The example is simply: after 30 seconds a single-digit counter increments to 1, after a further 15 seconds it increments to 2, after a further 7.5 seconds it increments to 3, and so on for 60 seconds, resetting to 0 at every tenth increment. — Michael

I guess I misunderstood your example. It is obviously not consistent with the OP. That little part where you say "and so on for 60 seconds" is unclear. The OP lays out the conditions in steps, but your "and so on" tells me very little.

The obvious point is that we can describe a scenario which is logically possible, but physically impossible. When working with this scenario, we need to bare in mind, the fact that it is physically impossible, and adhere rigidly to the logic of the scenario, only. If one's mind gets influenced by other principles, such as what is physically possible in the universe, and what is going on in the physical universe, this will surely create confusion.

60 seconds will pass in the universe. The counter is just one thing that exists in the universe and it changes according to the prescribed rules.

So given the prescribed rules, when the universe is 60 seconds older, what digit will the counter show? — Michael

Yes, that is the point. Your expressed conceptualization "60 seconds will pass in the universe" is not consistent with the conceptualization prescribed by the OP. But this conceptualization "60 seconds will pass in the universe" is not part of the example. So your introduction of it is not valid. We could call it an equivocation fallacy. We have "time passing" as prescribed in the example, and "time passing" in the universe. The two are not consistent. To introduce the latter into the example, is to equivocate.

Sorry Lionino, I am not a biologist, and spoke hastily without understanding what I was saying. Google has told me that viruses are not alive, so I apologize for the misleading comment.

Let's recast Zeno's ideas using contemporary terminology. In his era, the dominant philosophical view was presentism, which posits that only the present moment is real, and it unfolds sequentially, moment by moment. — keystone

I wouldn't say that. If you read Aristotle's Physics, you'll see that he describes the principal definition for "time" being used at his time, as a sort of number, used for measurement. That, he distinguished from a secondary sense, as something measured. So the secondary sense might be consistent with what you say, but it's not the primary definition for "time" at that time.

No end to the staircase but the end is reached - Yes, this is the very issue I'm trying to highlight. And this has nothing to do with continuous acceleration or motion. — keystone

But the end is not reached. According to what is stipulated Icarus always has more steps before a minutes passes. Here's what I wrote in the other thread:

"For Icarus a minute cannot pass because he always has steps to cover first, just like Achilles cannot pass the tortoise for the same reason. Maybe if we call the staircase a line, and the steps are "points" it would make more sense to you. No matter where Icarus stands on the prescribed line, he has to cover an infinite number of points before a minute can pass. And to traverse each point requires a non-zero amount of time. Therefore no matter where Icarus is on the line (stairs), there will always be time left before a minute passes. A minute cannot pass, and Icarus' journey cannot end."

You only claim that the end is reached, because you assume that a minute passes. But that assumption is not provided for, as explained. Therefore, the valid conclusion is that Icarus never reaches the bottom, just like Zeno concluded that Achilles never surpasses the tortoise. The required premises about space and time, to conclude otherwise, are not provided.

I suggested that movement was discrete, not that space was discrete. — Michael

This is a very good point, to keep in mind when we get a good understanding of, and move beyond, the appearance of paradoxes like Zeno's. What is indicated is that motion is discrete. To account for the reality of this, we need to model either space or time as discrete, but not necessarily both. So when we employ the concept of "space-time" we deny ourselves the capacity of separating time from space, and considering the possibility that one is continuous, and the other is discrete.

To me, what works best for understanding the nature of reality is to allow for a continuous time, with a discrete space. This means that the so-called "quantum jump" is a feature of space. As time passes, the things which we know as having spatial (material) existence change in discrete jumps. Those discrete jumps limit our empirical capacity to understand the true nature of time, because no change can be observed to occur during the time which passes in between such jumps. However, since time would be conceived as continuous, while spatial motion is discrete, we can still conceive of time as passing in between such jumps.

Those premises allow us to understand the "immaterial realm of Forms", as the activity which is occurring between the spatial jumps. The immaterial realm of Forms is what determines how the spatial world will be, at each moment of ("observable") time. The human being as a free willing agent, has causal power within the immaterial realm of Forms, to influence what will be spatially present at any moment as time passes. Notice the requirement of real points in time. These are the points when the observable (spatial) world is materialized as discrete "jumps" during the passage of time.

The issue we have is that if there is no smallest unit of time then the counter is metaphysically possible, but this entails a paradox as the answer to what the counter shows after 60 seconds is undefined yet the counter will show something after 60 seconds. Assuming that paradoxes are metaphysically impossible then the counter is metaphysically impossible, and that suggests that it's metaphysically impossible for time to be infinitely divisible. — Michael

I don't think this is correct, I think Andrewk is correct. The counter is not programed to reach 60 seconds, that is outside its described capacity. Here's what you said:

What digit does the counter show after 60 seconds?

If there is no answer then perhaps it suggests a metaphysically necessary smallest period of time. — Michael

.
See, the counter is not programmed to show anything after 60 seconds. "There is no answer", because if the counter were to do as prescribed, it would never get to 60 seconds. There is no such things as 60 seconds for the counter, it can never get there if it does what its supposed to do. The assumption that 60 seconds will pass, is the mistaken conclusion of the OP, because this requires a premise about time which is not provided in the example. That premise being that time will pass at some rate which will surpass the actor in the example. That's what creates the appearance of paradox, if you allow yourself to be influenced by the contradictory idea, that time will surpass the actor.

The paradox is that given the premise(s) what happens at the limit is undefined, and yet something must happen at the limit. — Michael

This is the mistaken assumption. There is no limit prescribed. The premises set up an infinite process, which means "no limit". The issue exposed now, is that training in mathematics (calculus specifically) inclines one to see the scenario as a limit at 60 seconds, when the example simply does not state it that way. Someone who knew no complicated mathematics, only simple arithmetic, would work through the prescribed process, adding up the periods of time, and then realize that the sum gets closer and closer to 60 seconds, without at all thinking that 60 seconds is "a limit" here.

This imaginary "limit" is added by the mathematical way of looking at the scenario. It is "the intent" in producing the example. Start with the limit, and set something up which approaches the limit but does not reach it. The limit though, is not part of the example, it was only employed by the mind which produced the example, as a guiding principle which does not enter into, or become part of the example. In other words, we need to read the premises exactly as they are written, and there is no mention of 60 seconds as a limit. It's only when you take the short cut, don't read, but jump to the end, the intent, that you think of 60 seconds as a limit.

You're suggesting that the issue lies in the impossibility of a minute passing? — keystone

I wasn't saying that this is "the issue", only that it is the logical outcome. For Icarus a minute cannot pass because he always has steps to cover first, just like Achilles cannot pass the tortoise for the same reason. Maybe if we call the staircase a line, and the steps are "points" it would make more sense to you. No matter where Icarus stands on the prescribed line, he has to cover an infinite number of points before a minute can pass. And to traverse each point requires a non-zero amount of time. Therefore no matter where Icarus is on the line (stairs), there will always be time left before a minute passes. A minute cannot pass, and Icarus' journey cannot end.

No end to the staircase but the end is reached - Yes, this is the very issue I'm trying to highlight. — keystone

No, the end is not reached, as explained above. This is what Andrewk neatly explained in the other thread. That a minute will pass, and the end will be reached, is a presumption outside the prescribed scenario. You are assuming that from some other principles.

What thread are we on? Did you combine this one with the other one? Maybe you could ask a mod to do that for you.

Hi andrewk. It's good to see you, been a while. Doing well? I hope.

This is not true. Perhaps you are reading a different account of the story than I did, which is the one on wiki, which says simply:
"In a race, the quickest runner can never over­take the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead". The 2nd bolded part is the non-sequitur, and the first bolded part follows from the 2nd. None of it makes the assertion you claim. The non-sequitur makes the argument invalid. There are ways (such as with the light switch) that make it seem more paradoxical. — noAxioms

Sorry no Axioms, I can't follow what you are saying, perhaps you could spell out your supposed "non-sequitur" in a clear explanation, instead of simply asserting it. In Zeno's paradox, the tortoise is given a head start.

Same non-sequitur. It is not true that Icarus always has more steps to take, only that he does while still on a step, but the time to complete all the remaining steps always fits in the time remaining in his minute. — noAxioms

That Icarus always has more steps to take is the valid conclusion from the premises. Yes, "the time to complete all the remaining steps always fits in the time remaining in his minute", as you say. However, the remaining steps are indefinite. Likewise the amount of divisions which can be made to the remaining time are indefinite. Therefore Icarus' minute is never completed, and he never completes his steps. That is the conclusion we must make.

However, the OP concludes that the minute passes, and the bottom reached. The OP therefore relies on a sense of physical reality, that a minute must pass, which is outside of the premises. That's why it's not a valid conclusion. There is nothing within the premises to indicate that a minute must pass, and everything indicates that a minute will never pass.

OK, which premise then is false in the Zeno case? The statement is really short. One premise that I see: "the pursuer must first reach the point whence the pursued started", which seems pretty true to me. — noAxioms

The false premise for Zeno is that each distance, and each time period will always be divisible. That's the problem points out. Think of the way a runner actually runs. One foot hits the ground, then the next foot hits the ground some distance further ahead. The runner does not cover every inch of ground in between, the motion of the feet in contact with the ground, takes place in increments.

I believe other animals are capable of reasoning and presymbolic language. The only difference I see is the advent of symbolic language with humans. I also think this is pretty much the standard view, so I'm not sure why you seem to think it isn't the standard view. — Janus

What does "presymbolic language" mean? Isn't all language by the meaning of "language", symbolic in some way? Adding "symbolic" to language, to say that human language is "symbolic language" is just redundancey.

"A man can do what he wants, but not want what he wants", which I take to mean that, apart from external constraints, you are free to do whatever you want but you are not free to choose what it is that you want. — Janus

Why not? I see no problem with a man choosing ones wants. That's what we learn how to do in moral training, mastering our habits.

Well, you could make an essentialist argument that understanding is exactly the discontinuity between humans and other animals, even if understanding itself is a power among others like movement etc. One can find many features that is shared by all (not deficient) humans and absent in other animals and claim that as the discontinuity, no matter whether the feature chosen is important. — Lionino

I do not agree. I think its' very clear that other animals "understand". We had a dog which clearly understood that it ought not get on the table, and so it did not ... as long as someone was around. But as soon as we went to bed it would be on the table. To me, that's obviously a form of "understanding". Of course, you can tailor a definition of "understand" to suit your purpose, but what's the point in that?

I'm just pointing out that there are many lines that can drawn between us and animals. — Lionino

And I'm just pointing out that the vast majority of those lines are arbitrary. In a similar way, we could draw a line between child and adult, and say that only an adult is responsible for one's actions, because an adult understands. But such boundaries are arbitrary.

Is there? What do you make of viruses? Specially something like a mimivirus. — Lionino

I think viruses are quire clearly living. You should ask about something like cancer, or prions, and things like that.

That's beautiful, simple and eloquent.

Sure, I already acknowledged that in the post above about Schumacher's ontology. — Wayfarer

"Mineral" = m
"Plant" = m + x
"Animal" = m + x + y
"Human" = m + x + y + z

In his theory, these three factors (x, y and z) represent ontological discontinuities — Wikipedia

This is what I think is not at all objective and obvious, and I also disagree with it. I see an ontological discontinuity between inanimate and alive. That discontinuity (signified as x above) is what Aristotle explained with his concept of "soul", and which forms the basis of vitalism. And, it is this ontological discontinuity which renders the common notion of abiogenesis as inadequate.

The other differences mentioned above as y and z display no such discontinuity. In fact, there is very much evidence for a continuity between them, as demonstrated by Darwin in support of his evolutionary theory. Furthermore, the continuity between them is described by Aristotle in "On the Soul". He describes all the powers of living beings as potentials, capacities, the powers of self-nutrition, self-movement, sensation, and intellection. Notice that intellection is classed with the others.

Each of these various potentials, are dependent on the material body, matter as potential, but they are properly attributed to the soul which is the active principle that activates and operates them. So there is a continuity between all the powers of the soul (intellection included), as shown by Darwin, each being dependent on the material body which provides the specific potency/act relation, as described by Aristotle, and these are all understood through their similarity.

However, there is a distinct discontinuity between living and inanimate, and this is understood through a principle of actuality, the active principle responsible for the causation of the material body which provides the potential, and this is known as the soul.

Objective - and obvious, isn't it? Again, actual language, as distinct from linear communication through calls or displays, is unique to h. sapiens. As is tool-making, philosophy, technology, art, science, mathematics, music, drama. As is the capacity to reflect on the nature of being and question the meaning of existence. — Wayfarer

Well Vera Mont clearly doesn't think that it is objective and obvious, and I'm not convinced either way. Let me see if I can put this in another way.

Look at the difference between plants and animals. If there is such a thing as a "highly significant difference" which marks a threshold in evolving life forms, wouldn't this qualify as such a threshold? Plants are rooted in the ground, whereas animals are free to move around and sense things. Now, look at the difference between human beings and other mammals. Human beings communicate, socialize, cooperate, and build things. So we might also say that this is a highly significant difference which marks a threshold. But how many other things can we look at as highly significant differences which mark a threshold? do the development of a heart, lungs, brain, legs, wings, hands, not qualify as highly significant differences? It appears to me like we may call the difference between human beings and other mammals a "highly significant difference", but that's just one in a multitude highly significant differences we observe between life forms. Therefore, in reality life is rife with "highly significant differences" and "thresholds". But this makes that one specific difference or threshold, just another difference, and nothing special.

Agree that humans and other species are on a biological continuum, but I also believe that humans crossed a threshold with the advent of language, tool use, and so on, and that it is a highly signficant difference, that though we're related to other animals, we're more than 'just animals'. — Wayfarer

I've seen you state this before, and I find it interesting and would like to see it better supported. What type of "threshold" are you talking about here? would this be an objective, or a subjective threshold, and in what form does it exist?

By "subjective threshold", and "objective threshold" let me give you an example of what I mean. Suppose that within a given species there is a significant degree of variation, but not enough variation to warrant sub-classes, as sub-species within a species, the sub-classes are only variations. Now suppose one particular variation refuses to interbreed with the other variations, and only breeds amongst others of that particular variation. Then, suppose that this variation branches off and becomes a distinct species. When it was a variation within a species, the "threshold" was subjective, because it was by choice that they bred only amongst themselves avoiding the other variants. But when it became a distinct species, it can no longer breed with the other variety, by physical impossibility, so the threshold is an objective threshold, supported by that physical impossibility.

So what I am asking about your claim "that humans crossed a threshold with the advent of language, tool use, and so on", is to say whether this is objective or subjective. Is it the case that we, as human beings, have subjectively decided to say that we are different (perhaps referring to human intellect), and that our minds have produced some sort of mental, or psychological threshold, or barrier, or is it the case that there is real physical principles (opposing thumb?) which supports your claim of a threshold?

What do you mean stipulated? That Achilles cannot overtake is a non-sequitur. It simply doesn't follow from there being a way to divide the journey into infinite segments. — noAxioms

It's not a non-sequitur, the conclusion follows logically from the way that Achilles' movement is described. From the description there is always further distance for Achilles to move before he overtakes the tortoise. Therefore he cannot overtake the tortoise. The issue is not that the argument is invalid, it is that the argument is unsound. The description of motion employed provides false premises.

Time not being allowed to pass was never a specification in the OP. — noAxioms

In the OP, it is not the case that time is not allowed to pass, but the premises imply that a minute cannot pass for Icarus, who always has to take more steps before a minute can pass. Just like in Zeno's paradox, the premises which describe how Icarus moves down the stairs are faulty.

So, in the OP, the false premise is the description of acceleration. Acceleration from rest is described as continuous and open ended (infinite). But this is false, acceleration does not happen like this in reality. Imagine if the OP was expressed in the following way. Someone states that the universe is infinite in size. Then the person states that a rocket accelerates from being at rest on earth at a rate of acceleration which will take it to the edge of the universe before a minute passes. Then the person concludes that after a minute passes the rocket is at the edge of the universe. Do you see the incoherency? That's what's going on in the OP. The premises are arranged so that there cannot be an end to the staircase, just like there cannot be an end to pi. Then it concludes, that after a minute has passed, the end has been reached.

So the OP makes a non-sequitur by concluding that the end is reached. Zeno on the other hand, concludes that Achilles cannot overtake the tortoise, which is the valid conclusion. And the absurd conclusion reveals the falsity of the premises.

The dichotomy thing was better illustrated by something that actually seems to be a paradox.
You are at location x < 0. The goal is to traverse the space between x=0 and x=1.
Thing is, a magic barrier appears at x=1/2 if you are at x <= 1/2, but x > 1/4.
A second barrier appears at x=1/4 if you are at x <= 1/4, but x > 1/8.
And so on. Each barrier appears only if you're past the prior one.
Furthermore, for fun, the last barrier is red. The prior one blue, then green, then red again. Three colors in rotation, all the way up the line.

Per the dichotomy thing (and Keystone's stairs), there can be no first barrier. So you walk up to x=0 and are stopped, despite there not being anything there to stop you. I mean, if there's a barrier, you'd see it and know its color, which is like suggesting a remainder if you divide infinity by three.

So paradoxically, you are prevented from advancing despite a total lack of a first barrier. You can see the goal. But you can't move. — noAxioms

I don't think that this is representative of the OP at all. You have changed the divisibility of time in the OP to a divisibility of space in your interpretation. Then, instead of dealing with the problem of acceleration, which the OP is concerned with, you have to employ "magic barriers" to make sense of the steps. There are no such magic barriers employed by the OP, only steps, and each step is made in half the time of the prior step. So clearly, the OP deals with the issue of infinite acceleration.

I don't think the intention was for physics to be a problem. — flannel jesus

If a person does not take into account what is physically possible in this type of thought experiment, then one can make up false premises however one wants, and create the illusion of a "mathematical problem" when no such problem actually exists. The real problem is that the premises are false (physically impossible), and by employing the false premises the illusion of a mathematical problem is created.

Do you truly believe that Achilles is unable to surpass the tortoise? — keystone

By what is stipulated, yes, Achilles cannot surpass the tortoise. But, the stipulations are not a true representation and that is why there is a problem. The issue is with the way that motion is described. We employ a conception of time and space as a continuity which is infinitely divisible. However, if motion actually consists of discrete changes like a "quantum jump" for example, then the representation of a continuous existence, is false.

Do you think that Icarus's deeds influence the passage of time? — keystone

No, I do not think that Icarus's deeds influence the real passing of time. However, the passing of time is a subject in your example, and it is determined by the premises of the example. So. according to the premises of the example, half as much time is covered each time Icarus makes a step, as compared to the previous step, and Icarus can keep on stepping forever. Therefore the passage of time is defined in relations to Icarus's deeds in the example. That is what is stipulated in the example, That the passage of time is relative to Icarus's steps. Whether it is a truthful representation of the passage of time is irrelevant at this point.

It looks like a simple question, but it isn't. I wouldn't want to reply without looking up his argument for a start. One reply might start from the argument here, that solitary thinking (which may or may not be what he is talking about) doesn't produce the best ideas on its own. The answer from that stand-point would be, no. But that might mean rejecting his argument about "contemplation". That is thinkable. I'm not a fan of his hierarchical argument for the Supreme Good. — Ludwig V

For what it's worth, I believe you'll find it in Bk 6 of Nichomachean Ethics. A lot of any such argument is a sort of stipulation of intuitive principles, so of course the premises are debatable. I think the general idea is that contemplation produces the most universal, principles of theory, and these are required to ground practical principles, and practical principles are required for moral actions. Therefore contemplation produces the highest principles because these are a requirement for all the other virtues. So contemplation is the highest virtue. Then, he moves to show how contemplation is consistent with "happiness" at the end of Bk 10.

After a minute, yes. Do you contend otherwise, that the sum of 60/2**n is not 60? — noAxioms

The specifications do not allow for a minute to pass, that's the problem. It's just like Zeno's Achilles and the tortoise paradox. What is specified by Zeno, disallows the possibility of Achilles passing the tortoise. Here, what is specified in the op by keystone, disallows the possibility of a minute passing.

So it's like you're saying, "after Achilles passes the tortoise...", when Achilles cannot pass the tortoise, because of what is specified, he must pass an infinite number of spaces first. Here, you are saying "after a minute..." when a minute cannot pass because of what is specified, Icarus must pass an infinite number of steps fist.

So it's just like the Achilles and the tortoise paradox, with a different conclusion. Here, instead of concluding that a minute cannot pass, as Zeno concluded that Achilles cannot pass the tortoise, keystone changes things up to say that after a minute has passed the infinite number of steps has been reached. But @keystone has made a invalid conclusion, and should have stuck to Zeno's formulation, to say that a minute cannot pass for Icarus because he always has another step to make first, and that step will be made in a shorter time than the last.

So her argument is that traditional philosophy privileges one kind of human experience, typified by Descartes' solitary thinker (and, perhaps Rodin's statue, which also suggests the thinking is a solitary occupation) or Virginia Woolf’s desire for a room of her own. — Ludwig V

So, philosophy, as the ideas which are produced from the solitary thinker, is a representation of that kind of human being, the solitary thinker. Now, Aristotle shows how contemplation is the highest virtue. So can we conclude that philosophy provides us with the very best ideas?

Despite the staircase being endless, he reached the bottom of it in just a minute. — keystone

But also, there is a slight of hand that occurs when we are encouraged to imagine Icarus's position immediately after he's finished traversing the infinitely long staircase in the original direction. If he would have traversed the staircase in Zeno like fashion, as specified, although he would have stepped on all the steps in a finite amount of time, there would be no definite position along the staircase that he was at immediately before he had arrived at his destination. — Pierre-Normand

Yes, there is a "slight of hand" involved. The real solution is that the only "finite time" in the description is the starting time, and the formula for figuring the increments. And, according to the prescribed formula for figuring the increments, there can be no finish time. It's analogous to finding the end of pi, you just keep going. Despite the defined, and finite starting point, Icarus is currently covering an infinite number of steps in an infinitely short period of time, and by adhering strictly to the description we must conclude that the bottom will never be reached. Bye bye Icarus, enjoy the "black hole's core".

He reaches the bottom of something with no bottom. It taking a minute is fine, but there being a bottom is contradictory. Hence I think resolution. Just as there is no first step to take back up, there is no last step to reach, even if it is all reached in a minute. — noAxioms

How does that work? He's traveling by steps. Each step takes a discernible amount of time which is a different time from the prior step. You say he reaches the bottom, yet there is not "last step". Clearly he doesn't do a bunch of last steps at the same time, so ambiguity is not the problem. How do you think it is possible that he got finished with all the steps, in the described order, yet there was no last step?

Peter Wohleben, a career forester has a very well written, bestselling book called "The Hidden life of Trees: What they feel, How they communicate". In it he talks as if trees act with intention, and he describes how trees communicate with each other through electrical impulses that travel through mycelium which grow around their roots. The electrical impulses of trees have now been studied scientifically.

To communicate through the network, trees send chemical, hormonal and slow-pulsing electrical signals, which scientists are just beginning to decipher. Edward Farmer at the University of Lausanne in Switzerland has been studying the electrical pulses, and he has identified a voltage-based signaling system that appears strikingly similar to animal nervous systems (although he does not suggest that plants have neurons or brains). Alarm and distress appear to be the main topics of tree conversation, although Wohlleben wonders if that’s all they talk about. “What do trees say when there is no danger and they feel content? This I would love to know.” Monica Gagliano at the University of Western Australia has gathered evidence that some plants may also emit and detect sounds, and in particular, a crackling noise in the roots at a frequency of 220 hertz, inaudible to humans. — Smithonian

https://www.smithsonianmag.com/science-nature/the-whispering-trees-180968084/

Wohleben now has a book called "The Inner Life of Animals: Love, Grief, and Compassion: Surprising Observations of a Hidden World". If it's as good as the tree one, it's well worth the read.

You're missing the point. The act, which is called "interpretation", "to interpret", requires a relationship of representation of some sort. This is commonly understood as the relationship between sign and what is signified by the sign. It could also be understood as information and what the information says. To "interpret" is to bring out the meaning which is apprehended as being inherent within this relationship between sign and signified. So any act of "interpretation" requires these two aspects, with this relationship. For simplicity we could say these two are signs and what is signified, representation, and what is represented, or, the information and what the information says, or means.

So if the body/mind "interprets what is given to it", then what is given to it is the signs, information, or representation. But we still must consider the separation between the representation given to the body/mind and what is represented by that representation, or, the separation between the information given, and what the information says, signs and what is signified.

In the act of interpretation, "what is represented", or, "what the information says", is something created by the mind of the interpreter. The interpreter looks at the representation or information, and produces (creates) what is thought to be the meaning of it. "What is represented", "what the information says", "what is signified by the signs", is a creation of the interpreting mind.

Therefore, if "the bodymind interprets what is given to it precognitively", as you say, and what is given to it is a representation, sign, or information (as implied by the concept "interpret"), then what is represented by that information which is given to the mind precognitively, is something created by the mind in this act of interpretation. And so, if "what is given to it precognitively" is determined to be a representation of "the world", or information about "the world", then the world as what is determined as being represented, through the act of interpretation, is something created by the mind which interprets the representation, signs, or information.

People generally prefer to recognize difference over similarity. It feeds the ego and cultivates the superiority complex derived form the person's denial, or refusal to accept oneself as a very small part of a very large whole. Brute or savage, same difference.

The way I see it the world is always already interpreted, so we are not going to agree about this. — Janus

How do you make that consistent with what you said earlier:

It is true that the way we perceive the world is conditioned by the ways in which our sentient bodies and brains are constituted. The suggestion that the mind creates the world, rather than merely interprets it seems absurd and wrong. — Janus

If, "already interpreted" is a prerequisite of there being such a thing as "the world", and minds do the job of interpreting, how would you dismiss the proposition that the mind also creates the world, being prior in time to the world? Since a mind is already necessarily prior to the world to perform that interpretation which is already done in order for there to be such a thing as the world, it seems very likely, rather than absurd, that a mind also creates the world.

Our interpetations are constrained by the nature of the world including ourselves, so it's not right to say that we create the world. — Janus

If the world is always already interpreted, then an interpretation is prior in time to the world. Why would you think that the interpretation which is prior in time to the existence of the world, would be constrained by the world? As is the case with cause and effect, the posterior is constrained by the prior, not vise versa.

No, representing the world to ourselves just is interpreting it. — Janus

To "interpret" is to bring out, or explain the meaning of. To "represent" is to stand for, signify, or correspond to. In no sense are the two the same thing. As I explained, one can interpret a representation, but a representation is not an interpretation. This is because representation is meaning without the requirement of understanding, whereas interpretation requires understanding.

So, in relation to your prior statement, we can only interpret meaning, which we find in the representation of the world. We never actually interpret the supposed independent world, only the representation of it. Therefore the world which we interpret is just an artificial representation, a creation. And when we analyze the representation process, we find that the representation is always a representation of a further representation, in what appears to imply an infinite regress. This is why skepticism cannot be ruled out.

This is going too far. It is true that the way we perceive the world is conditioned by the ways in which our sentient bodies and brains are constituted. The suggestion that the mind creates the world, rather than merely interprets it seems absurd and wrong. — Janus

The primary problem with this statement is your use of "interprets". What is present to the mind, is just a representation which is created by the mind. The thing represented is supposed to be "the independent world". But the relationship between a representation and the thing represented cannot be called an "interpretation". An "interpretation" would be an explanation of the representation, which may attempt to describe that relation between the representation and the thing represented. But we cannot truthfully say that the relation between the conscious representation and the supposed independent world is anything like an interpretation.

Furthermore, if we proceed to a deeper level in our analysis, and attempt a true interpretation of that relation between the representation and the thing represented, we find a secondary problem. If we look at what is actually represented by the conscious mind, when it creates its representation which is supposed to be a representation of the independent world, we see that what is represented is just the information which the subconscious part of the mind, along with the sense organs and neurological system, provide to it. Now we have a distinction between the conscious part of the mind which creates what we know as the representation, and subconscious part (the neurological system), which creates the raw material which is being represented by the conscious representation.

Therefore it is really correct, and not at all absurd or wrong, to say that the mind creates the world, even though this may seem extremely counter intuitive to you. The conscious mind creates a representation of "the independent world", but what is actually represented here is just something created by the subconscious part of the mind. The analysis I provided above shows that the conscious mind creates something which is a representation of what is supposed to be "the independent world". However, what that representation really represents is the information provided to it by the subconscious part of the mind, and this part of the mind produces that information through the various acts of sensation. So what is really represented by the conscious mind's representation, which is claimed to be "the independent world", is just something created by the subconscious part of the mind.

Ok, let me break down more clearly what I do and do not mean. To your credit, value is always assigned but, to my credit, it is not always extrinsic value. Intrinsic value is value assigned to a thing because, and to the degree that, it innately insists (or demands) on being valued. Extrinsic value is value a thing has been assigned relative to how well it fulfills a (subjective) purpose.

Intrinsic value, unlike extrinsic value, is objective because, although we assign it, it is being assigned because the thing actually (mind-independently) motivates people to value it for its own sake and not for the sake of something else: a person is motivated, even if they overcome it, to value a thing with intrinsic value despite what they believe or desire to value it at. It is external motivation (for the subject) which they can not think or desire away.

Another way to put it, is that intrinsic value is value a thing has (1) for its own sake and (2) is attributable to the thing (which exists mind-independently) from its natural ability to motivate people of #1. — Bob Ross

I still do not see how this description of "intrinsic value" makes any sense. You seem to be saying that there are some things in the world, which demand of people, that the people want them, and they want them simply for the sake of having the thing, itself, and not for anything else. But doesn't this really just say something about people in general, that people exist in such a way that there are specific types of things which they will want, simply for the sake of having that thing.

Notice, that I say "specific types of things" that people want, but you portray particular things as having this intrinsic value, rather than types. If it is a type of thing which is valued in this way, then the value is not really intrinsic to the things themselves, but it is attributable to the type.

So take food for example, as such a type. Food appears to be valued for its own sake. This type of thing is inherently good. But what is the case, is that we make a category of things judged as good to eat, we name this category "food", and then we judge which things ought and ought not be placed in this category. So "good" is a defining feature of the category, and its definition is based on what is needed by the human being, it is not based on what is intrinsic to any particular thing.


We might say that nutrition is a good which is intrinsic to particular things, but it is only classed as "nutrition:, or "good", based on how it is received by human beings. It appears like the good is intrinsic to the thing, but it is really only "good" in its relation to humans. These chemical compounds are ones needed by humans. Isn't this very similar to pleasure and pain? These two are categories, one of good feelings, the other bad feelings. They are types of feelings, the good type and the bad type. Then particular instances of feelings need to be judged as to whether they fit one category or the other. So they are really only good or bad as a result of their relation to the conscious mind which does the judging.

I would simply want to speak about what is correctly valued as opposed to what is incorrectly valued; or what is rightly done for its own sake as opposed to what is wrongly done for its own sake; or what is the highest good/end as opposed to what appears to be the highest good/end.

* This last sentence seems to represent Aristotle's thought. Plato, Augustine, Aquinas, and others go beyond Aristotle in this, but Aristotle's position is careful and easily defensible. He does not commit himself to goodness simpliciter in any substantial sense. — Leontiskos

Yes, I think Aristotle was the first to distinguish between the apparent good, and the real good. Aquinas followed him on this distinction, and I believe Augustine did too, to a large degree. Plato was more vague on his notion of "the good".
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I don't agree with the use of random here. Stochastic phenomena are just simply not precise (this is the word I was looking for) as an analysis. Commonly, (and I say erroneously) it is the precision upon which we judge whether something is random, or in the case of Heisenberg, uncertain. But to further judge a phenomena as undetermined is really troubling. — L'éléphant

I agree with this. The appearance of randomness is created by the system which analyzes, it is not a feature of the thing being analyzed. That the analyzing system does not apprehend the patterns being searched for and produces the conclusion of "random", is an indication that the system is not properly formulated for the application it is put to.

You have a very strange way of reading 180 Proof. Did bert1 say that "capacity" = "structure and function"? That's an odd interpretation, to assume that a capacity is a structure or function.

Aristotle says that eudaimonia is the highest end because of its nature, not because subjects happen to value it. But Aristotle and Aquinas immediately address the most obvious objection, namely that different people are made happy by different things (↪Leontiskos).

Here is how Aquinas puts the quandary:

So, then, as to the aspect of last end, all agree in desiring the last end: since all desire the fulfilment of their perfection, and it is precisely this fulfilment in which the last end consists, as stated above. But as to the thing in which this aspect is realized, all men are not agreed as to their last end: since some desire riches as their consummate good; some, pleasure; others, something else. Thus to every taste the sweet is pleasant but to some, the sweetness of wine is most pleasant, to others, the sweetness of honey, or of something similar.
— Thomas Aquinas — Leontiskos

Yes, this is a problem. If "last end" is defined as happiness, then we need a separate description of happiness or else the two words just become representative of each other. Then "happiness" means "last end", and "last end" means "happiness", and all we have is a vicious circle.

So if we look at the broader context, to get an understanding of exactly what happiness is, we see that it is something which is produced in a variety of different ways for the various different people. This appearance of a multitude of differences prevents that mode of inquiry from proceeding, and we are forced to look back at the more general, to find a description with a more universal application, instead of referring directly to all the specific differences.

Notice that Aquinas mentions "the fulfilment of their perfection". Developed from Aristotelian principles, the goal of "perfection" becomes the last end for Aquinas. Every existing thing, by the nature of its very own form, has a perfection which is proper to it, and it alone. So that is what could bring a person true happiness, the perfection of one's very own form, the unique form which is proper to oneself, and this becomes the last end, the goal of each individual.

So this defines "happiness" in "perfection", and leads us toward the need to understand this concept, "perfection" which is revealed as a sort of ideal form.

But math itself does not refer. — fishfry

Math is a field of study, it's not a symbol, sign, or even a group of such, so it's not used to refer to anything. But that's irrelevant. So this discussion is useless from the start

In the evolution of thought, people are going to decide math is wrong because it doesn't actually refer to anything? I thought that was a feature. — fishfry

In practise the math always refers to something. In theory it is designed to be applicable to a very wide range of circumstances. When the theory is not being used to refer to anything, it sits idle. So it only "doesn't actually refer to anything" if it never gets used, in reality it refers an endless number of things.

From what I can see, the Lounge is now the best part of this site. — fishfry

It is a pretty cool place to hang out, lots of activity down there. And they call it The Lounge. Now that's a misnomer.

Law of identity, that each thing is identical with itself, isn't actually math, but general philosophy. So I guess the law of identity is simply a=a or 1=1. Yet math it's actually crucial to compare mathematical objects to other (or all other) mathematical objects. Hence defining a set "ssu" by saying "ssu" = "ssu" doesn't say much if anything. Hence the usual equations c=a+b. — ssu

This is the crucial point, which I'd like to bring to your attention. The law of identity is an ontological principle which deals which "objects" as we meet them in our daily lives, all the different objects which we sense around us, and it forms a defining principle of what it means to be an object. It is meant to recognize the reality of these objects, in the face of skepticism, and offer guidance as to the type of existence which they have. It is probably the most universal of general principles, applying to all the different types of objects that we might possibly encounter.

On the other hand, supposed "mathematical objects" are distinctly different, and the law of identity does not apply. Now we might simply consider that the so-called mathematical objects are not even objects, therefore they don't have any identity as such, and they are really just thoughts and ideas. That seems like a reasonable approach. However, some people want to compose a special type of "identity", specifically designed for these thoughts and ideas, and through reference to this special type of identity they argue that these thoughts and ideas actually are a special type of object, mathematical objects.

However, it ought to be clear to you, that this is just smoke and mirrors sophistry. The special type of identity is formulated for the special purpose of creating the illusion that these thoughts and ideas are a type of object. But it is actually impossible that these ideas are a type of object because the law of identity applies to all types of objects which we might possibly encounter, and this supposed special type of object requires a distinct form of identity which is incompatible with the law of identity.

It's like comparing what in Physics is work and what in economics / sociology is work. The definitions are totally different. — ssu

I don't think that's true true, "work" in physics is consistent with "work" in economics/sociology, physics is simply a broader sense, and "work" in sociology is narrowed down to work is done by human beings.

In the case of "identity" in mathematics, it is inconsistent with, (in violation of), "identity" in the law of identity.

Suppose I owe a creditor a certain amount of money, and ask them, "I have record of my balance as being 582 dollars plus 37 dollars. Do you have the same number?" They say, "Yes, your balance is 619 dollars and 0 cents." It would be ridiculous for me to say, "No! 582 plus 37 is not the same number as 619.00!" — TonesInDeepFreeze

Obviously, you do not understand the law of identity. By the law of identity, the symbols printed here, 582, are distinctly different from the symbols printed over here, 582. Although they appear very similar there is a different position, context, etc., so it is very clear that this is not two instances of one and the same thing, 582. By the law of identity two separate occurrences of the printed symbols, are not the same thing, they are two similar things. Under the conditions of the law of identity we cannot say that 582 printed here is the same thing as, or has the same identity as, 582 printed here.

Therefore I recommend that any wise person would completely disregard the following statement, as coming from the mind of someone who does not know what they are talking about.

The law of identity is a philosophical principle.

It is adopted in mathematics. — TonesInDeepFreeze

Your thesis is that someday, Internet archeologists are going to discover this thread and go, "My God, math is wrong!" — fishfry

It's actually an ongoing process, the evolution of thought. Look at Russel's paradox for example.

Even if the discussion has moved on, I'll just point out this, what identity in math is and why math does deal with identity:

In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables within a certain range of validity.[1] In other words, A = B is an identity if A and B define the same functions, and an identity is an equality between functions that are differently defined. — ssu

All right, you just confirmed what I thought. "Identity" in mathematics is equality. That clearly violates the law of identity. The law of identity allows that identity is a relation between a thing and itself, so there is only one thing involved. Equality on the other hand allows that two distinct things may be equal to each other. So unless you can provide this distinction between equality and identity, or else show that to be equal necessarily means to be one and the same thing, in set theory, then you ought to accept this violation. And, as I mentioned already, we know that the latter cannot be done, because set theory allows that two sets with the same elements in different orders are equal. Therefore I think we ought to just conclude that "identity" in mathematics is a violation of the law of identity. Agree?

You just described your own posting style. — fishfry

That's very observant of you fishfry. Generally speaking, one's language use is a reflection of the conventions and habits which the society has immersed that person in. I like to seek, determine, and then exaggerate within my own usage, the various ambiguities, misleading implications, false representations, and overall misgivings of deceptive habits and conventions which permeate our communications, thereby laying them bare, exposed for the world to see, so that perhaps, at some point in time, the general population will start to realize that something needs to be done about this situation. Wayfarer knows me as the obfuscator.

Bob, in my own moral theory, I believe everything has intrinsic value by the fact of its existence. — Philosophim

This is a fair proposal. It bases value in existence, allowing for "intrinsic value" by the very fact that a thing's existence is intrinsic to it. The problem now would be how to scale different values. By what principles would you say that one type of existence is higher or lower than another type of existence?

My analysis doesn't determine what has intrinsic value based off of what is done for its own sake: — Bob Ross

Since value is relative, in the way I described, your discussion of "intrinsic value" doesn't make any sense. It's an oxymoron. Things like pain and pleasure do not have value, they would be better described as "invaluable", meaning beyond valuation, or impossible to value.

Do you see that "value" implies the ability to scale the worth of a thing relative to the worth of other things? The idea that things have "intrinsic value" would negate the idea that the thing's value is determined by the scale of worth. So this, "intrinsic value" cannot be "value" as we know it.

You are trying to overload the word with metaphysical baggage that it simply does not have in math. — fishfry

What I've argued is that this use of "same", is not consistent with "same" as defined by the law of identity. And if this sense of "same" is claimed to be constitutive of "identity", as Tones argues, then this is a violation of the law of identity. If this is what you want to call "metaphysical baggage", that's ok with me. There are many words with similar forms of "metaphysical baggage". The use of a specific word in one field may contradict its use in another field, and it only becomes a problem if people start to believe that the two uses are consistent with one another.

They are NOT implying any kind of metaphysical baggage for the word "same." If pressed, they'd retreat to the formal syntax. — fishfry

You may want to take this up with Tones, and his notion of "identity theory", which obviously is a kind of metaphysical baggage.

Make sense? You are using "same" with metaphysical meaning. Set theorists use "same" as a casual shorthand for the condition expressed by the axiom of extensionality. It's a synonym by definition. The set theorist's "same" is a casual synonym; your "same" is some kind of ontological commitment. So all this is just confusion about two different meanings of the same word. — fishfry

That completely makes sense. However, not every mathematician is as reasonable as you are. If you look at what TonesoffTheDeepEnd is writing here, you'll see great effort to support some kind of formal identity theory. That is not a "casual shorthand for the condition expressed by the axiom of extensionality".

Also, meta: This thread, "Infinity," is active, and I keep getting mentions for it and replying. But this thread does not show up in my front-page feed! Anyone seeing this or know what's going on? — fishfry

What has happened is that there was a new policy initiated which was to relegate a whole lot of these rambling, bickering, blah. blah, blah, type of threads to The Lounge. And threads in The Lounge don't show on the front page. You'll find The Lounge in the list of Categories on the left side of the front page.