Did you bother even reading the rest of what was said? — Michael

Yes, and read a few chapters on pred logic and free logic. :brow: The white sauce nearly caught in the pan - I shouldn't read while cooking.

I tried to formulate a few versions of your argument to see if I could get it to work in a formal system, but could not.

Q(a)→∃x(x=a)

Q(a) already assumes that a exists, so of course it follows - from the definition of ∃x.

Try it this way: can you conceive of a proposition that does not exist?

Then what does it mean for a proposition to exist?

And can you remind my why we started on this argument?

Okay, thanks for the discussion.

Q(a) already assumes that a exists, so of course it follows - from the definition of ∃x. — Banno

Then the argument is valid. From the premise ∀p: T(q) ↔ p it follows that ∀p: ∃x(x=q). For all p, the proposition that p exists.

And can you remind my why we started on this argument? — Banno

We didn't. This argument was a response to Pie's OP where I wanted to draw a distinction between these two related claims:

1. "p" is true iff p
2. "'p' is true" means "p"

The former has a possibly problematic entailment as my argument shows.

But as I said to Srap, the simple resolution is to specify that the T-schema is saying ∀q: T(q) ↔ p, i.e. for all propositions that p, the proposition that p is true iff p. The conclusion is then the truism that ∀q: ∃x(x=q), i.e. for all propositions that p, the proposition that p exists.

So...

1. "p" is true iff p
2. "'p' is true" means "p"
— Michael

If you have an understanding of the state under which p is true, then what more could you want in order to have the meaning of p? (Davidson) — Banno

I don't understand what that question has to do with the point I'm making. The point I am making is that if for all p, the proposition that p is true iff p, then for all p, the proposition that p exists.

Cool.

I was addressing

I think a distinction needs to be made between these two claims:

1. "p" is true iff p
2. "'p' is true" means "p" — Michael

Which was your original point...

And I don't understand how your question is related to what I was saying.

Aporia. A wonderful thing.

1. "the cat is on the mat" is a true sentence written in English iff the cat is on the mat
2. "'the cat is on the mat' is a true sentence written in English" means "the cat is on the mat"

These mean different things. And (1) is true but (2) is false.

Now consider:

3. "the cat is on the mat" is a true sentence iff the cat is on the mat
4. "'the cat is on the mat' is a true sentence" means "the cat is on the mat"

If (3) and (4) also mean different things, with presumably (3) being true and (4) being false, then what of these two?

5. "the cat is on the mat" is a true sentence
6. "the cat is on the mat" is true

Do (5) and (6) mean the same thing? If they do, and if (3) and (4) mean different things, then (7) and (8) mean different things:

7. "the cat is on the mat" is true iff the cat is on the mat
8. "'the cat is on the mat' is true" means "the cat is on the mat"

Good idea. A bit of depth.

We can perhaps see the difference most clearly if we look to the use of each rather than meaning. Let's look at an example in which it might make sense to separate truth from belief.

There's a tree over the road. Suppose Fred believes the tree is an English Oak. But it is a Cork Oak.

We might write, in order to show the bivalency of the belief:

Believes ( Fred, The tree over the road is an English Oak)
And
True (The tree over the road is a Cork Oak). — Banno

You haven't gotten very far yet. The difference between "it is a Cork Oak" and "it is an English Oak", is that the former is justified. Yet you say that the difference is that the former is true. This makes "true" nothing other than "justified", in practise. But in theory you insist on a difference between justified and true. How do you describe that difference? Where do you turn to place "true", to God's belief (absolute truth), or to the individual's belief (honest subjectivity)?

I think the best way to define the "mention operator" as I called it, and had yet to be able to answer your question, is to say what it does is it converts a natural-language string into a name for that said string using the same alphanumeric characters, but changing its function from a proposition to a name. — Moliere

Where does mention or use come into it?

One thing I'm noticing here, in your examples, is you like to treat existence like a predicate. So the existence of things gives propositions used their truth-value. — Moliere

Hopefully we can avoid that rigmarole. According to the correspondence theory, the truth of a proposition is determined by whether or not a proposition corresponds to the empirical facts of the world. On the other hand, the deflationary claim made by @Pie and @Banno(?) is that true propositions are identical with the empirical facts of the world. Opposing this deflationary claim, I argued that language and the empirical facts of the world are distinct. It is difficult to try and draw this distinction without attempting to use language to gesture at the existence or instantiation of things in the world other than language.

"This river contains many fish" is true iff there exists a river, and the river contains, and the object contained by the river are fish, and the relationship of said fish to the numerical predicates in the context its within is such that speakers would say "many". — Moliere

Sounds okay to me. I was thinking more along the lines that "this river" has to refer to something outside the sentence and that, in order for the sentence to be true, it should be in principle verifiable that there are indeed many fish in the river.

You agree with this:

So non-existent rivers are not facts? I might agree with you there.
— Luke

On your account of correspondence, how is it that "There is no river on this dusty plane" true? The fact is the dusty plane, rather than the no-river. — Moliere

I said I might agree that "the no-river" is not a fact; not that it is a fact. On my account of correspondence, the proposition is true because no fact (of a river) corresponds to the proposition.

Or, the classic "The present king of France is bald". There is nothing to which this proposition refers as we speak it today. So you'd likely say something like the proposition is either obviously false, given there is no fact to the matter, or does not have a truth-value, or something like that. — Moliere

There is no present king of France, so I'd agree with what you say here. The proposition proposes nothing (presently) verifiable and so it cannot be verified as either true or false.

But that's something I liked about the plums example -- here was something that would matter, and is a lot more natural to our way of thinking. When you open up the fridge and see nothing in it, the no-plums have an effect on your state, at least. The nothing has an effect on us. And especially the no-plums, if we wanted plums. The no-plums have a relationship to the believed proposition. The fact is the empty fridge, and yet the sentence is "There aren't any plums in the ice box", and it's true. — Moliere

Right, but this example is the same as "the no-river". We can verify whether or not it's true by seeing for ourselves; that's what "empirical" means, and that's the strength of the correspondence theory.

The arguments for the deflationary theory given here seem to illicitly assume the approach (or "truth") of the correspondence theory without admitting it. If deflationism is no more than endorsing a sentence that one believes to be true, then there is no place for correspondence, verification, "finding out" whether or not a proposition is true, truthmakers, or facts. There is nothing more to truth than endorsement and, therefore, no way of determining or discovering the truth of a given proposition. According to deflationism, looking for plums in the freezer has nothing to do with the truth or falsity of the proposition about plums in the freezer. There is then nothing "outside" the proposition that counts for or against the truth of a given proposition. A T- sentence is then no more than an abstract equation with absolutely no relation or reference to reality, as several here have noted already.

1. "the cat is on the mat" is a true sentence written in English iff the cat is on the mat — Michael

That's not a T-sentence, of course.

So what are you doing here?

So what are you doing here? — Banno

Check the rest of the comment. You may need to refresh your page as I made some substantial edits about half an hour ago.

The main point is that, prima facie, these are different claims:

1. X is Y iff Z
2. "X is Y" means "Z"

So, prima facie, these are different claims:

3. "p" is true iff p
4. "'p' is true" means "p"

And, as my argument from that original comment shows, (3) has possibly undesirable implications – implications which may not follow from (4) – hence the importance of distinguishing (3) and (4).

I don't know why you are making these claims. They don't seem related to anything.

You said

I think a distinction needs to be made between these two claims:

1. "p" is true iff p
2. "'p' is true" means "p"


Now Davidson pointed out that if you have a true T-sentence such as

1. "S" is true iff p

then you have in p, in effect, the meaning of S.

Hence my comment.

And I don't understand how Davidson's comment has anything to do with me making a distinction between these two claims:

1. "p" is true iff p
2. "'p' is true" means "p"

So could you actually clarify what it is you are trying to say? Are you saying that, according to Davidson, (1) and (2) are equivalent?

What's the difference between seeing the sheet and seeing the sheet-as-sheet? — creativesoul

I was going to say no difference, other than some extra accounting being redundantly performed, but I think I like this answer too:

Sheet-as-sheet is stronger :strong: — magritte

:D

No. Rather that on Davidson's account, p gives the meaning of S.

Fine, but that has nothing to do with what I was saying so I don't understand why you're bringing it up as a response to my comment.

Ok. I give up.

Where does mention or use come into it? — Luke

From the examples that we'd be looking at, as persons interested in some meta-lingual predicate, like truth. The example sentences aren't going to be used by us, but they will serve as examples for clarifying, between us, what is meant by the meta-lingual predicate.

So on the left-hand side you have what is mentioned by us (converted into a name for the calculus), and on the right-hand side you have what is used by whoever or whatever our source is.

If deflationism is no more than endorsing a sentence that one believes to be true, then there is no place for correspondence, verification, "finding out" whether or not a proposition is true, truthmakers, or facts. There is nothing more to truth than endorsement and, therefore, no way of determining or discovering the truth of a given proposition. According to deflationism, looking for plums in the freezer has nothing to do with the truth or falsity of the proposition about plums in the freezer. There is then nothing "outside" the proposition that counts for or against the truth of a given proposition. A T- sentence is then no more than an abstract equation with absolutely no relation or reference to reality, as several here have noted already. — Luke

I think what I'd say is that it just leaves those questions open. In the context of the plums, the method for verifying, finding out, and such wouldn't be pre-specified by deflationary accounts. So one could, for instance, go check for themselves. Or they could ask their friend who just came back from the fridge if there are any left. The method of justification is left open with respect to deflationary accounts -- not denied. Clearly for someone to say they believe such-and-such, we'd have to do something to provide a justification in the game of reasons. The deflationary account is just attempting to put that game of reasons to the side of an understanding of the concept of truth -- so that the two are distinct.

So when you say:

According to the correspondence theory, the truth of a proposition is determined by whether or not a proposition corresponds to the empirical facts of the world. On the other hand, the deflationary claim made by Pie and @Banno(?) is that true propositions are identical with the empirical facts of the world. Opposing this deflationary claim, I argued that language and the empirical facts of the world are distinct. — Luke

I don't think I'd say that true propositions are identical to the *empirical* facts. I'd say that true propositions and facts are one and the same, but that doesn't mean I'd discount reality. Reality just isn't the totality of facts, in that case -- as you note, they're just true propositions, so I certainly wouldn't want to reduce the entirety of reality to them. I don't think either @Banno or @Pie have said they'd do the same, either.

Why would I make a distinction between facts and reality? Well, because we cannot count how many facts there are. There could, after all, just be one fact -- the fact of reality itself. All of existence is what makes our sentences true or false. That Mars is the fourth planet in our solar system is related to the empty fridge and so makes "there are no plums in the ice box" true, being the one big fact that's there.

After all, it's not like reality is divided up into English sentences, right? As you say, language and the world are distinct. So we have access to the world on one side, and language on the other, and we match them up. But the world isn't made up of linguistic constructs, so it leads me to ask "what is this matching? What matches what? Where does the fact end and the language begin?" It seems like I'd have to be able to specify what facts are distinct from language to hold up this claim, but I am unable to do so -- as you noted:

It is difficult to try and draw this distinction without attempting to use language to gesture at the existence or instantiation of things in the world other than language. — Luke

I agree! :D I suppose I think the correspondence theory sits on "this side" of language -- that it doesn't say anything about reality, but rather about how we think about reality, because I am completely unable to specify the difference between a fact and a true sentence in speech. But I don't deny reality: just this one way of talking about reality, through correspondence, since we are unable to specify the difference between true sentences and facts.

What's the difference between seeing the sheet and seeing the sheet-as-sheet?
— creativesoul

I was going to say no difference — Moliere

Sheet-as-sheet to me indicates naming and descriptive practices accompanying the seeing. This eliminates language less seeing of the sheet, which - of course - is a problem.

Sheet-as-sheet to me indicates naming and descriptive practices accompanying the seeing. This eliminates language less seeing of the sheet, which - of course - is a problem. — creativesoul

Is it?

If truth is linguistic, and animals don't speak, then those animal behaviors won't tell us about truth.

Perhaps a better tact, though: if truth is more general than linguistic -- say it is a correspondence between some animal belief and facts or reality, construing belief broadly to indicate that it could be linguistic or not so as to make explicit that we're interested in this -- then we are the types of creatures that rely upon linguistic truth, and only by understanding this kind of truth would we even be able to make statements more general about this bigger-picture truth.

EDIT:

Accidentally cut off the link to the post in my reply.

So, I believe that what seems self-evident in logic is so because of what we perceive and what we can imagine perceiving, and what we can consequently imagine being the case. To my way of thinking this is the essence of modal logic; what is impossible in all worlds just is what we find impossible to imagine, and I think what we can imagine is constrained by the general characteristics we are able to identify in what we perceive. If we perceived very different images of the world with very different characteristics, then we would be able to imagine what for us, as we are, is unimaginable, and our logics would be correspondingly different

The problem with using the imagination as a basis for logic is that people have different capacities for imagining -- so a logic, then, would only be understandable insofar that we have the imaginative capacity. If our imaginations are a bit dim, then our logic will also be a bit dim, and if our imaginations are incredibly active, then our logic will be incredibly active.

But logics don't have that variability to them. That's precisely what's interesting -- we already know that more clever persons will be more clever. But logic, in general, is nothing more than how we make inferences whether we are clever or dim or not. All we need to do is check the validity of the argument using rules that can be taught. No need to rely upon our imaginative powers to define a logic.

After all, even though I think I have a notion of what it means to imagine possibilities, to take a similar tactic as I did with @creativesoul -- we'd have to understand linguistic truth first to be able to share those imagined possibilities.

Basically it's easier to talk about linguistic truth than it is to talk about the possible limits of our imaginations, especially since our imaginations seem to morph over time depending upon how much we might use them (or not).

Very interesting point there.

@Moliere, @Luke

According to the correspondence theory, the truth of a proposition is determined by whether or not a proposition corresponds to the empirical facts of the world. On the other hand, the deflationary claim made by Pie and Banno(?) is that true propositions are identical with the empirical facts of the world. Opposing this deflationary claim, I argued that language and the empirical facts of the world are distinct.
— Luke

I don't think I'd say that true propositions are identical to the *empirical* facts. I'd say that true propositions and facts are one and the same, but that doesn't mean I'd discount reality. Reality just isn't the totality of facts, in that case -- as you note, they're just true propositions, so I certainly wouldn't want to reduce the entirety of reality to them. I don't think either @Banno or @Pie have said they'd do the same, either. — Moliere

I certainly don't advocate any form of idealism, and don't wish to be misunderstood as advocating that there are only propositions, with no world. I am advocating realism as the best way to talk about the stuff around us.

So it is incorrect to say that I have claimed "that true propositions are identical with the empirical facts of the world".

And this is an example of where the nuance found in logic is indispensable. There is a difference between material equivalence, "≡", and identity, "=". Folk can use Google if they are unsure of this.

In a T-sentence the true proposition on the left is found to be equivalent to the fact on the right.

This does not mean that they are identical.

Nor does it imply that "language and the empirical facts of the world are distinct"; clearly that the kettle is boiling is not the same as "the kettle is boiling", The first is an empirical fact, the second a piece of language.

I think, Moliere, this is the point you are making. I'm wondering, @Luke, at the wisdom of trying to do philosophy without logic.

Poverty of correspondence

According to the correspondence theory, the truth of a proposition is determined by whether or not a proposition corresponds to the empirical facts of the world. — Luke

What's interesting is how this dissipates when examined. So on this account, say, the truth of the proposition "The kettle is boiling" is determined by whether or not "the kettle is boiling" corresponds to the empirical facts of the world. But when one asks what those empirical facts are, one is told that they are that the kettle is boiling...

Which is exactly to say that The kettle is boiling" is true only if the kettle is indeed boiling.

The salient point here is that this correspondence account says pretty much the same as the T-sentence.

But there are cases where the correspondence theory becomes opaque. It is not at all clear what the "empirical facts of the world" are that make the propositions "four is twice two", "no married men are bachelors " or "this note is worth ten dollars" true. Yet the appropriate T-sentence will still hold.

Yes, I know there are explanations for these issues in correspondence theory, but that ad hoc explanations are needed shows the poverty of correspondence.

It's not that correspondence is wrong, but that it does not work in all case, that leads to the need for a better theory of truth.

I think, Moliere, this is the point you are making — Banno

Yup!

One approach that might be helpful here is to point out that deflation need not commit to correspondence being wrong.

So such sentences as "that the kettle is boiling corresponds to the facts" aren't wrong, but just an obtuse way of saying that "the kettle is boiling" is true. The deflationary view here unpacks "corresponds" as material equivalence between a fact and a true sentence.

This view would not be acceptable to those who see correspondence as an ontology; those who invoke the existence of a category of things called "facts", sitting somewhere between boiling kettles and the sentences about them.

The problem with using the imagination as a basis for logic is that people have different capacities for imagining -- so a logic, then, would only be understandable insofar that we have the imaginative capacity. If our imaginations are a bit dim, then our logic will also be a bit dim, and if our imaginations are incredibly active, then our logic will be incredibly active. — Moliere

That's not what I had in mind. No one can imagine a round square, or that something could be both red and green all over. In general, we are unable to imagine the actual existence of contradictory states of affairs, or, perhaps better, we are unable to imagine what a contradictory state of affairs could look like..

The deflationary view here unpacks "corresponds" as material equivalence between a fact and a true sentence. — Banno

It isn't clear what this means. What's a material equivalence? Why not just an equivalence?

And why not call it an equivalence theory of truth if that's what you mean?

What's a material equivalence? — Tate

*despair*