TonesInDeepFreeze

Thank you very much for that, and for saying it. Refreshing to read something like that in this forum. 'S' is true iff X is the general definitional f...

'set' is no more technical than 'list' I usually take 'list' as 'sequence' or 'series' or 'enumeration'. And since we're interested in hewing to Tarsk...

What difficulties of opacity and circulaity? I don't know what sense of 'opacity' you have in mind. And Tarski's formulation is not circular. Indeed h...

Right. But recall that my unpacking was a conditional: If 'snow' stands for blahblahblah and 'white' stands for 'bleepbleepbleep', then 'snow is white...

That is the basic idea. For a 0-place function symbol, the denotation is a member of the domain. For an n-place (n>0) function symbol, the denotation ...

That's an excellent point. I like the second because it's illustrative. And I like the third because, as you observe, it is getting closer to the actu...

Of course the denotation is not the expression. The denotation is, formally, as given by the method of models.

I don't know why you regard it as the most close. All three seem reasonable to me. Though the first is Tarski's own form. The advantage of Tarki's for...

I don't know where you're headed with this, but in case my hunch is right, I would say: Tarski is not saying how we know that 'snow is white' is true....

They have the same denotation and extension (but not the same intension). There's perhaps a slight problem with the choice of 'snow' for the Tarski ex...

Indeed, the second is a formal way of saying the first. But necessity and sufficiency (the biconditional) does not enter there, in the semantics, but ...

For uniformity of style we could say 'relation symbol' rather than 'predicate symbol'. Then have: The model maps n-place (n any natural number) relati...

I just now added: I think we could say that the extension of a predicate or function symbol is the relation or function the symbol maps to. (?)

The denotation of a word is the thing the word refers to. In formal semantics, the model maps n-place (n any natural number) predicate symbols of the ...

'snow' is not denoted as snow, and 'white' is not denoted as white. 'snow' denotes snow, and 'white' denotes white.

Denotations are stipulated. Though it is not as clear cut in natural languages as with semantics for formal languages. Do you mean the denotation of '...

What, no leminscate to go with that?

Just to let you know that I haven't disregarded your post. I wish to give it more thought. I hope eventually to reply.

Too bad I don't have an emoticon to express that for you.

You did it again! You falsely twisted what I said to reflect it in the worst possible way, little doubt as a spite you're exercising. You are incorrig...

(1) In set theory, there is no completeness axiom. Rather, we prove as a theorem that the system of reals is a complete ordered field. (2) We assume a...

I glean a thing or two here and there. But posting is only a side hobby. I don't have ambitions for philosophy. Sometimes, though, I see things in dis...

I don't usually support the affirmative because I'm humble enough to admit that I don't have the vision, education, confidence and constancy to arrive...

Having no philosophy is not a disqualifier. Posting is not paintball where you can't participate unless you you are on one of the teams. Not having a ...

Okay, you were joking with the 'formal' part. Maybe because you perceive me as asking posters to back up with formal proofs? Or you think I can be cha...

Except in formal mathematics, definitions are purely syntactical. Indeed.

Of course not. It's not a formal claim. Anyway, I think the burden of argument is on the side saying that infinitistic mathematics does require a plat...

Whether by that name or not, the idea goes at least as far back as Aristotle.

I don't believe that infinitistic mathematics requires a platonist commitment.

NASA telling me what's the largest number I can use is like the Department Of Agriculture telling me how many taste buds I can have.

If we agree that there's a largest number we'd ever need to use, then still, what's the harm in having all the rest of the larger numbers in the attic...

He's "The Crank With The Friendly Face".

I don't know definitively that that is the case, but it seems to me to be so. There are systems - such as intuitionistic* ones and others - that are s...

https://thephilosophyforum.com/discussion/comment/737931 That message is retracted by me.

It's a conceptual issue. He seems to think that, because mathematics is infinitistic, it has a thing that is called 'infinity'. As if the leminscate s...

Got started with what? I don't know where you're going with this.

I don't know what it means to not "want" more than monadic logic. You can't do much mathematics with just monadic logic.

You can reduce n-ary predicate symbols (n>2) to 2-ary predicate symbols. But you have to have at least 2-ary if you want more than the monadic predica...

He would eliminate n-ary relations (n>1) from the method of models?

But it's only an example of a principle. Presumably, the principle applies to n-place for any natural number n, as indeed it does in model theory.

Predicate symbols can be n-place for any natural number n. Relations can be n-place for any natural number n. Of course, in the case of the 'snow is w...

n-ary for any natural number n n-ary for any natural number n

No, I'm just unpacking what's already there. 'Snow is white' is true if and only if snow is white. I merely unpacked, pedantically really, the right s...

Whatever is meant by 'predicate' and 'property' there, you asked about model theory. Predicate symbols map to relations on the domain. So, yes, if I w...

Means "Whatever, dude", eh?

I don't know what that means. I'd have to read the rest of the context.

I don't know what that means.

Yet you asked me to comment on your post that includes: So I took the time to write a post about that. Then you say the opposite, that definitions are...

0 is a number. I don't understand why you keep skipping my point that using the leminscate as if it stands for an object makes no sense the way you do...

I don't see any improvement in your revision.