Right, but they could have been born in the past. Right? — Arcane Sandwich

No because their parents were not born then. It's an infinite regress of impossibility.

There you are!!! I thought I’d let my mouth get away from me, there, I didn’t hear back. Done went and pissed you off somehow. — Mww

No, it was simply my forgetfulness—

If something could be conditioned by the good alone, would that not entail that the good could not be conditioned by any further thing?
— Janus

No, that statement only says the something cannot be conditioned by any further thing, which makes that something good in itself, not good for the attainment of something else. — Mww

My statement and yours here seem to be saying the same thing. Perhaps I am misreading you.

Thing is, it is said there is only one thing that can be good in itself, for the attainment of no other end, except to duty according to law. Hence the limit of this good to a moral disposition alone. Got nothing to do with good things, of good feelings or good anything. Except a good will. — Mww

Kant's deontological ethics seems to me to be a kind of consequentialism—pertaining to the whole human condition, not to particular circumstances. He seems to be saying that if lying, for example, was acceptable then human society could not function because there would be no trust to act as a social binder. That makes the acceptance of lying (and theft, murder, rape, assault and so on) a kind of self-contradiction for a society, because acceptance of such things contradicts the very idea of social harmony.

I think that Kant is right in the universal context—for me the mistake he makes is transferring that truth to all particular situations as a rigid notion of duty.

My heuristic, and it is only that, is that numbers, laws, etc, are real but not existent as phenomena. They do not appear amongst phenomena, but can only be discerned by the intellect (nous). So they are, in the Platonic sense, but not the Kantian, noumenal objects, object of nous. — Wayfarer

The problem I find here is that number does appear in the phenomenal world—we encounter great numbers of phenomena, and you seem to be ignoring that fact. Also what does it mean to say that number, laws etc are objects of nous? Does it simply mean that they are ideas?

Whereas the archetypal forms exist in the One Mind and are apprehended by Nous: while they do not exist they provide the basis for all existing things by creating the pattern, the ratio, whereby things are formed. They are real, above and beyond the existence of wordly things; but they don't actually exist. They don't need to exist; things do the hard work of existence.

If numbers, laws etc., and all other objects are ideas in the "One Mind" then surely, they exist as such. Do you believe they stand out for the "One Mind" ? If so then they must exist for that mind, no?

I have often said to you that your position needs a universal mind or God in order to explain how we all experience the same world. But you always seem to pass this over and to be reluctant to posit such a mind. That is why your position seems confused and inadequate to me—you seem to want to make a claim, but then when asked just what your substantive claim is, you seem to have no answer.

Sure. I guess this is a common sense account. By the way, I have no commitments either way, I am just interested to hear more. — Tom Storm

Do you think it is more plausible that our formulations are completely arbitrary or that they are constrained by what we actually experience—that the whole logic (grammar) of our language evolves in keeping with the primordial, given nature of that experience.

Note I am referring to the logical structure of language, not to the particular sounds and marks that conventionally represent this and that—they are, onomatopoeia aside, seemingly mostly arbitrary.

Well, sometimes it should be a conversation terminator, I suppose. If you've already solved the problem of the OP, what more is there to talk about, in this Thread? I'd continue the conversation in some other Thread. — Arcane Sandwich

:up:

You never answer the question so often posed to you. How could something that does not exist in space and time be real? Real in what sense?

Is the "domain of natural numbers" more than merely an idea? The set of all sets, is it real?

We try to imagine it as a literal domain or place, which doesn't make sense, but then, only things that exist in space and time are considered real. So the 'platonic realm' then becomes imagined as a kind of ghostly palace with ethereal models of ideal objects, when it is not that at all. — Wayfarer

That may be how you try to imagine it. I have no doubt your imagination is not representative, given human diversity, so I think there is an element of narcissism in your thinking we all imagine in this kind of way.

OK, that's cool. But agreement often seems to be a conversation terminator. Where do we go from here?

I find this some of the most interesting ideas on the forum. The notion that scientific laws and maths are contingent human artifacts rather than the product of some Platonic realm seems more intuitively correct to me. But as an untheorized amateur, I would say that. — Tom Storm

I don't think it's so black and white—either this or that. We formulate the laws of nature, but we are constrained in those formulations by what we actually observe to be so. We see regularities and invariances everywhere we look. We encounter number in our environments simply on account of the fact that there are many things.

So mathematics has its roots in experience—the world really is mathematical, but not (obviously) explicitly so—it is we who make it explicit, and it is not a contingent enterprise, but must be in accordance with what we actually experience. What we actually experience is not up to us. It's like we speak the language that the world teaches us, a language it does not know or articulate by itself.

Because I said "sweet chicken" at the end? Who says that seriously? — Arcane Sandwich

I don't know you and thus I have no idea what you might be serious about.

Then why are you hassling me, matey-mate? — Arcane Sandwich

I have and have had no intention of hassling you. You have been responding to my posts and I to yours. It's called a conversation, or at least an attempt at one.

It was a joke. You know that, right? — Arcane Sandwich

How would I know?

Have you solved the problem of the OP? If yes, cool. If not, what are we arguing about, you and me? Clue me in, as I've no idea. — Arcane Sandwich

I've solved the OP to my own satisfaction, which no doubt will count for little for others. It's not clear to me that we are arguing about anything.

I have jumped to no assumptions about you. Ironically it seems to be you who is projecting some concerns onto me such as that you seem to think I think my solution is the correct one, or that I'm concerned about having it "certified" somehow.

What I present is nothing more than how I look at it—for me the purported problem regarding whether mathematical entities exist in any platonic sense is a non-issue, a collateral result of reificational thinking.

So what are you asking me, Janus? If your solution is the right answer to the question in the OP? Because there's also @Banno's proposed solution, as well as the one that I proposed myself (mathematical fictionalism). How do you propose to solve this, in practical terms? — Arcane Sandwich

The only question in the post you are respionding to is this:

How much lerss would we need to think of infinitesimals as actual existents, and how incoherent is the idea of an actual existent being "outside of spacetime itself in some mysterious way that is incomprehensible to modern science" ? — Janus

and it is a rhertorical question. So I wasn't asking you anything.

You ask me how I proposed to solve this in practical terms—the only solution (more a dissolution) I am offering was the one at the top of the post you were responding to:

As I said earlier: "If the infinitely many integers are understood to be merely potential as a logical consequence of a conceptual operation—in this case iteration—and are not considered to be actually existent, then the need for a Platonic 'realm' disappears." — Janus

Does that count for you as a practical solution? If you are seeking an empirical solution to such questions, I'd say you are wasting your time. Seems it would be impossible to establish a fact of the matter.

Then he’s already shot himself in the foot, insofar as the uncondition-ed is beyond human reason, and the uncondition-al is itself a rather suspicious conception. — Mww

An unconditional good would be a good that was good in itself—a good that relied on no other conditions to establish its goodness. Perhaps it could also be referred to as an unconditioned good. I don't believe there is anything either unconditional or unconditioned—the very ideas seem incoherent—or at least I can make no sense of them beyond being able to say what I said in the first two sentences.

Better he propose a claim that there is that which is conditioned by good alone, which makes good a quality under which the conceptual object of the claim is subsumed, rather than the condition of that conceptual object’s possibility. Thereby, he is justified in claiming that in which resides good as its sole quality, serves as the singular necessary condition for that which follows from it. — Mww

I am not sure I'm grasping what you want to say here. If something could be conditioned by the good alone, would that not entail that the good could not be conditioned by any further thing? Would that not lead us directly back to the idea of an unconditional, unconditioned good?

That there is that in which resides good as a sole quality is a claim restricted to mere opinion, yes, but the justification for that which follows from it, in the form of pure speculative metaphysics, can be logically demonstrated as a prescriptive practice, which is not mere opinion. — Mww

While that which is claimed to be good in itself is mere opinion, it can still be the case that whatever follows from it, iff logically consistent hence irrational to deny, that the ground for the claim is the subsequent affirmative justifications given from it. — Mww

So the premise that there could be a pure, unconditioned good is a claim restricted to opinion, but if that opinion be granted the logical entailments that follow from it are not? If that is what you meanI would say that is true of any premise, however unsound.

But, as in any speculative domain, it’s off to the rodeo, and the commoners get lost in the minutia paving the way. — Mww

So, it would seem!



.

Right but then if it's plain old oddness that you want to talk about, I'd say that Mathematical Platonism in general is far more odd than Mathematical Fictionalism. It is less odd to say "infinitesimals are just fictions, which means that they are a series of brain processes" than to say "infinitesimals exist in some sense in the external world, structuring reality itself from outside of spacetime itself in some mysterious way that is incomprehensible to modern science." — Arcane Sandwich

As I said earlier: "If the infinitely many integers are understood to be merely potential as a logical consequence of a conceptual operation—in this case iteration—and are not considered to be actually existent, then the need for a Platonic 'realm' disappears."

How much lerss would we need to think of infinitesimals as actual existents, and how incoherent is the idea of an actual existent being "outside of spacetime itself in some mysterious way that is incomprehensible to modern science" ?

The problem I have with some platonists is that they want to say that the forms are real, but not existent, and the idea of a "realm" is an incoherent reification, but they cannot say how the forms (or numbers) could be real in any sense other than the merely logical or the empirical.

Not perplexity, just plain old oddness. I'm not suggesting anything about essences; I think the very idea is problematic. Identity is just an idea. The odd thing is that the "in itself' the very thing which is conceived as having no identity or identifiability for us, is an expression couched in terms of identity.

The odd thing about the idea of "in itself" is that it is saying "in its identity". Identity suggests integrity. When we eat the oyster, it is broken down, loses its integrity, and thus loses its identity. Once eaten it is "in us" now a part of our identity. We cannot eat the oyster's identity, because the act of eating progressively destroys it—in eating the oyster we do not digest the oyster's identity, but its brokenness.

I agree with the conclusion of that argument, really. We cannot eat oysters as they are in themselves. That is true. I only wish the premises were true as well. — Arcane Sandwich

Because once eaten they are no longer "in themselves" but in us?

UNE — Banno

Is that University of New England?

3. The “I think” is not experienced at all. It is a condition of thought, a form of thought, in the same way that space and time are conditions of cognition. Self-consciousness, in Rödl’s sense, is built in to every thought, but not as a content that must be experienced.

4. If your report is accurate, then the thesis that “the ‛I think’ accompanies all our thoughts” has been proven wrong. — J

3. seems to be a post hoc judgement. Of course every thought is thought by me, because they are my thoughts, right? But what am I? It's like the cogito: I think therefore I exist—and further— I exist in every thought. But 'I' is really just another thought, even if some would like to paint it as the transcendental master thought if not as some substantive entity.

4. is right because there is no clear sense in which the so-called "I think" could be present in or inherent in every thought.

But the question of the OP literally asks if they exist in a "Platonistic" (sic) Platonic way. — Arcane Sandwich

If the infinitely many integers are understood to be merely potential as a logical consequence of a conceptual operation—in this case iteration—and are not considered to be actually existent, then the need for a Platonic 'realm' disappears.

Salient bit is that it's not a pretence that there is no largest integer, it's just what we do with integers. — Banno

I agree it's not a pretence, it's a logical entailment.

I don't know, maybe. But if so, then you're no longer doing mathematics, you're doing something else. — Arcane Sandwich

What we are doing here is not mathematics but philosophy of mathematics. So, all I'm saying is that I think what I outlined is the best way to understand the situation regarding what is a given in mathematics—that there are infinitely many integers.

We pretend that there are infinitely many integers even though we can think of only finitely many of them - and this because we assign the set of all integers definite properties, such as that of being included in the set of rational numbers. — Bunge, Ontology II: A World Of Systems, page 169)

We don't pretend that there are infinitely many integers, because there are infinitely many integers. That's how integers work. And they work that way not just in this or that mind, but as an activity performed by our community. — Banno

The solution to this is to say that there are potentially infinitely many integers. Once the logic of iteration is in place, there are potentially infinitely many integers just because there is no inherent logical limit to iteration.

This was made unavoidably obvious by the observer or measurement problem in quantum physics. Although that is a special case of a far wider issue, which is also a subject in philosophy of science. — Wayfarer

Firstly, in QM the so-called "observer problem" is not recognized uncontroversially as entailing that human consciousness is paradigmatically the observer.
Secondly, it is not at all controversial that science begins with observation. How else could it possibly begin? Seems like clutching at straws.

If anything is said to be good, we can always ask on what grounds is it deemed to be good. If someone claims there is an unconditional good, then you might ask "can that be more than a mere opinion?" or "what grounds do you have for claiming that there is an unconditional good?"

Are you saying divisibility cannot be "divided up" and/or sets displaying "evenness" cannot be divided up? For example, the set of even numbers can be divided up into those even numbers having exactly two 2s. — jgill

I'm not sure what led you to think I was saying anything like that. It seems to me that arithmetic has its genesis in playing around with groups of actual things and inducing the basic concepts of adding dividing, subtracting and multiplying. Once we have generalized and abstracted those notions and represented them symbolically and formulated the rules that govern them, then all of the elaboraqtions of mathematics become possible.,

In my opinion none of math exists in some Platonic realm independent of human brains. These are ideas, not physical objects. — jgill

Totally agree.

The irony in all this is that I sort of am a fan of hierarchical notions of "being," if by hierarchy we just mean structure or grounding. My idea, not to belabor it to death, is that we'll do a better job by dropping the word "being" to the extent that we can. — J

I also am fine with the notion of hierarchy in the sense of structure or grounding—I just reject the spiritualist notion of degrees of being—you know, the idea that humans are at a higher degree of being than animals, and angels at a higher degree of being than humans, and so on. The "great chain of being" idea I reject.

For me the word 'being' just means, if taken as a noun 'existent' or 'existence' and if taken as a verb, 'existing'.

I'm sorry, I can't resist a good typo. Yes, I too find small numbers to be prim, even reticent. But then there's π, which is small but goes on and on forever . — J

:lol: Nice!

:up: I like the article, since it is saying just what I have been. It's the middle ground between Platonism and nominalism.

.

I wasn't equating the 'elements' of the verses with the five elements. I never had that in mind at all.

I'm not saying mathematical proofs are empirical. Divisibility, and thus oddness, evenness and the primeness of small numbers can be directly observed in the ways groups of things can and cannot be divided up. From there abstract rules are formulated. Remember, calculations used to be done on an abacus.

Not deduced. it is induced by what is discovered in what is observed.

. Does it make more sense -- is it more conducive to good thinking -- to speak of "justice" or "instances of justice"? A good question! "Do rocks exist in a superior way to justice?" Not a good question! — J

Right, I wasn't asking the second question. I don't think in terms of superior ways of existence—I am not a fan of hierarchical notions of being.

Rocks and justice exist in different ways—rocks are spatiotemproally existent and justice like goodness is conceptually existent. So, depending on circumstance you could have good and bad rocks—if you are trying to build a certain kind of ashlar wall, for example.

If numbers are just abstractions, how do you distinguish "3" from "The second even prime". The first "exists", the second doesn't. What distinguishes these two abstractions?

Second, how do you account for numeric laws? If numbers were all in the head, how are laws discovered that were most certainly not in anyone's head until they were discovered? — hypericin

Primeness, evenness and oddness can be observed in the ways that groups of objects can and cannort be divided up.

Then what did you want to refer to by 'elements'? — Arcane Sandwich

Man, Earth, Heaven, Tao and Nature—the five 'elements' of the verse.

Politely, kindly, genuinely, candidly, honestly, I ask you: who is to be faulted, for your lack of sureness (or degree of certainty) in where I am going with the rest of my post? — Arcane Sandwich

I don't know. Must it be somebody's fault?

In Wuxing (Chinese philosophy), there are five elements: Fire, Water, Wood, Metal, and Earth. — Arcane Sandwich

Right I was aware of that, but it wasn't what I wanted to refer to by 'elements' and nor did I want to draw any analogy.

Not sure where you are going with rest of your post.

Of course you're right. There are five 'elements'. I guess the difference I see is that there is no difference between any of those and thus to follow any one is really to follow all the others. And that seems to follow from the way the text is set out, too: to follow Man is to follow Earth, to follow Earth is to follow Heaven, to follow Heaven if to follow Tao and to follow Tao is to follow Nature. Perhaps we could continue: to follow Nature is to follow Man.........

I do understand the Tao and nature as being the most general or universal or overarching, though. Still, I nonetheless can't see the way (Tao) as something different from nature or the way of nature as different from nature. Maybe it's a pedantic point. I am no Dao De Ching scholar and i can only guess at the intentions of the author.

Nice! I agree.

OK, as I understand Hegel the idea is that consciousness evolves according to a dialectic which is so rationally or logically constrained that it serves as a kind of telos. I never understood the logic of his idea of the end of history and the advent of absolute knowledge, though, since I see the process of the evolution of understanding as having no end in both senses: as not having a final goal and as never being finished.

I always aim to be charitable towards others' interpretations. But no matter how comprehensive explanations are from both sides the possibility of diagreement remians. Doesn't mean one is right and the other wrong of course.

Language is not a thoroughbred, though, but a mongrel.
— Janus

Ok... Can you explain that? — Arcane Sandwich

I mean language usage has evolved not in an ordered and planned (selective breeding) way, but in an ad hoc (free for all mating) manner.

Yes, if I thought there was a hope of ever settling it. But using the "existence" terminology to do so just doesn't seem to get anywhere. Instead, let's talk about the ways that rocks show up in our lives, and what we can say about them -- also the ways that justice shows up in our lives, and what we can say about that -- and whether there might be various grounding relations obtaining between physical things and values -- but do it all without trying to award the Grand Prize of Existence to anything. — J

Is it justice that shows up or merely actions that are deemed to be just or not? It is common parlance to speak of injustices, but we don't generally speak of justices, which is itself a little strange, and speaks to the inconsistency of language usages.

In any case instances of both justice and injustice do appear, and that seems somewhat disanalogous with rocks since we don't speak of instances of rock showing up. Language is not a thoroughbred, though, but a mongrel.

I'm comfortable with saying that rocks exist and that ideas and instances of justice exist.

The third premise is that one follows the Tao if one follows heaven. The fourth premise is that if the Tao follows what is natural then one follows what is natural. This all seems to me to suggest non-duality. Man, The Earth, Heaven, the Tao and nature are all one, so I can't see how saying one follows something that is not the Tao follows from saying that one follows what is natural.

Are you suggesting that what is natural is over and above and something thus different than the Tao (and by implication over and above and different from Man, the Earth and Heaven?

Ok, do you have a moment, then? I could explain it to you, but it's just my point of view. It has errors, I'm sure of it. But it's not without merit, if I may say such a thing. — Arcane Sandwich

I'd be happy to get some more explanation. We all have different points of view, and all with some merit, no doubt.

I still don't know what you are talking about.

It was not an "appeal to the stone" I simply don't understand what you are trying to say by translating the verse into propositional logic.

Thanks, but the translation into propositional logic made no sense to me. I understand the way of the Tao to be the way of nature, pure and simple.

So, if you "believe" in the Tao, you must, at the very least on logical grounds (to say nothing of moral grounds) follow what is natural, instead of following the Tao, because the Tao itself follows what is natural. — Arcane Sandwich

I have never read it that way. "Tao (the way) follows what is natural" means the way is just natural, in other words nothing over and above nature itself. So it is not following the natural "instead of following the Tao".

– ergo reality is necessarily more-than-subjective. — 180 Proof

:up: Right there must be something we subjects are being subjected to.

Which is why, if someone were to prove that the evil demon argument leads to a contradiction, then such a person would have also demonstrated that it is not possible to doubt logic. And whoever demonstrates that, deserves the Fields medal. Well, maybe I'm being too extreme in my judgement, but it would certainly be a monumental achievement to prove that logic cannot be doubted. — Arcane Sandwich

The only thing going for the 'evil demon' is that he is not a logical contradiction. Just as it is impossible to prove the existence of anything by logic alone, so it is also impossible to logically prove the non-existence of anything.

If we attempted to doubt logic, what would we be using but logic? Logic is merely a formal procedure. There is no reason to entertain the idea of the evil demon or the brain in a vat or the flying teacup at the other end of the universe. They are all logical possibilities, though.