Well, again, that needs some finesse: — Banno

If you keep reading, the SEP explains that the arguments that he wasn't a finitist are weak.

This is well worth working through, as well as was he right? — Banno

He would say there's no fact of the matter regarding who is right. As you mentioned before, there is no change in practice if we accept or reject finitism.

I'm happy to call him a finitist, for what that's worth - the interesting thing is how that plays out.

My contention - and I haven't put it together into a PhD yet, so it is incomplete - is that he lacked, or missed, the mechanism that allows us to move from a rule to a quantification, the "counts as" of the constitutive definition.

That's the direction taken by Austin, and then Searle, and a large part of why their work is worth considering alongside that finitism. We bring things into existence by with we do with words, in a way that Wittgenstein might not have recognised.

I'm happy to call him a finitist, for what that's worth - the interesting thing is how that plays out. — Banno

It's a rejection of set theory. We wouldn't even talk about the extension of the real numbers. There is no extension.

Well, finitism doesn't automatically reject set theory. Arguing in terms of 'isms' will not get us as far as setting out the detail. some might see ZFC or other set theories from a finitist perspective, treating infinite sets as symbolic devices or potentialities, without committing to their actual existence. Finitism rejects the Platonist reading of infinite sets, but I think I've shown that there is at least one alternative.

Well, finitism doesn't automatically reject set theory. Arguing in terms of 'isms' will not get us as far as setting out the detail. some might see ZFC or other set theories from a finitist perspective, treating infinite sets as symbolic devices or potentialities, without committing to their actual existence. Finitism rejects the Platonist reading of infinite sets, but I think I've shown that there is at least one alternative. — Banno

It kind of looks like your alternative involves people walking into a fictional world and pretending it's all real, drawing conclusions based on it's reality, when they know good and well it's all a lie.

Is that how you see math?

It kind of looks like your alternative involves people walking into a fictional world and pretending it's all real, drawing conclusions based on it's reality, when they know good and well it's all a lie. — frank

That's were you live.

That's were you live. — Banno

Don't bait me into giving my sociological report on this thread. :cool:

No, I'll leave the baiting to you.

No, I'll leave the baiting to you. — Banno

Ok. I'm going fishing.

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

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

I'm actually Socrates. I forgot to tell you.

I'm actually Socrates. — frank

Everyone here uses that excuse.

Both misunderstand mathematics, which consists in public techniques governed by rules. — Banno

That's insignificant drivel. We could say it about any discipline, they all consist of techniques governed by rules. That's education, learning the rules. The issue here however, is what do the rules say. If the rule says that "the natural numbers" refers to a completed object, that's platonism. If the rule says that "the natural numbers" refers to a count which can never be completed, then this refers to a mental act. The problem is that we cannot have both rules in the same system without contradiction within the system.

Depends on whether the first symbolism is time dependent. Does counting actually require temporal steps. Can you think of 1,2,3 as instantaneous? Just speculating. — jgill

This is the issue of platonism which Banno intentional avoids. The only way to believe that "N" could refer to a non-temporal, eternal object, is platonism.

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.

If the rules of a single system contradict each other, as in the example, then "learning to use the rules" has a nuanced meaning, which includes choosing which of the opposing rules best suits one's purpose. Providing for an individual to choose from contradictory rules, according to one's purpose, allows subjectivity to contaminate the discipline which is supposed to provide for objective knowledge.

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

Which system? What contradiction?

Go back and finish reading my post, instead of just replying to the second sentence.

Stay cryptic. It's your only defence.

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).

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

This is what we call trying to have our cake and eat it too.

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

Frege and Godel both believed something similar to this:

Quine Putman Indispensability Argument

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...

I don't really have the burden of proof here.

I'll give you time to read the article.

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?

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

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...?

So let's take Wittgenstein's objection to set theory.

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

If you claim the full extension exists in space and time, where? and when? It's not part of any social practice, so where is it?

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?

@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.