But it says what can be said. — Banno

But not what only can be said. We're not required to just stop at "snow is white" is true iff snow is white. A rigorous account should cash out the consequent of that biconditional.

If you need a metaphysics before you can decide if the kettle is boiling — Banno

I don't. I need a metaphysics to understand that a boiling kettle is a mind-independent material object, or that it's a mental phenomenon, etc.

IS there a way to determine X? — Banno

Well, is there a way to determine which metaphysics is correct? If materialism is correct then the truth of "the kettle is boiling" depends on the existence of a material object; if idealism is correct then the truth of "the kettle is boiling" depends on the existence of a mental phenomenon.

This is why, as I have said many times, that the T-schema doesn't say much. It doesn't answer a question like the above, which is important. We need to cash out the consequent of the biconditional. I made a start at that here:

We've been taking as a starting point "snow is white" is true iff p and then discussing p, whereas I think we should instead take as a starting point snow is white iff q and then discuss q.

Snow is white iff snow appears white, or
Snow is white iff snow reflects all wavelengths of light, or
Snow is white iff snow has a mind-independent sui generis property of whiteness, etc.

We can then bring this back to truth-predication by understanding that if "p" is true iff p and if p iff q then "p" is true iff q.

"Snow is white" is true iff snow appears white, or
"Snow is white" is true iff snow reflects all wavelengths of light, or
"Snow is white" is true iff snow has a mind-independent sui generis property of whiteness, etc.

But not in all cases. — Banno

I was referring to the sentence "the kettle is boiling".

I have mentioned before that I'm not talking about every sentence. Obviously the truth of a sentence like "1 + 1 = 2" does not depend on a material object and its properties. A coherency theory would be more fitting for formal system like maths.

The error I see in what Michael proposes is that he thinks we can talk about the kettle outside of language. He needs a "non-linguistic kettle" to make his account work. — Banno

When I say that kettles are non-linguistic I mean that they are not words or sentences or any other feature of language. I’m addressing those who say that the truth of a sentence is determined by some other sentence, like some kind of coherency theory, which is false in the case of a sentence like “the kettle is boiling”. The truth of the sentence is determined instead by a material object and its properties.

Once we fix the meaning of a sentence such that it refers to that material object and its properties, changes to that material object and its properties change the truth value of that sentence without changing the meaning of that sentence, and so the truth of that sentence depends on more than just its meaning.

Sometimes “it is raining” is true and sometimes “it is not raining” is true. This isn’t explained by us continually revising the terms in our language: it’s explained by events in the material world; events which occur irrespective of language.

It was. Using "normal set theories" like ZF or ZFC was your suggestion, not mine. I was evaluating your proposal from a much more generalized perspective and showing how it's untenable even with a set theory tamed to be "physicalist-friendly"- this was discarded per your call — Kuro

Then you need to be more explicit with your argument. What sort of things are members of your premised set of all that exists? Urelements like apples, in which case we’re not using ZFC, or only sets, in which case it has no relevance to real life where non-sets exist.

What's that got to do with the slingshot? — Banno

That’s my understanding of the slingshot. All it says is that all true sentences refer to the same world, just as all true sentences about the kettle refer to the same kettle. It doesn’t follow from the latter that the kettle is black iff the kettle is metal and so it doesn’t follow from the former that the kettle is black iff snow is white.

But if my understanding of the slingshot is incorrect then I think Tate’s link is a good response. “Clark Kent” refers to Superman but it doesn’t follow from this that if Lois Lane knows that Clark Kent is Clark Kent that she knows that Clark Kent is Superman. Davidson is wrong in asserting that co-referring terms are logically equivalent.

Trouble is you would also have to agree that "snow is white" is true because the kettle is boiling. — Banno

I don’t. Both “the kettle is black” and “the kettle is metal” refer to the same kettle but it doesn’t follow from this that the kettle is black because the kettle is metal.

Then I think the problem is with the wording of the discussion. In ZFC, urelements are not allowed. Everything is a set. But in the real world things exist which aren’t a set, e.g apples. If you had worded this as saying that the universal set in ZFC is impossible then I wouldn’t have even bothered replying. I thought this was talking about more than just pure maths.

The physicalist takes that all that exists is physical. In set theory, the universal set is the set of all that exists. Therefore, per extensionality, these are substitutable salva veritate and, per the axiom, the same. — Kuro

But sets don’t exist if physicalism is true, and so following your reasoning the physicalist cannot define any set. Given that the physicalist does define sets when using set theory, his physicalism plays no role, and so, when using set theory, sets exist and the set of all that physically exists isn’t a universal set (as the universal set includes sets, which don’t physically exist).

Then the mathematical anti-realist can use set theory to define the set of all that physically exists in my cupboard, or all that physically exists in England, or all that physically exists in the one and only universe. None of these are a universal set within ZFC.

So how is it that mathematical anti-realists, like physicalists, can use set theory?

This is an explanation of a relatively simple set-theoretic result, since we've already fixed the set theory we're operating in. I'm quite appalled that it requires this many replies and/or elaborations. — Kuro

The set theory we’re operating on is the one in which sets exist, and so the set of all that physically exists isn’t a universal set.

The universal set is the same as "the set of all that exists". In physicalism, "all that exists" is just physical stuff (though this does not mean "existing" and "being physical" having the same meaning, just that they coextend)

This is contradictory because, as explained to you several times, it would violate the pairing axiom, the foundation axiom as well as Cantor's theorem which I spoke of earlier. — Kuro

We can assume, when doing maths, that sets exist even if sets do not exist. A physicalist, who doesn’t believe that sets exists, can make use of ZFC set theory.

In using ZFC set theory, this physicalist can define the set of all that physically exists. Within ZFC this isn’t contradictory because it isn’t a universal set.

But if physicalism is true then everything that exists in the real world is a member of the set of all that physically exists within ZFC set theory.

The non-existence of the universal set in ZF, ZFC and so on is a well established mathematical theorem in those set theories. — Kuro

I’m not talking about the universal set. I’m talking about the set of all that physically exists. These are not the same thing.

So, in ZFC, why is the set of all that physically exists contradictory?

This "physicalism-constrained set theory" fails — Kuro

I’m not taking about that though. Use normal set theory. The set of all that physically exists is not contradictory. It might not be, within set theory, the set of all that exists, but if physicalism is true then everything that actually exists is a member of the set of all that physically exists.

Anti-realists can pretend that sets exist for the sake of the maths to then talk about everything that actually exists.

The set of all that exists is contradictory. — Kuro

The set of all that physically exists isn’t contradictory (at least with respect to the power set), which is what that argument shows.

No? I'm saying that the non-existence of the set of all that exists is an issue far prior to the philosophy of mathematics (namely because it's an issue provable in mathematics): the existence of the set is contradictory, so both platonists, who are realists about other sets, and nominalists, realists about no sets whatsoever, would agree it doesn't exist. — Kuro

Where’s the contradiction here?

1. The set of all that physically exists is {apple, pear, ...}
2. The power set of this is {{}, {apple}, {pear}, {apple, pear}, ...}
3. No member of the power set physically exists
4. Therefore, the power set is not proof that there are things which physically exist and are not members of the set of all that physically exists — Michael

Your response before was just to say that if physicalism is true then there are no sets.

It is not simply that the material belongs to the national archives, it is that the material contains classified documents. Having them in his personal possession raises national security issues. The fact that he did not protect them from a whole host of people raises national security issues. Is it that you are not able to see why it is of concern, or are you just pretending not to? — Fooloso4

I am not concerned. He was the president of the United States, the commander in chief, and had the unilateral power to do whatever he wanted with those documents, including taking them home. — NOS4A2

"He was legally allowed to do it, therefore there is no national security issue".

That's a fallacious inference.

And he had no legal right to retain them, or to defy the subpoena for their return, after losing the Presidency.

The set itself asserted by that premise doesn't exist. — Kuro

So you're saying that if mathematical anti-realism is true then there is no set of all that exists, because there are no sets? And so your very argument, which uses sets, depends on mathematical realism being true?

The members of the set in (2) physically exist, but the set itself doesn't per physicalism. — Kuro

I'm aware. What is the relevance of that? I'm not saying that the set physically exists. I'm only saying that the power set doesn't prove that some things physically exist which are not in the set of all that physically exists.

In even asserting that the set is anything, like having the property of "containing apple as a member", you get back to existential commitments. — Kuro

Mathematical anti-realists and physicalists are quite capable of doing maths with sets.

Perhaps a clearer example:

1. Physicalism is true (assumption)
2. The set of all that physically exists is {apple, pear, ...}
3. The power set of this is {{}, {apple}, {pear}, {apple, pear}, ...}
4. No member of the power set physically exists
5. Therefore, the power set is not proof that there are things which physically exist and are not members of the set of all that physically exists

(1) entails that no sets exist, including that set in (3) — Kuro

I think there's a difference between saying "there is a set of all that exists" and saying "the set of all that exists, exists". The mathematical anti-realist will assert the former but reject the latter.

the assumption in 5, that the powerset is literally empty — Kuro

I didn't say that it's empty. Similar to the above, there's a difference between saying "the set has members" and saying "the members of this set exist". The mathematical anti-realist will assert the former but reject the latter.

So, the power set isn't empty, but as all of its members are sets, and as sets don't exist, none of its members exist. As such, it doesn't follow from the fact that the power set has more members that there exist things which aren't in the set of all that exists.

As I said before, I think you're equivocating on the word "exists". Being a member of a set isn't the same thing as existing (if physicalism and mathematical anti-realism are true).

If you assume physicalism, the set of all that exists, let alone the set of anything, since sets are not physical objects neither identical to their physical members nor the collection of their physical members (the proof of this is simple: suppose it is the case, then submerge that same set under a further set, which is mathematically non-identical!) — Kuro

I don't understand how this addresses my argument. Can you specify which step you disagree with?

1. Physicalism is true (assumption)
2. Everything that exists is a physical object (from 1)
3. The set of all that exists is the set of all physical objects (from 2)
4. The power set has more members than the set of all that exists
5. No member of the power set exists (from 2)
6. Therefore, that the power set has more members than the set of all that exists does not prove that some things exist which are not in the set of all that exists (from 5)

( 1 ) A total determination of the referent "the kettle" by the underlying collective standards of interpretation.
( 2 ) A partial determination of the referent of "the kettle" by those same standards.
( 3 ) No dependence of the referent of "the kettle" by those same standards.

By the looks of it, no one here is arguing that ( 3 ) is true and no one here is arguing that ( 1 ) is true. (@Michael, correct me if I'm wrong). — fdrake

From the argument here:

a. The meaning of the sentence at T₁ is the meaning of the sentence at T₂
b. The truth value of the sentence at T₁ is the not the truth value of the sentence at T₂
c. Therefore, the truth value of the sentence is determined by something other than (even if in addition to) the meaning of the sentence
d. The only other thing that differs at T₂ is a material object
e. Therefore, the truth value of the sentence is determined by (even if only in part) that material object

I think the argument is valid and that the conclusion refutes (3) and is consistent with (1) and (2). It might not be clear which material object(s) determine (even if only in part) the truth of the sentence, but it is still the case that it is some material object(s) which determine (even if only in part) the truth of the sentence.

You didn't look at the slingshot argument, did you? — Tate

But if I were to take a shot at it, I would say that the “Great Fact” that true sentences refer to is the world.

Just as “the kettle is black” and “the kettle is metal” refer to the same kettle, “the kettle is black” and “snow is white” refer to the same world. In a sense the sentences are “the world is such that the kettle is black” and “the world is such that snow is white”.

But even though in one sense “the kettle is black” and “the kettle is metal” refer to the same thing (the kettle), there’s another sense in which they don’t refer to the same thing: one refers to the kettle being black and the other to it being metal.

I think the slingshot arguments address the first sense of reference, whereas correspondence-like theories address the second.

But I admit that I can’t quite grasp the logic of the slingshot arguments. This is just my intuitive understanding.

It's the reason we say the extension of any sentence is it's truth value — Tate

And how does this account for the truth value of a sentence changing? Truth values don’t change apropos of nothing. The truth value of some sentences change because a particular physical event happens. So why is it that physical event that changes the sentence’s truth value and not a different one? Because the sentence refers to that physical event and not a different one.

I think either the slingshot arguments are mistaken or they’re not addressing the same kind of extension that I’m addressing. See here and here.

2. — Isaac

Then why did the truth value change if the meaning didn’t? It seems to me to be a contradiction to argue both that a) the truth of a sentence is determined entirely by its meaning and that b) the truth of the sentence changed but its meaning didn’t.

The truth value changed because I painted the kettle red. The material object changed. Therefore the truth of that sentence depends on that material object.

No, I agreed to that. — Isaac

Then it is exactly as I said:

1. The meaning of the sentence didn't change at T₂ but its truth value did.

2. If the truth value of a sentence can change without the meaning of that sentence changing then the truth value of that sentence depends on more than just its meaning.

3. In this specific case the truth value changed because a material object changed, and so the truth of that sentence depends on that material object.

Which of these three claims do you disagree with?

No. I don't see how you're getting that. — Isaac

Because you're rejecting my claim that the sentence "the kettle is black" means the same thing at T₁ and at T₂. If it's not me painting the kettle red that changes the meaning then what does change the meaning?

Are you saying that me painting the kettle red changes the meaning of the sentence "the kettle is black"? That's an absurd claim.

Which doesn't refute my point.

We agree to fix the meaning of the sentence "the kettle is red" such that it is unambiguously false at T₁. I paint the kettle red at T₂. The sentence "the kettle is red" is unambiguously true at T₂. The meaning of the sentence "the kettle is red" didn't change at T₂ but its truth value did. Therefore, its truth value depends on more than just its meaning. It also depends on the kettle and its properties.

Doesn't that just beg the question a little — Isaac

You agreed above that we can decide what words mean. So, for the sake of this example, we decide that the screw in the drawer is not part of the kettle, and to use a spectrophotometer to measure the kettle's colour, agreeing which range of results indicates the kettle being black or not-black.

Otherwise I don't understand the point that you are trying to make. That the sentence "the kettle is black" is neither true nor false? Or both true and false? Or true for some and false for others?

If the truth value of a sentence can change without the meaning of that sentence changing then the truth value of that sentence depends on more than just its meaning. — Michael

I wonder if this is inconsistent with the redundancy theory.

Is it. — Isaac

Yes. For the sake of argument we have fixed the referent of the phrase "the kettle" (and "black", and "red") such that the truth value of "the kettle is black" is unambiguously true at T₁ and false at T₂.

The meaning of the sentence didn't change at T₂ but its truth value did. Therefore, the truth value of the sentence depends on more than just its meaning. It also depends on the material object referred to by the phrase "the kettle".

Yes. But since it could be literally any matter at all, to claim that the truth of any sentence involving kettles depends on this fact would render all statements about kettles always true, since there's always some matter. — Isaac

The sentence "the kettle is black" is true at T₁. I paint the kettle red at T₂. The sentence "the kettle is black" is false at T₂.

The meaning of the sentence "the kettle is black" did not change at T₂. So why did the truth value of the sentence "the kettle is black" change at T₂? Because the material object changed.

If the truth value of a sentence can change without the meaning of that sentence changing then the truth value of that sentence depends on more than just its meaning.

And I honestly don't know how you make the inference you do in the above quote.

We determine that by language use. — Isaac

But it's still the case that whichever matter we decide 'counts' as being the kettle must exist for the sentence "the kettle exists" to be true.

The "sure" was actually a response to the rest of your comment. Sorry for not being clear.

Does this particular matter the kettle depends on include the screw in the drawer or not? — Isaac

That's for us to decide.

I really don't understand the point you are trying to make. That words and phrases can be ambiguous isn't that the truth of a sentence like "the kettle is black" doesn't depend on the existence of a material object (or the occurrence of a sensory experience).

You said "yes" when I asked if the material particular matter was any particular matter. — Isaac

Did I? Where? If I did then it was a mistake.

I agree with that. My recent comments are a response to @Tate saying that "truth is a matter of comparing a statement to another statement". A sentence like "the kettle is black" isn't made true by another sentence but by the existence of a particular material object (if materialism is true), or by the occurrence of a particular sensory experience (if idealism is true), etc.

What particular particles? Do they include the screw in the drawer or not? — Isaac

Possibly, it's ambiguous. But if there are no particles, just the sentence "the kettle is black", then is it true?

What sensory experience? The one I say is that of a kettle, or the one you say is that of a kettle? — Isaac

Either. But if there were neither, just the sentence "the kettle is black", then is it true?

Do you? Or do you get damp when you stand out in drizzle? If you're wearing a coat are you still getting wet? Does the sentence "I didn't really get wet, just a bit damp" make no sense to you? — Isaac

Yes, yes, a little, and no.

But if there is no water falling from the sky, just the sentence "it is raining", then is it true?

Your arguments for the ambiguity of language do not refute my point. It still requires that there is something in addition to the sentences "it is raining" and "the kettle is black" for these sentences to be true. Truth depends on more than just language.