However, their brains were pretty much like ours by the time the flute was made, so maybe... but we just don't know what kind of quantitative thinking they did. — Bitter Crank

Musical instrument makers think in terms of ratios, so there is necessarily measurement involved, to get the right notes.

Since when would a metaphysician think a thing as immaterial as theoretical moral philosophy have any kind of deterministic force incorporated in it, as a means of its justification? — Mww

That was your argument, that moral laws determine one's volition through the means of "moral constitution". I was merely pointing out the inconsistency in what you were saying, your self-contradiction.

Moral law is the source of the form of determinism you said you don’t see. The laws conform to the agent’s innate qualifications, and determine one’s moral constitution, that which the will uses to formulate its volitions. — Mww

First you say people can behave in opposition to moral law, then you said that moral law determines ones volitions. How can moral law be said to determine one's volitions if people can behave in opposition to moral laws?

The sentence "they both describe the same set and therefore they are extensional" is therefore in accordance with the axiomatic foundation of ZFC set theory. — alcontali

Right, but as I noted, this theory is deficient. The two sets are not the same set by any rigorous standard of "same", though they are "the same set" according to the deficient standard of ZFC set theory; the law of identity being the appropriate standard for "same", not ZFC theory. ZFC theory allows that two distinct things are the same, contrary to the law of identity. Since they are not the same, your argument, which requires that they are the same, to reach its conclusion, fails. Therefore they are not even equal.

You conclude that the two sets are equal based on the assumption that the two distinct descriptions describe "the same set". They do not describe the same set, by a rigorous standard of "same", therefore you cannot even conclude that the two sets are equal.

S1 and S2 describe the same set. Therefore, S1 = S2. — alcontali

That two things are equal does not mean that they are the same. This is a known deficiency of mathematics, equality cannot replicate identity. Anyone who argues that 2+2 is the same as 4 needs to learn the law of identity, and respect the difference between equality and identity. The two sets are not "the same" in the sense of "same" used in philosophy, they are "the same" in the sense of "same used by mathematicians (i.e. equal). In philosophy, an actual thing is not the same as a possible thing, and we have a law of identity to prevent this type of sophistry, employed by mathematicians who creep into philosophical discourse without the appropriate discipline.

Yes, now what about the way that mathematics links space and time, when will that be overturned?

Morality speaks to what is good, not what is right. What people commonly do that is not right is with respect to an objective want, called inclination, in opposition to cultural acceptance, thus not necessarily against moral disposition. What people much less commonly do that is not good is with respect to a subjective interest, called obligation, in opposition to moral law, which is very much so against moral disposition. — Mww

Now you leave "moral disposition" as meaningless.

Moral law is the source of the form of determinism you said you don’t see. The laws conform to the agent’s innate qualifications, and determine one’s moral constitution, that which the will uses to formulate its volitions. — Mww

This is not true, by what you've said above. People behave in opposition to moral law, so moral law cannot act as a determinist force.

All possible sentences you can say in English is a set. — alcontali

No it isn't. A set consists of objects, not possible objects.

But what do i have to do to make them one, tie the laces together - glue the soles together - crush them into a singularity? — unenlightened

That's quite simple, to make them one, you have to refer to them as one, and not as two. if you refer to them as two things, a pair, or any such thing, then you are talking about two distinct things. But if you refer to them as one, then you are talking about one thing. But you cannot talk about them as two things and one thing at the same time without contradicting yourself. So either "two" refers to one object, a mathematical object, in which case it does not mean two distinct things, or "two" refers to two distinct things. You can use the word either way, but you must be careful not to equivocate, so you can't use it both ways at the same time.

So don't do it. — unenlightened

The problem is with the people who want to make mathematics do the impossible, not with the people who point out that what the mathematicians are doing when they're tying to make mathematics do the impossible, is contradictory.

The concept of infinite set is abstract and very Platonic but not contradictory. — alcontali

It is contradictory, because a set is closed, complete, (as an object it is bounded, defined) whereas an infinity of anything is open, incomplete, unbounded and indefinite. I went through this in another thread recently, you weren't there.

C’mon, man, really? Nonsense? Look at what you wrote...river still flows according to the direction of the tide. If the tide is the major determinant factor, then the necessity resides in the tide, not the river, re: estuary. I can see one from my deck, complete with lobster boats. Navigational charts call it a river because shoreline proximity precludes calling it a bay, cove, inlet or sound. — Mww

So it's not a river you're talking about, it is an "estuary". Make up your mind, because my analogy did not refer to estuaries, it referred to rivers. Show me a definition of "river" which does not contain 'flow" or something synonymous. Then you might have an argument that some rivers don't flow.

Ahhh.....now we’re getting somewhere. There is a kind of determinism in play. Granting that a moral disposition is predicated on certain qualifications, whether innate genetically or instilled very early on from experience, then in order for proper moral agency to manifest, the agent must conform to whatever those qualifications happen to be. Hence, a form of determinism. It follows that the volitional determinations of the will must adhere to one’s moral disposition in accordance with his pre-established personal qualifications. Hence, a form of determinism. — Mww

I really don't see how this is a form of determinism. We can choose to go against our moral disposition. This is called doing what one knows is wrong, and people do it commonly. So one's moral disposition cannot act as a determinist force.

All well and good, peachy, have a nice day.......right up until the will is called upon to determine a proper moral volition in direct conflict with a vested interest of the agent called upon to act. Here, the will is not free to relieve the conflict at the expense of the agent’s moral constitution. To do so is the epitome of immorality, which manifests in the agent as “guilty conscience”, “dishonor”, ill-will” and the like. And NOT....oh jeez, can you believe people actually think so???......as farging court appearance!!!!! (Gaspsputterchoke) ‘S-ok, though; they can’t separate ethics from morality either, so what can you expect? — Mww

So this is where you're wrong. We often act against what our moral disposition dictates, and your appeal to "guilty conscience" does nothing to resolve this. A person may or may not feel a guilty conscience, but this is irrelevant to the fact that one is free to go against the dictates of one' moral disposition, and is evidence of this freedom.

but if you find no value in any of what’s been said, there’s no point in continuing, right? — Mww

I don't know, you seem to be arguing both sides of incompatible positions, as if they are compatible.

OK, you have two shoes. By what principle are these "two" things, one object? If they are a "pair" of shoes, this does not make them into an object, it is just another way of saying that they are two, a specialized form of "two". They are still not one object.

The first evidence of a musical instrument that was made to purpose is an ivory instrument with holes drilled at regular intervals. This instrument belong to 'modern man' and was made 45,000 years ago.
...
But the first applications of math were (as far as I know) applied to trade, which is very recent, 5,000 years ago, after the invention of writing. — Bitter Crank

Are you sure that the construction of that ancient musical instrument was not an application of mathematics, as is the case with the construction of all musical instruments today?

It is not necessary to adopt platonism to accept that there are infinite sets. One may regard infinite sets as abstract mathematically objects, while one does not claim that abstract mathematical objects exist independently of consciousness of them. — GrandMinnow

There is a metaphysical problem with claiming that there are objects which do not exist independently of consciousness, and that is that these objects are imaginary. And imaginary objects are subjective, property of individual subjects. Such objects could be false, contradictory, or a logical impossibility. So if mathematical objects have this type of existence, each one needs to be justified, or else anyone could make up any imaginary thing, asserting that it exists as a mathematical object.

That is the problem with the infinite set. It is self-contradictory, an impossibility, which someone has asserted as an existing object, and other people have blindly accepted it because it is useful, without requesting justification. When we request justification, we see that "infinite set" is contradictory, as are most mathematical objects. And many which are not contradictory are irrational , like the principles of geometry.

Here's an example as to how mathematical objects are self-contradictory. Take the number 2. As an object, it is a simple unity. However, it is necessarily two distinct unities, as that's what 2 signifies, two distinct objects. So either 2 signifies two distinct things, or it signifies one unity, a mathematical object. It cannot signify both or else 2 would be 1, and that's contradictory. And so we cannot conceive of "mathematical objects" as objects, without loosing the meaning of the symbol. There is an inherent contradiction in asserting that a symbol like 2 signifies an object, because the unifying agent which makes 2 into one object has not been identified, therefore that two are one object has not been justified, and there really is no such object.

Space and time are mathematically linked. — fishfry

The link is synthetic, we link space and time with mathematics. How space and time are really related we haven't the foggiest idea. That's because we do not know what neither of these is, nor can we even describe what space or time is.

Why does Trump flirt with Putin and Kim, but he harasses Iran? Real question. — frank

Trump is, in his own eyes "the greatest deal maker ever". His MO as president is to nullify or cancel as many deals which were made before him as possible, asserting that they are terrible deals, and then he sets to renegotiating them with the tactics of a bully. He has cancelled the "Iran deal", calling it, "the worst deal ever" (which of course is what he called NAFTA, and probably many other deals he's cancelled like TPP). Now he's in the bullying stage, which is his route to negotiating a new deal. In the case of Putin and Kim, there's been no cancelled deal to renegotiate and he's buttering them up, probably hoping to get something from them (unless the rumours are true, that Putin already has something on him, then it's a different story).

The concept “flow” is a condition of the concept “river”, but it is not a necessary condition, for a river that does not flow, i.e., tidal access rivers, is still a river. — Mww

This is nonsense, a tidal river still flows according to the direction of the tide. You've just rejected the generally accepted definition of "river", for personal reasons, to say that "flow" is not a necessary condition of a river. Anyway, it's not relevant to the discussion. Either you accept the analogy or you do not, and obviously you do not.

The concept “free will” is a misnomer, because a free will that is not free in its volitional determinations cannot be a “free will”, but nonetheless a will. — Mww

I can't see your point. You seem to be suggesting that there is such a thing as a will which is not free, such that "free" is not a necessary condition of willing. How could that be, without accepting determinism. Care to explain, or are you just arguing determinism?

Freedom is an indirect condition of the will, insofar as it is a necessary condition for autonomy, which in its turn is the necessary condition for the will to operate in conformity to its prerogatives. Forgive me; I took liberties with the theoretical philosophy of morals by not specifying the distinction between conditions and necessary conditions. — Mww

If freedom is a condition of the will, as explained here, wouldn't this contradict your prior statement, where you talk about a "free will that is not free in its volitional determinations"? Isn't this contradictory in the first place, to refer to a free will which is not free?

I gave no indication that free will is displaced; I specifically itemized free as being separated from will. — Mww

OK, I do not mind separating "free" from "will", but then we must dispose of the idea that freedom is a necessary condition of will. If "free" is separate from and not a necessary condition of "will", then we have a will which may or may not be free. But if freedom is a necessary condition for will, then the will cannot be anything other than free. Which are you proposing? You seem to be talking both, which is contradiction.

If "freedom is the condition the will takes place under", then why is "free will" a misnomer? For example, lets say that "flow" is the condition a river takes place under. Why would it be a misnomer to talk about a flowing river?

That being the case, it is more apt to say, “freedom is the condition the will takes place under”, which still isn’t quite right, but is close enough to work with, and incorporates the added bonus of showing how and why free and freedom both are necessarily separated/displaced from will. Logically separated because free will is always susceptible to self-contradiction, and temporally displaced because freedom is always antecedent to the will for which it is the condition. — Mww

Of course "free" is logically separable from "will", the former is the predicate and the latter the subject. So "free" may be predicated of subjects other than will. Because of this, we can see that there were free things prior to there being a free will, and therefore conclude that freedom is antecedent to the will. But this does not mean that free will is temporally displaced, nor is this conclusion produced by any self-contradiction. The claim that free will is susceptible to self-contradiction represents a misunderstanding of free will.

Lots of gas in me! Actually gas is dissolved in liquids, and can be locked up in solids, so there is a lot of gas in a living being. You already named it with breathing gas, the oxygen gets absorbed into the blood, and moved around to the various body parts. The human being really is solid-liquid-gas. And I wouldn't be surprised if they discovered some form of plasma within us as well.

It's not good to be perogied?

The problem here is that the charting technique puts time as distinct from all three dimensions of space. So if dimensionality is defined by spatial existence time would be better represented as non-dimensional, or the 0th dimension.

The will existing as an autonomous casual means in no way requires it to be separate from time itself. It acts in time, is constrained by it, and to say it is temporally displaced is nonsensical. — Pathogen

This concept of free will requires a particular understanding of the nature of time and change. We see that time passes, and as time passes, time which was to the future of us becomes to the past of us.

Now, we understand a continuity of existence, which is at the base of determinism. What has existed in the past will continue to exist onward into the future, unless there is a force which acts to cause change. This is expressed by Newton's first law, the law of inertia. However, we also can conclude that anything, and/or everything, including Newton's law, could possibly change at any moment of the passing time. This indicates that Newton's first law, which is the basis of causal determinism, is not itself a necessity.

So we have the brute fact that the continuity of existence, expressed by Newton's first law, which is fundamental to determinism, has no support as a universal law. This is sufficient to support the reality of the observations which produce this statement:

4.) Non-deterministic factors do exist in the physical universe. — Pathogen

Furthermore, we observe that these non-deterministic factors, things which are not subject to Newton's first law, are very active within the internal parts of living beings, and this supports the thesis of free will.

No it doesn't. It requires a definition of determinism that implies prediction-making. — Harry Hindu

Right, the faulty definition of "deterministic", which you added is the premise required. It's a false premise though because it's not an acceptable definition of "deterministic".

Predictions can only be made if occurrences that we observe are consistently determined by prior causes. — Harry Hindu

This is not true though, as I explained, a prediction could be made randomly and be correct by chance. Or, a prediction could be made using many other strategies, some of which I described, without the need for determinism. That the actions of a human being may sometimes be correctly predicted does not prove determinism, nor disprove free will, which would be the case if prediction could only be made when actions are predetermined.

I think you are assuming "prediction" which has absolute infallibility, no chance of failure. This might require a deterministic system, but human prediction is unable to obtain such perfection. So, determinism is not required for a correct prediction.

Yes, agreed, the discovery of new knowledge is mostly carried out with other, non-knowledge, tools/mental faculties. — alcontali

Good, but you're still not making the distinction which I asked you to make, between the thing, the tool, (knowledge in this case), and the activity which uses the thing. A tool is not the same as the activity which uses the tool. Knowledge is not the same as the mental activity which uses knowledge. If you make this distinction, then the same thing, an axiom for example, may be considered to be knowledge when it is used as a tool, put to work toward some goals, or it may be consider to be not-knowledge, not a tool, when it is considered to be arbitrary, and used as a toy in play like you described. The same thing is apprehended in a different way, depending on the activity which is using it.

Likewise, if we take one specific type of activity, using knowledge as a tool toward a goal for example, we could potentially use many different tools toward reaching the same goal. Each tool (axiom, or piece of knowledge) selected to be used would be useful, but some would be better than others, specifically the tools designed for that particular type of task. And, no matter how good the tool appears to be, we ought to respect the fact that a metaphysician might find a better tool. However, more likely than not, this would involve changing the task (the activity). An activity is a means to an end, and analysis of the end might determine that the end itself is slightly misguided, or that the activity is not the most efficient way of reaching that end, so a change to the activity would be required, also requiring a change to the tool.

Ha, but if we could "know" the nitty-gritty of these other, non-knowledge mental tools, then they are actually knowledge, and that would be contradictory. Therefore, I am opposed to any strategy that consists in trying to systematize these other mental tools, because in order to do that, we would need to thoroughly "know" them, which is is not possible, because they are not knowledge. — alcontali

I see that, but I wasn't talking about tools (knowledge) at that point, I was talking about the mental activity which uses the tools. So let's say that some mental activity employs "strategy", that's a word you've introduced. Strategy is a tool which is often comprised to a large degree, of intuition. So we cannot say that all strategy is knowledge. Strategy is a tool which is applicable toward bringing about a desired end. It dictates the way we act, in the sense that it is used to determine the way that the mental activity uses the tools, knowledge, and how the tools are chosen. So strategy is more closely aligned to the end (the goal) than it is to the activity (the means to the end), because it is used to determine the activity.

Notice, I am not trying to "systemize" these mental tools, only to understand them. They are already systemized by the mental activity which uses them, and that's what makes them understandable, they are systemized. Therefore you've made an important error in the passage above. You have stated that it is not possible to know these tools because they are not knowledge. But there is an activity which brings knowledge into existence, so just because something is not knowledge doesn't mean that it is impossible to know it. A particular strategy for example may begin as not-knowledge (being based in intuition), but after being tried and tested it becomes knowledge. What this indicates is that there are mental activities which are not understood, because the tools employed are not knowledge, but these tools are not unknowable, our knowledge just has not progressed to the extent of knowing them.

am heavily "epistemized" and deeply invested in the idea of the existence of various knowledge-justification methods. — alcontali

What do you mean by "deeply invested"?

Still, I completely acknowledge that non-knowledge mental faculties are key, not just for the discovery of new knowledge, but in general. But then again, systematization means converting things into knowledge. If it is not knowledge, but rather intuition, this is guaranteed to be a failing strategy. — alcontali

Again, I think I need to stress the difference between knowledge, and mental activity. Do you agree that mental activity is not knowledge, but it uses knowledge? Furthermore, there must be mental activity which does not even use knowledge, as this would be required to account for the coming into existence of knowledge, unless you place knowledge as prior to mental activity (but this could only be intuition, which you deny as knowledge).

So we must respect the fact that if we exclude intuition as knowledge, then we necessarily have mental activity which does not use knowledge, but can itself bring knowledge into existence. The strategy by which this mental activity proceeds cannot be "guaranteed to be a failing strategy", because it is responsible for the existence of knowledge. Therefore, the mental process which proceeds without the use of knowledge ought not be denigrated as a guaranteed failure.

In the end, this kind of research rather amounts to playing with "cool toys". But then again, it is not possible to know what people will find unless they actually try. Furthermore, this type of research nicely emphasizes the true nature of axioms as fundamentally arbitrary starting points. — alcontali

I do not believe that this does show that axioms are arbitrary. This is because there is a difference between playing with toys, and working with tools. Playing with toys is random and arbitrary, but working with tools is purpose driven. Axioms are tools, they are not toys.

Suppose we create an analogy in this way. Knowledge is a tool, and the thinking mind uses knowledge in its purposes driven activities as a tool. But the mind engages in other activities as well, more like playing with toys. The "toys" here are not knowledge, but in a way they are still tools, because the playing is in some ways purpose driven and it's just the case that toys are used by the mind instead of knowledge. The toys are the arbitrary axioms which you refer to, axioms which are not adopted for the purpose of doing any particular sort of work, which would make them tools. But they are used for the purpose curiosity and wonder, for play, like an artist playing with different colours, or a composer playing with different notes. So new axioms are discovered through this activity of creative playfulness, which because it is not putting tools to work it is not an act of using knowledge in thinking, it's more like thinking for the purpose of finding interesting things, playing. .

If you predicted that it would break down, and it eventually does, then that is deterministic. — Harry Hindu

That's not true. When you predict that something will happen, and it does, this does not mean that the thing is deterministic. This conclusion would require a further premise which states that something can only be predicted if it's deterministic.

Deterministic means that the outcome of some system is capable of being predicted by some mind. It follows some logical pattern. It is logical. — Harry Hindu

Neither is this true. Minds can predict things which are not deterministic by many different means, like chance, by some system of statistics and probabilities, or through vagueness in terms . I can predict the outcome of a coin toss. If I am right, I've successfully made the prediction. I can also predict that if I flip the coin 100 times half will be heads and half tails. If the score is 51 to 49 I can employ vagueness to claim that it's close enough to count as half and half, therefore my prediction was correct. For a prediction to be correct, it is not required that the thing predicted is deterministic, nor that the thing follows any logical pattern, it only requires a successful strategy by the predictor.

Well, the link with classical, Euclidean geometry has long ago been abandoned in contemporary number theory. I suspect that it was completely gone by the end of the 19th century, at the same time as they dumped Euclid's Elements. I have never had to carry out arithmetic using a straightedge and compass, like the Greek in antiquity apparently did. — alcontali

And what do you think lead to that move? Metaphysics.

I believe that there must be ingredients in the process of knowledge discovery that are fundamentally unknowable, because if we could know them, then we could even systematize the discovery of new knowledge, while this is fundamentally not possible. — alcontali

This would only be the case if you restrict the act of knowing, in the manner that you have proposed. Let's say that there is a system or method for producing knowledge, the axiomatic system you described. The system cannot know itself, so the "ingredients" of knowledge which are unknowable, as you say are those things which comprise the system. A logician cannot know what makes the logic employed, work, without going outside of the logic. So this is why metaphysics is important, it employs a completely different method, to evaluate the axiomatic systems. If it were a specific system which metaphysicians employed, then metaphysics would run into the same problem. Metaphysicians do not use any specific system, it is more like intuition, so metaphysics appears to be random nonsense to the uninitiated.

Yes, I did refer to non-knowledge mental faculties. Intuition is clearly one. — alcontali

It is necessary to distinguish between knowledge, as an object desired or possessed, and the activities which bring knowledge into existence. When we allow for the existence of non-knowledge based mental activities, we allow for a process which could bring knowledge into existence. If, for simplicity sake, we generalize and call this intuition, then we have something named, which we can discuss, and analyze toward understanding it. We can say now, that principles, axioms, are not chosen arbitrarily, but they are chosen by intuition. Intuition would assess the applicability of various possible principles, in relation to various goals, ends. Now we have separated the means from the ends, and this produces the necessity of assessing the ends themselves. That's the endeavour which pragmatism forces onto the metaphysician. Pragmatism brings light to the fact that axioms are chosen for a purpose, now the metaphysician must identify and evaluate the purpose.

For example, they did not start building the first computers because there were errors in the old mechanical calculators that preceded them. — alcontali

Since a machine is designed to give the human being what one wants, the inability of a machine to give the human being what the person wants, is an error in the machine. It is not an error in the machine's processing activity, but an error in the design. You might say, that an error in design is a human error, but all errors are human errors, and if the machine's processing activity screws up, it is just an error in design.

The universe would be the closed system. — Harry Hindu

The existence of free will demonstrates that the universe, as we know it, is not a deterministic system, nor closed system. To say that there are multiverses which comprise a closed system is nonsense, indicating that you do not know what a "system" is..

The car is epistemically deterministic in the sense that the problem can be identified and the car repaired or an irreparable part replaced. On the other hand the human body is not like this; many things can go wrong that we do not fully understand and repair is often impossible. — Janus

The fact that human beings can identify the problem after the fact, and repair it by replacing the worn parts, does not make the system deterministic. After all, human beings built the system in the first place, and it is the fact that the machinery will break down which makes it non-deterministic.

Irrational just means that a number cannot be reached by merely applying the standard arithmetic operators (+ - x /) to integers. — alcontali

"Irrational" refers to an incommensurable ratio. This means that the two things being related to each other cannot be measured by the same system of measurement, such as the examples I gave you, the circumference and diameter of a circle, as well as the sides of a square and it's hypotenuse. What this indicates is that there is incommensurability between one spatial dimension and another.

Still, the algebraics are not enough when you look, for example, at the roots of polynomials with rational coefficients. You will need to keep adjoining additional field extensions if you want to close the splitting field — alcontali

And you claim that the efforts of the metaphysician are pointless due to infinite regress. It appears like in reality the efforts of the mathematician are pointless due to infinite regress.

So, in this context, "irrational" just means that the problem cannot necessarily be solved by using basic arithmetic, but that it may requiring adjoining to the rationals Q, other numbers produced with more complicated operations. — alcontali

You mean the problem can be solved by hiding the infinite regress behind "complicated operations". A good metaphysician is trained to recognize such sophistry.

Existing knowledge cannot possibly be the main ingredient in the discovery of new knowledge, because in that case humanity would never have discovered any knowledge at all, or else, discovered all possible knowledge already. — alcontali

I see we agree on something anyway.

We simply do not know how to discover new knowledge, and we can certainly not justify how we managed to do it anyway. — alcontali

But we do know how to discover new knowledge. It is basically a process of trial and error. It requires an assumption, a presupposition, which is not taken as true or false (knowledge), but is taken as a principle to be tried, like an hypothesis. You explained this above, in your explanation of what science is.

The issue here, between us, is where do these principles to be tried come from. We cannot just choose them randomly because there would be an infinity of possibilities. Therefore we must proceed with some guidance in choosing the principles to be tried, this is metaphysics. The metaphysician recognizes the failures, errors of others, and narrows the pathway with this form of trial and error.

Gödel's first incompleteness theorem also provably dismisses the idea of running through all possible well-formed formulas as to question a knowledge machine whether the formula is provable or not. For example, in the language required to axiomatize the existence of numbers, it is possible to produce formulas that are logically true but impossibly provable by the knowledge machine. So, if you enumerate the well-formed formulas in that language (which happens to be first-order logic), from first to last, the knowledge machine will run into examples of formulas of which the provability is simply undecidable.

So, it is just not possible to run new candidate knowledge claims through a knowledge machine filled with existing knowledge to check if these new claims happen to be justifiable. Gödel proved that this is not a legitimate knowledge discovery procedure. We will undoubtedly have to keep doing it with leaps and bounds, through serendipity, trial and error, and what have you, to slowly, gradually, and painstakingly, but surely, acquire new justifiable knowledge claims. — alcontali

This is exactly why we cannot choose the principles to be tried, arbitrarily, as you seem to think that we do. We need some intuition as to which of the proposable principles are credible. This comes from a thorough examination of the existing knowledge, the flaws within reveal the errors, and therefore where new proposals are required. So your "knowledge machine" requires a method of analysis of the already existing knowledge to determines errors. This is where new knowledge comes from, determining errors in the old knowledge, not from introducing new proposals and checking for consistency with the old. A new proposal which is inconsistent with the old knowledge is not necessarily wrong, it could be that the old knowledge is wrong.

I agree, but from what you've said, I think you and I have different reasons for thinking so. — T Clark

That we come to the same conclusion from different approaches is good support for the conclusion.

For example, the internal combustion engine is epistemically deterministic. That just means it is a simple system whose function is reliably predictable. — Janus

It isn't though, because the car breaks down when you least expect it. You're over simplifying "deterministic", and "predictable", in order to say that if you can predict something there is a deterministic system involved.

That is only the nature of falsificationist knowledge. That is absolutely not the nature of axiomatic knowledge. The Pythagorean theorem was provable 2500 years ago. It still is provable today. The same holds true for Thales' theorem. It is as provable today as 2500 years ago. Once provable, always provable. Hence, that particular view on the nature of knowledge is epistemically completely incorrect for axiomatic knowledge. — alcontali

When the two sides of a right angle are of equal length, the hypotenuse is irrational. Therefore the Pythagorean theorem as a first principle of geometry is deficient. Pythagoras himself grappled with this problem, and the fact that he could not resolve it bothered him. That the hypotenuse remains irrational indicates that the Pythagorean theorem remains unproven, just like the value of pi remains unproven.

For mathematics, these rules are arbitrarily chosen. — alcontali

If the rules are arbitrarily chosen then why choose a rule which results in the contradiction which is an irrational ratio? The fact is that the rules are not really chosen arbitrarily, they are chosen for purpose, pragmatics. The circle is useful, and pi is the result of the rule which creates the circle. The right angle is useful for making parallel lines, and the Pythagorean theorem is the result of the rule which creates the right angle. That each of these results in an irrational ratio indicates that they are lacking in truth and reality, despite the fact of being very useful.

So, then where is that elusive progress visible? Any link? — alcontali

I gave you the example, we now have a better understanding of the solar system. If you are unfamiliar with metaphysics behind this, you are not the only one. But that's because few people today study ancient metaphysics, they prefer modern metaphysics.

The initially hypothetical knowledge was very often stumbled upon, through serendipity, trial and error, and sheer luck. — alcontali

Actually, most of the initial hypotheses are sheer metaphysics. Take a look at Einstein's special theory of relativity for example. And today there is much metaphysical speculation into the nature of the universe, and the micro world of quantum mechanics.

So, yes, a better understanding of the solar system and other parts of the visible universe took a lot of observation. In fact, it first took quite a bit of haphazard progress in optics and construction of telescopes just to be able to observe these things in sufficient detail. So, yes, if they had had proper telescopes 2500 years ago, they would obviously have seen it too. It wasn't a problem of following the wrong principles at all. — alcontali

Actually, telescopes came after it was theorized that the earth revolved around the sun, and not vise versa, so understanding the heliocentric nature of the solar system was not the result of telescopes. The idea was floated around 2500 years ago, but the planets were given perfect circular orbits according to the principles of Aristotelian metaphysics. The assumption of perfect circles resulted in inconsistencies which could not be reconciled until Copernicus. The point though, is that metaphysical theory preceded the fine tuning observations which were required to adjust the theory.

Sure, I can see that the equations may be strictly deterministic. but that doesn't mean the system in the real world is. — T Clark

That's right, there is no such thing as a completely deterministic system. That's a fantasy.

(1) No ontological uncertainty in deterministic systems because... — fdrake

There is a very real problem with this assumption, and that is that such a system is not real. A system cannot be completely deterministic, because it is always subject to outside influence. A completely deterministic system would be a completely closed system, which is impossible to construct, and even if it does exist somewhere naturally, it couldn't be observed. There is no such thing as an absolutely "fixed", or determined system, so it makes no sense to talk about what does or does not exist within such a system.

Remember, with time the boundaries of the fixed system will break down. Keep rolling the dice and after a while you won't be able to tell which side is which..

Keep hammering away

Oh that's right this is why I don't respond to you, ever. My mistake. — StreetlightX

Transgression! How did you loose your will? Unpredictability seeps in, to even the most predictable things. Why?

Possible answers:

1. Jesus is a human being
2. A human being is Jesus — TheMadFool

How about "Jesus was a human being"? This allows us to deny 2), and it's more truthful. But what is Jesus now? I think that's a more interesting question.

But how do you know it is truly "first"? You do not. So, you will keep trying to find the really "true" first that comes before the current first. It just keeps going on. Ad nauseam. That is why it does not work. — alcontali

Of course, that's the nature of knowledge. Proceeding from the first principle has a similar problem,. There's no infinite regress, just some degree of uncertainty within knowledge, such that knowledge is forever evolving as we move forward.

The most widespread and successful approach to morality is what the three offshoots of second-temple judaism propose, i.e. religious law. — alcontali

OK, now the point is that someone must determine the rules, the law. It makes no sense, to argue as you do, that all respectable knowledge proceeds from first principles in an axiomatic way, because this neglects the fact that someone must determine the principles, in the first place, from which the axiomatic knowledge will proceed.

If you assume that all of the first principles for all divisions of knowledge have already been produced, this contradicts your original statement above, that we cannot know it's really "true", and therefore we must keep searching, in an endless way. You can't argue both sides of the contradiction. But this fact, the fact that we cannot know with absolute certainty that the accepted first principles are really true, is the reason why there is always a need for metaphysics. We cannot just accept as absolute truth, the first principles from which we proceed, in the other forms of axiomatic knowledge.

Read up on it, and then you will understand that what you are doing in the realm of morality, i.e. "metaphysics", is just un-methodical bullshit. Seriously, that is why there has been no progress whatsoever in metaphysics for over 2500 years. That was to be expected, because there is simply no logic in that madness. — alcontali

What is bullshit is your claim that there has been no progress in metaphysics in 2500 years. Do you think that human beings developed the current knowledge of the solar system, and the rest of the universe, by following the principles which were accepted 2500 years ago?

A fixed system can and does capture real phenomena. — StreetlightX

Sure, just like any artificial thing is real.

A great deal - if not all - of experiments in science involve fixing possible variables in order to isolate some dynamics of some system or another. That does not make scientific results artificial. — StreetlightX

What? Scientific results are not artificial? Artificial means produced by human beings. Are you suggesting that scientific results just pop into existence without being produced by human beings. You've degenerated to new levels of nonsense StreetlightX.

He didn’t state it publicly. Like many of these stories some “official” told the press, they sensationalized it, the Danish prime minister criticized it. More misinformation. — NOS4A2

As far as I can tell, telling the press is a way of making it publicly known.

If you reason toward first principles, you will look for the principles underlying these first principles, and again, ad nauseam. It obviously leads to infinite regress. — alcontali

That's contradiction, "first" means first, the possibility of infinite regress is therefore excluded.

That is why this particular direction is forbidden in axiomatic systems. — alcontali

Metaphysics does not operate on an axiomatic system, as I explained above, so whatever it is that is forbidden in axiomatic systems is irrelevant to metaphysics.

The metaphysicist is wasting his time, simply because the direction of reasoning is necessarily incorrect. — alcontali

Unless you can justify this claim, it's nothing more than an opinion of an uneducated person.

Justifying the starting-point rules is an exercise in infinite regress and futility. Can you give even one example of where an approach like that has worked? — alcontali

I gave you the example, moral ethics.

Epistemology really works, while metaphysics is nonsense. We know that for a fact, because after 2500 years of metaphysics, it has never produced anything else but nonsense. — alcontali

I see, morality is nonsense to you.

That a coin toss is random is entirely a real, and not artificial property of a series of coin tosses. — StreetlightX

A coin is something natural?

What happened to you claim that "randomness can only be spoken of in relation to a fixed system"? A "fixed system" is an artificial system.

One thing that follows from this understanding is that randomness can only be spoken of in relation to a fixed system. — StreetlightX

This is important, randomness is only a property of an artificial system. It is something created. The randomness in QM and other microsystems, discussed in this thread, is a property of those systems which have been created by physicists. Randomness itself, because it only exists within the confines of a created system and therefore cannot be absolute, is necessarily determined in the sense of being created intentionally. That is why it is an epistemic, and not an ontological matter. It only takes on the appearance of an ontological issue, as an illusion, when misguided metaphysicians such as C.S. Peirce, posit randomness as a fundamental ontological principle.

Such misinformation is good reason for outrage.