I am pretty sure that oysters don't know they are oysters. — Corvus

They don't. But just because an entity cannot know much (i.e., oysters), that doesn't mean that it doesn't have certain features, which it cannot know. I don't know how many individual hairs I have on my head. That doesn't mean that I don't have hair.

I don't know how many individual hairs I have on my head. That doesn't mean that I don't have hair. — Arcane Sandwich

If you managed to count them, you would know how many. It is not infinity for sure.

If you managed to count them, you would know how many. It is not infinity for sure. — Corvus

In that case, I will offer a different example: I have never seen my own heart, but that doesn't mean that I don't have one. An oyster cannot know what it is, but that doesn't mean that it is not an oyster.

In that case, I will offer a different example: I have never seen my own heart, but that doesn't mean that I don't have one. — Arcane Sandwich

It is an inductive statement with very high probability. You have never seen your heart, but from the empirical fact that all living humans have heart, therefore you must have one. No problem with that.

An oyster cannot know what it is, but that doesn't mean that it is not an oyster. — Arcane Sandwich

OK, it sounds valid. (Had to edit my initial comment)

An oyster cannot know what it is, but that doesn't mean that it is not an oyster. — Arcane Sandwich

If oysters don't know they are oysters, then is it right to call them oysters?

↪Sam26 You don't seem to have said anything of substance with which I would disagree, so long as you agree that hinge propositions are true. — Banno

I thought the whole point of hinge positions , language games and forms of life was that the concept of truth was precisely irrelevant to them? Hinge propositions, as the grounds of truth-apt assertions, are themselves neither true nor false.

94. But I did not get my picture of the world by satisfying myself of its correctness; nor do I have it because I am satisfied of its correctness. No: it is the inherited background against which I distinguish between true and false.
199. The reason why the use of the expression "true or false" has something misleading about it is that it is like saying "it tallies with the facts or it doesn't", and the very thing that is in question is what "tallying" is here.
200. Really "The proposition is either true or false" only means that it must be possible to decide for or against it. But this does not say what the ground for such a decision is like.
205. If the true is what is grounded, then the ground is not true, not yet false
(On Certainty)

why is it that mathematical predictions so often anticipate unexpected empirical discoveries? He doesn’t attempt to explain why that is so, as much as just point it out. — Wayfarer

Apparently he has some ideas concerning why that is so.
Wigner wrote:

“It is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena."He adds that the observation "the laws of nature are written in the language of mathematics," properly made by Galileo three hundred years ago, "is now truer than ever before.”

I myself am a critic of ‘scientism’, the attempt to subordinate all knowledge to mathematical quantfication, but I don’t think that invalidates Wigner’s point. — Wayfarer

If Wigner’s point is that the laws of nature are written in the language of mathematics, then that’s precisely what I’m trying to invalidate. It’s the human-constructed norms of nature that are written in the language of mathematics, not anything to do with nature ‘in itself’.

If oysters don't know they are oysters, then is it right to call them oysters? — Corvus

I think so, yes. Because we're the ones calling them "oysters", they don't call themselves that. They can't. But a stone can't call itself a stone either, and it's still a stone nonetheless.

I think so, yes. Because we're the ones calling them "oysters", they don't call themselves that. — Arcane Sandwich

I thought you were discussing about the identity of oysters, hence asked the question. I know what your saying, but questions still remains.

Identity means the owner of the identity claims who it is. They don't get given identity by some authorities like hey arcane sandwich this is your identity. But arcane sandwich applies for the identity to his local council or passport office, saying name is arcane sandwich, date of birth is 25 12 1985, place of birth Argentina. Marital Status: maybe, Job tittle: Professional Metaphysician ... etc etc.

But in oysters case, I am pretty sure they don't claim their identity details to anyone. They might have all the details for their identity, but maybe they don't see the point of applying for identity, or simply aren't able to due to lack of resources whatever.

They still get called as oysters, even if they don't know they are oysters, and that is fine, no problem with that. But when you said identity of oysters blah blah, I thought wait a minute here, something is not right, and did ask you the question.

I think that one might coherently say that oysters have an identity, sure. They have something that makes them oysters and not stones, for example. Perhaps everything does. For example, one might suggest, as Kripke does, that the essence or identity of gold is having one or more atoms that each have 79 protons in its nucleus. I'm sure that oysters have a distinguishing property, we can call that essence, identity, essential property, etc. And they have that property independently of humans and their languages.

If Wigner’s point is that the laws of nature are written in the language of mathematics, then that’s precisely what I’m trying to invalidate. It’s the human-constructed norms of nature that are written in the language of mathematics, not anything to do with nature ‘in itself’. — Joshs

But doesn’t that assume the very separation between mind and world that elsewhere you’re very keen to criticize? Humans are, after all, part of the very world which mathematics describes so effectively. While it’s true that ‘not everything that counts can be counted’, the human ability to intuit the quantifiable forms of nature seems, as Wigner says, tantamount to a miracle. (Plato has Socrates say it is something the soul learns before the descent into the material world.)

Applied mathematics has been extraordinarily effective because it enables us to connect mathematical with physical principles. Schopenhauer noted in passing that science ‘really teaches nothing more than the relation of one idea to another’ because, for him, the entire domain of phenomenal experience comprises ideas. He also says that science cannot get at the ‘inmost truth of things’, with which I also agree. But it nevertheless enables an enormous range of powers. That’s the sense in which Plato deems Dianoia (mathematical and geometrical knowledge) higher than sense perception, although not the highest form, which is noesis.

I thought the whole point of hinge positions , language games and forms of life was that the concept of truth was precisely irrelevant to them? — Joshs

Ask @Sam26.

But doesn’t that assume the very separation between mind and world that elsewhere you’re very keen to criticize? Humans are, after all, part of the very world which mathematics describes so effectively. — Wayfarer

On the contrary, it is because mind-body and world are inseparable that the world we perceive is a world that matters to us in particular ways We are not just part of the world, we interact with our portion of the world in normative ways. as does one aspect of the world with another. There is no one way the world is in itself , it world can show up for us in many different ways, depending on how we choose to cut it up. If we carve it up by way of idealisms like mathematical logic , bodies ina geometric space and physical causality, it will appear to ‘miraculously’ conform to our calculative specifications. If we burrow beneath these idealisms, the world will show up for us not as conforming to mathematical rules and laws, but as amenable to an infinite variety of patterns of normative relationality with respect to our practices or knowing.

↪Banno This is one of the main points of OC. We often refer to things as true without being justified, just as we can use the word know without it being JTB. They're just different language games. In other words, you can hold them as true in practice, e.g., chess rules — Sam26

Chess rules are not true or false in themselves, the moves in the game which these rules specify are true or false.

94. But I did not get my picture of the world by satisfying myself of its correctness; nor do I have it because I am satisfied of its correctness. No: it is the inherited background against which I distinguish between true and false.
199. The reason why the use of the expression "true or false" has something misleading about it is that it is like saying "it tallies with the facts or it doesn't", and the very thing that is in question is what "tallying" is here.
200. Really "The proposition is either true or false" only means that it must be possible to decide for or against it. But this does not say what the ground for such a decision is like.
205. If the true is what is grounded, then the ground is not true, not yet false
(On Certainty)

Since the laws of chess are the ground in the basis of which moves in the game can be correct or incorrect, the laws of chess are ‘not true, not yet false’. Is this what you meant?

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.

why is it that mathematical predictions so often anticipate unexpected empirical discoveries? He doesn’t attempt to explain why that is so, as much as just point it out.
— Wayfarer

Apparently he has some ideas concerning why that is so.
Wigner wrote:

“It is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena."He adds that the observation "the laws of nature are written in the language of mathematics," properly made by Galileo three hundred years ago, "is now truer than ever before.”

I myself am a critic of ‘scientism’, the attempt to subordinate all knowledge to mathematical quantfication, but I don’t think that invalidates Wigner’s point.
— Wayfarer

If Wigner’s point is that the laws of nature are written in the language of mathematics, then that’s precisely what I’m trying to invalidate. It’s the human-constructed norms of nature that are written in the language of mathematics, not anything to do with nature ‘in itself’. — Joshs

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.

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. — Janus

I'm just asking how you propose to solve the problem of multiple answers to the OP, that's all. Don't jump to conclusions or assume things about me, sweet chicken. If your solution is the correct one, then what do you propose that we do? Should we vote? Should a mod step in and mark you solution as the correct one? What?

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. — Tom Storm

I agree.

But as an untheorized amateur, I would say that. — Tom Storm

We are all amateurs in this regard. Mathematicians rarely spend their time discussing or arguing the issue. It has so little to do with traditional math research. But times change for any human endeavor, and "modern" mathematics, category theory e.g., is an elevated and abstract perception of the way the subject has been for millennia and is possibly closer to the Platonic conundrum, although I can't see how.

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

And can you see how this notion doesn’t take away from science the usefulness that we know it has in our lives? People tend to go into a panic when you suggest his to them, as if the ground has been pulled out from under them and suddenly cats will be mating with dogs and murderers will run rampant in the streets. But accepting this idea of science as contingent artifact leaves everything exactly as it has been. It just gives us further options we didn’t see before.

The notion that scientific laws and maths are contingent human artifacts rather than the product of some Platonic realm — Tom Storm

Artefacts are made from the stuff around us. It's not an either-or.

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.

↪Arcane Sandwich
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. — Janus

It was a joke. You know that, right?

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. — Janus

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.

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.

How would I know? — Janus

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

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. — Janus

Then why are you hassling me, matey-mate?

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's called a conversation, or at least an attempt at one. — Janus

Ok. Lets converse then. I believe that you have offered a good solution to the question of the Platonistic (sic) existence of infinitesimals.

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.

some Platonic realm — Tom Storm

I think there is confusion around the term 'platonic realm'. There is a domain of natural numbers, right? Where is it? Obviously a silly question; 'domain' is in this context a kind of metaphor, like a 'place' or 'realm', when there really is no such place or realm. Nevertheless the domain is a real one, in that it includes integers but not imaginary numbers. Go back to that essay What is Math I quoted right at the start of this thread. We read 'Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous.' And that, I reckon, is what is behind the myth of the 'platonic realm'. 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. It is a domain of 'objects' that can only be grasped by reason.

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.

Which is why I keep mentioning Thinking Being. This book has been put online, in reality it's out of print and when available was very expensive. The online unauthorised copy is a fully bookmarked .pdf. The chapters on Parmenides and Plato are well worth the effort of reading, they will set anyone straight on the origin of the platonic forms. (This book is highly recommended by John Vervaeke, that's how I found it.)

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? — Janus

What do you mean, 'I never answer it'? I have >23k posts on this forum, and a significant proportion are devoted to just this question. I've said already in this thread:

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. Of course, we rely on them automatically, transparently, and continuously, in the operations of discursive thought, whenever we make inferences or judgements. But the elements of those judgements do not, themselves, exist in the way that tables and chairs and Banno's beloved crockery exists. Without them, though, we could not even converse, let alone pursue philosophy. — Wayfarer

So there's my answer to it, it was the substance of my first forum post. Criticize it all you like, but don't say I haven't tried to answer the question! Which is, a distinction between what is real, and what exists, where the latter is a small sub-section of the former.

This was my first ever forum post, around 2008: