In that sense, it is a just a further step along the path Aristotle discovered when he noted the structural similarity of classes of arguments, setting aside the specific contents of the premises and conclusions. — Srap Tasmaner

Perhaps the difficulty is to do with how a model-theoretical account relaters to intuitionist mathematics. On the on hand we have a clear idea of truth as satisfaction, and considerable progress in math. On the other, we have truth as relative to proof. It'd make for a good topic. But not here, with so many clowns.

(among people who know what they're talking about) — frank

We did this already.

https://survey2020.philpeople.org/survey/results/5030?aos=47

That's the data from philosophers of mathematics. 43 respondents. Structuralism was ahead, with 18 agreeing. Platonism is in the alternatives, with 15 respondents.

Not perfect data, but far from a consensus for platonism.




What's the supposed contradiction?

Sounds accurate. If the observer is aware of the delay, then they are aware that they see the apple as is was ten seconds previously. They are under no compulsion to conclude that they only ever see a mental reconstruction of the apple, and never the apple.

So metaphysician undercover is now saying numbers are not ordinal, only cardinal.

While Frank continues to say very little.

I agree that during the second interval I will judge that the apple is still there, and that this judgment will be false. — Esse Quam Videri

Oh, so the observer is unaware of the ten-second delay?

Then that's the problem. The causal and epistemic stories differ.

:meh:

The pain and c- fibres firing stuff needs a detailed look. Pain has a different grammar to colour, despite what Michael seems to suppose. So it's tempting to say Kripke's argument assumes we have direct or immediate access to our own mental states; but take care - do we "access" our mental states, as if they were somehow seperate from us? Or is it more that we are our mental states - they are constitutive of us? And that's not so far from the distinction between only ever seeing a mental model of an apple, the indirect realist error, and seeing as constructing a model of an apple, the alternative.

Intersting offshoot.

For a start, Kripke's causal theory of reference plays against indirect realism in much the same way it plays against descriptivist theories of reference. A rigid designator picks out the extension, not some mental image or sense-data or whatever. That collapses much of the fussing between semantics and a supposed ontology. "Nixon" refers to Nixon, not to some intermediary.

Not a refutation, so much as a rejection of any advantage.

yes indeed. Existential qualification functions within a domain. So if it’s univocal then it’s univocal only within that domain...

So we might think that it moves the “question of existence” back a step, back to asking what it is to be part of the domain. And the domain is a construct; this or that counts as an item within the domain.

:meh:

What are your thoughts?

:meh:

I'd reject the term "mental image of an apple". It's already floating free of application, already private.

I do occasionally see apples. When I do so, there is invariably an apple. I can also imagine an apple, or perhaps I might hallucinate an apple, and such cases would be noteworthy, given a different grammar, precisely because there is no apple.

Once we treat “phenomenal character” as a constituent or item in an inner realm, we’ve already built the indirect realist ontology into the starting point. The grammar invites reification. — Esse Quam Videri

So the point becomes one of pedagogy - how to have Michael or Amadeus understand their mistake. But his involves a change away from thinking of private mental states, a habit ingrained since before Descartes. Our comments get interpreted through that window.

There might be a place here for a discussion of pedagogic method.

You've claimed I don't, but haven't set out anything to support such a view. I have asked. What, for you , is realism? Technically, it's the commitment to statements being either true or false, with antirealism the view that some statements are neither true nor false. Meta, and perhaps you, suppose a slightly different realism in which truths are made true by a mind-independent domain of entities, whose existence and nature do not depend on our practices, languages, or activities.

But you are fishing again. What happened to indispensability?

Whatever it take for you to commit.

Treating phenomenal character as an intermediary object is exactly the indirect realist move I’m resisting. — Esse Quam Videri

Nice.

To my eye the mistake is to treat "phenomenal character" as an item, to quantify were quantification is illicit. To suppose that there exists a phenomenal character, it has such-and-such properties, it stands in relations to neural states, and so on, a whole ontology mushrooming from a grammatical slip.

“Phenomenal character” isn’t a thing over and above our perceptual and behavioural capacities, but a mode of description. We abstract from how someone sees, reacts, discriminates, reports, and then pretend the abstraction names an inner object. That’s exactly the move Wittgenstein warns against: turning an adjective or an adverbial construction into a noun and then asking what sort of thing the noun refers to.

An admirable approach.

...that distal objects are not constituents of experience... — Michael

, I hope you haven't conceded this - that we never see apples, or taste oysters, or hear birdsong.

Following Quine,

• There is exactly one whole number between one and three.
• Therefore, our theory quantifies over at least one whole number.
• Hence, we are ontologically committed to whole numbers.

Unfortunately, you do not agree, having said:

This supposition that you have, that there are numbers between numbers is very problematic. — Metaphysician Undercover

Quine's approach has a distinct advantage over your own, in that it allows us to do basic arithmetic.


Nothing in the above commits us to numbers existing independently, in the way of chairs or mountains. Nothing commits us to a hard platonic world of floating numbers. It is open for mathematical entities to be more akin to property, money or countries, a convenient way of talking about how things are.

Quine's approach does not commit us to Platonism in any robust or traditional sense.

What you post shows is your failure to follow the argument.

What do you take Quine to have said about ontological commitment with regard to mathematical entities? It'd be helpful to understand how you think it differs from the view I expressed, which makes use of his "To be is to be the value of a bound variable."

I've no clear idea of what you are getting at here.

ok.

You said your constructivism was compatible with realism — frank

This?

This view preserves mathematical realism (mathematical statements have objective truth values) while avoiding the metaphysical commitments of Platonism (no need for causally inert, spatiotemporally transcendent entities). — Banno

Tell me what you think realism is - how you are here using it... Ontological realism (Platonism), Semantic realism, Quantificational or something else/combined? I've been pretty explicit that the 'reality' of numbers is little more than our ability to quantify over them.

...?

I don't think you understand what math realism is. — frank

Do you?

Well then, tell me. Say something. Commit.

@frank

π is not 3.1415926... but it is the ratio of the circumference of a circle to its diameter. — Banno

Compare your interpretation of quus. There are multiple ways for us to continue the sequence 3.1415926... but only one is π. This is were Kripke starts to slip.

Quus: scepticism arises if meaning is tied to finite behaviour alone.
π: determinacy is secured by publicly available rules and standards.

Here:

“Direct realism” is not a position that emerged from philosophers asking how perception is best understood, so much as a reaction to dialectical pressure created by a certain picture of perception, roughly: the idea that what we are immediately aware of are internal intermediaries, be they sense-data, representations, appearances, mental images, from which the external world is inferred.

Once that picture is in place, a binary seems forced: either we perceive the world indirectly, via inner objects; or we perceive it directly, without intermediaries. “Direct realism” is then coined as the negation of the first horn. It is not so much a positive theory as a reactive label: not that. This already suggests the diagnosis: the term exists because something has gone wrong earlier in the framing.

What those who reject indirect realism are actually rejecting may not be indirectness as such, but the reification of something “given” — an object of awareness that is prior to, or independent of, our conceptual, practical, and normative engagement with the world. Once you posit sense-data, qualia as objects, appearances as inner items, you generate the “veil of perception” problem automatically. “Direct realism” then looks like the heroic attempt to tear down the veil. But if you never put the veil there in the first place, there is nothing to tear down.

You see the cat. Perhaps you see it in the mirror, or turn to see it directly. And here the word "directly" has a use. You see the ship indirectly through the screen of your camera, but directly when you look over the top; and here the word "directly" has a use. The philosophical use of ‘indirect’ is parasitic on ordinary contrasts that do not support the theory. “Directly” is contrastive and context-bound, it does not name a metaphysical relation of mind to object, it does not imply the absence of causal mediation.

What you do not see is a sense datum, a representation, an appearance, or a mental image. You might well see by constructing such a representation, and all the physics and physiology that involves. But to claim that what you see is that construct and not the cat is a mistake.

One can admit that neural representations exist and denying that such things are the objects of perception. These neural representations are our seeing, not what we see. — Banno

He says we can talk about what goes in in the first 10,000 decimal places of pi, but it makes no sense to talk about the full extension. — frank

Where?

“The decimal expansion of π is not a completed object. It is an instruction for producing digits.” RFM I §32

“It is not as if all the digits were already there and we merely hadn’t yet discovered them.” RFM I §35

Wittgenstein is certainly not saying that talk of the value of π does not make sense. It does make sense to talk of the value of π. We do so all over mathematics. Consider: which digit are we not able in principle to determine? There is no digit that is in principle undeterminable; but there is also no completed totality of digits waiting to be surveyed.

The response is not to reify the procedure that produces each digit; yet π is a quantified value within mathematics. It figures under quantifiers, enters inequalities, is bounded, approximated, compared, integrated over, etc. None of that is in dispute, and none of it commits us to Platonism. π is quantified intensionally, via its defining rules and inferential role — not extensionally, as a completed set of digits.

π is not 3.1415926... but it is the ratio of the circumference of a circle to its diameter.

How is your catch of the day? Indispensability not such good bait?

So in what specific ways are you different from a platonist? — frank

:brow:

...platonism is the view that mathematical stuff, numbers and triangles and so on, exist independently of human minds, language, and thought, and are located outside of space and time. — Banno

Platonism is not just "numbers exist", as Meta supposes.

Why are you changing the topic back away from indispensability...?

I'm familiar with the article. What I am not sure of is how you see it as problematic for the account I gave.

Just to be clear, the indispensability argument gives us reason to commit to the existence of mathematical entities. The proffered account does just that.

So, where's the issue?

And this somehow shows my proposal is problematic?

If you were willing to set this out as an argument, rather than just wave at it, we might have an interesting discussion.

Failure to...

The straw man to which I referred is the one proffered as the only alternative to indirect realism, is the contentious "direct realism" of their imaginings.

So can you show, or even suggest, a problem with it? Something more than mere disparagement ?

Mathematical platonism is the view that mathematical stuff, numbers and triangles and so on, exist independently of human minds, language, and thought, and are located outside of space and time.

The proffered alternative is that mathematical statements are true, and we can talk about mathematical objects existing, but this doesn't require positing some separate realm outside space and time where numbers "live." Instead, mathematical language works the way it does - we can truly say "there is a prime number between 7 and 11" - without needing to tell some grand metaphysical story about what makes this true. The truth of mathematical statements is connected to their role in our practices, proofs, and language games rather than correspondence to abstract objects in a Platonic heaven.
This view preserves mathematical realism (mathematical statements have objective truth values) while avoiding the metaphysical commitments of Platonism (no need for causally inert, spatiotemporally transcendent entities).

Stay cryptic. It's your only defence.

If the rules of a single system contradict each other — Metaphysician Undercover

Which system? What contradiction?

That's education, learning the rules. — Metaphysician Undercover

Better, education is learning to use the rules. And the issue is, what can we do with the rules.

Opening up, instead of closing off.

I'm actually Socrates. — frank

Everyone here uses that excuse.

Baloney — frank

...as bait? Maybe. Oily, so it'll attract something...

You always are fishing. It's what you do. What I so rudely call "failure to commit".