I still think we're a bit apart on the terms. Let me see if I can define them more clearly.

Firstly, the use of "possibility" and "plausibility" in the sense that you have defined it seems, to me, to not account for certain meaningful distinctions. — Bob Ross

The meaningful distinctions should be:

Possibility - the belief that because distinctive knowledge has been applicably known at least once, it can be known again.

Plausibility- the belief that distinctive knowledge that has never been applicably known, can be applicably known.

In an earlier post, I mentioned knowledge chains. I believe this was before we had clarified the distinction between the two inductions. Lets take your example here:

For example,let's consider two scenarios: person one claims that a new color could be sensed by humans if their eyes are augmented, while person two claims that iron can float on water if you rub butter all over the iron block. I would ask you, within your use of the terms, which is more cogent? — Bob Ross

First, we cannot compare cogency between different branches of claims. This is because cogency takes context into account as well, and the difference between evaluating the human eye, and an floating iron block, are two fairly separate contexts. Recall that inductions are cogent when we reach the limit of what can be applicably known, so we could have a situation in which a plausibility is the most cogent conclusion within that context, while in another context, a possibility is the most cogent.

The more important question, is how can we determine what is most cogent in the belief of what will happen in an attempted application, with a claim within the same context? This is where knowledge chains, and their comparisons come into play.

What we know or believe often times implicitly relies on prior beliefs or applicable knowledge. If I am making a judgement about the human eye, then I am taking my knowledge and inductions about the eye into my assessment.

I applicably know the eye can see X colors.
I applicably know we can improve the eye's ability to see with greater focus.
Therefore I believe we can improve the eye to see greater than X colors.

We have 2 knowledge claims, then we leap to a plausibility. We don't know if its possible yet, as we haven't tried applying it to reality. But we believe that if we attempt to, we will discover that we can improve the eye to see more than X colors.

Now, lets think prior to the availability of eye surgery.

I applicably know the eye can see X colors.
I think its plausible we can improve the eye's ability to see with greater focus.
Therefore I believe we can improve the eye to see greater than X colors.

Here we have 1 knowledge claim, a plausibility, then another plausibility built on the first plausibility. Comparing the two chains, the first chain is more cogent than the second chain. Even though the conclusions are the same, it is the chain of logic that determines our conclusion, which determines which end statement is more cogent than the other.

This is valuable, because this destroys the Getter problem. It doesn't matter if either claim happens to be true or not. We could of course refine the context. Perhaps include some prior statements that we are implicitly glossing over. But it is about taking a belief, thinking about all of the alternative ways we can arrive at that belief (or the negation of that belief), and taking the most rational logic chain of events.

I believe the above should cover what you meant by "qualitative likelihood". Hierarchial induction determines which of the inductions within consideration of a conclusion is most rational. And it is more rational to consider outcomes that involve possibilities, over outcomes that involve plausibilities. But more importantly, we need to examine the chain of rationality one took to arrive at one's induction as well. This should provide all that's needed for a strong and measurable basis of cogency.

Moreover, there is knowledge that we have that we cannot physically directly experience, which I am sure you are acquainted with as a priori, that must precede the subject altogether. I haven't, and won't ever, experience directly the processes that allow me to experience in the first place, but I can hold it as not only a "possibility" (in my sense of the term) but also a "highly plausible" "truth" of my existence. — Bob Ross

According to this, there is no apriori. Everything is distinctively or applicably known by our experience. I you believe there is something that must exist prior to your current existence, then like every other other induction, it must be some variation on probability, possibility, plausibility, or an irrational belief.

I would say that this reveals what I think lacks in your terminology: we can't determine what is more cogent to pursue. In my terminology, I would be able to pursue trying to augment the eye to see more shades of colors because it is "possible". — Bob Ross

Under the old terminology, you wouldn't be able to state it was possible either. It may very well be that we cannot modify a human eye to see greater color, because it ends up that color is observed in the brain, and we would have to rewire that as well. As such someone would ask, "How do you know that is possible?"

With the chain of reasoning comparisons I noted above, we can definitely determine which is most cogent to pursue. In fact, it might help us realize we have underlying assumptions that we need to discover first.

I understand what you mean to a certain degree, but I think that it isn't fallacious to say that something could potentially occur: I think it becomes fallacious if the subject thereafter concludes that because it could occur it does occur. — Bob Ross

Every induction is a claim that something might be. An induction, by definition, is a conclusion that is not necessarily concluded from the premises involved. If I'm going to predict the sun will rise tomorrow, because its risen several times, I know that it is possible. If I say the sun will not rise tomorrow, that is plausible, as the sun has always risen. My plausibility might be correct, and my possibility might be incorrect. The point of cogency is to evaluate the inductions, and evaluate which one is more reasonable to hold to when you are deciding what will happen in the future.

There was a lot that went in many directions on your post. I couldn't cover it all in one post, but I thought if I tried to direct back to the meaning of the terms, and answer some of the repeating themes, it would clarify most of the issues.

Hello @Philosophim,
The dots have finally clicked for me! I think I understand what you are stating now and, so, most of what I said has been negated (I apologize for the confusion). However, I do still have a couple quarrels, so I will elaborate on those in a concise manner (that way, if I am still not understanding it correctly, you can correct me without having to address too many objections).

Possibility - the belief that because distinctive knowledge has been applicably known at least once, it can be known again.

Plausibility- the belief that distinctive knowledge that has never been applicably known, can be applicably known.

I have no problem with the underlying meaning of "possibility", however I think it still leaves out potentiality, but more on that later. With respect to "plausibility", I think you just defined, in accordance with your essays, an "applicable plausibility", contrary to an "inapplicable plausibility", which is not just a "plausibility". You defined it in the quote that it "can be applicably known", which is what I thought an "applicable plausibility" was. Maybe I am just misremembering.

First, we cannot compare cogency between different branches of claims. This is because cogency takes context into account as well, and the difference between evaluating the human eye, and an floating iron block, are two fairly separate contexts

I think you are sort of right. I think that you are thinking of the hierarchical inductions within a particular context as a linear dependency (i.e. a possibility -> plausibility is more cogent than a possibility -> plausibility -> plausibility); However, I think it is more of a plane, contexts engulfing contexts, style of hierarchies: no context is strictly isolated from any other context as they all are dependent on a more fundamental context which engulfs them together. Think of it as the evaluating the human eye context and the floating iron block context as separate contexts, indeed, but residing within a shared context(s) which is where they can be cross-examined from. A great example is the context in which the law of noncontradiction is a valid axiom: this contextual plane would engulf, because it is more fundamental, the two aforementioned contexts. Therefore, in the abstract, if context A and B reside within the law of noncontradiction context, and A does not abide by the law of noncontraction while B does, then A is less cogent than B on a more fundamental contextual plane--regardless of the fact that their hierarchical inductions are considered separately. Their are always parent contexts that engulf a given context unless you are contemplating the axioms from which all others are derived (then it gets tricky).

Before I continue to your post, let me briefly try to explain the difference between "possibility" (in your terms) and potentiality. Let's use two examples:

I applicably know what two "things" are.
I applicably know what three "things" are.
I applicably know that the underlying meaning of "two" and "three" are not synonymous.
Therefore, "two" "things" and "three" "things" are synonymous.

I applicably know the eye can see X colors.
I applicably know we can improve the eye's ability to see with greater focus.
Therefore I believe we can improve the eye to see greater than X colors.

Although they are to be considered separate from one another, in the sense of the induction chains, because they are two totally different contexts, we can still compare them because they both reside within a parent (or more than one parent) context; The law of noncontradiction, assuming the subject holds that as a fundamental axiom, would be a great example of a parent context that engulfs these two examples and, therefore, the former example is less cogent than the latter, despite their clearly different contexts, due to the parent context's negation of the former example's potentiality. Normally this would be called "possibility", but since you use it differently I think we are safe using potentiality instead. But, most importantly, notice that these two examples are not mutually exclusive, in a holistic sense, as they stem from more fundamental parent contexts.

I applicably know the eye can see X colors.
I applicably know we can improve the eye's ability to see with greater focus.
Therefore I believe we can improve the eye to see greater than X colors.

I understand your hierarchical induction chains, and they are brilliant (and great example)! However, consider this:

1. I see a round object at the top of a hill.
2. I have never experienced this round object before.
3. I applicably know that it is windy out.
4. I have experienced a round log fall down a hill during a windy day.
5. I have never experienced a round log fly up off of a hill during a windy day.
6. I have experienced "things" flying off of a hill.
7. The round object is similar in size to the log, but isn't a log.

Consider the following conclusions:
1. The round object is going to fly off of the hill
2. The round object is going to roll down the hill

Now, I think that you are perfectly right in stating that the cogency of these two conclusions, since they are within the same context, can be evaluated based off of the induction chains. However, in this example, let's try it out:

For conclusion 1:
I applicably know that some "things" can fly off of hills.
I applicably know that this round-object is a "thing".
Therefore, the round-object will fly off the hill.
I can apply this belief to reality to see if it holds.
Therefore, I am holding an "applicable plausibility" based off of two possibilities.

For conclusion 2:
I applicably know that some round-like objects, such as a log, can roll down a hill.
I applicably know that some round-like objects, such as a log, will roll down a hill in windy climates.
Therefore, the round-like object will roll down the hill.
I can apply this belief to reality to see if it holds.
Therefore, I am holding an "applicable plausibility" based off of two possibilities.

Notice that these are (1) both within the same context and (2) they both are at the same point in the induction chain. However, the latter is more cogent than the former because we have to evaluate the parent context(s) that they share: in this case, a good example is the law of similarity. If the subject holds that a generic "thing" is less cogent to base correlations off of than more particular groups of concepts, aka (I believe) the law of similarity, then they hold a more fundamental, parent context, that engulfs the two aforementioned conclusions and, thereby, one is more cogent than the other. Likewise, if the person held a parent context that directly contradicts the engulfed context, then that engulfed context would have to go (or the parent one would have to be refurbished to allow it to live on) and, more importantly, that context would be based off of the law of noncontradiction, which resides within another context: it is a hierarchy of planes that are engulfed by one another where the most fundamental is the most engulfing.

Similarly, with respect to your example prior to eye surgery, that requires a more fundamental acceptance, a parent context, that the context of the situation nullifies the ability for me to say they were truly wrong or right, or that I am truly right compared to them (because it depends on the context). If I didn't hold that context, then I wouldn't agree with you in this sense and neither would be truly wrong: I would just be disagreeing with you at a more fundamental context that engulfs the other.

I believe the above should cover what you meant by "qualitative likelihood".

I am going to refrain from elaborating on "qualitative likelihoods" to restrict the amount of objections I give in this post (that way it is easier for you, hopefully). But we can most definitely talk about this after.

According to this, there is no apriori.

Originally I was going to object, but I think that a priori is perfectly compatible with your view (or at least how I understand it) and can elaborate on this further if you would like.

With the chain of reasoning comparisons I noted above, we can definitely determine which is most cogent to pursue.

Only within the particular context and not considering the parent contexts.

In general, I like your epistemology! I think it is an empiricist leaning view that is more "sure" of the chick and less "sure" of the egg. I just think we can improve it (:

Bob

reply="Bob Ross;638715"]

Great response Bob, my apologies for the delay. I caught "The Covid," and have been fairly sick. Fortunately I'm vaccinated, so recovery is going steady so far.

With respect to "plausibility", I think you just defined, in accordance with your essays, an "applicable plausibility", contrary to an "inapplicable plausibility", which is not just a "plausibility". You defined it in the quote that it "can be applicably known", which is what I thought an "applicable plausibility" was. Maybe I am just misremembering. — Bob Ross

An applicable plausibility is something which can be applied to reality if we so choose. For example, "If I go outside within five minutes, it will rain on me as soon as I step outside of the door." I do not know if it is raining, nor can I figure it out from within the house. There is nothing preventing me from going outside within the next five minutes. Its an applicable plausibility that I will be rained on, because I can test it.

An inapplicable plausibility is a plausibility that either cannot be tested, or is designed not to be able to be tested. If for example I state, "There is a unicorn that exists that cannot be sensed by any means," this is inapplicable. There is nothing to apply to reality with this idea, as it is undetectable within reality. Perhaps there is a unicorn that exists that cannot be sensed in reality. But we will never be able to apply it, therefore it is something that cannot be applicably known.

Therefore, in the abstract, if context A and B reside within the law of noncontradiction context, and A does not abide by the law of noncontraction while B does, then A is less cogent than B on a more fundamental contextual plane--regardless of the fact that their hierarchical inductions are considered separately. — Bob Ross

Just because two built contexts are dissimilar, it doesn't mean they cannot have commonalities. But commonalities do not mean they can necessarily be evaluated against the different inductions within their independent contexts. The human eye and iron floating on water with butter are just too disparate to compare. The law of non-contradiction simply means you have an irrational inductive belief, which is completely divorced from rationality. I suppose if there's nothing stopping a person from placing comparative contexts in planes, but I would think the end result would be the same.

To add, the comparison is about finding the best induction to take within that context. So if my only recourse in one instance, lets say iron floating on water, is a plausibility over an irrational induction, its more cogent to choose the plausibility. If in the case of an eye, I have a probability vs a possibility, its more cogent to take the probability. But there's really no comparing the probability of improving the eye, the the options of plausibility vs irrationality with iron floating on water with butter. We could state that within the context of the eye, we have more cogent inductions to select from than in the context of iron floating on water, but that's really about it.

I applicably know what two "things" are.
I applicably know what three "things" are.
I applicably know that the underlying meaning of "two" and "three" are not synonymous.
Therefore, "two" "things" and "three" "things" are synonymous. — Bob Ross

Can you clarify this? I interpreted this as follows.

I applicably know A and B.
I applicably know C, D, and E.
I applicably know that the numbers two and three are not synonymous.
Therefore A and B, and C,D, and E are synonymous.

I don't believe that's what you're trying to state, but I could not see what you were intending.

For conclusion 1:
I applicably know that some "things" can fly off of hills.
I applicably know that this round-object is a "thing".
Therefore, the round-object will fly off the hill.
I can apply this belief to reality to see if it holds.
Therefore, I am holding an "applicable plausibility" based off of two possibilities.

For conclusion 2:
I applicably know that some round-like objects, such as a log, can roll down a hill.
I applicably know that some round-like objects, such as a log, will roll down a hill in windy climates.
Therefore, the round-like object will roll down the hill.
I can apply this belief to reality to see if it holds.
Therefore, I am holding an "applicable plausibility" based off of two possibilities. — Bob Ross

I still wasn't quite sure what you meant by parent contexts in these examples. I think what you mean is the broader context of "things" versus "round objects". Please correct me here. For my part, it depends on how we cut hairs so to speak. If the first person does not applicably know that things can roll down a hill as well, then neither statement is more cogent than the other. If the first person knows that "things" can also roll down hill, then there's no cogent reason why they would conclude the "thing" would fly off the hill over roll down the hill.

What might help is to first come up with a comparison of cogency for a person within a particular context first. Including two people complicates comparing inductions greatly, but generally follows the same rules as a person comparing several inductive options they are considering within their own context.

You may be on to something by the way. You're the first person I've had the opportunity to really dig in with the inductive hierarchy, and I will be the first to say it is only a foundation. I just want to make sure the foundation is understood first. While I feel the hierarchy chain is a good start, the second step, which is much more difficult to establish, is comparing two inductions of the same hierarchy and determining which one is more cogent. I think there is something that might be needed beyond the hierarchy chains, such as a further subdivision of the base four inductions. I'm eager to hear more of your ideas!

Hello @Philosophim,

I caught "The Covid," and have been fairly sick. Fortunately I'm vaccinated, so recovery is going steady so far.

Oh no! I am glad that you are recovering and I hope you have a speedy recovery!

An applicable plausibility is something which can be applied to reality if we so choose. For example, "If I go outside within five minutes, it will rain on me as soon as I step outside of the door." I do not know if it is raining, nor can I figure it out from within the house. There is nothing preventing me from going outside within the next five minutes. Its an applicable plausibility that I will be rained on, because I can test it.

An inapplicable plausibility is a plausibility that either cannot be tested, or is designed not to be able to be tested. If for example I state, "There is a unicorn that exists that cannot be sensed by any means," this is inapplicable. There is nothing to apply to reality with this idea, as it is undetectable within reality. Perhaps there is a unicorn that exists that cannot be sensed in reality. But we will never be able to apply it, therefore it is something that cannot be applicably known.

This is all and well, but I think you defined "plausibility" (in your previous post) as exactly what you just defined as an "applicable plausibility"--and that was all I have trying to point out. You defined "plausibility" as "the belief that distinctive knowledge that has never been applicably known, can be applicably known". A "plausibility", under your terms (I would say), is not restricted to what "can be applicably known" (that is a subcategory called "applicable plausibilities"), whereas "plausibility" is a much more generic term than that (as far as I understand your terms).

Just because two built contexts are dissimilar, it doesn't mean they cannot have commonalities. But commonalities do not mean they can necessarily be evaluated against the different inductions within their independent contexts.

I agree in that two contexts can be dissimilar and still have commonalities, but those commonalities are more fundamental aspects to those contexts and, therefore, although they are dissimilar, they are not separate. Even the most distinct contexts share some sort of dependency (or dependencies). An induction (within a context) that contradicts a parent context is less cogent than an induction (within a different context) that doesn't.

The human eye and iron floating on water with butter are just too disparate to compare.

You can compare them relative to their shared dependencies (such as the law of noncontradiction). You could say that, since iron floating on water (even if you haven't experienced it before) cannot occur based off of what you have learned (experienced) about densities in chemistry and your acceptance of the law of noncontradiction, then this is not as cogent as the eye example since it violates thereof. This is a comparison of potentiality, where both are compared to an accepted principle that engulfs both of them (which are part of the context, but is shared). From what I understand from your hierarchical inductions, the idea that (1) A can be A and not A and that (2) A will have the same identity as another A are both not possible unless we experience it, with no distinction between the two (preliminarily). However, I am saying that #1 has no potential to exist while #2 does because I have accepted the law of noncontradiction and law of identity as underlying principles which rules out #1 and allows for #2. However, if I did not accept the law of noncontradiction and I did not accept the law of identity, then #1 has the potential to be "true" while #2 does not. It is also relative to the parent contexts: the shared dependencies (more fundamental concepts that the given contexts at hand depend on).

The law of non-contradiction simply means you have an irrational inductive belief, which is completely divorced from rationality

I would say that it means that the subject has accepted the axiom as "true" and, therefore, it will be a dependency for many future ideas (or beliefs) they will have (as they will build off of it). It isn't necessarily "true" in all contexts, we just share that more fundamental principle.

To add, the comparison is about finding the best induction to take within that context.

I think that that is one goal, but the comparing of all contexts is also desired. All knowledge stems from the same tree, therefore one can derive any given contexts back to a common node. I am just saying that the idea that you strictly cannot compare contexts eliminates potentiality. When I say something can potentially exists, or happen, it means that it does not violate any of my parental contexts (any underlying principles that would be required for the concept to align with my knowledge as it is now). Hitherto, your epistemology eliminates this altogether: you either have a possibility or plausibility (probability encompasses the idea of a possibility) and you can't preliminarily determine whether one plausibility has the potential to occur or not.

no comparing the probability of improving the eye, the the options of plausibility vs irrationality with iron floating on water with butter

You would be comparing it one step deeper than that: iron floating on water has no potential to occur whereas improving the eye does (I would call this "possibility").

Can you clarify this? I interpreted this as follows.

I applicably know A and B.
I applicably know C, D, and E.
I applicably know that the numbers two and three are not synonymous.
Therefore A and B, and C,D, and E are synonymous.

I don't believe that's what you're trying to state, but I could not see what you were intending.

You are absolutely right: I was trying to keep it as fundamental as possible, but I see how that was confusing. I was merely pointing out essentially that the law of noncontradiction is an underlying principle (which is apart of the context) that can determine one context more cogent than another because they exist within a plane. I was just making up a contradictory example off the top of my head and I apologize--as it wasn't very good at all.

I still wasn't quite sure what you meant by parent contexts in these examples. I think what you mean is the broader context of "things" versus "round objects". Please correct me here. For my part, it depends on how we cut hairs so to speak. If the first person does not applicably know that things can roll down a hill as well, then neither statement is more cogent than the other. If the first person knows that "things" can also roll down hill, then there's no cogent reason why they would conclude the "thing" would fly off the hill over roll down the hill.

At its most fundamental level, I was trying to convey that the law of similarity could be another example of a parent context, where one may determine two completely even contexts (i.e. possibility -> plausibility and one that is a possibility -> plausibility) based off of an underlying principle that governs both contexts. If I have witnessed a "thing" fly and roll off of a hill, but the "things" that I have seen fly look less similar to the "thing" on the hill now and the "thing" looks more similar to the "things" that I have seen roll down a hill, then I might determine one context more cogent than the other based off of the fact that I accept the law of similarity as an underlying principle that engulfs both the contexts in question. It is a more fundamental examination then the hierarchical inductions.

What might help is to first come up with a comparison of cogency for a person within a particular context first. Including two people complicates comparing inductions greatly, but generally follows the same rules as a person comparing several inductive options they are considering within their own context.

I agree. I think that, within an individual context, the subject will compare their knowledge based off of a tree like structure (or plane like structure where principles engulf other principles) and decide their credence levels based off of that (which includes your hierarchical induction chains). I think that multiple subjects do essentially the same thing, but they will accept their own experiences are more cogent than others (because it is more immediate to them as the subject) and, therefore, that is the most vital factor.

Look forward to your response.
Bob

Thanks for the well wishes Bob. I almost feel like my normal self again today.

This is all and well, but I think you defined "plausibility" (in your previous post) as exactly what you just defined as an "applicable plausibility"--and that was all I have trying to point out. You defined "plausibility" as "the belief that distinctive knowledge that has never been applicably known, can be applicably known". A "plausibility", under your terms (I would say), is not restricted to what "can be applicably known" (that is a subcategory called "applicable plausibilities"), whereas "plausibility" is a much more generic term than that (as far as I understand your terms). — Bob Ross

In both cases, the person believes that the plausibility can be applicably known. The difference between an applicable, and inapplicable plausibility, is whether it is designed so that it can be applied to reality. You can craft a belief about reality that can never be actually applied to reality. Its plausible, but inapplicable. It doesn't mean that the plausibility isn't true either. All of these labels are for inductions, which by nature, may or may not be true. The goal is to find which inductions are most rational to hold. An inapplicable plausibility is pretty low on the hierarchy, as it is a claim to what is real when you can never actually apply it to reality.

I agree in that two contexts can be dissimilar and still have commonalities, but those commonalities are more fundamental aspects to those contexts and, therefore, although they are dissimilar, they are not separate. Even the most distinct contexts share some sort of dependency (or dependencies). An induction (within a context) that contradicts a parent context is less cogent than an induction (within a different context) that doesn't. — Bob Ross

If you have two identical underlying building blocks between two compounded inductions, then you can compare those. But if you add anything else on top to make them different, they are no longer fair comparisons.

For example, I hold the law of non-contradiction as true. From this I believe it is plausible that the moon is made out of green cheese. Separately from this, I believe it is plausible that the sun is really run by a giant lightbulb at its core. The basis of the law of contradiction between them has no bearing on the evaluation of comparing the plausibilities.

That being said, you can compare the belief in the law of non-contradiction, versus the belief of its denial. If you hold the law of non-contradiction as applied knowledge, or an induction that you believe in, you can evaluate an inductions chain, and reject any inductions that relay on the law of non-contradiction being false within its chain.

I "think" this is what you are going for. If so, yes, you can determine which inductions are more cogent by looking in its links, and rejecting links that you do not know, or believe in. But this is much clearer if you are trying to decide whether the moon is plausibly made out of green cheese, or something else, then trying to compare the moon and the sun. Does that make sense?

When I say something can potentially exists, or happen, it means that it does not violate any of my parental contexts (any underlying principles that would be required for the concept to align with my knowledge as it is now). Hitherto, your epistemology eliminates this altogether: you either have a possibility or plausibility (probability encompasses the idea of a possibility) and you can't preliminarily determine whether one plausibility has the potential to occur or not. — Bob Ross

You can't preliminarily determine whether one plausibility has the potential to occur or not, because it is an induction. And an induction is when we conclude a result that does not necessarily stem from the premises. Any prediction about the future for example, can always be wrong. Hypotheses, even the most educated ones, about what will happen in a science experiment can also be wrong. Holding to a cogent induction does not guarantee it will actually happen either. Cogency is simply deciding which induction is more reasonable to hold. The nature of holding an induction is always a gamble, no matter how much you might rationalize prior to holding one.

That isn't limited to the epistemology proposed here either. At least this epistemology has a way of rationally measuring inductions. Prior to this, I don't believe there is any epistemology that can claim which inductions are more rational to hold. So if I believe the bird in front of me can fly, because I have applicably known things with wings can fly, its more cogent then stating that the bird in front of me could plausibly levitate off the ground with psychic powers. That being said, if I'm looking at a penguin, my induction will be wrong once applied. With inductions, nothing is certain.

If I have witnessed a "thing" fly and roll off of a hill, but the "things" that I have seen fly look less similar to the "thing" on the hill now and the "thing" looks more similar to the "things" that I have seen roll down a hill, then I might determine one context more cogent than the other based off of the fact that I accept the law of similarity as an underlying principle that engulfs both the contexts in question. — Bob Ross

We can break the chain down as follows.
Thing X which has Y traits I have seen fly off of hills.
Thing A which has B traits I have seen roll off of hills before.

(These are both based on our contexts of what we have applicably known)
It is possible that a thing with B traits can roll off of hills.
It is possible that a thing with Y traits can fly off of hills.
I have never seen a thing with B traits fly, and I have never seen a thing with Y traits that can roll.
It is plausible that a thing with B traits can roll, and plausible that a thing with Y traits can fly.

Since it is possible that a thing with B traits can roll, but only plausible that a thing with B traits can fly, it is more cogent to assume the thing with B traits, will likely fly.
Apply the same reasoning to Y.

I don't think there is a law of simularity, but there is a chain of probabilities and possibilities within this context. And with this context, we can conclude certain beliefs would be more cogent. Does that mean the thing with B traits will roll and the thing with Y traits will fly? No. We can only applicably know the answer by applying our induction to reality without contradiction.

I hope that clears up the process a bit more! Let me know what you think.

Hello @Philosophim,
I am glad that you are feeling well!

In both cases, the person believes that the plausibility can be applicably known.

I don't think this is necessarily true. It depends on what you mean by "applicably known": lots of people believe in things that they claim cannot be "applicably known". For example, there are ample amounts of people that believe in an omnipotent, omniscient, etc (I call it the "omni" for short) God and actively claim that these traits they believe in are necessarily outside of the scope of what we can "applicably" know. Another, non-religious, example is a priori knowledge: most people that claim their are a priori knowledge also actively accept that you necessarily cannot applicable (directly) know the components of it. At its most generic form, they would claim that we there is something that is required for experience to happen in the first place, for differentiation to occur, but you definitely will never be able to directly "applicably" know that. I guess you could say that they are indirectly "applying" it to reality without contradiction, which I would be fine with.

For example, I hold the law of non-contradiction as true. From this I believe it is plausible that the moon is made out of green cheese. Separately from this, I believe it is plausible that the sun is really run by a giant lightbulb at its core. The basis of the law of contradiction between them has no bearing on the evaluation of comparing the plausibilities.

I think that, because the law of noncontradiction is one of the (if not the) fundamental axiom there is, it is easy to consider it irrelevant to the comparison of two different plausibilities; however, nevertheless, I think that it plays a huge, more fundamental, factor in the consideration of them. For example, if my knowledge of physics (or any other relevant subject matter) that makes it "impossible" (aka has no potential to occur) for green cheese to be able to make up a moon, then, before I have even started thinking about hierarchical inductions, I have exhausted the idea to its full capacity (which, in this case, isn't much). Furthermore, if I have knowledge that both examples (the giant lightbulb and the green cheese moon) are "impossible" (have no potential to occur), then they are equally as useless as each other, but, more importantly, notice that I still compared them to a certain degree. Now, I could hold that the law of noncontradiction isn't as black and white as I presume we both think: maybe I have a warped understanding of superpositioning, for example. Maybe I believe, prior to even having the ideas of the green cheese or light bulb sun, that A can be and not be at the same time as long as there is no observant entity forcing an outcome. Now, this is not at all how superpositioning works (I would say), but someone could, nevertheless, hold this position. Moreover, with the stipulation that there are no observers, even if I have solid evidence that green cheese can't make up a planet, the planet could be made of green cheese and green cheese can't "possibly" makeup a planet at the same time. This refurbished understanding of the law of noncontradiction poses whole new problems, but notice that they wouldn't be objectively wrong: only wrong in the sense that we don't share the same fundamental context (i.e. the same understanding of the law of noncontradiction).

That being said, you can compare the belief in the law of non-contradiction, versus the belief of its denial. If you hold the law of non-contradiction as applied knowledge, or an induction that you believe in, you can evaluate an inductions chain, and reject any inductions that relay on the law of non-contradiction being false within its chain.

This is, essentially, what I am trying to convey. That would be a consideration prior to hierarchical inductions and would provide an underlying basis to compare two different plausibilities. I think we do this with a lot more than just the law of noncontradiction.

I "think" this is what you are going for. If so, yes, you can determine which inductions are more cogent by looking in its links, and rejecting links that you do not know, or believe in. But this is much clearer if you are trying to decide whether the moon is plausibly made out of green cheese, or something else, then trying to compare the moon and the sun. Does that make sense?

Correct me if I am wrong, but I think that you are trying to convey that, once all the underlying beliefs are evaluated and coincide with the given belief in question, you can't compare two different contexts' hierarchical induction chains. I don't think this is necessarily the case either, but I want to focus on the more fundamental disputes first before segueing into that.

My main point is that potentiality is completely removed when "possibility" is refurbished in your epistemology. The problem is that there are no distinctions between applicable plausibilities. For example, imagine I have 2,000 5 ft bricks. Now, imagine two claims: (1) "you can fit 200 of these bricks in a 10 x 10 x 10 room" and (2) "you can fit 2,000 of these bricks into a 10 x 10 x 10 room". Let's say that I've never experienced filling a room with 5 ft bricks. I think, according to your definitions, both claims would not be possibilities but, rather, applicable plausibilities because I haven't ever experienced either (and "possibility" is something that has been experienced before). However, I don't need to attempt to apply both directly to reality to figure out which one has the potential to occur. Even though they are plausibilities, #1 has the potential to occur (meaning that, although I could be wrong since it is an induction, all my knowledge aligns with this having the potential to occur) while #2 does not (because, assuming my math is sound, 1000 Sq Ft / 5 Ft only allows for 200 5 ft bricks). So, even if I haven't directly attempted to fill a room with 200 nor 2,000 5 ft bricks, I can soundly believe that one claim is more cogent than the other because one aligns with my current knowledge while the other does not. If we were to put them both as plausibilities, then I would say one is "highly plausible" while the other is "highly implausible" to make a meaningful distinction between the two.

Another fundamental problem is what constitutes experiencing something before? How exact of a match does it have to be? If it is an exact match, then we hold very little possibilities and a vast majority of our knowledge is ambiguously labeled as "plausibilities". For example, I have internal monologue. I think that it is "possible" (in accordance with my use of the terms) that other people have internal monoloqes too; however, I have never experienced someone else having an internal monologue, therefore it isn't a "possibility" in accordance with your terms. I think the obvious counter argument would be that I have experienced my own internal monologue, therefore it is "possible". But my experience of my own internal monologue is not an experience that is an exact match to the claim in question ("other people have internal monologue"). Someone could walk up to me and rightly claim that my own experience of my own internal monologue is in no way associated with the experience of someone else having an internal monologue, therefore I don't know if it is possible (according to your terms): and they would be correct. However, I would still hold that other people have the potential to have internal monologue because they have the necessary faculty (very similar to mine) for it to occur. As of now, I am not saying that they definitely have internal monologue, or that they can, just that they have the potential to. To take this a step further, the belief that other people can have internal monologue is an "inapplicable plausibility" (I can't demonstrate any other than my own). However, although I can't claim that another person can have internal monologue, I would not tell someone else who claims to have internal monologue that that is "impossible" (according to your terms), even though I haven't experienced someone else having internal monologue, because I have a more fundamental parent context that I abide by: empathy. If I were in their shoes, and I actually did have internal monologue (regardless of whether, in my current state, I can actually claim it is "possible"), I would want the other person to give me the benefit of the doubt out of respect. So my empathetic parental context would overrule, so to speak, my factual consideration and, therefrom, I would walk around claiming that it is "possible" for someone else to have internal monologue although technically I can't claim that within your definitions. So basically: I can claim that they have the potential to have internal monologue and, although I can't claim they can have internal monologue, I will claim they can regardless.

This brings up a more fundamental issue (I think): the colloquial term "possibility" is utterly ambiguous. When someone says "it is possible", they may be claiming that "it can occur" or that "it can potentially occur", which aren't necessarily synonymous. To say something "can occur", as you rightly point out, is only truly known if the individual has experienced it before, however to say something "can potentially occur" simply points out that the claim doesn't violate any underlying principles and beliefs. I think this is a meaningful distinction. If I claim that it is "possible" (in my terms) for a rock to fall if someone drops from a mountain top, it depends on if I have directly experienced it or not whether I am implicitly claiming that it "can occur" (because I've experienced it) or that it "can potentially occur" (because, even though I haven't experienced it before, my experiences, which are not direct nor exact matches of the given claim, align with the idea that it could occur). I think this can get a bit confusing as "can" and "can potentially" could mean the same thing definitions wise, but I can't think of a better term yet: it's the underlying meaningful distinction here that I want to retain.

Also, as a side note, I like your response to the object rolling off hills example, however this is getting entirely too long, so I will refrain from elaborating further.

Look forward to hearing from you,
Bob

I don't think this is necessarily true. It depends on what you mean by "applicably known": lots of people believe in things that they claim cannot be "applicably known". For example, there are ample amounts of people that believe in an omnipotent, omniscient, etc (I call it the "omni" for short) God and actively claim that these traits they believe in are necessarily outside of the scope of what we can "applicably" know. — Bob Ross

Then what they are describing is an inapplicable plausibility. It is when you believe that something that exists, but have constructed it in such a way that it cannot be applicably tested. I can see though that my language is not clear, so I understand where you're coming from. Applicable knowledge is when you apply a belief to reality that is not contradicted. All inductions are a belief in something that exists in reality. The type of induction is measured by its ability to be applicably applied or known.

So people believe that God exists in reality, like all inductions. The type of induction is an inapplicable plausibility, because the essential properties of God are things that cannot be applied to reality. There is no way to discover if a God outside of space and time exists, because we cannot go outside of space and time.

Another, non-religious, example is a priori knowledge: most people that claim their are a priori knowledge also actively accept that you necessarily cannot applicable (directly) know the components of it. At its most generic form, they would claim that we there is something that is required for experience to happen in the first place, for differentiation to occur, but you definitely will never be able to directly "applicably" know that. I guess you could say that they are indirectly "applying" it to reality without contradiction, which I would be fine with. — Bob Ross

I think this is largely ok. Maybe a more specific example would help me to determine if you have the right of it. As I noted earlier, a priori knowledge doesn't really exist under this theory. There is distinctive knowledge, and there is applicable knowledge. You cannot have applicable knowledge, without first applying distinctive knowledge. You can create whatever distinctive knowledge you want, but it is not applicable knowledge until it is tested against reality.

I think that, because the law of noncontradiction is one of the (if not the) fundamental axiom there is, it is easy to consider it irrelevant to the comparison of two different plausibilities; however, nevertheless, I think that it plays a huge, more fundamental, factor in the consideration of them. For example, if my knowledge of physics (or any other relevant subject matter) that makes it "impossible" (aka has no potential to occur) for green cheese to be able to make up a moon, then, before I have even started thinking about hierarchical inductions, I have exhausted the idea to its full capacity — Bob Ross

Even though you did not actively think about hierarchial induction, you practicied it implictly. You noted that on the chain of reasoning, the law of non-contradiction proves that the moon is not made of green cheese. Therefore, you have no need to continue that chain of reasoning. No one has ever applicably known a situation in which the something was both itself, and its negation. Further, its definition makes a contradiction impossible. If you define something as one way, then define it as its negation, you have created a situation that can never be applied to reality.

That is because it is impossible even as distinctive knowledge. Recall that distinctive knowledge is what is held within a particular context that is not contradictory. I cannot claim that "A" is not "A" when I mean A and not A within the same context of equality. Something provably impossible ends any further thinking along the lines of it being possible.

Moreover, with the stipulation that there are no observers, even if I have solid evidence that green cheese can't make up a planet, the planet could be made of green cheese and green cheese can't "possibly" makeup a planet at the same time. — Bob Ross

If we cannot observe it, we cannot apply this to reality. Therefore it is an inapplicable plausibility. It is something we can consider, but it will fail in an inductive hierarchy test against something possible, probable or even applicably plausible.

That being said, you can compare the belief in the law of non-contradiction, versus the belief of its denial. If you hold the law of non-contradiction as applied knowledge, or an induction that you believe in, you can evaluate an inductions chain, and reject any inductions that relay on the law of non-contradiction being false within its chain.

This is, essentially, what I am trying to convey. That would be a consideration prior to hierarchical inductions and would provide an underlying basis to compare two different plausibilities. — Bob Ross

Again, you are doing the practice of hierarchial induction here, whether you are aware of it or not. I don't think its a consideration prior, but a consideration of it.

Correct me if I am wrong, but I think that you are trying to convey that, once all the underlying beliefs are evaluated and coincide with the given belief in question, you can't compare two different contexts' hierarchical induction chains. — Bob Ross

This is correct.

I can soundly believe that one claim is more cogent than the other because one aligns with my current knowledge while the other does not. If we were to put them both as plausibilities — Bob Ross

This is essentially what the hierarchy does. In one case of your induction, you founded it upon applicable knowledge. In another, you did not.

Chain one: Applicable knowledge => plausibilty
Chain two: Possibliity => plausibility.

It is more cogent to believe in the first plausibility, then the second. We can do a little math to prove it.

Lets say that applicable knowledge counts as 100% being an accurate assessment of reality without contradiction. An induction is less than 100 percent. When you have a chain of beliefs, you can multiply the percentage chance of the beliefs together. For example, getting one result out of a roll of six dice is 1/6* 1/6 or 1/36 chance (individual values for each die, so five on die one is different from 5 on die two).

Every induction is either 1, not contradicted by reality, or 0, contradicted by reality. We do not applicably know whether it is a 1, or a 0, we we will make it a binary variable with 1 as true, and 0 as false.

So the first chain is:
1 * X
The second chain is:
X * Y

The first chain's chance of being correct using probability, is 50% The second chains chance is .5*.5 or .25% chance of being correct.

A probability and possibillity are more cogent, because they are really a chain based off of applicable knowledge. There is only one binary uncertainty, will what was applicably known be applicably known again.

Possibility chain:
Applicable knowledge => induction that it will still be applicably known

Plausibility chain:

Take something possible (For example, the moon will still exist when I look for it) => create induction (It is made out of green cheese) => Can be applied v Can't be applied

A possibility is essentially always 1* X of it still being applicably known.
A plausibility is essentially always predicting another induction off of what is possible, or X * Y

If I continue and say, The moon is made of green cheese, and this green cheese has green bacteria, then my induction of green bacteria can be seen as:

X * Y * Z or .125 chance of not being contradicted by reality.

For example, I have internal monologue. I think that it is "possible" (in accordance with my use of the terms) that other people have internal monoloqes too; however, I have never experienced someone else having an internal monologue, therefore it isn't a "possibility" in accordance with your terms. — Bob Ross

Correct, depending on the context. You do not know if people have internal monologues in their head like yourself. Fun fact, there are people who cannot visualize inside of their head. They literally cannot imagine a vision of anything when they close their eyes. So what do we do here? Do we fall into solipsism? No, we simply adjust the context of what it means to have internal monologues between two different people.

First, we can determine a conclusion or experience that could only happen if one had an internal monologue. For example, I could ask a person, "Can you invent a story of two people talking to each other in your head?" A person who can internally monologue, can create a conversation of two people talking in their mind. A person who could not understand the question, or was unable to fulfil the request (with the possibility that they were telling the truth depending on how deep we want to go) would not be able to have an inner monologue in their head. If however, they could fulfil the request, then they must be able to have an inner monologue in their head.

Do we know what that inner monologue sounds or looks like in their head? No. We likely never will. This is the "hard problem" of consciousness. We can determine a bat can think, but we can never have the experience of thinking like a bat.

Finally, also recall that cogency is the highest level of induction we can make. Imagining what it is like to have the experience of being a bat is an inapplicable plausibility, and there is no real alternative. There is no confirmation or denial of applicable knowledge, no probability or even possibility beyond the idea that it is possible brains can have consciousness. Perhaps as we improve the science of the mind, this will change, but for now, this is what we have.

This brings up a more fundamental issue (I think): the colloquial term "possibility" is utterly ambiguous. When someone says "it is possible", they may be claiming that "it can occur" or that "it can potentially occur", which aren't necessarily synonymous. — Bob Ross

Agreed. Colloquially, the term possiblity is a bad term, because we have not had a viable means of assessing knowledge. This colloquial term of "possibility" causes confusion, and ambiguous arguments that those without this method of knowledge, are not equipped to handle.

To say something "can occur", as you rightly point out, is only truly known if the individual has experienced it before, however to say something "can potentially occur" simply points out that the claim doesn't violate any underlying principles and beliefs. I think this is a meaningful distinction. If I claim that it is "possible" (in my terms) for a rock to fall if someone drops from a mountain top, it depends on if I have directly experienced it or not whether I am implicitly claiming that it "can occur" (because I've experienced it) or that it "can potentially occur" (because, even though I haven't experienced it before, my experiences, which are not direct nor exact matches of the given claim, align with the idea that it could occur). I think this can get a bit confusing as "can" and "can potentially" could mean the same thing definitions wise, but I can't think of a better term yet: it's the underlying meaningful distinction here that I want to retain. — Bob Ross

I think you've nailed it. This is really the separation between what is possible, and what is plausible. It takes time to wrap your head around it. Perhaps an applicable plausibility is better described as "an inductive claim of potentiality". That seems to clash with "probability" though, and honestly, all inductions could be argued as "potential". So I'm not sure the generic term of potential works well anymore either. But the underlying meaningful distinction you are describing, is the difference between what is possible, and what is plausible. It is a distinction we have not had in epistemology until now, and I believe the introduction of this distinction is a real key in unlocking some of the problems epistemology has had over the years.

Also, as a side note, I like your response to the object rolling off hills example, however this is getting entirely too long, so I will refrain from elaborating further. — Bob Ross

Not a worry. I was sick, and having difficulty finding the time and effort to cover larger posts. I am feeling much better now, and more energized! My apologies if I was not able to drill down or cover ideas as much as I normally would. Please continue to drill into every nook and cranny.

How do you prove Socrates' (paradoxical) statement? — Agent Smith

Hello Agent Smith. I appreciate your contribution, I just had not gotten around to it yet. For this forum post, I would be glad to answer your question, but you need to understand the knowledge theory first. Have you read the papers? I could give you an answer, but if you haven't read the papers yet, you will not understand it. If you are against reading the papers at first, feel free to start with Bob's posts. We cover a lot of questions and answers, and it may help you. Thanks!

Hello @Philosophim,

Then what they are describing is an inapplicable plausibility. It is when you believe that something that exists, but have constructed it in such a way that it cannot be applicably tested. I can see though that my language is not clear, so I understand where you're coming from. Applicable knowledge is when you apply a belief to reality that is not contradicted. All inductions are a belief in something that exists in reality. The type of induction is measured by its ability to be applicably applied or known.

I agree with you here, but my point was that it is an inapplicable plausibility (which means we are on the same page now I think). A couple posts back, you were defining "plausibility" as "the belief that distinctive knowledge that has never been applicably known, can be applicably known", which I am saying that is an "applicable plausibility", not "plausibility". I am now a bit confused, because your response to that was "In both cases, the person believes that the plausibility can be applicably known", which that is why I stated people can have plausibilities that they don't think can be applicably known. You are now saying, as far as I am understanding it, that if they think it can't be applicably known, then it is an "inapplicable plausibility" (I agree with that, but notice that doesn't align with your previous definition of "plausibility", as it was defined as "can be applicably known"--unless you think that "inapplicable plausibilities" are not a subcategory of "plausibility", I don't see how this isn't a contradiction).

Upon further reflection, I think that if we define every "plausibility" that has no potential as an "irrational induction" (and, consequently, all plausibilities have potential), rather than an "applicable/inapplicable plausibility", then I have no objections here. So, using my brick example, the claim that one can fit 2,000 5 ft bricks in 1000 sq ft is an "irrational induction" (not a "plausibility") because 1000 / 5 = 200, which necessarily eliminates any potentiality. However, I still think that there are meaningful hierarchies between claims (between plausibilities, for example) that relate to sureness apart from cogency which can be evaluative tools.

Even though you did not actively think about hierarchial induction, you practicied it implictly.

Fair enough. But I would say that the fundamental comparison with respect to the law of non-contradiction is a valid comparison across all hierarchical chains.

No one has ever applicably known a situation in which the something was both itself, and its negation.

This is true, but also notice that no one has ever applicably known a situation in which, in the absence of direct observation, something necessarily was not both itself and its own negation.

If you define something as one way, then define it as its negation, you have created a situation that can never be applied to reality.

Let's say we have these two claims:
1. Absent of direct observation, things abide by the law of noncontradiction.
2. Absent of direct observation, things do not abide by the law of noncontradiction.

Firstly, I could apply both of these indirectly to reality without any contradiction because, using the law of noncontradiction, I can create situations where the law of noncontradiction doesn't necessarily have to occur (mainly absent of sentient beings). Don't get me wrong, I agree with you in the sense that both are inapplicable plausibilities, but that is with respect to direct application. I may decide, upon assessing the state of a currently unobserved thing, to decide that the outcome should calculated as if they are superpositioned (this is how a lot of the quantum realm is generally understood). This can be indirectly applied to reality without any contradiction. Or, on the contrary, I could decide the outcome should be calculated as if they are either/or (this is generally how Newtonian physics is understood).

If we cannot observe it, we cannot apply this to reality.

We cannot directly apply it to reality, but we can produce meaningful calculations based off of superposed states which necessarily imply A being, only in the theoretical, in two contradictory states. Even if we could not produce meaningful calculations, it is equally as much of an "inapplicable plausibility" as claiming it does abide by the law of noncontradiction.

Again, you are doing the practice of hierarchial induction here, whether you are aware of it or not. I don't think its a consideration prior, but a consideration of it.

I think that if these underlying principles, which engulf other contexts, are a consideration of it, contrary to prior to it, then you are agreeing with me that hierarchical chains, to some degree or another, can be compared. I was merely trying to distinguish between the underlying, engulfing, principles and the point at which the induction chains can no longer be fairly compared.

It is more cogent to believe in the first plausibility, then the second. We can do a little math to prove it.

I agree with you here, but now we are getting into another fundamental problem (I would say) with your terminology: if a "possibility" is what one has experienced once before, then virtually nothing is a possibility. And, to be more clear, I think it is a much bigger disparity then I think your epistemology tries to imply. It all depends, though, on what one defines as "experiencing before". I don't think we experience the exact same thing very often (potentially at all) and, consequently, when one states they have "experienced that before" what they really mean is they've "experienced something similar enough to their current experience for them to subjectively constitute it as a match". For example, under your terms, the claim that "that car, which I haven't experienced run, will run, when started, because I've experienced my car run before" is not a "possibility" but, rather, a "plausibility". I think that we would both agree that that is the case. However, this directly implies that I also can't claim that "this apple is edible, although I haven't taken a bite yet, because I've experienced eating an apple before" is a "possibility": not even in the case that I have good reason to claim that this apple resembles another apple I've eaten before. Similarly, I also can't claim that it is "possible" that my car will start because I've experienced it start before because, directly analogous to the apple example, my car is not the exact same, within the exact same context, as when I experienced it start (at least, the odds are that it most definitely is not). In more philosophical terms, the problem is that almost all experiences are of particulars, not universals. A previous experience of thing A cannot be constituted as a previous experience of B, ever, because A is a separate particular from B and, therefore, "possibilities" would be constrained to only that experience after it occurs and never before its occurrence. However, I would say that a previous experience of thing A can be constituted as a previous experience of B if it qualifies, potentially with reference to objective evidence but necessarily contingent on subjective determination, as similar enough, within the context, to a previous context. Notice how "possibility" is no longer a zero sum game, a binary question, and, subsequently, becomes a matter of passing a subjectively determined threshold (which could be, in turn, based off of objective claims) by necessity: this is what I would call the spectrum of sureness. It isn't a question of whether something (1) has been experienced before or (2) it hasn't but, rather, a question of how sure are you of the similarity between what you just experienced and a past experience: does it constitute as similar enough. I think there is rigidity within your epistemology that mine lacks, as I see it more as an elastic continuum of sureness. I don't know if that makes any sense or not.

Correct, depending on the context. You do not know if people have internal monologues in their head like yourself.

Not depending on the context, but every context that contains such a claim. Asking someone if they have internal monologue, no matter how you end up achieving it, doesn't prove it is "possible" in the sense that you "have experienced it at least once before". "Hard consciousness", as you put it, is exactly what I am trying to convey here in conjunction with your "possibility" term: by definition, I can never claim it is "possible" for someone else to have internal monologue. Even if you knew that the person could not physically lie about it, you would never be able to claim it is "possible" because you have never experienced it yourself (even if you have experienced internal monologue, you haven't experienced it particularly within them).

We can determine a bat can think, but we can never have the experience of thinking like a bat.

We cannot, under your terms, claim that a "bat can think", only that it is a plausibility. Even if we scanned their brains and it turns out the necessary, similar to ours, faculty exists for thought, we would never be able to label it as a "possibility" because we have not experience a bat thinking. This is, to a certain degree, what I was trying to convey previously: how incredibly narrow and limited "possibility" would be. It would essentially only pertain to universals (that which has an objective, or absolute--depending on how you define it--basis) or subjective universals (that which is true for all experience for a particular subject). An example of this would be numbers in terms of quantity: one abstract "thing" is the exact same experience as one abstract other "thing" because quantity is derived from the same subjective universal called differentiation. Differentiation, at its most fundamental level, is the same for all particulars for that subject--as they wouldn't even be particulars, but rather a particular, if this wasn't the case.

I look forward to hearing from you,
Bob

:up:

I agree with you here, but my point was that it is an inapplicable plausibility (which means we are on the same page now I think). A couple posts back, you were defining "plausibility" as "the belief that distinctive knowledge that has never been applicably known, can be applicably known", which I am saying that is an "applicable plausibility", not "plausibility". I am now a bit confused, because your response to that was "In both cases, the person believes that the plausibility can be applicably known", which that is why I stated people can have plausibilities that they don't think can be applicably known. — Bob Ross

Fantastic point. I need to revise what an inapplicable plausibility is. What would be more accurate is the belief that something exists that cannot be applicably known. Would we call this faith? I'm hesitant to use that word, as it is loaded with a lot of other emotions. But I think you are right. An inapplicable plausibility is different enough from a plausibility to warrant a separate identity in the heirarchy. That would leave us with probability, possibility, plausibility, faith, and irrational inductions.

Upon further reflection, I think that if we define every "plausibility" that has no potential as an "irrational induction" — Bob Ross

This is correct. An irrational induction is a belief that something exists, despite applicable knowledge showing it does not exist.

This is true, but also notice that no one has ever applicably known a situation in which, in the absence of direct observation, something necessarily was not both itself and its own negation. — Bob Ross

As you are aware, this would be an induction then.

Firstly, I could apply both of these indirectly to reality without any contradiction because, using the law of noncontradiction, I can create situations where the law of noncontradiction doesn't necessarily have to occur (mainly absent of sentient beings). — Bob Ross

What does indirect application to reality mean? I only see that as an inductive belief about reality. This isn't an applicable knowledge claim, so there is no application to reality. If there are no sentient beings, then there is no possibility of application knowledge.

Don't get me wrong, I agree with you in the sense that both are inapplicable plausibilities, but that is with respect to direct application. — Bob Ross

Can you describe what an indirect application to reality would be?

I may decide, upon assessing the state of a currently unobserved thing, to decide that the outcome should calculated as if they are superpositioned (this is how a lot of the quantum realm is generally understood). This can be indirectly applied to reality without any contradiction. — Bob Ross

Superpositioning, to my understanding, is essentially probability. There are X number of possible states, but we won't know what state it will be until we measure it. The measurement affects the position itself, which is why measuring one way prevents us from measuring the other way. You won't applicably know the state until you apply that measurement, so the belief in any particular outcome prior to the measurement would be an induction.

I agree with you here, but now we are getting into another fundamental problem (I would say) with your terminology: if a "possibility" is what one has experienced once before, then virtually nothing is a possibility. — Bob Ross

Great! We might be nearing a limitation for where I've thought on this. Just as we can construct detailed contexts to the point we could hardly claim applicable knowledge on anything, we can do so with inductive cogency. For example, I could state that to know a particular car is mine, it needs to be identical to the atomic level. Once I've measured that, I could say, "The quantum level". Of course, elections are moving around constantly, so from one moment to the next, I would say I had a brand new car.

The point of identity, the ability to discretely experience in a meaningful way, is to construct limitations of context that allow us to understand and interact with the world in an accurate and helpful way to us. This can be called, "rational". If I construct a context that is so detailed, it takes years to conclude even one discrete claim of knowledge, or the requirements are impossible to apply, what use is it?

I can identify a field of grass, a blade of grass, a piece of grass, ad infinitum. The point is to define it in such a way and context, as to be useful. The same goes with inductions. If I define a car as X, know that an attribute of a car is that it starts, I can say it is possible that a car can start. If I define what a car is as needing 10 hours of poking prodding, and dismantling to applicably know it, the distinctive knowledge useless in my every day application. If I define each car as separate entities, and only insist I know it is possible for this car to start, but not possible for any other car to start, then I make it a plausibility.

Is that useful to me? Depends on my context, but for most context of every day use, probably not. At that point I remove a hierarchy. So everything I have left over at that point is comparative plausiblities. Even though its a car, I'm trapped in my inability to analyze plausibilities. Maybe the car doesn't turn on. Maybe it turns into a demon. Maybe the ignition is actually in a hidden panel undeneath the floor board. Without a possibility comparison, I'm rationally trapped in my inability to justify one plausibility as being more cogent than another.

The addition of the hierarchy of induction is not to state, "This is true." Its the introduction of distinctive definitions, that have examples of being applied to reality without contradiction. To my mind, this distinction is useful. To another, perhaps it is not. Perhaps there are better words and phrases depending on your context that would be more useful to you. This is how all new claims work. A new distinctive knowledge is introduced that can be applicably known. Do we amend our context to use it, or reject it? You cannot force an individual to accept or reject it. You must show them it is a tool that can be useful.

I think there is rigidity within your epistemology that mine lacks, as I see it more as an elastic continuum of sureness. I don't know if that makes any sense or not. — Bob Ross

No, this makes perfect sense, and I hope you see that I agree with you that distinctive knowledge is infinitely elastic. There are infinite possibilities of how to define the world. Infinite contexts. Infinite sounds, language, etc. The question is, can you construct something that is useful? That fits the needs of your context at the time? Can it be used between more than one person? There is no reason the word "sheep" has to mean anything. There is nothing in reality that necessitates it. It just just an agreement we hold, because the word "sheep" has a use to us that we can use in our own lives, and in communicating to others.

"Hard consciousness", as you put it, is exactly what I am trying to convey here in conjunction with your "possibility" term: by definition, I can never claim it is "possible" for someone else to have internal monologue. Even if you knew that the person could not physically lie about it, you would never be able to claim it is "possible" because you have never experienced it yourself (even if you have experienced internal monologue, you haven't experienced it particularly within them). — Bob Ross

Full agreement. I do not think there is anything wrong with applicably knowing the limits of what you can applicably know. I find it a strength of the theory.

We cannot, under your terms, claim that a "bat can think", only that it is a plausibility. Even if we scanned their brains and it turns out the necessary, similar to ours, faculty exists for thought, we would never be able to label it as a "possibility" because we have not experience a bat thinking. — Bob Ross

Again, this depends upon your context. I could state that thinking is not just brain activity, but the ability to react to stimuli in a way that does not kill the creature. So I could place a bad smelling and rotten piece of fruit next to a fresh piece of fruit, and see what the bat does. If we state "thinking" is having the ability to reason at the level of an average human, than a bat will never be applicably known as thinking.

Again, fantastic assessment. I think you understand the theory pretty well now. The question to you is, is it useful for you? Is it logically consistent? Can it solve problems that other theories of knowledge cannot? And is it contradicted by reality, or is it internally consistent? Thanks again, I look forward to hearing from you.

Hello @Philosophim,

An inapplicable plausibility is different enough from a plausibility to warrant a separate identity in the heirarchy.

It is completely up to you, but I think that inapplicable plausibilities should be a plausibility; It is just that, in order to avoid contradictions, "plausibility" shouldn't be defined as what can be applicably known, just what one believes is "true" (or something like that). What can be applicably known would, therefore, be a subcategory of plausibility, namely "applicable plausibilities", and what cannot be applicably known would be another subcategory, namely an "inapplicable plausibility". On a separate note, the potentiality of a belief would be differentiated between irrational inductions and all other forms (as in it is irrational if it has no potential). And it is not necessarily always the case that a belief that cannot be applied to reality has no potential to occur and, thusly, there is a meaningful distinction between irrational inductions and inapplicable plausiblities (as in the latter is guaranteed to have potential, but cannot be applied). I just think that a contradiction arises if you define "plausibility" as always applicable (can be applied). You could, on the flip side, decide that the belief in what cannot be applied to reality is irrational and, consequently, that would make it an irrational induction.

This is correct. An irrational induction is a belief that something exists, despite applicable knowledge showing it does not exist.

Fair enough.

What does indirect application to reality mean? I only see that as an inductive belief about reality. This isn't an applicable knowledge claim, so there is no application to reality. If there are no sentient beings, then there is no possibility of application knowledge.

What I meant by "indirect" and "direct" seems to be, in hindsight, simply an inductive belief about reality (you are right). But my point I was trying to convey is that we produce meaningful probabilistic models based off of the idea that something is in multiple states at once, which doesn't really abide by the law of noncontradiction in a traditional sense at least.

Superpositioning, to my understanding, is essentially probability. There are X number of possible states, but we won't know what state it will be until we measure it. The measurement affects the position itself, which is why measuring one way prevents us from measuring the other way. You won't applicably know the state until you apply that measurement, so the belief in any particular outcome prior to the measurement would be an induction.

I agree. I was merely conveying that, to build off of what you said here, we don't assume the law of noncontradiction in terms of some quantum "properties" (so to speak), but the contrary. For example, a 6-sided die is considered to have 6 states. Even when the subject isn't observing the die, they will assume the law of noncontradiction: it is in one of the 6 states. Whereas, on the contrary, electrons can have two spin states: up or down. However, unlike the previous 6-sided die example, the subject, if they are quantum inclined (:, will assume the electron is equally likely in both positions (thus, not assuming the law of noncontradiction in the same sense as before).

Great! We might be nearing a limitation for where I've thought on this.

I think that, to supplement what you stated, possibility really isn't defined as clear as it should be. Instead of what "has been experienced before", it should be what "is similar enough to what one has experienced before". This is what I mean by rigidity (although I understand you agree with me on it being elastic): "possibility", as defined as what has been experienced before, implies (to me) that you have to experience it once before in a literal, rigid, sense. On a deeper level, I think it implies that experiences tend to be more like universals and less like particulars. For me, defining it in the previously mentioned refurbished way implies that subjective threshold.

Further, I think that the terminology is still potentially somewhat problematic. Firstly, your essays claim that probabilities are the most cogent, yet they actively depend on possibilities. There is no validity in probabilities, or honestly math in its entirety, if we weren't extrapolating it from possibilities (numbers in actuality, in reality). To say that the probability of 1/52 is more cogent than a possibility seems wrong to me, as I am extrapolating that from the possibility of there being 52 cards. Maybe it is just a difference between cogency and sureness, but I am more sure that 52 cards are possible than any probability I can induce therefrom. Secondly, it seems a bit wrong to me to grant probabilities their own category when there can be plausible probability claims and possible probability claims. For example, it becomes even more clear (to me) that I am more sure of the possibility of 52 cards when I consider it against specifically 1/N probability where N is a quantity that I haven't experienced in actuality (in reality). 1/N would be a probability that is really just a "plausible probability", contrary to a "possible probability" which would be a quantity, such as 52, that I can claim is possible. One is, to me, clearly a stronger claim than the other. Furthermore, probabilities are really just a specific flavor of mathematical inductions, which it seems odd that they have their own category yet mathematical inductions aren't even a term. For example, if I have a function F(N) = N + 1, this is a mathematical induction but not a probability. So, is it a plausibility? Is it a possibility? Depends on whether N is something experienced before or not (or how loosely we are defining similar enough). Probabilities are considered the most cogent, but is 1/N probability, where N is an unexperienced number in actuality, really more cogent than F(N), where N is a number experienced in actuality? I think not. On the flip side, is F(N), where N is an unexperienced number in actuality, more cogent than a 1/N probability where N is a number experienced in actuality? I think not. What if F(N) and 1/N are a number, N, that has not been experienced in actuality before? Are they equally as cogent? F(N) would be a plausibility, and I would say probability too, but probability would be considered more cogent simply because it has its own term (at least that is how I am understanding it). In reality, I think mathematical inductions (which includes probability) are subject to the same, more fundamental, categories: possibility, plausibility (and its subtypes), and irrational induction. Also, F(N) and 1/N where N is unexperienced and so large it can't be applied to reality would both be inapplicable plausibilities. Therefore, I think we are obligated to hold the position that an inapplicable plausibility mathematical induction (such as F(N) where N is inapplicable) are less cogent than an applicable plausibility (such as I can apply the existence of this keyboard without contradiction to reality) because fundamentally, mathematics, abides by the same rules. But, however, an applicable plausibility mathematical induction (such as F(N) where N is applicable) would be more cogent than probably every other non mathematical plausibility I can come up with because the immediateness of numbers, and its repetition, surpasses pretty much all others.

Thirdly, it also depends on how you define "apply to reality" whether that holds true. Consider the belief that you have thoughts: is your confirmation of that ever applied to "reality"? It seemed as though, to me, that your essays were implying sensations outside of the body, strictly, which would exclude thoughts. However, the claim that you even have thoughts is a belief and, therefore, must be subject to the same review process. It seems as though your thoughts are the initial beliefs being applied to "reality", which seems to separate the two concepts; Do you applicably know that you think? I don't apply my thoughts to reality in the sense that I would about whether a ball will roll down a hill: my thoughts validate my thoughts. If my thoughts validate my thoughts, then we may have an example of one of the most knowable beliefs for the subject that is technically inapplicable. However, if we define the thinking process as an experience, then we can say it is possible because we have experienced it before. However, most importantly, that directly, and necessarily, implies that you are not thought but, rather, you experience thought. On the contrary, if you don't experience thought, and subsequently the separation between the two isn't established, then you cannot claim that your own thoughts are possible, since you are incapable of experiencing them.

he question to you is, is it useful for you? Is it logically consistent? Can it solve problems that other theories of knowledge cannot? And is it contradicted by reality, or is it internally consistent?

I think that it is an absolutely brilliant assessment! Well done! However, I think, although we have similar views, that there's still a bit to hash out.

I look forward to hearing from you,
Bob

It is completely up to you, but I think that inapplicable plausibilities should be a plausibility; It is just that, in order to avoid contradictions, "plausibility" shouldn't be defined as what can be applicably known, just what one believes is "true" — Bob Ross

I agree with this! I got caught up in my own verbiage, and need to separate the inductions by the ability to apply applicable knowledge, that I forgot one does not believe one can applicably know something to believe it is real.

On a separate note, the potentiality of a belief would be differentiated between irrational inductions and all other forms (as in it is irrational if it has no potential). — Bob Ross

Here, I am very careful to not use the word potentiality, because I think it loses meaning as an evaluative tool in the inductive hierarchy. Colloquially, I think its fine. I understand what you mean. But the reason why I don't think it works in the hierarchy is because the inductive hierarchy is not trying to assert what has more potential of being true, only which induction is more rational.

I believe this is a very important distinction. Recall that what is applicably known is based upon our context as well. A very narrow context might lead us to some strange probabilities and possibilities. It doesn't mean they are potential, as reality may very well defy them. They are simply rational inductions based on the applicable knowledge we have at the time.

Further, potentiality is not something the hierarchy can objectively measure. Let say that in a deck of 52 cards, you can choose either a face card, or a number card will be drawn next. You have three guesses. Saying number cards is more rational going by the odds. But the next three cards drawn are face cards. The deck was already shuffled prior to your guess. The reality was the face cards were always going to be drawn next, there was actually zero potential that any number cards were going to be pulled in the next three draws. What you made was the most rational decision even though it had zero potential of actually happening.

Lets go one more step. Same scenario. Only this time, I didn't put any number cards in the deck, and didn't tell you. You believe I made an honest deck of cards, when I did not. You had no reason to believe I would be dishonest in this instance, and decided to be efficient, and assume the possibility I was honest. With this induction, I rationally again choose number cards. Again however, the potential for number cards to be drawn was zero.

An induction cannot predict potentiality, because an induction is a guess about reality. The conclusion is not necessarily drawn from the premises. Some guesses can be more rational than another, but what is rational within our context, may have zero potential of actually being. That being said, generally acting rationally is a good idea, because it is based on what we do applicably know about the world, versus what we do not. It is less uncertainty, but has no guarantee.

So, I do understand your intention behind using potentiality, and in the end, it might boil down to semantics and context. For the purposes of trying to provide a clear and rational hierarchy, I'm just not sure whether potentiality is something that would assist, or cloud the intention and use of the tool.

Whereas, on the contrary, electrons can have two spin states: up or down. However, unlike the previous 6-sided die example, the subject, if they are quantum inclined (:, will assume the electron is equally likely in both positions (thus, not assuming the law of noncontradiction in the same sense as before). — Bob Ross

Not to get too off on a tangent here, but I believe the only reason we calculate it as having both, is because it is equally likely they could be either prior to measurement. It is like calculating what would happen for each side of a six sided die prior to rolling the die. But perhaps we shouldn't wade into quantum physics for examples, as I believe it mostly to be a field of conceptual land mines in any conversation, much less while addressing a new theory of knowledge!

To say that the probability of 1/52 is more cogent than a possibility seems wrong to me, as I am extrapolating that from the possibility of there being 52 cards. — Bob Ross

Probability does not assert there are possibly 52 cards, it asserts that there are 52 cards, whether this be based on applicable knowledge or belief. Of course, what if I'm having a thought experiment? This is a great time to get into math.

Math is the language of discrete experience, and distinctive knowledge. 1, is "a discrete experience" One blade of grass. A field of grass. One piece of grass. It is the abstraction of our ability to discretely experience "a" thing. "Two" is the idea that we can create 1 discrete experience, and another discrete experience. The discrete experience of both together as one identity, is two.

Math is the logic of discrete experience. It is why it fits so well into our world view, because it is an abstraction of how we view the world. When I say, "two blades of grass," this relies on a context of two identities that are similar enough to be labeled "blades of grass". It does not assert their equality on a mass or atomic level. This is because it is an abstraction of our ability to contextualize identities down to their essential properties for the purposes of addition and subtraction, while throwing out all non-essential properties.

The proofs of math work, because they can be confirmed by our discrete experience being actively applied. Therefore I can abstract that if I have 20 bushels of hay, and take away 2 bushels of hay, I have 18 bushels of hay. I can discretely experience that in my head right now. I'm not claiming what constitutes a bushel. I have no need for the weight of each bushel down to the ounce, its color, smell, etc. I just need a discrete experience of a bushel, and this is enough to abstract something useful for reality.

Even so, just like language, math must be applied to reality without contradiction to be applicably known. I can predict that a feather will fall at 9.8 meters a second, but may find in my measurements it does not . I might state that my 5 bushels of hay at 20 pounds each will result in 100 pounds of hay, but upon actual measurement, I find they only weigh 98 pounds.

For example, if I have a function F(N) = N + 1, this is a mathematical induction but not a probability. So, is it a plausibility? Is it a possibility? — Bob Ross

This is a known function. This is an observation of our own discrete experience. If I take N identities, and add one more, then this will equal the identities added together. So, 2+1 are the same as the identity of 3. This applies to the abstract of discrete experience, which when applied to reality could specifically be bushels of hay, sheep, etc. As it is in its functional form, it is only a descriptive logic of discrete experiencing.

This leads to,

Thirdly, it also depends on how you define "apply to reality" whether that holds true. Consider the belief that you have thoughts: is your confirmation of that ever applied to "reality"? — Bob Ross

This goes back to the beginning of the essay. Recall that what we discretely experience, we know. That is because it is impossible to deny that we discretely experience. When I discretely experience something that I label as "thoughts" in my head, I distinctively know I have them. Applicable knowledge is when we apply our distinctive knowledge outside of our own ability to create identity as we wish. I might believe that the apple in front of me is healthy for me, but when I bite into it, I find it rotten. The apple is something apart from my own identifiable control in this way. Your thoughts are also reality.

Distinctive knowledge occurs, because the existence of having thoughts is not contradicted. The existence of discretely experiencing cannot be contradicted. Therefore it is knowledge. I label this special type of knowledge distinctive, because it is something within our control. I can create a world of magic and unicorns distinctively, but there is a limit when applied to that which I do not have control over, reality.

So, going back again to abstracting the idea of 1/52 playing cards, I can distinctively create the limitation in my head that there are 52 playing cards, that they are randomly shuffled, and 1 is pulled without applicably knowing which card it is. I can then establish the limitations of what the necessary possibilities are knowing what each card is within the deck. But, if I applicably apply this probability to any one particular deck in reality, what actually happens is what actually happens.

Perhaps some of the cards were not all the same weight or smoothness, and it causes some of them to stick in the shuffle. Perhaps there is some strange law of physics we didn't know about in reality that causes the Ace of spades to come up more frequently. Math is the ideal of distinctive knowledge, but it must still be applied to reality when it makes a prediction about a particular reality to see if it is applicably known.

Secondly, it seems a bit wrong to me to grant probabilities their own category when there can be plausible probability claims and possible probability claims. — Bob Ross

We cannot meaningfully understand what plausible probability is, without first distinctively and applicably knowing what plausibility, and probability are first. Recall then, that a plausible probability is a chain of reasoning. I have a plausibility, and from that plausibility, I assert a probability. I have a possibility, and from that I assert a probability. I have applicable knowledge, and from that applicable knowledge, I assert a probability.

If I could compare all three inductions, it would be most rational to use the one that has applicable knowledge as its base.

1. Its plausible the dark side of the moon is on average hotter than the light side of the moon, therefore it is probable any point on the dark side of the moon will be hotter than any point on the light side of the moon.
2. Its possible the side of the moon facing away from Earth is on average colder than the light side of the moon, therefore it is probable any point on the dark side of the moon will be colder than any point on the light side of the moon.
3. The dark side of the moon has been measured on average to be cooler than the light side of the moon at this moment, therefore it is probable any point on the dark side of the moon will be colder than any point on the light side of the moon.

As you can see, intuitively, and rationally, it would seem the close the base of the chain is to applicable knowledge, the more cogent the induction.

I think that it is an absolutely brilliant assessment! Well done! However, I think, although we have similar views, that there's still a bit to hash out. — Bob Ross

Thank you! Yes, please continue to drill into the theory as much as you can. Its usefulness is only as good as its ability to withstand critiques. Again, greatly enjoying the conversation, and my thanks for your pointed assessment and crticism!

Hello @Philosophim,

Further, potentiality is not something the hierarchy can objectively measure. Let say that in a deck of 52 cards, you can choose either a face card, or a number card will be drawn next. You have three guesses. Saying number cards is more rational going by the odds. But the next three cards drawn are face cards. The deck was already shuffled prior to your guess. The reality was the face cards were always going to be drawn next, there was actually zero potential that any number cards were going to be pulled in the next three draws. What you made was the most rational decision even though it had zero potential of actually happening.

Although I understand what you are saying, and I agree with you in a sense, potentiality is not based off of hindsight but, rather, the exact same principle as everything else: what you applicably know at the time. Prior to drawing three face cards, if you applicably know that there is at least one number card in the 52 (or that you have good reason to believe that there is one regardless of whether you directly experienced one), then there is a potential that you could draw it. Regardless of whether it is the most rational position, it is nevertheless a rational position. However, if you applicably know that there are no number cards in the 52 (or you have good reason to doubt it), then it has no potential and, therefore, it is irrational.

Only this time, I didn't put any number cards in the deck, and didn't tell you. You believe I made an honest deck of cards, when I did not. You had no reason to believe I would be dishonest in this instance, and decided to be efficient, and assume the possibility I was honest. With this induction, I rationally again choose number cards. Again however, the potential for number cards to be drawn was zero.

Again, I understand what you are saying and I agree. However, within the context (in the heat of the moment) the numbers do have the potential to be in the deck if you have assessed that your knowledge deems it so. In hindsight, which refurbishes the context and maybe a new context depending on how one looks at it, you can now claim that there was no potentiality. But with respect to whether it had potentiality prior to this new knowledge that they lied, it is more rational to conclude that it has potentiality. I would argue, furthermore, that this assessment is actually necessary for one to even pick numbers in the first place (in terms of your example): if they don't think there is any potential for there to be a number, then they wouldn't pick numbers (and if they did, then it would be irrational). Although sometimes potentiality and "possibility" (in your terms) coincide, it isn't necessarily the case that something only has potential if you have "experienced it once before".

An induction cannot predict potentiality, because an induction is a guess about reality.

It is a part of the guess. First I make an educated guess that there is potential for water to exist on another planet somewhere, then I guess on how likely that is and, thereafter, whether it really constitutes as knowledge or not (with consideration to my discrete and applicable knowledge). Potentiality is the first (or at least one of the first) considerations when attempting to determine knowledge. If the subject determines there is no potential, then they constitute any further extrapolations as irrational and thereby disband from it.

Some guesses can be more rational than another, but what is rational within our context, may have zero potential of actually being

It isn't about what can potentially occur in light of new evidence afterwards, it is about what can potentially occur in light of the current evidence. It is perfectly fine if we find out later that what we thought had no potential actual does have some, or vice-versa. This is how it is for all contexts and even the induction hierarchies. Potentiality is a guide to what one should pursue (as one of the first considerations), and I would argue we all implicitly partake in it: that's why if you can convince someone that they hold a contradiction, they will feel obligated to refurbish their beliefs (most of the time). It is the fact that they know they are holding an irrational belief, due to the potentiality being nonexistent, that motivates their will to change. This would be, colloquially speaking, "possibility". I agree that this may just be a sematical difference, but I think defining possibility as "what one has experienced once before" eliminates the other meaningful aspect of the term (potentiality).

It is less uncertainty, but has no guarantee

Nothing is guaranteed. It could very well be that in five years we will look back, in hindsight, and "know" our understanding of induction hierarchies was utterly wrong (with consideration to new evidence). This doesn't mean that we can't use the induction hierarchies now, does it? I don't think so. So it is with potentiality. In my head, this would be like claiming that we can't utilize "possibilities" because, in the future, it may be the case that we find out it never actually was possible.

For the purposes of trying to provide a clear and rational hierarchy, I'm just not sure whether potentiality is something that would assist, or cloud the intention and use of the tool.

Personally I think it is necessary, but of course do what you deem best!

Math is the logic of discrete experience.

I agree for the most part: math deductions are the logic of discrete experience and we inductively apply that in the abstract. But I think the problem remains: where does mathematical inductions fit into the hierarchy?

This is a known function. This is an observation of our own discrete experience

It is an observation of our own discrete experience (when it is a deduction), but that doesn't exempt it from the hierarchy (when it is an induction). 1 + 2 = 3 is an observation of our own discrete experience, whereas X + Y = Z (where all of them are numbers never discretely experienced before) is based off of our own discrete experience (it's an induction, as you are probably well aware). When I state that 1 + 2 = 3, I know that these numbers are possible, whereas I don't know that is the case in terms of X + Y = Z for all numbers. Furthermore, there is actually cases where I know that they aren't possible, in the case of imaginary numbers (i), such as 1 + √-25 = 5i. We also apply math to actual infinities that may not actually exist (such as infinity and negative infinity and even PI and E, which are irrational numbers). When we take the limit approaching infinity, are you claiming that that is an observation of our own discrete experience (or a distant extrapolation)? Therefore, the function F(N) is not an observation of our own discrete experience (that would be a deduction) but, rather, an induced function meant to predict based off of our deducible knowledge (it is literally an induction put into a predictive model). This directly implies that, for N in F(N) it could either (1) be a possible number, (3) applicable plausible number (with regards to your terms: has potential and can be applied but isn't proven to be possible), (4) inapplicable plausible number (has potential and hasn't been proven to be possible but cannot be applied), or (5) an irrational number (has no potential, isn't possible, and has no potential). I think you are right in the sense that, in the abstract, X + Y = X + Y will always hold, but saying it will always hold is an induction (it is just so ingrained, as you stated, into our discrete experience itself that we hold it dear--in my terms it is one of the most immediate things, closest to our existence). Most importantly, none of this exempts it from the hierarchy of inductions and, therefore, I would like to know where you were classify it?

When I discretely experience something that I label as "thoughts" in my head, I distinctively know I have them.

My intention is not to try and put words in your mouth, but I think you are, if you think this, obliged to admit that you and thought are distinct then. I don't think you can hold the position that we discretely experience them without acknowledging this, but correct me if I am wrong. If you do think they are separate, then I agree, as I think that your assessment is quite accurate: we do apply our belief that we have thoughts to reality, because the process of thinking is apart of experience (reality). It is just the most immediate form of knowledge you have (I would say): rudimentary reason.

Distinctive knowledge occurs, because the existence of having thoughts is not contradicted. The existence of discretely experiencing cannot be contradicted. Therefore it is knowledge.

I agree!

We cannot meaningfully understand what plausible probability is, without first distinctively and applicably knowing what plausibility, and probability are first.

If I follow this logic, I still end up with a problem: without first distinctively and applicably knowing what mathematical induction is, I cannot meaningfully understand what a probability is. Therefore, why isn't mathematical inductions a category on the induction hierarchy? Why only probabilities?

Furthermore, I apologize as my term "plausible probability" is confusing: I am not referring to a chain plausibility -> probability. What I was really referring to was something we've previously discussed a bit: there are different cogencies within probabilities since they are subject, internally and inherently, to the other three categories (irrational, possibility, and plausibility). Same goes for math in general. Two separate probabilities, with the same chances, could be unequal in terms of sureness (and cogency I would say). You could have a 33% chance in scenario 1 and 2, but 1 is more sure of a claim than 2. This would occur if scenario 1 is X/Y where X and Y are possible numbers and scenario 2 is X/Y where X and Y are plausible numbers (meaning they have the potential to exist, but aren't possible because you haven't experienced them before). My main point was that there is a hierarchy within probabilities (honestly all math) as well.

Moreover, another issue I was trying to convey is why does probability have its own category, but not mathematical inductions? I think what your "probability" term really describes, in terms of its underlying meaning, is mathematical inductions. If I induce something based off of F(N), this is no different than inducing something off of 1/N chances, except that, I would say, anything induced from the former is more cogent. This is because if I base a belief on there being a 90% chance, that will always be less certain (because it is a chance) than anything based off of F(N) (directly that is). For example, if I induce that I should go 30 miles per hour in my car to get to may destination, which is 60 miles away, in 2 hours, that is calculated with numbers that are a possibility or plausibility (the mathematical operations are possible, but not necessarily the use of those operations on those particular numbers in practicality). But this is more cogent than an induction that I should bet on picking a number card out of a deck (no matter how high the chances of picking it) because the former is a more concrete calculation to base things off of (it isn't "chances", in the sense that that term is used for probability). Don't get me wrong, the initial calculation, because it is also math, of probability is just as cogent as any other mathematical operation (it's just division, essentially), but anything induced from that cannot be more cogent than something directly induced from a more concrete mathematical equation such as 60 miles / 30 mile per hour = 2 hours. Notice that these are both inductions but one doesn't really exist in the induction hierarchies (mathematical inductions) while the other is the most cogent induction (probability). Why?

1. Its plausible the dark side of the moon is on average hotter than the light side of the moon, therefore it is probable any point on the dark side of the moon will be hotter than any point on the light side of the moon.
2. Its possible the side of the moon facing away from Earth is on average colder than the light side of the moon, therefore it is probable any point on the dark side of the moon will be colder than any point on the light side of the moon.
3. The dark side of the moon has been measured on average to be cooler than the light side of the moon at this moment, therefore it is probable any point on the dark side of the moon will be colder than any point on the light side of the moon.

This may be me just being nit picky, but none of those were probable (they are not quantitative likelihoods, they are qualitative likelihoods). If you disagree, then I would ask what the denominator is here. But my main point is there is a 4th option you left out: if I can create a mathematical equation that predicts the heat of a surface based off of it's exposure to light, then it would be more cogent than a probability (it is a mathematical induction based on a more concrete function than probability) but, yet, mathematical inductions aren't a category.

Furthermore, #2 isn't possible unless you've experienced the side of the moon facing away from the earth being colder than when you experienced it on the light side. This is when we have to consider what we mean by "what we have experienced before". This is more of potentiality than possibility (in your terms). I think that your use of "possible" is more in a colloquial sense in #2.

As you can see, intuitively, and rationally, it would seem the close the base of the chain is to applicable knowledge, the more cogent the induction.

I agree!

Look forward to hearing from you,
Bob

Although I understand what you are saying, and I agree with you in a sense, potentiality is not based off of hindsight but, rather, the exact same principle as everything else: what you applicably know at the time. — Bob Ross

I have been thinking about this for some time. I like the word "potential". I think its a great word. The problem is, it comes from a time prior to having an assessment of inductions. Much of what you are describing as potential, are a level of cogency that occurs in both probability, and possibility. The word potential in this context, is like the word "big". Its a nice general word, but isn't very specific, and is used primarily as something relative within a context.

Perhaps this is why I'm shying away from implementing it as something measurable within the hierarchy. Logically, I can only say inductions are more cogent, or rational than another. I have absolutely no basis to measure the potential of an induction's capability of accurately assessing reality. At the most, I suppose I would be comfortable with stating that "potential" is anything that is the realm of probability or possibility, as these directly rely on claims of applicable knowledge in their chain of rationality, but I cannot use it as anything more than that before it turns into an amorphous general word that people use to describe what they are feeling at the time.

Potentiality is the first (or at least one of the first) considerations when attempting to determine knowledge. If the subject determines there is no potential, then they constitute any further extrapolations as irrational and thereby disband from it. — Bob Ross

This is what I mean by saying the word begins to morph into something too general. Now a word which could describe a state of probability or possibility, becomes an emotional driving force for why we seek to do anything. I could hold an irrational belief, and say its because its potentially true. Potential in this case more describes, "I believe something, because I believe something (It has potential). Its not that potential is a poor word, its just as its been used, its too poorly defined and amorphous. Without concrete measurement, it can be used to state that any belief in reality could be true. So until a more concrete and defined use of the word can be created, I think I'm going to stick with evaluating inductions in terms of rationality, instead of potentiality.

If I induce something based off of F(N), this is no different than inducing something off of 1/N chances, except that, I would say, anything induced from the former is more cogent. — Bob Ross

But I think the problem remains: where does mathematical inductions fit into the hierarchy? — Bob Ross

So earlier, I was trying to explain that math was the logical conclusions of being able to discretely experience. I remember when I learned about mathematical inductions, I thought to myself, "That's not really an induction." The conclusion necessarily follows from the premises of a mathematical induction. I checked on this to be sure.

"Although its name may suggest otherwise, mathematical induction should not be confused with inductive reasoning as used in philosophy (see Problem of induction). The mathematical method examines infinitely many cases to prove a general statement, but does so by a finite chain of deductive reasoning involving the variable n, which can take infinitely many values."
https://en.wikipedia.org/wiki/Mathematical_induction

N + 1 = F(N) is a logical process, or rule that we've created. Adding one more identity to any number of identities, can result in a new identity that describes the total number of identities. It is not a statement of any specific identity, only the abstract concept of identities within our discrete experience. Because this is the logic of a being that can discretely experience, it is something we can discretely experience.

We could also state N+1= N depending on context. For example, I could say N = one field of grass. Actual numbers are the blades of grass. Therefore no matter how many blades of grass I add into one field of grass, it will still be a field of grass. I know this isn't real math, but I wanted to show that we can create concepts that can be internally consistent within a context. That is distinctive knowledge. "Math" is a methodology of symbols and consistent logic that have been developed over thousands of years, and works in extremely broad contexts.

My intention is not to try and put words in your mouth, but I think you are, if you think this, obliged to admit that you and thought are distinct then. I don't think you can hold the position that we discretely experience them without acknowledging this, but correct me if I am wrong. If you do think they are separate, then I agree, as I think that your assessment is quite accurate: we do apply our belief that we have thoughts to reality, because the process of thinking is apart of experience (reality). It is just the most immediate form of knowledge you have (I would say): rudimentary reason. — Bob Ross

I don't believe you did in this case. If you recall, thoughts come after the realization we discretely experience. The term "thought" is a label of a type of discrete experience. I believe I defined it in the general sense of what you could discretely experience even when your senses were shut off. And yes, you distinctively know what you think. If I think that a pink elephant would be cool, I distinctively know this. If I find a pink elephant in reality, this may, or may not be applicably known. Now that you understand the theory in full, the idea of thoughts could be re-examined for greater clarity, definition, and context. I only used it in the most generic sense to get an understanding of the theory as a whole.

Two separate probabilities, with the same chances, could be unequal in terms of sureness (and cogency I would say). You could have a 33% chance in scenario 1 and 2, but 1 is more sure of a claim than 2. This would occur if scenario 1 is X/Y where X and Y are possible numbers and scenario 2 is X/Y where X and Y are plausible numbers (meaning they have the potential to exist, but aren't possible because you haven't experienced them before). My main point was that there is a hierarchy within probabilities (honestly all math) as well. — Bob Ross

I think again this is still the chain of rationality. A probability based upon a plausibility, is less cogent than a probability based on a possibility.

Back to your idea of using math inductively.

For example, if I induce that I should go 30 miles per hour in my car to get to may destination, which is 60 miles away, in 2 hours, that is calculated with numbers that are a possibility or plausibility (the mathematical operations are possible, but not necessarily the use of those operations on those particular numbers in practicality). But this is more cogent than an induction that I should bet on picking a number card out of a deck (no matter how high the chances of picking it) because the former is a more concrete calculation to base things off of (it isn't "chances", in the sense that that term is used for probability). — Bob Ross

You distinctively know that if you travel 30 miles per hour to get to a destination 60 miles away, in 2 hours you will arrive there. Now, if you get in your vehicle, can you consistently travel 30 miles per hour? Is the destination exactly 60 miles away, or is it 60 and some change? If say that any decimals are insignificant digits, and you can travel exactly 20 miles per hour, and the distance is exactly 60 miles away, then you will arrive in exactly two hours, because we have defined distance and time and applied it to reality to work that way without contradiction.

A probability is not a deduction, but an induction based upon the limitations of the deductions we have. Probability notes there are aspects of the situation that we lack knowledge over. As noted earlier, a randomly shuffled deck of cards is not really random. We call it "random" because we distinctively and applicably know that we lack the ability to observe the order it was shuffled in. We induce what is rationally most likely when we lack this information, based on the other information we do know.

As such, the first case is actually a deduction, the second is an induction.

This may be me just being nit picky, but none of those were probable (they are not quantitative likelihoods, they are qualitative likelihoods). — Bob Ross

You are correct! I was being sloppy. I was more interested in conveying the idea of chains of rationality. Instead of average, I should have said "median". In that case we know we have a majority of spots on one side that would be above or below the temperature of the other side, and could create a probability.

But my main point is there is a 4th option you left out: if I can create a mathematical equation that predicts the heat of a surface based off of it's exposure to light, then it would be more cogent than a probability (it is a mathematical induction based on a more concrete function than probability) but, yet, mathematical inductions aren't a category. — Bob Ross

I think most of the conversation has boiled down to induction vs deductions with math. Math is a tool that can be used to create deductions, or inductions, just like distinctive knowledge. Looking at distinctive knowledge, everything inside of itself that is internally consistent is deduced. But I can induce something. I can state, "This distinctive knowledge applies to reality without contradiction, even though I haven't applied it to reality yet." This is the impetus of all beliefs. Trying to find a way to measure more rationally which beliefs we should spend the time and effort pursing is why we develop a system of knowledge, and use the inductive hierarchy.

Math is merely the logic of discrete experience. Meaning you can use math deductively, and also use some of those deductions to make predictions about reality. These aren't mathematical inductions, these are inductions based on math within its chain of rationality. Does this make sense?

Absolutely fantastic deep dive here Bob. I've wanted to so long to discuss how the knowledge theory applies to math, and its been a joy to do so. I also really want to credit your desire for "potentiality" to fit in the theory. Its not that I don't think it can, I just think it needs to be more carefully defined, and serve a purpose that cannot be gleaned with the terms we already have in the theory. Thank you again for the points, you are a keen philosopher!

Hello @Philosophim,

Absolutely fantastic deep dive here Bob. I've wanted to so long to discuss how the knowledge theory applies to math, and its been a joy to do so. I also really want to credit your desire for "potentiality" to fit in the theory. Its not that I don't think it can, I just think it needs to be more carefully defined, and serve a purpose that cannot be gleaned with the terms we already have in the theory. Thank you again for the points, you are a keen philosopher!

Thank you Philosophim! You are a marvelous philosopher yourself! I am also thoroughly enjoying our conversation. I agree in that our dispute is really pertaining, at a fundamental level, to two concepts: potentiality and math.

I have been thinking about this for some time. I like the word "potential". I think its a great word. The problem is, it comes from a time prior to having an assessment of inductions. Much of what you are describing as potential, are a level of cogency that occurs in both probability, and possibility. The word potential in this context, is like the word "big". Its a nice general word, but isn't very specific, and is used primarily as something relative within a context.

I agree, I definitely need to define it more descriptively. However, with that being said, at a deeper level, the term possibility is also like the word "big": it is contingent on a subjective threshold just like potentiality. Although I like your definition of it (what has been experienced once before), that very definition is also utterly ambiguous (from a deeper look). Just like how I can subjectively create a threshold of when something is "big", which you could disagree with (cross-referencing to your own threshold), I also subjectively create a threshold of what constitutes as "experiencing it before". Furthermore, I also subjectively create a threshold of what constitutes as having the potential to occur. I think we can definitely get further into the weeds about "possibility" and "potentiality", but all I am trying to point out here is that their underlying structure is no different.

Logically, I can only say inductions are more cogent, or rational than another.

I agree, I think potentiality is an aspect of rationality. If it has no potential, just like if it isn't possible, then it is irrational. Potentiality isn't separate from rationality (it is apart of rational thinking).

I have absolutely no basis to measure the potential of an induction's capability of accurately assessing reality

The basis is whether you think it aligns accurately with your knowledge. For example, although this may be a controversial example as we haven't hashed out math yet, I can hold that, even though I haven't experienced it, lining up (side by side) 2 in long candy bars for 3,000 feet has the potential to occur because it aligns with my knowledge (i.e. I do applicably know that there is 3,000 feet available to lay things and I do applicably know there are 2 in long candy bars); however, most importantly, according to your terminology, this is not possible since I haven't experienced it before. Likewise, without ever experiencing it, I can hold that it is irrational to believe that one can fit 7,000 2 in long candy bars, side by side long ways, within 1,000 feet (because, abstractly, 1,000 feet can only potentially hold 6,000 2 inch candy bars side by side). Yes, there is a level of error (mainly human error) that needs to be accounted for and, thusly, it is merely an ideal. But, nevertheless, I can utilize this assessment of potentiality to determine which is more cogent and which to not pursue (although both are not possibilities--as of yet--I should not sit there and try to fit 7,000 2 in long candy bars--side by side--within 1,000 ft since I already know it has no potential). Notice though, and this is my main critique, that the use of solely possibility (in your terms) within your epistemology strips the subject of being capable of making such a distinction (they are both not possible without further elaboration).

Much of what you are describing as potential, are a level of cogency that occurs in both probability, and possibility

I am failing to understand how this is the case? Potentiality is the component of colloquial use of "possibility" that got removed, implicitly, when your epistemology refurbished the term. Therefore, it does not pertain, within your terms, to possibility directly at all. Yes, in the sense that potentiality branches out to plausibility, possibility, and probability is true. But that is because it is a requisite (if it has no potential, it necessarily gets redirected to the irrational pile of claims). Something can't be plausible if it can be proven to have no potential (and it doesn't necessarily have to be "I've experienced the exact, contradictory, event to this claim, therefore it is an irrational induction": I don't have to experience failing to be able to fit 1,000,000 5 ft bricks into a 10 x 10 x 10 room to know that it is an irrational inductive belief). Moreover, something can't be probable (with an actual denominator) if it doesn't have potential. And, finally, it can't be possible (you couldn't have experienced it before) if it has no potential (and if you did experience it, legitimately, then it has potential). I think the main issue you may be having is that your new definition of possibility implicitly stripped this meaningful distinction out of "possibility" in favor of a new, less ambiguous term. However, now we must determine, assuming you agree with me, how to implement this distinction back into the epistemology. Otherwise, the subject is incredibly limited in what they can meaningfully induce about the world.

but I cannot use it as anything more than that before it turns into an amorphous general word that people use to describe what they are feeling at the time.

I agree: people could use it with no real substance. However, this is also true for possibility. I could make subjective thresholds for what constitutes "experiencing something before" that renders possibilities utterly meaningless. I think "rationality" isn't merely determining something a possibility, plausibility, or any other term: it is also about how one reasoned their way into the thresholds for those terms. I can dereference any term into a meaningless distinction, but how can we keep it meaningful for all subjects when it isn't a rigid distinction? I think we just have to agree, as two subjects conversing, on the underlying reasoning behind our subjective thresholds: that is rationality (what we both constitute as valid reasoning).

Now a word which could describe a state of probability or possibility, becomes an emotional driving force for why we seek to do anything.

I see where you are coming from and you are totally correct: people can de-value anything. However, I don't see how it is actually a probability or possibility: only that the distinction between what is irrational and rational (rational being probability, possibility, and plausibility) is necessarily potentiality (to one degree or another). All three terms within rational beliefs (not considering which is more rational than another, which could technically make a rational belief actually irrational if one determines another rational belief to be a better choice) inherent from this concept of potentiality: it is a requisite.

I could hold an irrational belief, and say its because its potentially true.

If we are defining an irrational belief as what has no potential to be true, then this statement is an irrational belief, within our subjective determination of what the term "irrational belief" should imply, because it directly contradicts the definition.

Potential in this case more describes, "I believe something, because I believe something (It has potential).

Awe, I see. This is what I was referring to a while ago (in our posts): people tend to make an illegitimate jump where they claim that "since it has potential, it is possible, therefore I believe it". This is not necessarily true though. Honestly, your defining of possibility as "experiencing it once before" is so brilliant for this very reason: something can have potential but yet never have been experienced, therefore it isn't possible (yet). Therefore, consequently, merely claiming something has potential ergo I believe it is true is irrational because, rationally speaking, something can't be constituted as "true" if it first isn't possible. Potentiality doesn't pertain to the "truth" of the matter, just a requisite to what one should rationally not pursue. It is a deeper level, so to speak, of analysis that can meaningfully allow subjects to reject other peoples' claims just like what you are describing.

Without concrete measurement, it can be used to state that any belief in reality could be true.

Not everything could be true. Firstly, not everything is possible (because we either (1) haven't experience it or (2) we have experienced contradictory events to the claim). Secondly, not everything has potential (because we may have experienced enough knowledge to constitute it as not having the capability to occur). Admittedly, potentiality and possibility are incredibly similar and that's why, traditionally, they are but one term. However, potentiality is a more broad claim, less bold and assertive, than possibility (if we define it as having experienced it before). Now, within this new terminology, we can boldly and assertively claim something is possible (assuming we agree on the subjective thresholds in place) because we have experienced it before. In regards to potentiality, we aren't boldly claiming that it can occur, just that there is potential for it to occur. This is more meaningful in terms of negation and not positive claims: we can meaningfully claim that something is irrational if it has no potential (assuming the subjective thresholds are agreed upon, like everything else). It isn't as meaningful in terms of two things that have potential and that's where the other terms come into play, but they only come into play once it is accepted that it has potential (that's why it is a requisite).

I think I'm going to stick with evaluating inductions in terms of rationality, instead of potentiality.

That is absolutely fine! My intention is not to pressure you into reforming it, but I do think this is a false dichotomy: this assumes potentiality is a separate option from rationality. Potentiality, and its consideration, is engulfed within rational thinking and the negation thereof is why it becomes irrational. We can't claim that something that has no potential is irrational if we aren't also claiming that if it does that it is rational to continue the analysis.

So earlier, I was trying to explain that math was the logical conclusions of being able to discretely experience. I remember when I learned about mathematical inductions, I thought to myself, "That's not really an induction." The conclusion necessarily follows from the premises of a mathematical induction. I checked on this to be sure.

"Although its name may suggest otherwise, mathematical induction should not be confused with inductive reasoning as used in philosophy (see Problem of induction). The mathematical method examines infinitely many cases to prove a general statement, but does so by a finite chain of deductive reasoning involving the variable n, which can take infinitely many values."
https://en.wikipedia.org/wiki/Mathematical_induction

This is true, but that is with respect to the mathematical operations, not the numbers themselves. I can say it is possible to perform addition because I have experienced it before, I cannot say that it is possible to add 3 trillion + 3 trillion because I haven't experienced doing that before with those particular numbers: I am inducing that it still holds based off of the possibility of the operation of addition. But, yes, you are correctt in the sense that philosophical induction is not occurring with respect to the operations themselves, but I would say it is occurring at the level of the numbers.

N + 1 = F(N) is a logical process, or rule that we've created. Adding one more identity to any number of identities, can result in a new identity that describes the total number of identities. It is not a statement of any specific identity, only the abstract concept of identities within our discrete experience. Because this is the logic of a being that can discretely experience, it is something we can discretely experience.

We could also state N+1= N depending on context. For example, I could say N = one field of grass. Actual numbers are the blades of grass. Therefore no matter how many blades of grass I add into one field of grass, it will still be a field of grass. I know this isn't real math, but I wanted to show that we can create concepts that can be internally consistent within a context. That is distinctive knowledge. "Math" is a methodology of symbols and consistent logic that have been developed over thousands of years, and works in extremely broad contexts.

I agree, but this doesn't mean it holds for all numbers. We induce that it does, but it isn't necessarily the case. We assume that when we take the limit of 1/infinity that it equals 0, but we don't know if that is really even possible to actually approach the limit infinitely to achieve 0. Likewise, we know that if there are N distinct things that N + 1 will hold, but we don't if N distinct things are actually possible (that is the induction aspect, which I think you agree with me on that, although I could be wrong).

I don't believe you did in this case. If you recall, thoughts come after the realization we discretely experience. The term "thought" is a label of a type of discrete experience. I believe I defined it in the general sense of what you could discretely experience even when your senses were shut off. And yes, you distinctively know what you think. If I think that a pink elephant would be cool, I distinctively know this. If I find a pink elephant in reality, this may, or may not be applicably known. Now that you understand the theory in full, the idea of thoughts could be re-examined for greater clarity, definition, and context. I only used it in the most generic sense to get an understanding of the theory as a whole.

Yes, I may need a bit more clarification on this to properly assess what is going on. Your example of the pink elephant is sort of implying to me something different than what I was trying to address. I was asking about the fundamental belief that you think and not a particular knowledge derived from that thought (in terms of a pink elephant). I feel like, so far, you are mainly just stating essentially that you just think, therefore you think. I'm trying to assess deeper than that in terms of your epistemology with respect to this concept, but I will refrain as I have a feeling I am just simply not understanding you correctly.

I think again this is still the chain of rationality. A probability based upon a plausibility, is less cogent than a probability based on a possibility.

Yes, but your essays made it sound like probability is its own separate thing and then you can mix them within chains of inductions. On the contrary, I think that "probability" itself is actually, at a more fundamental level, contingent on possibility and plausibility for it to occur in the first place.

You distinctively know that if you travel 30 miles per hour to get to a destination 60 miles away, in 2 hours you will arrive there.

Agreed, but, depending on if I've experienced it before, it may be an induction based off of possibility or plausibility.

A probability is not a deduction, but an induction based upon the limitations of the deductions we have. Probability notes there are aspects of the situation that we lack knowledge over.

Whether or not it is a deduction or induction, probabilities are derived from two separate claims that are not equally as cogent as one another. A calculation based off of a possibility is more cogent than a plausibility. Yes, this is still using the induction hierarchy, but notice it is within probabilities, which means probabilities itself is contingent on possibility and plausibility while the latter two are not contingent in any way on probability.

I look forward to hearing from you,
Bob

I agree, I definitely need to define it more descriptively. However, with that being said, at a deeper level, the term possibility is also like the word "big": it is contingent on a subjective threshold just like potentiality. — Bob Ross

All distinctive knowledge is formed subjectively. Why I think possibility is more clear and useful than potential as a discrete experience, is I have a clear definition that can be applied to reality without contradiction. How do I apply the definition of potential to applicably know it?

I agree, I think potentiality is an aspect of rationality. If it has no potential, just like if it isn't possible, then it is irrational. Potentiality isn't separate from rationality (it is apart of rational thinking). — Bob Ross

I think here we're along the same intuition. Intuitively, potentiality seems like a word that would be used to describe the likelihood of an induction being correct. But how do I determine that? How do I applicably know that? With probability, I have clear limitations in what can potentially be drawn. If I know the cards are set, but I don't know the outcome, I could say, "Potentially, I could draw a jack." Perhaps we could state potentiality is a description of the possible outcomes of a probability? Its clearly defined, and can be applicably known.

Perhaps with possibility, "potential" could be used as well. "Because the bear was here yesterday, its potentially here today." The only issue here is the word has changed meaning. What we're really stating in this instance is, "Its possible the bear is here today, because we applicably knew the bear was here yesterday. At that point, the word really is no different from "possibility".

I think that sums up my issues with the word. It needs a clear definition that can be applicably known. In regards to potentiality, it seems to be the same as the word possibility. So perhaps, we could call potential a synonym of possibility? Potential = possible?

I suppose I should also address why potential cannot work with plausibility at all. A plausibility has no means to evaluate its potential, because I believe potential evaluates a strong sense of what we believe can be real. A plausibility is almost an abandonment of potentiality as an evaluation, because the only way to know if a plausibility is possible/potential, is to applicably apply it to reality.

For example, although this may be a controversial example as we haven't hashed out math yet, I can hold that, even though I haven't experienced it, lining up (side by side) 2 in long candy bars for 3,000 feet has the potential to occur because it aligns with my knowledge (i.e. I do applicably know that there is 3,000 feet available to lay things and I do applicably know there are 2 in long candy bars); however, most importantly, according to your terminology, this is not possible since I haven't experienced it before. — Bob Ross

It is plausible. Its a claim about reality that has not been applicably tested yet. Maybe you aren't able to do it when you try. When applying a plausibility to reality, details come up that we haven't thought about. For example, what type of candy bar? Are we standing them vertically, or laterally? What is the surface, something inclined, rough, or flat? A possibility already has those answers. If you stand a candy bar, you can evaluate that candy bar and glean all the necessary information to show how it is applicably known.

So, if you have all of those answers, then you can state, since it is possible to line up a candy bar in X manner, then it is possible that a candy bar will be able to be lined up if X manner is repeated. Because there is no claim that the candy bar should not be able to stand if X manner is repeated, it stands to reason that if we could duplicate X manner many times, 3000 per say, the candy bars would stand aligned. But, if we've never aligned a candy bar one time, we don't applicably know if its possible.

Math alone does not evaluate the details of whether something is possible or plausible. For example, I can state 1 unicorn + 1 unicorn is 2 unicorns. That is distinctively known. But if I go looking for unicorns in reality, the fantastical magical horse kind, I do not know if its possible. The hierarchy of inductions is in relation to a beliefs application to reality. It is not a question of the distinctive knowledge that leads up to the belief itself.

Likewise, without ever experiencing it, I can hold that it is irrational to believe that one can fit 7,000 2 in long candy bars, side by side long ways, within 1,000 feet (because, abstractly, 1,000 feet can only potentially hold 6,000 2 inch candy bars side by side).

You can calculate that it is implausible abstractly. Lets even say we add details to make sure its impossible, such as ensuring the candy bars cannot be squished together. This again, is just like showing that just as a candy bar with X properties can stand, some object of unchangeable X dimensionality cannot fit into another area of X unchangeable dimensionality. But, we need to experience the possibility of two unchangeable dimensionalities, where one can fit inside of the other. Set it up correctly, and you are describing what is possible (or impossible in this case).

Just as an aside, it might be beneficial to describe what I consider distinctively impossible. What is distinctively impossible, is a plausibility that takes two possibilities, and results in a contradiction of at least one possibility. A plausibility, cannot claim a possibility is incorrect, as it is a lower level on the hierarchy due to its level of applicable knowledge relation. Applicable impossibility, is found when new applicable knowledge contradicts our previous possibilities.

Something can't be plausible if it can be proven to have no potential (and it doesn't necessarily have to be "I've experienced the exact, contradictory, event to this claim, therefore it is an irrational induction": — Bob Ross

So to adjust this sentence with the defined terms we have so far, "Something can't be plausible if it can be proven to be impossible (distinctive or applicable). Something can't be plausible if is contradicts what is possible both in our distinctive and applicable knowledge.

I could make subjective thresholds for what constitutes "experiencing something before" that renders possibilities utterly meaningless. — Bob Ross

True of everything. But can we turn it the other way, and make a threshold of what constitutes "experiencing something before" that renders possibilities meaningful when applied to reality. Yes. Can we do the same with potentiality? So far, I don't believe a definition of the word has been created so far that can be applied to reality consistently, clearly, and in a way that cannot be replaced by another word.

Potentiality doesn't pertain to the "truth" of the matter, just a requisite to what one should rationally not pursue. It is a deeper level, so to speak, of analysis that can meaningfully allow subjects to reject other peoples' claims just like what you are describing. — Bob Ross

Perhaps potentiality describes the hierarchy of induction itself then? In essence, the hierarchy allows us to rationally dismiss beliefs of a lower hierarchy that compete with ours. If I believe I have a 1/52 chance of pulling an ace of spades, and someone says, "Well its possible you could not pull an ace of spades," its not going to change the odds. The idea that an evil demon could change the result of the card, destroying my odds, is a plausibility that can be dismissed as well. And someone coming up with the idea that its actually 1/53 cards is an irrationality I can outright dismiss.

That being said, I do believe the level difference in the hierarchy should temper how quickly you dismiss a counter belief. One removed should always be considered to ensure your currently held belief is correct. But if you find upon re-evaluation that your level of hierarchy still holds, you may dismiss it. Perhaps this is what you mean by "potential"? The difference of the level of the hierarchy determines how much consideration you should give to it when rationally thinking about it?

I think I'm going to stick with evaluating inductions in terms of rationality, instead of potentiality.

That is absolutely fine! My intention is not to pressure you into reforming it, but I do think this is a false dichotomy: this assumes potentiality is a separate option from rationality. — Bob Ross

Please continue to defend your viewpoints on potentiality. I have not thought on it at length until now, and I may have mentioned that the hierarchy is a baseline that can be used to build something more. I think at this point to construct potentiality as a viable term it will need to

a. Have a clear definition of what it is to be applicably known.
b. It must have an example of being applicably known.
c. Serve a purpose that another applicably known term cannot.

I can say it is possible to perform addition because I have experienced it before, I cannot say that it is possible to add 3 trillion + 3 trillion because I haven't experienced doing that before with those particular numbers: I am inducing that it still holds based off of the possibility of the operation of addition. — Bob Ross

To clarify again, the process of addition is distinctive knowledge. Adding the abstract of 3 trillion identities to 3 trillion identities will always result in 6 trillion identities, because that is the logic of discrete experience. Induction only occurs when we apply this to reality. What essential properties make up each identity of the the first 3 trillion in reality? The second 3 trillion? What counts as adding them to become the new 6 trillion identity? It is their proximity? Ownership? Time and place? If we can applicably know these identities, then we can apply the logic of identities, math, and applicably know the outcome.

I agree, but this doesn't mean it holds for all numbers. We induce that it does, but it isn't necessarily the case. We assume that when we take the limit of 1/infinity that it equals 0, but we don't know if that is really even possible to actually approach the limit infinitely to achieve 0. — Bob Ross

In this case, we distinctively know the answer. A limit means that the calculation will never result in 0. It is not ascertaining specifically how small that calculation can get. Its just a deduction that it will never arrive at 0. An induction would be, "If I apply the calculation with X numbers, I will get the result .0000000124. You'll have to actually do the calculation to applicably know whether that belief is true or not.

Likewise, we know that if there are N distinct things that N + 1 will hold, but we don't if N distinct things are actually possible (that is the induction aspect, which I think you agree with me on that, although I could be wrong). — Bob Ross

This is correct. We distinctively know the abstraction of N identities plus one more will always result in F(N). But if we apply this math to reality, to see if there are actually N identities in existence, we are using an induction that must be verified.

Yes, I may need a bit more clarification on this to properly assess what is going on. Your example of the pink elephant is sort of implying to me something different than what I was trying to address. I was asking about the fundamental belief that you think and not a particular knowledge derived from that thought (in terms of a pink elephant). I feel like, so far, you are mainly just stating essentially that you just think, therefore you think. I'm trying to assess deeper than that in terms of your epistemology with respect to this concept, but I will refrain as I have a feeling I am just simply not understanding you correctly. — Bob Ross

I distinctively know that I think of a pink elephant. If I believe that a pink elephant exists in the next room, I have to go through the steps of applying that to reality to applicably know if that's true or not. This is just like math. I distinctively know N+1=F(N), but when I apply that to reality, I have to go through the steps that show it can be applied without contradiction by fleshing out exactly what it is I'm adding.

Yes, but your essays made it sound like probability is its own separate thing and then you can mix them within chains of inductions. On the contrary, I think that "probability" itself is actually, at a more fundamental level, contingent on possibility and plausibility for it to occur in the first place. — Bob Ross

Lets see if we can break this down. If I applicably know the cards in a deck, and applicably know I cannot know the order of shuffling, nor can the person doing the shuffling, then I can claim probability directly based upon applicable knowledge. Possibility is underneath probability in the fact that a probability is a calculated possibility with limits. A possibility alone has no assessment of calculated limitations. Its possible that I can draw a card. Its probable that its a 4/52 chance of being a jack.

Another great deep dive Bob! I hope that clarified numbers a bit, and also gave you a set of points you could use to define potential in a way that fits within the epistemology. I look forward to your responses as well!

Hello @Philosophim,

I think at this point to construct potentiality as a viable term it will need to

a. Have a clear definition of what it is to be applicably known.
b. It must have an example of being applicably known.
c. Serve a purpose that another applicably known term cannot.

I appreciate that you put your concerns (with respect to potentiality) in a such a concise manner, as it really helps me, on the flip side, really hone in on what I am trying to say. I've never been the best at explanations. So thank you! I will attempt to address this in my post hereafter.

I think, upon further reflection, we are both conflating potentiality and possibility to a certain extent in the process of trying to dissect the colloquial use of "possibility". Potentiality is "what is not contradicted in the abstract", whereas possibility is "what has been experienced before". When you define possibility in that manner, I think you are implicitly defining it as "I've experienced X before, because I've experienced X IFF X==X". Therefore, assuming we don't get too knit picky with a more strict comparison X===X, possibility is like "I've experienced an Orange before, because I've experienced an Orange IFF 'Orange'=='Orange'". Therefore, when you say:

So, if you have all of those answers, then you can state, since it is possible to line up a candy bar in X manner, then it is possible that a candy bar will be able to be lined up if X manner is repeated. Because there is no claim that the candy bar should not be able to stand if X manner is repeated, it stands to reason that if we could duplicate X manner many times, 3000 per say, the candy bars would stand aligned. But, if we've never aligned a candy bar one time, we don't applicably know if its possible

You are stating it is possible to line up X manner repeated because "You've experienced 'X manner repeated' before, because you've experienced 'X manner' IFF 'X manner repeated' == 'X manner'". But that IFF does not hold, just like how 'X + 1' != 'X'. Even if you have experienced lining up 2,999 of those particular candy bars in question, and you knew all the other things you mentioned were possible (such as aligning candy bars are possible, horizontally lined up, etc), you would not be able to claim, according to your definition, that it is possible to line up 3,000. What is missing here, and what I think you are also trying to maintain, is potentiality: the abstract consideration. What you claimed is correct, but it is because you abstractly determined, via mathematical operations of repetition, that there is the potential for lining up 3,000 candy bars. Likewise, when you define impossibility in this manner:

Applicable impossibility, is found when new applicable knowledge contradicts our previous possibilities.

What you are stating is the converse of possibility, something like "I've experienced X contradict previous experience Y, IFF X disallows Y". This would directly entail that you have to directly experience the converse, such that "I've experienced X before, which is contradicted by this experience Y, therefore X is impossible". Notice this also disallows abstract consideration. It is:

"I've experienced a cup holding water, therefore it is possible for a cup to hold water"
"I'm now experiencing cups not being able to hold water, therefore it is impossible for them to hold water"
"The most recent experience out of the two takes precedence"

But then I think you introduce potentiality here into impossibility:

Likewise, without ever experiencing it, I can hold that it is irrational to believe that one can fit 7,000 2 in long candy bars, side by side long ways, within 1,000 feet (because, abstractly, 1,000 feet can only potentially hold 6,000 2 inch candy bars side by side).

There is an asymmetry between possibility and impossibility in your usage of the terms: the former has no abstract consideration while the former does (aka, the latter allows for potentiality as a consideration whereas the former does not). What I am understand you to hold here, is that you can hold that it is impossible to fit 7,000 2 in long candy bars, side by side long ways, within 1,000 feet because you have abstractly considered its lack of potential. You have not determined this based off of "I've experienced the converse of X, which contradicts Y", therefore you haven't determined it an "impossibility" or "possibility", as they both are contingent on the experiences. No, you did not utilize anything except the abstract induction of mathematical operations to warrant it impossible (I'de say you actually warranted it, more specifically, as lacking potential). Admittedly, I have also been conflating potentiality and possibility in our discussion because it is a hard thing to separate. But they are two distinct things. Yes, I am still utilizing experience to do math in the first place, but I am not experiencing the direct converse for something to be considered lacking potential. But, according to your terms, I am also not stating that "I've experienced X before, which contradicts Y". I am stating "I've experienced X before, and the extrapolation of X contradicts Y in the abstract". For example, consider the following:

I claim something is either (1) green, (2) not green, or (3) other option

This does, eventually, boil down to the law of noncontradiction, but, in the immediate, it is the law of excluded middle. What I am trying to explicate is that the rejection of #3 as being a "possibility" isn't experiential based--as in I am not negating the usage of #3 in terms of "I've experienced X, which contradicts Y". I am considering this purely in the abstract and rightfully concluding it cannot have any potential to occur. The reason this feels like a sticky mess to me, and maybe for you too, is that this is traditionally how "possibility" was also used: it had multiple underlying meanings.

So let's go back to this:

I think at this point to construct potentiality as a viable term it will need to

a. Have a clear definition of what it is to be applicably known.
b. It must have an example of being applicably known.
c. Serve a purpose that another applicably known term cannot.

A is:

"what is not contradicted in the abstract"

Although I don't think abstraction has to be directly applicably known (like I would have to go test, every time, the usage of mathematical operations passed what has been previously experienced), but I think B is:

Abstraction is the distinctive knowledge, which is applicably known to a certain degree (i.e. I applicably know that my perceptions pertain to impenetrability and cohesion, etc), that is inductively utilized to determine potentiality.

C is:

The defining of "possibility" as "I've experienced X before, because I've experienced X IFF X==X" removes the capability for the subject to make any abstract determinations, therefore potentiality is a meaningful distinction not implemented already in possibility (and likewise for impossibility).

I think that this is a good start to spark further conversation, so I think we can revisit some of the other things you demonstrated in your post after we find some common ground on the aforementioned.

I look forward to hearing from you,
Bob

Very good work for a first, full-throated go at epistemology. However, if you haven't familiarized yourself with the first few chapters, at least, of Introduction to Objectivist Epistemology, I highly recommend you do so. Rand perfectly explicates the concepts you attempted to formalize here in this work. Nice job!

-G

Thank you! No, I have not read it. Due to time this morning, I got some general concepts. While we may have some similar beginnings, I believe we diverge. The first part of the epistemology I've proposed here is very similar to many other theories of epistemology. But, where people build from that tends to diverge. Have you read all four parts? I'm quite certain I take a few turns from Rand.

I did, yes. And I do think you both diverge, but the constituent elements are present in both epistemologies that hearken to the same objective process by which humans allocate information through abstraction via the senses, and then formulate those abstractions into applicable concepts. Plus, I like the eplication on "(3) other option," as this leaves room for Hume's problem of induction; which by the way, I believe I have actually solved after all these years.

Potentiality is "what is not contradicted in the abstract", whereas possibility is "what has been experienced before". — Bob Ross

I rather like your definition of potentiality here. I think it hammers home what we've been trying to get to. However, I think we can also see the problem with it. Almost every single belief of induction is not contradicted in the abstract. Meaning at best we describe all inductions besides irrational induction. Which, an irrational induction, is something that is not rational. This in turn implies that potentiality is a subset of rationality, "That which is not contradicted in the abstract."

It is not the identity I am critiquing, it is the word. Potentiality as a word, because it also implies something beyond this strict reading. Potentiality seems to also go along with "What is possible". What is not contradicted in the abstract, is not necessarily possible as we've discussed. The division between possibility and plausibility has been the focus of the last several posts of discussion. That is because there is an innate human desire to believe that if there is no contradiction in the mind, it must be possible in reality.

But that is a belief, and not rational. Rationally, something that is not contradicted in the mind may have no bearing as to wheather it is contradicted when applied to reality. But, perhaps we can create two identities that try to contain what you are saying while being consistent with the theory. As you can note, I have constantly divided beliefs into two camps, distinctive, and applicable. There are two identities that we could examine then.

1. A belief which is not contradicted by other beliefs.
2. Distinctive knowledge applied to reality which is not contradicted by other distinctive knowledge.

In the second case, this is a different way of describing applicable knowledge. The first case, is distinctive knowledge. Distinctive knowledge is exactly what you describe. When we create distinctive knowledge, we then have to have a reason to attempt to apply that to reality. Rationally, we would want to apply something that we believe to have no contradiction to reality, over a series of contradictory thoughts to reality.

Recall that to know something, there must be an application of essential properties. To apply our distinctive knowledge to reality while expecting an outcome, is always an induction; its always a belief. While it is more cogent, and arguably "safer" to stay within the higher tiers of inductions such as probability and possibility, you will never find new possibilities in the world if you do not explore plausibilities. When we explore plausibilities, we believe there is a chance they are real. But we must also temper our mind with the understanding that there is an equally unspecified chance that they are not real.

Perhaps "potentiality" could be used to describe the drive that pushes humanity forward to extend outside of its comfort zone of distinctive knowledge, and make the push for applicable knowledge. The drive to act on beliefs in reality. But what I think you want, some way to measure the potential accuracy of beliefs, is something that cannot be given. There is no way to measure whether one plausibility is more likely than another in reality, only measure whether one plausibility is more rational than another, but examining the chain of reason its built on.

This is because the nature of induction makes evaluation of its likelihood impossible by definition. An induction is a conclusion that does not necessarily follow the premises. As we've seen with probability, coming up with odds requires defined limits. An induction may be built upon deductions, which have defined limits, but there comes a part of the claim which is not defined by limits. Without limits, we cannot evaluate whether if it is more likely to pass than another claim which is not defined by limits. The only way to know, is to take that chance, that risk, and apply it to reality and see what happens.

"I've experienced a cup holding water, therefore it is possible for a cup to hold water"
"I'm now experiencing cups not being able to hold water, therefore it is impossible for them to hold water"
"The most recent experience out of the two takes precedence" — Bob Ross

For clarification, if you recall the second paper (Its been a while now!) when we are faced with a contradiction of our applicable knowledge with new applicable knowledge, we have several options of dealing with it. We could create a new term. Adjust our context, which essentially modifies the knowledge we use to avoid the contradiction. Or we can just state that one of the things we applicably knew, is wrong and can no longer be applicably known.

So while I could conclude that it is impossible for a cup to hold water, that is now a new belief that must be applicably known, not just concluded in your mind. What are the essential properties of a cup? Can you find objects that have those properties, but some hold water, and some don't? Do you need to adjust what you define by a cup? Perhaps the essential property of holding water, should become a non-essential property. There are lots of ways to approach it.

It is not that the most recent experience of the two takes precedence, it is that the most recent experience of a cup challenges your applicable knowledge. Right now you are making an induction as to what that means. You can induce, "It is impossible for a cup to hold water now," but is that applicable knowledge? You must apply that belief to reality, and see if it "holds water".

What I am understand you to hold here, is that you can hold that it is impossible to fit 7,000 2 in long candy bars, side by side long ways, within 1,000 feet because you have abstractly considered its lack of potential. — Bob Ross

If you are stating that the conclusion through distinctive knowledge is that you can't fit X > Y feet into Y feet is impossible, than yes. If you apply this to reality, you must be very specific with the properties of the material in use. A lack of known applicable knowledge in its application means you are working with a plausibility. Since candy bars are malleable, I very well could jam that many candy bars together. If I note I can only use material that is not malleable, then I would be creating a belief that is a possibility.

Since it is possible to find material that is not malleable, and can be stacked or lined together, then I know it is not possible to jam more of those material into a space that is smaller than the entire measurement of those materials. The possibility in this instance, is that it will not fit. We have never experienced in reality, a situation in which unmalleable material can fit in a space smaller than its dimensions.

I am stating "I've experienced X before, and the extrapolation of X contradicts Y in the abstract". — Bob Ross

You are stating a possibility or plausibility depending on how you word it. If you are combining two possibilities to show that a plausibility cannot occur, you have stated something distinctively impossible. If you are using a possibility to construct a plausibility, or something that is not contradicted by other possibilities in your mind, then you are not stating an impossibility, only a plausibility. Holding to a distinctive impossibility and applying it to reality, is an irrational belief.

But, what is impossible in our distinctive knowledge, may not be impossible when applied to reality. Because inductions are again, beliefs. We may believe something to be impossible, but it may not be impossible when applied to reality.

So, I think the difficulty is in separating the two types of knowledge. Impossibility, is no longer a general word that dictates what can, and cannot be. There is an impossibility within distinctive knowledge, and there is an impossibility within applicable knowledge.

With ALL of this covered, lets go to your break down of potentiality.

"what is not contradicted in the abstract"

Although I don't think abstraction has to be directly applicably known (like I would have to go test, every time, the usage of mathematical operations passed what has been previously experienced) — Bob Ross

You are correct. Distinctive knowledge does not have to be applicably known. Applicable knowledge is a claim that what we distinctively know, can be applied to reality without contradiction. But we can hold any distinctive knowledge as long as we don't assume it can be applied to reality without contradiction.

but I think B is:

Abstraction is the distinctive knowledge, which is applicably known to a certain degree (i.e. I applicably know that my perceptions pertain to impenetrability and cohesion, etc), that is inductively utilized to determine potentiality. — Bob Ross

There is no requirement of applicable knowledge for distinctive knowledge. Distinctive knowledge is what we use as a basis for our inductions about reality. But it can exist without such application.

C is:

The defining of "possibility" as "I've experienced X before, because I've experienced X IFF X==X" removes the capability for the subject to make any abstract determinations, therefore potentiality is a meaningful distinction not implemented already in possibility (and likewise for impossibility). — Bob Ross

I do not see this. Possibilities do not remove the capability of making abstract determinations. I can create the image of a unicorn in my head by taking the distinctive knowledge of a horn, and putting it on the distinctive knowledge of a horse. I can have it run around in my head casting magic and flying through the air leaving a rainbow behind it.

If I think I can find such a thing in reality, I just have to realize its not a possibility, just a plausibility. The hierarchy of inductions is all about assessing which are the more cogent beliefs about reality. It does not say we cannot use them.

I am out of time this morning, but I want to post this to you while it is fresh in my mind. Please feel free to follow up on this!

Part 1 The basics of knowledge
"Any discussion of knowledge must begin with beliefs. A belief is a will, or a sureness reality exists in a particular state." — Philosophim

Knowledge consists of facts, information and skills acquired through experience or education.
A belief is an acceptance that something exists or is true, especially one without proof.

Beliefs are not knowledge. And in most cases they do not reflect "sureness". Of course, I may say "I believe that ..." and state some fact or something I know well, but it's only an expression, a figure of speech.

Do you believe that "cats are animals" or you know that "cats are animals"? Do you believe that the "Earth is round" or you know that the "Earth is round"? Only people and Copernicus himself might not be certain about that before the later stated it as a fact. And after some time, it has become common knowledge. A belief is something like an hypothesis. When it is proved true, it is a fact.

I'm sorry for not being able to go further in this topic, because it starts and is based on a wrong assumption. I only wanted to point this out.

I'm sorry for not being able to go further in this topic, because it starts and is based on a wrong assumption. I only wanted to point this out. — Alkis Piskas

That's a fairly dishonest reading. I never claimed beliefs were knowledge. I claimed that before we start with knowledge, we had to start by looking at beliefs. Its just an introduction to a paper, not the claim you're presupposing. Knowledge indeed consists of facts, information, and skills acquired through experience. If you had read just until the end of the page, I think you would have understood where this was going.

I don't think that my reading was "dishonest" --actually, a more correct word would be "unfair"-- because I didn't read the whole thing. And I didn't say that the whole description of the topic was wrong. (Of course, since I didn't read everything!) I didn't criticize anything either. As I said, "I only wanted to point this out". I explained why stating that "A belief is a will, or a sureness reality exists in a particular state" is a wtong assumption, because belief is not sureness. I also gave examples why (something that most people don't) . But since you ignored all that, considering maybe that it is just a false idea of mine, here's another reference that describes well the difference between belief and certainty:

"Belief is the state of mind in which an individual is convinced of the truth or validity of a proposition or premise regardless of whether they have adequately proved or attempted to prove their main contention. Certainty is the state of mind in which an individual is convinced of the validity, truthfulness, or evidence of a proposition or premise. While believing is possible without warrant or evidence, certainty implies having valid evidence or proof." (https://www.newworldencyclopedia.org/entry/Belief_and_Certainty)

And as for my "dishonest reading", if your introduction started with something more plausible, I would certainly read more, since "knowledge" is a hot subject for me. But I always stop reading something when it starts and is based on a wrong assumption. Well, this is me! :smile:

But I always stop reading something when it starts and is based on a wrong assumption. Well, this is me! :smile: — Alkis Piskas

Fair. :smile:

I would say though that sureness is not the same as certainty. The intention is to use a word that conveys some conviction, assumption, or emotional indicator that compels a person that they believe X is worth holding. I even posted the word "will" next to it, so you would understand the context of what I was trying to convey.

Look at it this way, what makes you believe anything? For most beliefs, there is some type of conviction behind it. Regardless, you may not like the essay, because you have a prescriptive outlook on what I should be saying, instead of trying to understand what I'm intending to say. As this is an exploratory essay, and not a repeat of what is already known as fact, the latter intention is what is needed when approaching the paper. I do appreciate your comment, and your polite follow up!

I would say though that sureness is not the same as certainty. — Philosophim

"Sureness" from Merriam-Webster (My favorite dictionary, Oxford LEXICO, doesn't have it! :sad:)
"A state of mind in which one is free from doubt."
"Certainty" from the same dic:
"A state of mind in which one is free from doubt." !
(Check for your if you don't believe me! :smile: https://www.merriam-webster.com/thesaurus/sureness and https://www.merriam-webster.com/thesaurus/certainty)
Well, dictionaries are not perfect, of course. There may be nuances between them. But they are certainly (surely :smile:) synonyms.

Whatever is the case, both terms, as well as "belief", are certainly (surely :smile:) are totally different from "knowlwedge" and are connected to it only as a sequence, i.e. from a belief on can pass to knowledge, which was my main point. Again, I bring in the definition of knowledge, for s "fresh" comparison:
"Knowlwedge" from the same dic:
"Information, understanding, or skill that you get from experience or education"

Please note that I don't rely totally on dictionaries. I used them mainly as a common reference. If I now e a term well, i.e. it is "solidly real" for me, I rely more on my own undesrating of the term and sometimes I add elements to the dictionary definitions if I deem that they are important. But in the present case, I don't need to. Things speak for themselves! :smile:

I even posted the word "will" next to it, so you would understand the context of what I was trying to convey. — Philosophim

I have to confess that I have not undestood "will" in this context, even after having looked it up!
But see, this would create (more) confusion, anyway. Also, whatever you mean by it, the second part --or a sureness reality exists in a particular state-- was more important and enough to raise a protest in me! :grin:

Look at it this way, what makes you believe anything? — Philosophim

I gave you examples on this.

For most beliefs, there is some type of conviction behind it. — Philosophim

True. But this doesn't change much what I pointed out, does it? :smile:

you may not like the essay, because you have a prescriptive outlook on what I should be saying — Philosophim

This not true. I told you that I cannot judge the rest of the discussion and that I would have continued reading if I had read a more plausible introduction. I think this is fair, no?

And, as you can see, I like to converse with you! :smile:

And, as you can see, I like to converse with you! — Alkis Piskas

Thanks for the contribution to the OP! I'll see you around.

:up: I have contributed to 100 topics up to now. Only you and another OP owner have thanked me for that!

(There were even a lot (27) of OP owners who din't even respond to my reply on their topics!)

Hello @Philosophim,
I apologize for such a belated response: I've been quite swarmed recently.

Almost every single belief of induction is not contradicted in the abstract. Meaning at best we describe all inductions besides irrational induction.

I think that the first sentence here is sort of like survivorship bias: it isn't that almost every single induction has potential, it is that all beliefs of induction that hold any substance at all have potential, therefore all the ones that have survived enough for both of us to hear tend to have potential. Most people naturally revoke their own inductions that have no potential without ever verbalizing them, because it is the first aspect of consideration in the process of contemplation. What I am trying to say is that I wouldn't post an inductive belief on here if I was well aware that it had no potential. So I agree, but I don't think it implies what I think you are trying to imply: it doesn't mean that potentiality isn't a worthy, or relevant, consideration just because most don't make it out of our heads to other people. I agree with you that potentiality doesn't get the subject to a completely working, solid claim of knowledge.

With respect to the second sentence, I holistically agree! The point I am trying to make is that "irrational induction" is not just what is contradicted by direct experience but, rather, it is also about whether it is contradicted in the abstract. I think it may be the appropriate time to elaborate on what I mean by abstraction. A contemplation resides in the abstract, in a pure sense, if it isn't pertaining to particular experiences but, rather, is utilizing a combination of those experiences or/and a generic form of those experiences. For example, the consideration of 1 "thing" + 1 "thing" is 2 "things" is purely abstract because it doesn't pertain to particular experiences. Although we can dive in deep into what abstraction really is, I am going to intentionally keep it this vague so you can navigate the discussion where you would like. In light of this, the example of fitting malleable (as you rightly mentioned) candy bars in specific dimensions that cannot occur is not due to it having no possibility (I am not negating it based off of a direct experience), but actually because it lacks any potential. This is an irrational induction. What also is an irrational induction, but not based off of abstraction, would be if I were to hold the belief that some particular apple is poisonous, yet having experienced a person eating that exact apple and they showed 0 signs of poisoning. In this case, no abstraction is needed: the particular experience is enough to warrant it as an irrational induction. That is essentially what I was trying to convey.

Rationally, something that is not contradicted in the mind may have no bearing as to wheather it is contradicted when applied to reality.

I agree. I am not attempting to claim that something that has potential necessarily is possible (which is what I think you are getting at here). I am attempting to claim that something that has potential is more cogent than something that lacks potential.

Perhaps "potentiality" could be used to describe the drive that pushes humanity forward to extend outside of its comfort zone of distinctive knowledge, and make the push for applicable knowledge. The drive to act on beliefs in reality.

No I don't think it is the drive, it is what most subjects do inherently (and what everyone does who has subscribed themselves, legitimately, to the game of rationality--I would argue). It is an important aspect of what constitutes an irrational induction. Without it, I think your epistemology is constrained to the apple example I gave previously: what is irrational, is what is impossible. I am saying: what is irrational, is what is impossible and has no potential.

But what I think you want, some way to measure the potential accuracy of beliefs, is something that cannot be given.

To a certain degree, I agree with you. Potentiality in itself does not warrant a belief accurate, but the lack of potentiality warrants it necessarily inaccurate. In order for me to properly assess potentiality, I think that we ought to define the definition of possibility (define what it means to experience something before), because this greatly determines what is considered abstract. So, how are you defining what "you've experienced at least once before"?

There is no way to measure whether one plausibility is more likely than another in reality, only measure whether one plausibility is more rational than another, but examining the chain of reason its built on.

I think you are wrong, but actually right. I think we can most definitely compare plausibilities in terms of induction hierarchies within it--not in terms of probabilistic quantitative likelihoods. But before I can get into that, I need to do some defining. First, I need to define the relations within the induction hierarchies, so here's how I will be defining it (all of which are open to redefining if you would like):

The Induction = The induction being proposed.
the grounding inductions = The inductions that The Induction is contingent on, which ground it to the subject (derive back to the subject).
induction hierarchy = The Induction considered with respect to its grounding inductions, which can be considered a holistic analysis of The Induction.
components = The distinct claims within The Induction (more on this later).
characteristic = An attribute, descriptor within a component (more on this later).

To summarize what is defined above, The Induction is simply the actual induction that the subject is making, whereas the grounding inductions are, as we previously discussed, what the subject will consider in a holistic analysis of The Induction. The induction hierarchy should be pretty self-explanatory as it is that holistic analysis of The Induction. The components is where it gets interesting. The components are what essentially distinctively makeup The Inductions and the characteristics are, quite frankly (not to use the word to explain it, but I am definitely about to do that) the characteristics of the components.

Let's go through some examples real quick. So, for all intents and purposes right now, let's consider the induction hierarchy as a horizontal holistic analysis, like this:

possibility -> possibility -> plausibility

The two possibilities would be the grounding inductions, the plausibility The Induction, and the whole thing is the induction hierarchy. The components of The Induction are going to be formatted like this (I just made it up, no real rhyme or reason):

possibility -> possibility -> plausibility: (component1, component2, ...)

I am merely separating the components from The Induction with a colon and encompassing them with parenthesis. Also, I will put distinctive knowledge, although it isn't an induction, in the chain (for consistency) like this:

[distinctive knowledge1, distinctive knowledge2, ...] - possibility -> possibility -> plausibility: (...)

Note that I am not claiming that distinctive knowledge are apart of the induction hierarchy, just that they are grounds for it (one way or another). Also, the characteristics are within the components, so I won't have any special characters for those; instead, I am going to bold them.

Now that that is out of the way, let's dive in! Let's use our favorite example: unicorns (: . Let's say I claim this:

1. There are horses (distinctive knowledge)
2. There are horns (distinctive knowledge)
3. It is possible for animals to evolve into having horns (evolution) (possibility)
4. It is plausible that a horse with a horn could exist (plausibility)

Now, we can map this into our induction hierarchy like this:

[horses, horns] - evolution -> unicorn

But we can go deeper than this with components:

[horses, horns] - evolution -> unicorn: (horned horse)

The components are the specific distinctive claims within The Induction itself. In this case, I limited the claim to a horned horse: that is the sole component of my induction and the characteristic is horned. To really illuminate this, let's take a similar claim:

1. There are horses (distinctive knowledge)
2. There are horns (distinctive knowledge)
3. It is possible for animals to evolve into having horns (evolution) (possibility)
4. It is plausible that a horse with a horn and the ability to turn invisible could exist (plausibility)

I can map this one like so:

[horses, horns] - evolution -> unicorn: (horned horse, invisibility capabilities)

Now there are two components to my inductive claim. I think that this is incredibly useful for comparing two plausibilities. At first, I thought I could utilize the sheer quantity to determine the cogencies with respect to one another. I was wrong, it gets trickier than that because the components themselves are also subject to an induction hierarchy within themselves. I can claim that it is possible for an animal to evolve into having a horn, but I cannot claim that an animal has evolved into being invisible (assuming we aren't talking about camo but actual invisibility), so the components themselves are not necessarily as cogent as each other. Therefore, I must take this into consideration.

[horses, horns] - evolution -> unicorn: (horned {possible characteristic} horse)
[horses, horns] - evolution -> unicorn: (horned {ditto} horse, invisibility {plausible characteristic} capabilities)

Therefore, #1 is more cogent than #2, not due to the sheer consideration of quantities of components, but the quantity in relation to an induction hierarchy within the component itself. In other words, a plausibility that has one component which is based off of a possible characteristic is more cogent (doesn't mean it is cogent) than one that has component which is based off of a plausible characteristic.

For example:

[horse, horns] - evolution -> unicorn: (horned horse, has scaly skin)
[horse, horns] - evolution -> unicorn: (horned horse, invisibility capabilities)

The first is more cogent than the second because we can be more detailed with the components like this:

[horse, horns] - evolution -> unicorn: (horned {possible characteristic} horse, has scaly skin {possible characteristic})
[horse, horns] - evolution -> unicorn: (horned {possible char} horse, invisibility capabilities {plausible char})

Therefore, #1 is more cogent than #2 when analyzed from the perspective of quantities (which are equal in this case) and in relation to to type of induction the characteristic is. So:

[horse, horns] - evolution -> unicorn: (horned {possible characteristic} horse, has scaly skin {possible characteristic})
[horse, horns] - evolution -> unicorn: (invisibility capabilities {plausible char})

Even though #2 has only one component, that component is a plausible characteristic and #1 has two possible characteristics--therefore, #1 is more cogent because a possibility is more cogent than a plausibility. However, if it were the case that plausibility #1 had 3 plausible characteristics while #2 had 2 plausible characteristics, then #2 would be more cogent. I am simply applying the same induction hierarchy rules a step deeper to analyze plausibilities. When I state that a component contains a "possible characteristic", note that I am not trying to claim that that characteristic is possible with respect to subject it is describing; I am merely distinguishing characteristics that have been experienced before from ones that haven't been (some are just figments of our imagination, quite frankly). However, it isn't just about the relation to an induction hierarchy within the component itself: it is also about the quantity, but the quantity is always second (subordinate) to the consideration of the relation. For example:

[horse, horns] - evolution -> unicorn: (horned {possible characteristic} horse, has scaly skin {possible characteristic})
[horse, horns] - evolution -> unicorn: (horned {possible characteristic} horse)

First we consider the relation in terms of the characteristics within the components, as it takes precedence over quantity, and we find that both claims utilize possible characteristics. Now, since they are equal in relation, we must consider the quantity: #1 has two components while #2 has one. Now, we must keep in our minds at all times that these are components of a plausiblity and, therefore, a plausibility with more components of the same induction type is less cogent than one that has less of that type. This is because the more I add components, the more speculation I am introducing and, most importantly, in this case, I am adding more of the same type of speculation. Therefore, #2 is more cogent than #1.

I hope that serves as a basic exposition into what I mean by "comparing plausibilities".

This is because the nature of induction makes evaluation of its likelihood impossible by definition

We aren't really using likelihoods to compare plausibilities and if we are, then it is a qualitative likelihood of some sorts. I am going to stop here as this is getting quite long (:

I look forward to hearing from you,
Bob