UNE — Banno

Is that University of New England?

:up:

We can eat oysters only insofar as they are brought under the physiological and chemical conditions which are the presuppositions of the possibility of being eaten.

Therefore,

We cannot eat oysters as they are in themselves. (Stove, 1991, 151, 161) — Franklin

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.

Fifty posts a day is a lot. Make sure you take time to step away from the screen. — Banno

That's actually really good advice. I'll try to do that. Thanks.

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?

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

Hey, could be. Why not?

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

Mathematics is a very social endeavor. We explore, discover or create the subject, then place our results on paper, then digitalize and submit for others in the profession to read. Initially, it is a product of our minds, then when others read or hear about it, it becomes part of their minds, as well. If they find it interesting they may pursue the topic further and the process repeats itself.

Frequently, I can draw lots of images with pen and paper that help me understand a math idea. That helps make the topic "real". But there are limits. I can draw a line, an interval, and a point (you know what I mean), but I cannot draw an infinitesimal, no matter how tiny a point I can scratch on the paper. For me, infinitesimals are the metaphysics of math. Something I can work with but not develop an intimacy. I leave that to math people who indulge in non-standard analysis (NSA) or hyperreals.

Incidentally, there are very few universities that offer more than a course or two or independent study in NSA. The only two in the USA seem to be U of N Colorado, and U of Wisconsin - even there the pickings are slim.

Best not to be captivated by infinitesimals. The limit concept came along and did the little buggers in.

We cannot eat oysters as they are in themselves. That is true. I only wish the premises were true as well. — Arcane Sandwich

Could it be because they are the Kantian oysters? Oysters in themselves are in noumenon. They are not available in the physical world. You can only eat the oysters in phenomenon, which are are brought under the physiological and chemical conditions

The Russell Paradox was covered on this forum ...maybe a few times.
Something that applies to Mathematical Platonism is the unrestricted comprehension principle.
For me, Mathematical Platonism just leads to paradoxes. It leaves the door open for all sorts of problems.

I think mathematical objects can contradict.

Brains; (mathematical object 1)
Brains; (mathematical object 2)

No problems....they both exist as mental content.

They exist in the standard form of brains instantiating non-physical objects

Could it be because they are the Kantian oysters? Oysters in themselves are in noumenon. They are not available in the physical world. You can only eat the oysters in phenomenon, which are are brought under the physiological and chemical conditions — Corvus

Exactly. That is the correct answer. You can then add more recent metaphysical theory to that, for example Object-Oriented Ontology, also known as OOO, or simply Triple O.

But folks here don't seem to like Speculative Realism too much for some reason. I blame Alain Badiou for that.

Hinge propositions are said, but never quite rightly. "Here is a hand" isn't justified, at least not by other propositions. It's shown. "If you do know that here is one hand, we'll grant you all the rest".

So I keep coming back to PI §201. What's not expressible may nevertheless be enacted. Not just in following a rule, but in using language, deciding what to do, and generally in what he called a "form of life". You don't say it, you do it.

Any comments, Sam26? I suspect this is an older reading of Wittgenstein than is popular now. — Banno

I'll comment on this: I'm not sure why you would say this, viz., "Hinge propositions are said, but never quite rightly." They are often mischaracterized and taken as normal propositions, so in this sense they are often "never said quite rightly." However, they can be talked about if one understands what they are and how they function. Indeed, they aren't justified but neither are they true, i.e., they are outside of epistemological talk. This means that not only are they outside talk of justification, but they are outside talk of truth, at least in the epistemological sense. They are true in the sense that the rules of chess are true. This use of true is not epistemological.

The point of OC 1 is not about showing. It's about saying to Moore that if he does know as he claims, then Wittgenstein will grant the rest of his argument. But of course, Wittgenstein demonstrates that Moore doesn't know in the JTB sense. He's using the concept know, not epistemologically, but as an expression of a conviction. It's purely subjective. This is where people seem to get confused, i.e., they don't understand this point.

Where we do see the idea of showing in OC is that many hinges are shown in our actions even prior to the expression of the belief. Showing is prior to the expression in many ways, but not always. In the most basic of hinges, showing is bedrock.

I given a more detailed explanation in my most recent posts in my analysis of OC.

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.

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. — Janus

But you say that in a very perplexed way, and I'll I'm saying is that it's not that perplexing. What would be the perplexing "thing" about it? The possibility that essences can be destroyed? Why? Who says that essences have to be eternal, or even non-physical? Aristotle already dealt with this problem, way back in the day, so to speak. A small seed turns into a sapling, then into a mighty oak, then a lumberer cuts it down, hands it over to the carpenter, who then makes a table. The tree has lost its essence by that point, it has been destroyed. What exists now, in the form of a wooden table, is not a tree. So why is it so perplexing that the oyster's identity is destroyed once you digest the oyster?

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.

"never quite rightly" becasue they differ from mere assertions. You at least agree here, but phrase it oddly. You suggest that they do not have a truth value. I can't agree with that, since if they did not have a truth value then they could not be used as assumptions in an argument. One could not get from "Here is a hand" to "there are hands".

The difference is sometimes in the illocutionary force. So "Here is a hand" can be treated as a declarative rather than an assertion - as "This counts as a hand". And as such it can be true, and we can conclude that there are hands.

And treating "Here is a hand" as a declarative would indeed be a showing rather than a saying.

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. — Janus

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."

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.

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

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?

You still don't seem to follow my points. Of course, they could be used in arguments. We can talk about their truth values just as we can talk about the truth values of the rules of chess, they just aren't epistemological truth values, i.e., they're not justified and true. There are different language games for these words outside their epistemological use, and Witt points this out. It's in this sense you can use know, true, and even justified outside epistemology.

...they just aren't epistemological truth values, — Sam26

Not a good wording. If they are true, they have epistemic standing. "Here is a hand" justifies "There are hands". Hinges have truth values.

Forgetting the role such presuppositions play leads to such confusions as Wigner’s famous paper on the ‘unreasonable effectiveness’ of mathematics in the natural sciences. — Joshs

Can you explain what about Wigner’s famous paper you think is confused?

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.

@Wayfarer

Can you explain what about Wigner’s famous paper you think is confused? — Wayfarer

Wigner believed that mathematics is unreasonably effective at producing forms of description that ‘just so happen’ to fit the patterns of the physical world remarkably well. In so doing, he confused a passive representation of how things really are with an organizing scheme that forces us to see the world in a particular way (mathematical idealization) and to ignore other equally valid ways of conceiving it.

You mean, alternative mathematical systems that could produce similar results?

A big part of that paper is not that maths just happens to work, but that powerful predictions can arise from mathematical models that were not at all expected when the model was initially created, sometimes in subjects that seem remote from the one to which it was initially applied. So 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.

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.

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.

So 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

Indeed. My late ex-father-in-law, a Hungarian aristocrat - exchanged letters with Wigner, and he translated a few of these for me. I don't find it surprising that occasionally a development in math portends a scientific discovery. Mathematics arose from observing phenomena in the physical world, and those initial discoveries generated logical consequences, some of which provide insight into that same physical realm.

thereby highlighting an intriguing link between physical causation and logical necessity, which today’s philosophy generally describes in terms of separate domains.

Mathematics arose from observing phenomena in the physical world — jgill

And, more than ‘observing’. Cats and dog are quite capable of ‘observing’ the things humans observe. But only h.sapiens can measure and quantify.

(I read somewhere in my incessant stream of internet content that the basics of physical geometry were invented - or discovered - by the Egyptians, as a consequence of having to re-create fence lines on the Nile delta after the annual flood season. This involved apportioning highly irregularly-shaped parcels of land so that each landowner ended up with the right quantity, even though the shapes of their allotments were completely different to the year before. But then, they did build the Pyramids…..)

So why is it so perplexing that the oyster's identity is destroyed once you digest the oyster? — Arcane Sandwich

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