Pi is a particular real number, known to the ancients. Hardly a principle. — fishfry

This is clearly wrong. The ancients did not have real numbers, so they could not have known pi as a real number. They knew pi as the ratio of a circle's circumference to it's diameter. Further, they discovered that this ratio is irrational. You really amaze me with the nonsense you come up with sometimes fishfry.

Are you saying that because humans are physical and sets are a product of the human mind, that sets are therefore physical? — fishfry

No, I was saying that human actions are limited by the physical world, and mathematical thinking is a human action therefore it is limited by the physical world.

Well then your point is trivial and pointless. Everything is physical if we can imagine it. The Baby Jesus, the Flying Spaghetti Monster, the three-headed hydra, all physical because the mind is physical. Whatever man. Pointless to conversate further then if you hide behind such a nihilistic and unproductive point. — fishfry

Obviously, I wasn't saying "everything is physical". Metaphysically, I believe in the immaterial, or non-physical. But human thoughts, as properties of physical beings, do not obtain this status.

Can we please stop now? — fishfry

Sure, you seem to have run out of intelligent things to say.

How do I find out where my likes are?

Is this where we can come to get liked? Maybe the incels would benefit from something like this. A zero on your forehead might look pretty good to some people.

Some aspects of mathematics is so obviously fictional that it is UNREASONABLE that math should be so effective in the physical sciences. — fishfry

The vast majority of mathematical principles, like pi, and the Pythagorean theorem which we discussed, are not fictional, and that is why mathematics is so effective. So there is nothing UNREASONABLE in the effectiveness of mathematics. You can argue from ridiculous premises, as to what constitutes "true", and assume that the Pythagorean theorem is not true, as you did, but then it's just the person making that argument, who is being unreasonable.

If you drop a set near the earth, it doesn't fall down. Sets have no gravitational or inertial mass. They have no electric charge. They have no temperature, velocity, momentum, or orientation. In what sense are sets bound by the real world? — fishfry

The word "set" is a physical thing, which signifies something. And it only has meaning to a human being in the world, with the senses to perceive it. Therefore sets, as what is signified by that word, are bound by the real world.

except that -- stretching a point -- mathematical objects are products of the human mind and the human mind is bound by the laws of nature. So perhaps ultimately there's a physical reason why we think the thoughts we do. I'd agree with that possibility, if that's the point you're making. — fishfry

Now you're catching on. Consider though, that the physical forces of the real world are not the "reason why" we think what we do, as we have freedom of choice, to think whatever we want, within the boundaries of our physical capacities. The physical forces are the boundaries. So we really are bounded by the real world, in our thinking. We do not apprehend the boundaries as boundaries though, because we cannot get beyond them to the other side, to see them as boundaries, they are just where thinking can't go. Therefore it appears to us, like we are free to think whatever we want, because our thinking doesn't go where it can't go.

You will not understand the boundaries unless you accept that they are there, and are real, and inquire as to the nature of them. The boundaries appear to me, as the activity where thinking slips away andis replaced by other mental activities such as dreaming, and can no longer be called "thinking". We have a similar, but artificial boundary we can call the boundary between rational thinking and irrational thinking, reasonable and unreasonable. This is not the boundary of thinking, but it serves as a model of how this type of boundary is vague and not well defined.

Further, we have a boundary between conscious and subconscious, and this is closer to being a real representation of the boundary of thinking. The subconscious activity of the mind is not called "thinking", So dreaming is not thinking. You can see that the descriptions of these two types of boundaries are somewhat similar, being modeled on some form of coherency. A form of coherency marks the difference between reasonable and unreasonable, and a different type of coherency marks the difference between waking mental activity (thinking), and dreaming (mental activity outside the bounds of thinking). In the latter division, you ought to see clearly that it is the physical condition of the body (being asleep), which provides the boundary that we model with a description as to what qualifies as thinking, and what does not. However, there is a coherency or lack of it, within the mental activity, which corresponds with the physical boundary which we model as the difference between awake and asleep. In the case of reasonable/unreasonable, we have cases of physical illness, and intoxication, which demonstrate that the boundary, which is a boundary of coherency, has a corresponding physical condition.

So here's the point. We have mental activity which is thinking, and mental activity which cannot be classified as thinking. Therefore there must be a boundary to thinking which separates it from that other activity. The difference is described as a difference in coherency But, since there are real world physical differences which correspond with the described boundaries of coherency, I propose that it is the real world physical boundaries which impose upon our mental activity, the inclination to create corresponding mental boundaries of coherency. So for instance, the law of non-contradiction is a boundary of coherency. To violate the law is to put oneself outside a boundary of coherency. But the law of non-contraction is a statement of what we believe to be impossible, in the real physical world. So it is the acknowledgement of this physical impossibility, as being impossible, which substantiates the assumed mental boundary of coherent/incoherent.

Now, you are proposing a type of thinking "pure mathematics", which is not at all bounded by the real physical world. How could there possibly be such a thing? As I explained, the mental activity which is called thinking, is already bounded in order that it be separate from the mental activity which is not thinking, and there is a corresponding physical condition, being conscious, or awake, which provides the capacity for thinking. Since this physical condition is required for, as providing the capacity for, thinking, then thinking is necessarily bounded by the real physical world. A person cannot go in thought, beyond the capacity given to that person by one's physical body.

Suppose we allow that thinking might move past the boundaries of coherency, (which I admit we have created), to be not at all bounded by coherency. The problem is that there is a corresponding real world boundary which is responsible for the creation of the boundary of coherence. Do you allow that subconscious mental activity, and dreaming, are thinking? See, it makes no sense to say that thinking can go beyond the bounds imposed upon it by the real physical body which capacitates it.

Now suppose we say that there is a special type of thinking, "pure mathematics", which we give that privilege to. How can we even call this thinking? We create boundaries of coherency to define what "thinking" is, keeping "thinking" within the range of conscious mental activity, but now you want to allow a special type of thinking which is not bound by this rule. In reality, "pure mathematics" is a special type of thinking, so it has stricter binding of coherency than just thinking in general does. And, corresponding with those binds of coherency are features of the real physical world.

In math, violating the "fundamental principles" is how progress is made. — fishfry

I agree with this fully. But the need to violate fundamental principles just means that what was once considered to be a boundary of coherency can no longer be consider such. It does not negate the real physical boundaries, which the boundary of coherency was meant to represent. The boundary of coherency did not properly correspond, with the real world boundary, and therefore it needed to be replaced. The need to replace fundamental principles is evidence of faulty correspondence.

I've just shown that some of the greatest advances in math have been made by blowing up the opinions of the world. What happens is that the opinions of the mathematical world change. Or as Planck said, scientific progress proceeds one funeral at a time. Meaning that the old guard die off and the young Turks readily adopt the radical new ideas. — fishfry

Yes, yes, I think you truly are catching on. The need to change mathematical principles is a feature of poor correspondence. It is not the case that pure mathematics is thinking which is not bounded, because it truly is bounded, as described. But it is thinking which does not adequately understand the real world conditions which are its boundaries. It does not understand its boundaries, that's why it might even think as you do, that it is not bounded. Therefore it often poorly represents these boundaries, and when the boundaries become better understood, the representations need to be replaced. Understanding the true real world boundaries is what produces certainty.

Sure the pieces are made of atoms, but there is no fundamental physical reason why the knight moves that way. — fishfry

Yes there is a physical reason for this. The pieces cannot be floating in air, nor can they randomly disappear and reappear in other places, nor be in two places at once. There are real physical restrictions which had to be respected when the game was created. So a board and pieces, with specific moves which are physically possible, was a convenient format considering those restrictions.

This is the problem with your claim that mathematics is not bound by real world restrictions. You can assert that it is not, and you can create completely imaginary axioms, such as a thing with no inherent order, but when it comes to real world play (use of such mathematics) if these axioms contain physical impossibilities, it's likely to create problems in application. The creator of chess could have made a rule which allowed that the knight be on two squares at once. or that it might hover around the board. But then how could the game be played when the designated moves of the pieces is inconsistent with what is physically possible for those pieces?

I have full respect for the notion that mathematical axioms might be completely imaginary, like works of art, even fictional, but my argument is that such axioms would be inherently problematic when applied in real world play. You seem to think that it doesn't matter if mathematical axioms go beyond what is physically possible, and it's even okay to assume what is physically impossible like "no inherent order". And you support this claim with evidence that mathematics provides great effectiveness in real world applications. But you refuse to consider the real problems in real world applications (though you accept that modern physics has real problems), and you refuse to separate the problems from the effectiveness, to see that effectiveness is provided for by principles which are consistent with physical reality, and problems are provided for by principles which are inconsistent.

That math is inspired by the world and not bound by it? To me this is a banality, not a falsehood. It's true, but so trivial as to be beneath mention to anyone who's studied mathematics or mathematical philosophy. — fishfry

I've explained to you very clearly why it is false to say that mathematics is not bound by the real world. Perhaps if you would drop the idea that it is a banality, you would look seriously at what I have said, and come to the realization that what you have taken for a banal truth, and therefore have never given it any thought, is actually a falsity.

But it's still a formal game. — fishfry

I've gone through this subject of formalism already. No formalism, or "formal game", of human creation can escape from content to be pure Form. You seem to be having a very hard time to grasp this, and this is why you keep on insisting that there's such a thing as "pure abstraction". Content, or in the Aristotelian term "matter" is what is forcing real world restrictions onto any formal system. So when a formal system is created with the intent of giving us as much certainty as possible, we cannot escape the uncertainty produced by the presence of content, which is the real world restriction on certainty, that inheres within any formal system.

That's an interesting point. Yet you can see the difference between representational art, which strives to be "true," and abstract art, which is inspired by but not bound by the real world. Or as they told us when I took a film class once, "Film frees us from the limitations of time and space." A movie is inspired by but not bound by reality. Star Wars isn't real, but the celluloid film stock (or whatever they use these days) is made of atoms. Right? Right. — fishfry

Let's take this analogy then. Will you oblige me please to see it through to the conclusion? Let's say that abstract art is analogous to pure, abstract mathematics, and representational art is analogous to practical math. Would you agree that if someone went to a piece of abstract art, and started talking about what was represented by that art, the person would necessarily be mistaken? Likewise, if someone took a piece of pure abstract mathematics, and tried to put it to practice, this would be a mistake.

Bear in mind, that I am not arguing that what we commonly call pure math, ought not be put to practice, I am arguing that pure math as you characterize it, as pure abstraction, is a false description. In other words, your analogy fails, just like the game analogy failed, the distinction between pure math and practical math is not like the distinction between abstract art and representational art.

I recognize the difference between pure and applied mathematics. And you seem to reject fiction, science fiction, surrealist poetry, modern art, and unicorns. Me I like unicorns. They are inspired by the world but not bound by it. I like infinitary mathematics, for exactly the same reason. Perhaps you should read my recent essay here on the transfinite ordinals. It will give you much fuel for righteous rage. But I didn't invent any of it, Cantor did, and mathematicians have been pursuing the theory ever since then right up to the present moment. Perhaps you could take it up with them. — fishfry

I do not reject fiction, I accept it for what it is, fiction. I do reject your claim that pure mathematics is analogous to fiction. Here is the difference. In fiction, the mind is free to cross all boundaries of all disciplines and fields of education. In pure mathematics, the mathematician is bound by fundamental principles, which are the criteria for "mathematics", and if these boundaries are broken it is not mathematics which the person is doing. And, these boundaries are not dreamt up and imposed by the imagination of the mathematician who is doing the pure mathematics, they are imposed by the real world, (what other people say about what the person is doing), which is external to the pure mathematician's mind. This is why it is false to say that pure mathematics is not bound by the real world. If the person engaged in such abstraction, allows one's mind to wander too far, the creation will not be judged by others (the real world) as "mathematics". Therefore if the person wanders outside the boundaries which the real world places on pure mathematics, the person is no longer doing mathematics.

edit: This again is the issue of content. If the content is not consistent with what is judged as the content of mathematics, then the person working with so-called "pure" abstractions cannot be judged as doing mathematics. Therefore the abstractions cannot be "pure" as there are restrictions of content, as to what qualifies as mathematics.

The concept of infinite infinities is already part of mathematics today. Therefore, in your dubious distinction between mathematics and “imaginary fictions”, your placement of infinite infinities on the side of "imaginary fictions" makes no sense; infinite infinities is already on the side of mathematics. Your attempted stipulations to the contrary are pointless. — Luke

My argument is that such things are wrongly called mathematics, due to faulty conventions which allow imaginary fictions, cleverly disguised to appear as mathematical principles, to seep into mathematics, taking the place of mathematical principles. And obviously, it's not a stipulation but an argument, as I've spent months arguing through examples.

How can you argue with the truth of things that are not claimed to be true? Nobody claims that the axiom of replacement or the axiom of powersets is true. NOBODY says that. — fishfry

I don't see why this is a problem for you. You hand me a proposition, and I refuse to accept it, claiming that it is false. You say, 'but I am not claiming that it is true'. So I move to demonstrate to you why I believe it to be false. You still insist that you are not claiming it to be true, and further, that the truth or falsity of it is irrelevant to you. Well, the truth or falsity of it is not irrelevant to me, and that's why I argue it's falsity hoping that you would reply with a demonstration of its truth to back up your support of it.. If the truth or falsity of it is really irrelevant to you, then why does it bother you that I argue its falsity? And why do you claim that I cannot argue the falsity of something which has not been claimed to be true? Whether or not you claim something to be true, in no way dictates whether or not I can argue its falsity.

It's entirely analogous. Chess is a formal game, there's no "reason" why the knight moves as it does other than the pragmatics of what's been proven by experience to make for an interesting game. And there are equally valid variations of the game in common use as well. — fishfry

Either you are not getting the point, or you are simply in denial. Playing chess, is a real world activity, as is any activity. Your effort to describe an activity, like the game of chess, or pure math, as independent from the real world, as if it exists in it's own separate bubble which is not part of the world, is simply a misrepresentation.

Now, you admit that there actually is a pragmatic reason why the knight moves as it does, and this is to make an interesting game. And of course playing a game is a real world activity. so there is a real world reason for that rule. Now if you could hold true to your analogy, and admit the same thing about pure mathematics, then we'd have a starting point, of common agreement. However, the reason for mathematical principles beings as they are, such as our example of the Pythagorean theorem, is not to make an interesting game. It is for the sake of some other real world activity. Do you agree?

Of course math is inspired by the world. It's just not bound by it. A point I've made to you a dozen times by now. — fishfry

You keep on insisting on such falsities, and I have to repeatedly point out to you that they are falsities. But you seem to have no respect for truth or falsity, as if truth and falsity doesn't matter to you. Mathematics has been created by human beings, with physical bodies, physical brains, living in the world. It has no means to escape the restrictions imposed upon it by the physical conditions of the physical body. Therefore it very truly is bound by the world. Your idea that mathematics can somehow escape the limitations imposed upon it by the world, to retreat into some imaginary world of infinite infinities, is not a case of actually escaping the bounds of the world at all, it's just imaginary. We all know that imagination cannot give us any real escape from the bounds of the world. Imagining that mathematics is not bound by the world does not make it so. Such a freedom from the bounds of the world is just an illusion. Mathematics is truly bound by the world. And when the imagination strays beyond these boundaries, it produces imaginary fictions, not mathematics. But you do not even recognize a difference between imaginary fictions, and mathematics.

News to me. — fishfry

The reason why I can truthfully say that our discussion has never been about how math works, is that you have never given me any indication as to how it works. You keep insisting that mathematical principles are the product of some sort of imaginary pure abstraction, completely separated from the real world, like eternal Platonic Forms, then you give no indication as to how such products of pure fiction become useful in the world, i.e., how math works.

Wow! I am really impressed to realize Omar Khayyam (1048-1131) had the perspicacity to realize his efforts at Non-Euclidean geometry involved notions of space-time. Thanks, MU. I would not have guessed. :chin: — jgill

As I said, one can produce any sort of geometry depending on the particular purpose. My reference to space-time was in reply to fishfry's talk of a specific incidence, the use of non-Euclidian geometry in modern physics

And I'm insane to question the metaphysics of a person who rebukes the skeptic with 'it's science therefore your demonstrations of deficiency are irrational unless your a scientist' It doesn't take a scientist to understand metaphysics..

I'm not arguing my point of view is right, I'm not even arguing a point of view. I'm telling you how modern math works. It's like this, if you don't mind a Galilean dialog. — fishfry

This is not true. You've been making arguments about "pure math", and "pure abstractions". So it is you who is making a division between the application of mathematics, "how modern math works", and pure mathematics, and you've been arguing that pure mathematics deals with pure abstractions. You've argued philosophical speculation concerning the derivation of mathematical axioms through some claimed process of pure abstraction, totally removed from any real world concerns, rather than the need for mathematics to work. So your chess game analogy is way off the mark, because what we've been discussing here, is the creation of the rules for the game, not the play of the game. And, in creating the rules we must rely on some criteria.

Nowhere do I dispute the obvious, that this is "how modern math works". That is not our discussion at all. What I dispute is the truth or validity of some fundamental principles (axioms) which mathematicians work with. This is why the game analogy fails, because applying mathematics in the real world, is by that very description, a real world enterprise, it is not playing a game which is totally unrelated to the world. So the same principle which makes playing the game something separate from a real world adventure, also makes it different from mathematics, therefore not analogous in that way

I have a proposal, a way to make your analogy more relevant. Let's assume that playing a game is a real world thing, *as it truly is something we do in the world, just like scientists, engineers and architects do real world things with mathematics. Then let's say that there are people who work on the rules of the game, creating the game and adjusting the rules whenever problems become evident, like too many stalemates or something like that. Do you agree that "pure mathematicians" are analogous to these people, fixing the rules? Clearly, the people fixing the rules are not in a bubble, completely isolated from the people involved in the real world play. Of course not, they are working on problems involved with the real world play, just like the "pure mathematicians" are working on problems involved with the application of math in science and engineering, etc.. Plato described this well, speaking about how tools are designed. A tool is actually a much better analogy for math than a game. The crafts people who use the tool must have input into the design of the tool because they know what is needed from the tool.

In conclusion, your claim that "pure mathematicians" are completely removed from the real world use of mathematics is not consistent with the game analogy nor the tool analogy. Those who create the rules of a game obviously have the real world play of the game in mind when creating the rules, so they have a purpose and those who design tools obviously have the real world use of the tool in mind when designing it, and the tool has a purpose. So if mathematics is analogous, then the pure mathematicians have the real world use of mathematics in mind when creating axioms, such that the axioms have a purpose.

Modern math is what it is, and nothing you say changes that, nor am I defending it, only reporting on it. — fishfry

The problem is that you have been "reporting" falsely. You consistently claimed, over and over again, that "pure mathematicians" work in a realm of pure abstraction, completely separated, and removed from the real world application of mathematics, and real world problems. That is the substance of our disagreement in this thread. My observations of things like the Hilbert-Frege discussion show me very clearly that this is a real world problem, a problem of application, not abstraction, which Hilbert was working on. And, the fact that Hilbert's principles were accepted and are now applied, demonstrates further evidence that Hilbert delivered a resolution to a problem of application, not a principle of pure abstraction.

It was forced on math by the discovery of non-Euclidean geometry. Once mathematicians discovered the existence of multiple internally consistent but mutually inconsistent geometries, what else could they do but give up on truth and focus on consistency?

I'm curious to hear your response to this point. What were they supposed to do with non-Euclidean geometry? Especially when 70 years later it turned out to be of vital importance in physics? — fishfry

I can't say that I see what I'm supposed to comment on. The geometry used is the one developed to suit the application, it's produced for a purpose. With the conflation of time and space, into the concept of an active changing space-time, Euclidean geometry which give principles for a static unchanging space, is inadequate. Hence the need for non-Euclidean geometry in modern physics.

It's not good or bad, it is simple inevitable. What should math do? Abolish Eucidean or non-Euclidean geometry? On what basis? — fishfry

This is why there is a need for solid ontological principles, an understanding of the real nature of time, the real nature of space. Only through such an understanding will the proper geometry be developed.
This is why it makes no sense to place the "pure mathematician" in a completely separate realm of "pure abstraction". The "pure mathematician" could dream up all sorts of different geometries, and have none of them any good for any real purpose, if the "pure mathematician" had absolutely no respect for the real nature of space.

As evidence I give you "The unreasonable effectiveness of math etc." — fishfry

Sorry fishfry, but this is evidence for my side of the argument. "The unreasonable effectiveness of math" is clear evidence that the mathematicians who dream up the axioms really do take notice, and have respect for real world problems. That's obviously why math is so effective. If the mathematicians were working in some realm of pure abstraction, with total disregard for any real world issues, then it would be unreasonable to think that they would produce principles which are extremely effective in the real world. Which do you think is the case, that mathematics just happens to be extremely effective in the real world, or that the mathematicians who have created the axioms have been trying to make it extremely effective?

You've given me not the slightest evidence that you have any idea how math works. And a lot of evidence to the contrary. — fishfry

Our discussion, throughout this thread has never been about "how math works". We have been discussing fundamental axioms, and not the application of mathematics at all. You are now changing the subject, and trying to claim that all you've been talking about is "how math works", but clearly what you've been talking about has been pure math, and pure abstraction, not application.

Since you're refusing to address the issue, I'll take the time to characterize you, as you did me.

You present us with bad metaphysics, and call it "science", so that when a metaphysician demonstrates the flaws in your metaphysics, you can dismiss it all by saying that the metaphysician has no understanding of that field.

Seems you're incapable of sticking to the topic. Why? Is it because you actually know how completely ridiculous, and completely unscientific, your description of inflation between spatial points is, so you're eager to change the subject?

Until you can empirically demonstrate any real points in space, with inflation between them, I'll continue to assume an infinite number of points between any two points in space, therefore inflation necessarily at an infinite speed.

The best you can do is say "normal rules for inertial frames (including universal speed limits) don't apply". What hurts like a kick in the balls, is that you insist this is science. Oh yeah, science is the discipline where rules don't apply! Have you absolutely no respect for true science? Calling this crap science is the worst disrespect for science that I've ever seen. Call it what it is, will you please, "metaphysics". You will not though, because you know it would be rejected by educated metaphysicians, as terrible metaphysics.

I'm curious where you came across this. I've only seen it once, from Eva Brann, but don't recall if she cited any supporting evidence. — Fooloso4

I've read Plato, Aristotle, and other ancient Greek philosophy. Plato had "the good", and descriptions of how the mind, reason, must prevail over the material body, and Aristotle developed final cause as 'that for the sake of which', the end, but there was not yet a concept of "free will" in the modern sense. In the modern sense, "free will" is the source of activity in an intentional act.

I think the "Passion" of Christ refers in the first place to the suffering of Christ from late Latin passio "suffering, experience of pain". Though, I guess you can use it in the sense of "strong will" if you want to. — Apollodorus

I believe that the Latin passio means equally "enduring" as it means "suffering". So we cannot focus only on the suffering aspect, but we must also consider the enduring aspect. The Passion of Jesus was not a simple moment of suffering, but an extended period which he choose to endure. This is what will power is all about, to endure suffering for the sake of a higher good.

Yeah, I'm using the word an insane amount of times. But in this case, I just meant that you're quite mad. — Kenosha Kid

Sad preacher nailed upon the coloured door of time
Insane teacher be there reminded of the rhyme
There'll be no mutant enemy we shall certify
Political ends, as sad remains, will die
Reach out as forward tastes begin to enter you
— Yes, And You and I

Modelling, hypothesis, observation: so far, so scientific, not to mention that inflationary cosmology comes from scientific research groups, not philosophical ones, and the founders of the theory have won prizes for breakthroughs in science, not metaphysics. — Kenosha Kid

Those are not observations. They are interpretations made through the application of dubious theories. I know that you don't agree that the theories are dubious, but there is no reason to believe that general relativity is applicable toward understanding inflationary theory. Anomalies such as "dark energy" and "dark matter" demonstrate the inapplicability of the these theories which are applied in the interpretation of the observations.

So on that level, calling it metaphysics not science is insane — Kenosha Kid

I don't know why you think that calling cosmology "metaphysics", which is the conventional norm as I demonstrated with Wikipedia quote, is insanity. But I think that calling an hypothesis "science", when the hypothesis is not at all consistent with observations, as the need to assume mystical, magical entities like "dark matter" and "dark energy" demonstrates, is worse than insanity, it's intellectual dishonesty. Calling your metaphysics "science" and trying to back up that claim with faulty interpretations of observations, is nothing other than deception.

You are insane. — Kenosha Kid

Right, we know how you use that word "insane": " the 'inflationary period', while brief, was insanely rapid". When you don't understand something you designate it as "insane". You do not understand me therefore I am insane.

Since you have absolutely no idea as to any of the specifics concerning this "insanely rapid" expansion, it makes no sense for you to call this "science". Clearly, from your description, there might be an infinite number of spatial points, each with an infinite number of spatial points between them, with each spatial point receding from every other, at some absolutely arbitrarily designated speed. The designation of a speed is really irrelevant because if there's an infinity of these points to even the smallest parcel of space, then the speed of inflation is necessarily infinite.

Cosmology – a central branch of metaphysics, that studies the origin, fundamental structure, nature, and dynamics of the universe. — Wikipedia: Outline of Metaphysics

Inflationary theory, as you describe it, Kenosha Kid, is not science, but extremely bad metaphysics.

The spirited part of the tripartite soul in the Republic, for example, is not spiritual in the sense I think you are using the term. — Fooloso4

All perfectly sound, but note that your definition of it is given in a specific context, or domain of discourse, rather than an attempt to define the term 'spirit' in a general sense. — Wayfarer

Right, because Fooloso4 (sorry, I said Apollodorus) had mentioned Plato's tripartite soul as context, in the passage which your reply was in response to, indicated above. The op concerns Plato's cave allegory, and the idea of the tripartite soul as presented in The Republic is very important to grasping the reality of the intelligible realm As the medium between body and mind, this third aspect, passion or spirit, is the means by which dualism escapes the common charge of an interaction problem. The interaction problem is a strawman which monist materialists hold up in a feeble attempt to ridicule dualists.

Further, this is why "the good" becomes so important. The good is what is desired or wanted, and is what actually moves the will, if the will is not allowed to be free from pragmatic influences. ("Will" did not even exist as a philosophical concept at Plato's time, though the underlying principles were being exposed by Plato, becoming a commonly used philosophical term at a later time, around Augustine's exposition on free will).

The problem of the free will, is that while the will moves us to act, it may be bound to material desires and bodily habits, or we may free it from following such habits, allowing it to follow the reasoning of the intellect leading us toward truth and understanding. We may even allow the will enough freedom to contemplate the highest intellectual principles. But intellectual principles, immaterial objects themselves, must be judged for truth or falsity, by the reasoning mind, according to the skepticism of the Socratic method, or Platonic dialectics, and this judgement is itself an act of will. Therefore It is of paramount importance that the soul allow the will complete freedom from the influence of the material body (including even the brain activity which would be composed of acquired habits of thinking), in making those judgements.

We must escape the trap of what is known as "rationalizing". This is why pragmaticism cannot be accepted as providing first principles, because it has been oriented toward 'what works for giving us material luxury' rather than a true honest understanding of "good" which exposes this deficiency.

The reason I don't like 'spiritual' is because of its many different uses, and also the different and sometimes conficting meanings of 'spirit' — Wayfarer

This is why I prefer "passion" when speaking of Plato's tripartite soul. it is much more specific, and I believe completely consistent with what Plato had in mind, strong ambition and enthusiasm, which under the right guidance of a reasonable good, is a prerequisite for achieving the end. But without the guidance of reason, passion becomes contemptuous anger, or unruly lust Also, it is the same word used to describe the "Passion" of Christ, referring to the very strong will of Jesus, to proceed and continue in his course of action intended to deliver us from a corrupted spirituality.

It is what the education in music is supposed to moderate. — Fooloso4

That's right, this is why music becomes a very important aspect of Plato's republic. Nothing stirs the emotions (passion) like music does, and it is understood by Plato that different types of music might lead passion in different directions. So it is proposed that music be used to help direct passion.

I also am ambivalent in respect of the word 'spiritual'. The terms I'm familiar with are psyche, nous, and logos. — Wayfarer

I think what Apollodorus was referring to is the position of "spirit", sometimes translated as "passion" (which I prefer), in Plato's tripartite soul. Passion, or spirit, takes the position of intermediary between body and mind or reason. In the well-ordered, healthy soul, passion allies with reason to exercise control over the body, But in the unhealthy soul, passion is swayed by bodily functions, resulting in an unreasonable mind.

This is important in Plato's comparison between the composition of an individual person, and the composition of the State. His State has three parts just like the human being, being designed after the tripartite being. There is the ruling class, the guardians, and the artisans or trades people (working class I suppose). The guardians are the middle, highly bred like dogs, high-spirited warriors to defend the interest of the State, having great honour, loyalty, and allegiance to the rulers. But in time, as the State starts to degenerate (the cause of degeneration being something to do with numbers), the guardians come to see honour, bravery, courage, ambition, as the highest thing in itself, falling away from the noble and good principles of reason. which are actually higher. Then the guardians are no longer guided by the noble principles of the intellect, they have no allegiance to the rule of reason, and so they are swayed by money, and the material goods of the lower part of the State. This is the unhealthy State.

You can see how the three parts of the human soul, reason, passion or spirit, and body, are comparable to the three parts of the State, rulers guardians, and artisans.

When I was in my early teens, no one at school spoke of “Platonism”. It was always individual authors like Plato, Aristotle, Plotinus. So, when I first read Plato’s dialogues like Timaeus, Symposium, Republic, I was unaware of the existence of a system called “Platonism”. — Apollodorus

We didn't get any education in philosophy in high school, so I wasn't exposed to Plato or Platonism until university.

If we insist that there were major changes, for example, from Plato to Plotinus, we should be able to show what those changes are and to what extent (if at all) they are inconsistent with (a) the text of the dialogues and (b) with how Plato was understood in the interim. — Apollodorus

What I find, is that in Plato's dialogues, Socrates produces unanswered questions. So if Plotinus made some progress toward answering some of those questions, that would constitute a change between Plato and Plotinus.

And the focus of that way of life, at least within the Academy, was the positive construction of a theoretical framework on the foundation of UP. — Apollodorus

I had to do a Google search to find out what Ur-Platonism is:

;

Here I briefly sketch a hypothetical reconstruction of what I shall call ‘Ur-Platonism’ (UP). This is the general philosophical position that arises from the conjunction of the negations of the philosophical positions explicitly rejected in the dialogues, that is, the philosophical positions on offer in the history of philosophy accessible to Plato himself. — Platonism Versus Naturalism, Lloyd P. Gerson, University of Toronto

I really do not see how a "general philosophical position that arises from the conjunction of the negations
of the philosophical positions explicitly rejected in the dialogues", can be called "a theoretical framework". I think these two are miles apart. A position of skepticism, which rejects philosophical positions, cannot be said to provide a theoretical framework. So any supposed theoretical framework would have to come from some principles other than those found in Plato.

We might say that Aristotle build a theoretical framework on UP, but we wouldn't call Aristotelian metaphysics Platonism, it's Aristotelianism.

I'm very familiar with it. But cosmology is metaphysics, not science.

Well, much more than 37bn. Part of inflation theory is that the universe must be much, much larger than the observable universe. However, no magic necessary, just counting. 2c for two adjacent points. Next add a third. You have points A, B and C in a row. A is receding from B at almost the speed of light. B is receding from C at roughly the same speed. How fast is A receding from C? — Kenosha Kid

Don't forget that we might assume an infinite number of points between any two spatially separated points, then we really do have an insanely fast separation. More like a terrible hypothesis though. Anyway, this stuff is not even science at all, so it shouldn't be presented as an example of science, or, @counterpunch.an example of scientific failure.

There's no empirical evidence which indicates that the separation between two supposed points, due to expansion, is limited to c. We don't even know how to find the points which are supposed to be separating from each other. So we might assume an infinite number of such points within any volume of space, and then we have nonsense, Scientists don't even have a vague idea as to how light moves through space which is not supposed to be expanding, so how are they ever going to make theories about how light moves in a space which is composed of points moving rapidly away from each other in all directions? Maybe if they weren't so quick to reject ether theories, the expanding points could be the vibrating particles of a substance.

These issues were not completely resolved in Plato's times and had to be worked out later. — Apollodorus

Actually, if you look really closely, you'll see that the issues haven't been resolved yet. I think you have something to work on Apollodorus. Get back to your studies!

As already stated, followers of Plato already referred to themselves as "Platonists" (Platonikoi) in antiquity and it would be absurd to claim that they were something else. Of course there were some variations according to different schools but that doesn't make the Platonism of one historical period a different system to the Platonism of other periods. — Apollodorus

Even by the time of Aristotle there was no such thing as one consistent "Platonism". Aristotle claimed to refute "some Platonists" with his cosmological argument. But Neo -Platonists took a position more consistent with Aristotle. So there must have been some fine tuning of "Platonism" and rejection of certain types of Platonism Therefore we can assume a reason for the name "Neo-Platonism" rather than simply "Platonism". And Aristotle himself is, in a way, a Platonist. The thing is, Plato had a lot of different teachings which could be interpreted in different ways.

Is there such a thing as "pure imagination" that does not arise ultimately from observations and experiences in the physical world? — jgill

That's a good question. But if all such principles can be said to have empirical causes, then how can you say that you have a mathematical concept which was produced purely for aesthetic beauty? If there are experiential concerns which enter into your conception then how can you say that your intention of aesthetic beauty is pure?

This is essentially the freewill vs determinism question. To make your conception pure, you'd need the capacity to mentally make a clean break between past and future. It is the assumed continuity between past and future, which forces real world concerns into our thinking. We cannot escape the reality of what we experience as what has just happened, and how this bears on what is about to happen. But if we make a break between past and future, then past experience has no necessary bearing on what we produce for the future because what has just happened will not influence our thinking about what is about to happen. Then your goal for the future, a creation of pure aesthetic beauty, could be completely free from the notion that past occurrences put a necessary constraint on your future production, and you could draw from your past experiences, in complete freedom. The creation of your aesthetic beauty could be done purely without any real world concerns, i.e. knowing that the past has no necessary causal relation with the future, allowing you complete freedom from real world pressure.

This is the issue of inherent order, which we've discussed for months now, in a nutshell. If there is order which inheres within a thing, then that order puts a necessary constraint on future possibilities of order, due to the continuity (causal relation) which we assume to exist between past and future. Logically, we want to start with the assumption of unlimited possibility, to give us the capacity to understand any possible ordering. So, we start with the premise fishfry suggested of "no inherent order". But this is not a real representation of the necessity imposed by inherent order. To remove the necessity of inherent order in a more realistic way, I think, requires that we make a clean break between past and future, annihilating the supposition of continuity, thus allowing that the order which inheres within a thing has no real bearing on the thing's future order. This would allow for the true possibility of any order, it doesn't start with the premise of no inherent order, but it rejects the order which is imposed by the supposition of continuity.

These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but pure mathematicians are not primarily motivated by such applications. Instead, the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles. . . . — Wikipedia

I have a number of issues with this passage. Any concept which originates in real world concerns cannot be said to have been produced from an appeal to aesthetic beauty. And if we suppose that there are some of each, wouldn't it be the ones which deal with real world concerns which get accepted into the community. So, as much as I see the claim that "pure mathematicians" are motivated by aesthetic beauty, as opposed to real world concerns, I don't see that any such concepts as being produced purely for aesthetic beauty actually exist in mathematics.

The next is with the phrase " the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles". What we are discussing is the production of the basic principles themselves. If "pure mathematics" simply involves working out the logical consequences of already established principles, then it is not really relevant to what we were discussing, which is the derivation of those basic principles. The question is whether those principles ought to be derived from pure imagination, or ontology.

That is evidence that mathematics, and what fishfry calls "formal abstractions", are not separate, or independent from the world, as fishfry argues. They are not ideal perfections, separate Forms, but they must share in the imperfections of the material world, as only being useful in that world, if they are part of that world. The proposition that they could have independence from the material world is a false premise. So to create a formalism and present it as free from the negative influence of content, is to present a smoke and mirrors illusion, because the most one can do in this respect, is hide that negative influence.

I was just reading about the Frege-Hilbert dispute. As I understand it, Hilbert was saying that axioms are formal things and it doesn't matter what they stand for as long as we can talk about their logical relationships such as consistency. Frege thought that the axioms are supposed to represent real things. I'm not sure if I'm summarizing this correctly but this is the feeling I got when I was reading it. That I'm taking Hilbert's side, saying that the axioms don't mean anything at all; and you are with Frege, saying that the axioms must mean whatever they are intended to mean and nothing else.

https://plato.stanford.edu/entries/frege-hilbert/

Is this what you're getting at? — fishfry

Thanks for the reading material fishfry, I've read through the SEP article a couple times, and the other partially, and finally have time to get back to you.

I think Frege brings up similar issues to me. The main problem, relevant to what I'm arguing, mentioned in the referred SEP article, is the matter of content.

The difference of opinion over the success of Hilbert’s consistency and independence proofs is, as detailed below, the result of significant differences of opinion over such fundamental issues as: how to understand the content of a mathematical theory, what a successful axiomatization consists in, what the “truths” of a mathematical theory really are, and finally, what one is really asking when one asks about the consistency of a set of axioms or the independence of a given mathematical statement from others. — SEP

In critical analysis, we have the classical distinction of form and content. You can find very good examples of this usage in early Marx. Content is the various ideas themselves, which make up the piece, and form is the way the author relates the ideas to create an overall structured unity.

Hilbert appears to be claiming to remove content from logic, to create a formal structure without content. In my opinion, this is a misguided adventure, because it is actually not possible to pull it off, in reality. This is because of the nature of human thought, logic, and reality. Traditionally, content was the individual ideas, signified by words, which are brought together related to each other, through a formal structure. Under Hilbert's proposal, the only remaining idea is an ideal, the goal of a unified formal structure. So the "idea' has been moved from the bottom, as content, to the top, as goal, or end. This does not rid us of content though, as the content is now the relations between the words, and the form is now a final cause, as the ideal, the goal of a unified formal structure. The structure still has content, the described relations.

Following the Aristotelian principles of matter/form, content is a sort of matter, subject-matter, hence for Marx, ideas, as content, are the material aspect of any logical work. This underlies Marxist materialism

However, in the Aristotelian system, matter is fundamentally indeterminate, making it in some sense unintelligible, producing uncertainty. Matter is given the position of violating the LEM, by Aristotle, as potential is is what may or may not be. Some modern materialists, dialectical materialists, following Marx's interpretation of Hegel prefer a violation of the law of non-contradiction.

So the move toward formalism by Frege and Hilbert can be seen as an effort to deal with the uncertainty of content, Uncertainty is how the human being approaches content, as a sort of matter, there is a fundamental unintelligibility to it. Hilbert appears to be claiming to remove content from logic, to create a formal structure without content, thus improving certainty. In my opinion, what he has actually done is made content an inherent part of the formalized structure, thus bringing the indeterminacy and unintelligibility, which is fundamental to content, into the formal structure. The result is a formalism with inherent uncertainty.

I believe that this is the inevitable result of such an attempt. The reality is that there is a degree of uncertainty in any human expression. Traditionally, the effort was made to maintain a high degree of certainty within the formal aspects of logic, and relegate the uncertain aspects to a special category, as content.

Think of the classical distinction between the truth of premises, and the validity of the logic. We can know the validity of the logic with a high degree of certainty, that is the formal aspect. But the premises (or definitions, as argued by Frege) contain the content, the material element where indeterminateness, unintelligibility and incoherency may lurk underneath. We haven't got the same type of criteria to judge truth or falsity of premises, that we have to judge the validity of the logic. There is a much higher degree of uncertainty in our judgement of truth of premises, than there is of the validity of logic. So we separate the premises to be judged in a different way, a different system of criteria, knowing that uncertainty and unsoundness creeps into the logical procedures from this source.

Now, imagine that we remove this separation, between the truth of the premises, and the validity of the logic, because we want every part of the logical procedure to have the higher degree of certainty as valid logic has. However, the reality of the world is such that we cannot remove the uncertainty which lurks within human ideas, and thought. All we can do is create a formalism which lowers itself, to allow within it, the uncertainties which were formerly excluded, and relegated to content. Therefore we do not get rid of the uncertainty, we just incapacitate our ability to know where it lies, by allowing it to be scattered throughout the formal structure, hiding in various places, rather than being restricted to a particular aspect, the content.

I will not address directly, Hilbert's technique, described in the SEP article as his conceptualization of independence and consistency, unless I read primary sources from both Hilbert and Frege.

I take this to be a reference to the fact that geometers studied various models of geometry, such as Euclidean and non-Euclidean, and were no longer concerned with which was "true," but rather only that each model was individually consistent. And philosophers, who said math was supposed to be about truth, were not happy. — fishfry

Geometers, and mathematicians have taken a turn away from accepted philosophical principles. This I tried to describe to you in relation to the law of identity. So there is no doubt, that there is a division between the two. Take a look at the Wikipedia entry on "axiom" for example. Unlike mathematics, in philosophy an axiom is a self-evident truth. Principles in philosophy are grounded in ontology, but mathematics has turned away from this. One might try to argue that it's just a different ontology, but this is not true. There is simply a lack of ontology in mathematics, as evidenced by a lack of coherent and consistent ontological principles.

You might think that this is all good, that mathematics goes off in all sorts of different directions none of which is grounded in a solid ontology, but I don't see how that could be the case.

I'm saying that we can study aspects of the world by creating formal abstractions that, by design, have nothing much to do with the world; and that are studied formally, by manipulation of symbols. And that we use this process to then get insight about the world. — fishfry

I know you keep saying this, but you've provided no evidence, or proof. Suppose we want to say something insightful about the world. So we start with what you call a "formal abstraction", something produced from imagination, which has absolutely nothing to do with the world. Imagine the nature of such a statement, something which has nothing to do with the world. How do you propose that we can use this to say something about the world. It doesn't make any sense. Logic cannot proceed that way, there must be something which relates the abstraction to the world. But then we cannot say that the abstraction says nothing about the world. If the abstraction is in some way related to the world, it says something about the world. If it doesn't say anything about the world, then it's completely independent from any descriptions of the world, so how would we bring it into a system which is saying something about the world?

This is EXACTLY what you are lecturing me about! But as SEP notes, Hilbert stopped replying to Frege in 1900. Just as I ultimately had to stop replying to you. If you and Frege don't get the method of abstraction, Hilbert and I can only spend so much time listening to your complaints. I found a great sense of familiarity in reading about the Frege-Hilbert debate. — fishfry

Actually, I think that often when one stops replying to the other it is because they get an inkling that the other is right. So there's a matter of pride, where the person stops replying, and sticks to one's principles rather than going down the road of dismantling what one has already put a lot of work into, being too proud to face that prospect. You, it appears, do not suffer from this issue of pride so much, because you keep coming back, and looking further and further into the issues.

it is not the case that Frege and I do not get the method of abstraction. Being philosophers, we get abstraction very well, it is the subject matter of our discipline. You do not seem to have respect for this. This is the division of the upper realm of knowledge Plato described in The Republic. Mathematicians work with abstractions that is the lower part of the upper division, philosophers study and seek to understand the nature of abstractions, that is the upper half of the upper division. Really, it is people like you, who want to predicate to abstraction, some sort of idealized perfection, where it is free from the deprivations of the world in which us human beings, and our abstractions exist, who don't get abstraction.

i totally agree with that. i guess i just misunderstood your use of "see".

The Platonic Forms are "that which is seen" (eidos), they are not ideas or assumptions. — Apollodorus

I think Plato separates the intelligible objects (ideas and Forms) from the visible objecys.

The argument, laid out in the other thread, leads to the conclusion that there can only be opinion about the good itself. — Fooloso4

For Plato, opinion is still a type of knowledge.

The good is not something that is. — Fooloso4

What the good itself is in the intelligible realm, in relation to understanding and intelligible things, the sun is in the visible real, in relation to sight and visible things.
...
So what gives truth to the things known and the power to know to the knower is the form of the good. And though it is the cause of knowledge and truth, it is also an object of knowledge. Both knowledge and truth are beautiful things, but the good is other and more beautiful than they. In the visible realm, light and sight are rightly considered sunlike, but it is wrong to think that they are the sun, so here it is right to think of knowledge and truth as goodlike but wrong to think that either of them is the good - for the good is yet more prized. — 508, translation Grube

...as far as how Aristotle defined the good according to individual need...I would desire proof to believe it. The individual good, that is, the good for every man, is a product of the Enlightenment. — Leghorn

I believe the distinction between real good and apparent good (good as apprehended by the individual), was first presented in its primitive form by Aristotle. I do not have time now to look up a reference. However, it was definitely expounded on by Aquinas, who presented many thoughts on this distinction. So the idea was around long before The Enlightenment.

The problem as I understand it is with our inability to know the good itself. — Fooloso4

I guess that would depend on how you define "know". According to Plato In The Republic, the philosopher gets a glimpse of the good, enough to know of its existence. The good is what makes intelligible objects intelligible, just like the sun makes visible objects visible. In a way we see the sun, and in a way we know the good. So in the cave allegory, the philosopher sees that the things people look at, material objects, are just reflections, or shadows, of the immaterial objects, But the philosopher also sees the good, behind the real immaterial things, which is responsible for creating the shadows or reflections, the material things which the cave dwellers see as the real things.

From this, Aristotle proceeded to define the good, in the teleological terms of final cause, that for the sake of which. Plato gave priority to the immaterial ideas, in the cave allegory. But a principle is needed whereby material things might come into existence from the immaterial Forms (Timeaeus). This principle is "the good", which moves the will to act, in the case of human beings and artificial things, and also, the Divine Will in the case of natural things. Final cause (will) is an immaterial cause, which causes material things to come into existence from immaterial Forms.

Are all acts founded on reason? — jgill

No, not all acts are based in reason. Reason is a property of the conscious mind. But that they are not based in reason does not mean that there is not order to them, as there is order in the actions of the inanimate world. That's the difference I referred to. If all order is derived from consciousness, or "reason", we are lead toward panpsychism.

Is there an axiom in set theory that requires the display of elements of sets to be done in inherent order? — jgill

No I really do not believe there is such an axiom, as fishfry stated, a set has no inherent order. And regardless of the displayed order, one could express a statement like 'these elements without any order'. The issue is whether it is possible to conceive of something like that, 'elements without any order'. If not, it would be an incoherent concept. It is possible to state things which are contradictory, or something like that, making what is stated impossible to conceive.

But as simple symbols, rather than meaningful symbols, they may have no IO or a different IO. If I make up three random symbols from finite lines, say, would you then state the order in which I created them gives IO to the set? — jgill

You know it's an oxymoron to talk of a symbol without meaning. If it doesn't symbolize something we can't call it a symbol. Anyway, a physical symbol is not much different from any other physical thing, except it's produced with intention. Each symbol as a distinct entity has order inherent within as the relations of its parts, and as a group of three, there is order inherent in the relations between them, As symbols, with meaning, there is a reason for the order in which you write them. if they are supposed to be devoid of meaning, then why would you be making them in the first place? It's an intentional act, so there must be reasons, therefore order.

Yes, I think that's the distinction I've been describing to Luke, the difference between inherent order, and order as created by the human mind, what you call "ordering". The two are completely different, and how they relate is in some respects "unclear".

The issue I brought up with fishfry is the distinction between representation and imagination. Fishfry allows that "abstraction" might encompass both of these, such that imaginary ideas could be a useful part of a representative model. But this was not borne out by fishfry's map analogy. The purely imaginary in this case, is the thing with no inherent order, as a "set". Another example of the purely imaginary is infinity.

The point that I am making, is that the current order which a thing has, the inherent order, limits the possibility for future order. Therefore the possibilities for ordering (by the mind), in any true sense, must be limited by an assumed inherent order that a thing has. To remove the necessity of assuming an inherent order, for the sake of allowing infinite possibilities of ordering, is a fiction of the imagination, which has no place in a representative model.

So here's an example. Suppose there's a set which contains the "numbers" 3,4,5. The "numbers" are assumed to be abstract objects. As abstract objects, they necessarily have meaning. The meaning which the abstract objects have, necessarily gives them an order, an order which inheres within that group of objects, the set. You cannot have five without first having four, and you cannot have four without first having three. Or even if we define purely by quantity, there inheres within the meaning of "quantity", more and less. Therefore there is an order which inheres within that set of abstract objects, necessitated by the meaning of the objects. To assume to be able to remove that order, which is essential to the existence of those abstract objects, and therefore inheres with the set, for the sake of claiming that any ordering of the set is possible, is a mistaken adventure.

There is one thing about the relation between inherent order, and ordering, which is very clear. This is that to represent the possible orderings of any group of objects, one must have respect for the limitations imposed by the order that they already have. To deny that they have any inherent order is to produce a false representation based in imaginary fiction. And to give abstract objects a special status as fishfry does, to allow exemption from this rule, is to render them free from the restrictions of definition which enforces logical relations (order) between them, thus allowing the imagination to run free.

Anytime.

What do you think he believed? — frank

Socrates professed to know nothing, so his beliefs are scarce.

And could you explain the Euthyphro dilemma? What do you take away from it? — frank

I think that the Euthyphro dilemma was simply presented as an indication of the problems existing within the religious thinking of his day. It's not meant to be resolved, just like Zeno's paradoxes are not meant to be resolved, it's meant to show a problem in the habitual ways of thinking that are prevalent. It's a skeptic's tool, to show deficiency in the accepted ways of thinking.

If I remember correctly, the problem is in the relationship between God and good. I think the lesson is that it's wrong to even define "good" in relation to the gods, or even in relation to God, because it can't be logically done. And so with Plato and Aristotle there's a moving away from this, toward a pragmatic definition of "good", "that for the sake of which", in Aristotle, the end. This defines "good" in relation to what the individual person needs or wants. Then there's the further distinction of the real good, and the apparent good. The apparent good is what appears to the individual as what is wanted, and "real good" is an appeal to some reasoned or rational good, beyond the individual's wants. So the ethical human being seeks to produce consistency between the real good and the apparent good, such that what is wanted is the rational end.

You are assuming the existence of an inherent order that lies beyond conscious recognition. Is there another aspect of mind that might register this phenomena? Is the fact we can discuss IO due to this possibility? — jgill

I don't think I'd call it an aspect of mind, rather an aspect of life. It is evident, that at the most fundamental level, living beings make use of inherent order, by creating extremely complex molecules, etc.. I don't know how the inherent order is recognized at this level, but it must be, in some way, in order for this organizational activity to occur.

I wouldn't say it is an aspect of "mind" that recognizes it because then we get into panpsychism, or something like that, and I think that there is a clear separation, or difference between mind, along with consciousness, and what happens at this fundamental level. So I think it is good to keep them separate, and understand that this is not a part of mind though mind may be a part of this. But the part only performs its particular function, without understanding its relation to the whole.

To me, that means he did not uphold the conventional rules of what it means to be pious, in his society. I think it says very little about his beliefs, it says something about what he refused to believe. Do you acknowledge the difference between rejecting a belief, and replacing the believe with something else? Skepticism rejects beliefs, and many people would argue that skepticism is a matter of replacing those rejected beliefs with others, but I don't think that this is really a good description.

You would need to apprehend the inherent order in able to compare and judge the representation as good or bad. — Luke

This is not true, we use empirical evidence, and deductive logic. It's called science. The hypothesis is the representation, and it is judged according to the evidence and logic.

Hi Frank,
I wouldn't say that Socrates was atheist, I would say that his form of theism was non-conventional. Couldn't we say the same of Jesus, that his form of theism was non-conventional? But no one would say that Jesus was atheist. I think both were accused of blasphemy, but that doesn't make one atheist.

o you are saying that possibility has no regard for truth or falsity, i.e. no regard for the inherent order. I still have no idea what this means. — Luke

No, I am saying that the person who assigns possibility, in that situation, has no regard for truth or falsity, in that act. How could possibility be the type of thing which might have a regard for truth or falsity? Your interpretation is simply ridiculous, and I can't see any reason for such a ridiculous interpretation other than that you intentionally make an unreasonable interpretation in an attempt to make what I say appear to be unreasonable.

But what regard should the inherent order be given if it cannot be perceived or known? — Luke

You are ignoring the fact that I repeatedly said that we see the inherent order without apprehending it with the mind. You just can't seem to grasp this fact of reality, that we see things without understanding what is seen. To you, this is pure contradiction, but until you grasp it, you will never understand what I've been saying.

So, when the mind produces an order, which is supposed to be a representation of the inherent order, within the thing, the order which is being sensed must be regarded in order that the representation be a good one.

Yeah, that's why I asked. It's a bullshit assumption that can't be known. — Luke

If you are convinced that the assumption of an inherent order is a "bullshit assumption", then why didn't you just say this two months ago, and we could have avoided all of your nonsense bad interpretation, and out of context quotes, in your effort to make it look like what I am saying is contradictory?

But no, this you MO, to produce nonsense interpretations, and out of context quotes, with the intention of making it look like the author is inconsistent. So of course you couldn't have been up front with your difference of opinion. You had to carry on and on, in the pretense that you were trying to understand, but couldn't, to get more words, more phrases, sentences, and statements, as ammunition in your pointless attack, without any intention of trying to understand. And then you call me a troll!

Maybe it took you this long to figure it out, that the assumption of an inherent order is a bullshit assumption, but if this is what you believe, then there's no point in going any further with this discussion, because I have no desire to try to convince you otherwise. Because of this belief which you have, that inherent order is a bullshit assumption, there is no point in discussing the relation of inherent order to a set, because you do not believe there is any such thing as inherent order in the first place.

But isn't what is being measured simply the changes that take place in the relation objects have to one another? — Apollodorus

No, what is being measured is the passing of time, which is better described as the rate of such changes. The "rate" requires relations between changes themselves, not relations between objects, but relations between changes..

My question, again, what do you mean possibility has "no regard for truth or falsity"? — Luke

I replied to this, in the last post go back and read it. That is such an unreasonably bad interpretation of what I said, that I think any reasonable person could only have presented me with such a thing intentionally.

So tell me what is the order of the three coloured balls before they are drawn from the bag. — Luke

We've gone through this before. I can't tell you the inherent order.. Luke, you've got an extremely bad habit of getting me to spend endless time explaining something to you, then you start right back at square one, as if we've never talked about it before.

So, to assist you in understanding, I'll use different words than the last time. Then, you turn around to the last time, and say 'look, these words are different from the last time, therefore you contradict yourself'. And you say I'm a troll!

Can you tell us how the imperceptible, unapprehendable inherent order could be useful to anyone? — Luke

It's useful to recognize the reality of it, to understand the deficiencies of mathematics.