That's besides the point. — Banno

The only point I am making is that the T-schema isn't a definition of truth. From his 1969 paper:

In fact, according to our stipulations, an adequate definition of truth will imply as consequences all partial definitions of this notion, that is, all equivalences of form (3):

“p” is true if and only if p,

where “p” is to be replaced (on both sides of the equivalence) by an arbitrary sentence of the object language.

...

If all the above conditions are satisfied, the construction of the desired definition of truth presents no essential difficulties. Technically, however, it is too involved to be explained here in detail. For any given sentence of the object-language one can easily formulate the corresponding partial definition of form (3). Since, however, the set of all sentences in the object-language is as a rule infinite, whereas every sentence of the metalanguage is a finite string of signs, we cannot arrive at a general definition simply by forming the logical conjunction of all partial definitions. Nevertheless, what we eventually obtain is in some intuitive sense equivalent to the imaginary infinite conjunction.

That "imaginary infinite conjunction" (extended from his earlier example of a finite language) which is the definition of truth being:

For every sentence x (in the language L), x is true if and only if either
s₁, and x is identical to “s₁”,
or
s₂, and x is identical to “s₂”,
. . .
or finally,
s_∞, and x is identical to “s_∞"

Although, again, this only applies to formal languages.

This seems to be the only definition of truth that Tarski offers in that paper:

If the language investigated only contained a finite number of sentences fixed from the beginning, and if we could enumerate all these sentences, then the problem of the construction of a correct definition of truth would present no difficulties. For this purpose it would suffice to complete the following scheme: x E Tr if and only if either x = x₁ and p₁, or x = x₂ and p₂, ... or x = x_n and p_n, the symbols 'x₁', 'x₂', ... , 'x_n' being replaced by structural descriptive names of all the sentences of the language investigated and 'p₁', 'p₂', ... , 'p_n' by the corresponding translation of these sentences into the metalanguage.

He makes it clear that a definition of truth is impossible for colloquial language and a formal language with an infinite number of sentences, only offering the above for a formal language with a finite number of sentences.

He's right, since he is talking about formal languages. — Banno

He's not. That quote is from the section "The Concept of True Sentences in Everyday or Colloquial Language". Later on in that section he says:

The attempt to set up a structural definition of the term 'true sentence' - applicable
to colloquial language is confronted with insuperable difficulties.

...

If these observations are correct, then the very possibility of a consistent use of the expression 'true sentence' which is in harmony with the laws of logic and the spirit of everyday language seems to be very questionable, and consequently the same doubt attaches to the possibility of constructing a correct definition of this expression.

And again, from the 1933 paper:

(5) for all p, 'p' is a true sentence if and only if p.

But the above sentence could not serve as a general definition of the expression 'x is a true sentence' because the totality of possible substitutions for the symbol 'x' is here restricted to quotation-mark names.

Tarski does what you say only he makes it clear that this doesn't count as the definition of truth:

(T) X is true if, and only if, p.

We shall call any such equivalence (with 'p' replaced by any sentence of the language to which the word "true" refers, and 'X' replaced by a name of this sentence) an "equivalence of the form (T)."

Now at last we are able to put into a precise form the conditions under which we will consider the usage and the definition of the term "true" as adequate from the material point of view: we wish to use the term "true" in such a way that all equivalences of the form (T) can be asserted, and we shall call a definition of truth "adequate" if all these equivalences follow from it.

It should be emphasized that neither the expression (T) itself (which is not a sentence, but only a schema of a sentence) nor any particular instance of the form (T) can be regarded as a definition of truth. We can only say that every equivalence of the form (T) obtained by replacing 'p' by a particular sentence, and 'X' by a name of this sentence, may be considered a partial definition of truth, which explains wherein the truth of this one individual sentence consists. The general definition has to be, in a certain sense, a logical conjunction of all these partial definitions. — The Semantic Conception of Truth

Which authors disagree with Tarski?

Consider what it would take to be certain that your housemate was a bachelor. If it's never possible, then that's a Cartesian standard, not an ordinary standard. — Andrew M

I don't think it even needs to reach the "Cartesian" standard. It's really just the same point you made earlier (which I missed):

I agree. Alice can know the phone number qua a ten-digit number. But if when asked she says, "I think it's <number>", then that raises a question as to whether she really does know it. If she gets it right, we're probably inclined to say she did know it after all. However, given her qualification, she wasn't certain that she knew it, and thus not certain what the number was.

So in that case we could say that she didn't know that she knew it. — Andrew M

In the case of my housemate being a bachelor, I just have a greater conviction.

Something else worth mentioning from The Semantic Conception of Truth:

In fact, the semantic definition of truth implies nothing regarding the conditions under which a sentence like (1):

(1) snow is white

can be asserted. It implies only that, whenever we assert or reject this sentence, we must be ready to assert or reject the correlated sentence (2):

(2) the sentence "snow is white" is true.

Thus, we may accept the semantic conception of truth without giving up any epistemological attitude we may have had; we may remain naive realists, critical realists or idealists, empiricists or metaphysicians – whatever we were before. The semantic conception is completely neutral toward all these issues.

Tarski does say in his 1933 paper:

For the reasons given in the preceding section I now abandon the attempt to solve our problem for the language of everyday life and restrict myself henceforth entirely to formalized languages. These can be roughly characterized as artificially constructed languages in which the sense of every expression is unambiguously determined by its form.

So perhaps Tarski is right in referencing Godel. What's wrong is interpreting Tarski as having said something about the meaning of "true" in our natural language (at least with respect to his 1933 paper).

If you don't see how my clarification might prevent people from thinking you were talking about the word string "snow being green" not being a sentence... — bongo fury

Given that I didn't use quotation marks it should be obvious. Most of us understand the difference between use and mention.

a) snow being green isn't a sentence
b) "snow being green" isn't a sentence

These mean different things. That should be obvious to any competent English speaker.

Do you mean that some alleged (truth-making) non-word-string corresponding to or referred to by the word-string "snow being white", or indeed by the word-string "snow is white", isn't a sentence? — bongo fury

I mean exactly what I said; that snow being green isn't a sentence. What I'm unsure of is what snow being green is.

So you would clarify thus:

Although there may be times, like with (a), where the consequent is does correspond to a fact, — bongo fury

Here's a sentence:

a) Joe Biden is President

I would say that the subject of the sentence is a person. I wouldn't say that the subject of the sentence corresponds to a person.

So here's another sentence:

b) "snow is white" is true iff snow is white

Perhaps the consequent of (b) is a fact, similar to how the subject of (a) is a person.

Do you mean the word-string "snow being green" or something else? — bongo fury

Something else.

Snow being green isn't a sentence. Snow being white isn't a sentence. Vampires being immortal isn't a sentence.

Which one, then? — bongo fury

I'm unsure.

Snow being green isn't a sentence, so what is it?

Two very different questions that keep being mixed up:

What is "true"?
What sentences are true?

T-sentences answer the first. — Banno

Not exactly. I mentioned before that in The Semantic Conception of Truth (1944) Tarski only said that the T-schema must be implied by the definition of truth, and that he offered something else as the definition ("a sentence is true if it is satisfied by all objects, and false otherwise").

But also in Truth and Proof (1969), where he explains that the T-schema is only a partial definition:

(1) “snow is white” is true if and only if snow is white.
(1’) “snow is white” is false if and only if snow is not white.

Thus (1) and (1’) provide satisfactory explanations of the meaning of the terms “true” and “false” when these terms are referred to the sentence “snow is white”. We can regard (1) and (1’) as partial definitions of the terms “true” and “false”, in fact, as definitions of these terms with respect to a particular sentence.

...

Partial definitions of truth analogous to (1) (or (2)) can be constructed for other sentences as well. Each of these definitions has the form:

(3) “p” is true if and only if p,

where “p” is to be replaced on both sides of (3) by the sentence for which the definition is constructed.

...

The problem will be solved completely if we manage to construct a general definition of truth that will be adequate in the sense that it will carry with it as logical consequences all the equivalences of form (3).

...

First, prepare a complete list of all sentences in L; suppose, for example, that there are exactly 1,000 sentences in L, and agree to use the symbols “s₁”, “s₂”, . . . , “s_1,000” as abbreviations for consecutive sentences on the list.

...

(5) For every sentence x (in the language L), x is true if and only if either
s₁, and x is identical to “s₁”,
or
s₂, and x is identical to “s₂”,
. . .
or finally,
s_1,000, and x is identical to “s_1,000”.

We have thus arrived at a statement which can indeed be accepted as the desired general definition of truth: it is formally correct and is adequate in the sense that it implies all the equivalences of the form (3) in which “p” has been replaced by any sentence of the language L.

But, again, my example of "this sentence has thirty one letters" seems to be an exception to the partial definition given by (3) and the general definition given by (5). It doesn't seem that either (3) or (5) can fully account for self-referential sentences.

Also, I should add, even his 1933 paper explains that the T-schema is not a general definition of truth:

(5) for all p, 'p' is a true sentence if and only if p.

But the above sentence could not serve as a general definition of the expression 'x is a true sentence' because the totality of possible substitutions for the symbol 'x' is here restricted to quotation-mark names.

Your account now is "p" is true iff q. — Michael

It always was. Putting p on both sides is a special case. — Banno

Then it just seems to be saying that "p" is true iff its truth conditions obtain which is a pretty vacuous theory. So as I said earlier, a more substantial account of truth is needed. Correspondence, coherence, verificationism, etc.

You are tying a knot where one is not needed.

"this sentence has thirty one letters" is in the object language.

In the metalanguage, we name that sentence "Fred". Fred is true if Fred had thirty one letters.

Fred has thirty one letters.

Fred is true. — Banno

OK, but this is no longer deflation/disquotation/the T-schema, which are all just "p" is true iff p.

Your account now is "p" is true iff q.

Perhaps it could be tacit. If no doubt is exhibited in the use of knowledge, or the person would respond that they know something if asked, then that would count as knowing that they know. — Andrew M

I don't think it's a matter of doubt, just a matter of admitting fallibility. I would say that I know that my housemate is a bachelor, but I also accept that he could be lying to me and have a secret wife that he ran away from. Implausible, perhaps, but not unheard of. Does admitting of this possibility (and not just in the "there is a possible world" sense) somehow entail that I don't know that my housemate is a bachelor (assuming he isn't lying to me)? I don't think so. That I might be mistaken is simply an admission that I am not certain, not an admission of doubt.

So in such a scenario I would say that I know (and perhaps I do), but I'd also say that I might be wrong. Both claims are warranted.

In Tarski's case, by separating the metalanguage from the object language, so that such self-referential sentences cannot be constructed. — Banno

So it has limited applicability to natural languages as self-referential sentences can be constructed in English.

What theory of truth is able to make sense of the English sentence "this sentence has thirty one letters" being true then?

"this sentence has thirty one letters" is true iff that sentence has thirty one letters — Banno

That's not disquotation then. It isn't in the form "p" iff p. Yours is "p" if q.

But with the caveat of the liars paradox, right? I said it just because it seemed like the most obvious thing that would break the logic. — Moliere

"this sentence is false" is true iff this sentence is false

If we accept that the T-schema is true then, using the above, "this sentence is false" is false (assuming the consequent is referring to the biconditional as a whole).

How does the T-schema deal with self-reference?

"this sentence has thirty one letters" is true iff this sentence has thirty one letters

The above sentence has seventy one letters, but the quoted sentence has thirty one. Do we have to make the "this sentence" in the consequent refer only to the consequent and not the biconditional as a whole?

I don't agree that the distinction between fact and fiction corresponds to the distinction between true and false. It is true that Mickey Mouse wears red shorts and that vampires have no reflection. — Luke

That's true.

"vampires have no reflection" is true iff vampires have no reflection
"snow is white" is true iff snow is white

The T-schema doesn't really say anything about facts at all. It may, incidentally, be a fact that snow is white (or in some parallel world that vampires have no reflection), but the T-schema is silent on that.

As I mentioned before, we need a more substantive account of meaning (and perhaps truth) to actually get anywhere important.

I wonder also if the order in which the T-schema is presented affects our interpretation of it:

a) "snow is white" is true iff snow is white
b) snow is white iff "snow is white" is true

As a biconditional both are correct, but I have this intuitive sense that they can be interpreted differently. Perhaps this is related to the paradoxes of material implication.

The T schema does cover both of these cases. — Luke

I meant that when we make sense of the T-schema we cannot simply say that the consequent is a fact because sometimes it isn't.

For almost every case I can imagine, p is always a fact of our world, our conventions and/or our myths and stories. These might all amount to the same thing. — Luke

Is there some singular term we can use to describe the sort of thing p is? Maybe "narrative"? Sometimes that narrative is a fact and sometimes it is a fiction. Which is really just another way of saying that sometimes the narrative is true and sometimes it is false, making the T-schema just the deflationary theory that the sentences "'p' is true" and "p" mean the same thing.

Is what I say true, true
I make the performative utterance "I name this ship Queen Elizabeth".
I can then say that it is true that this ship is named Queen Elizabeth.
Is what I say is true, true ?
(What I say is true) is (this ship is named Queen Elizabeth)
So yes, (this ship is named Queen Elizabeth) is true

So yes, what I say is true is true. — RussellA

Sometimes something is true because you say it. You cannot apply the above reasoning to everything.

That snow is white does not represent a fact; it is a fact. — Luke

I'll mention it again as it bears repeating.

a) "snow is white" is true iff snow is white
b) "snow is green" is true iff snow is green

However we make sense of the consequent of the T-schema I think it should apply to both (a) and (b). It is not a fact that snow is green. Although there may be times, like with (a), where the consequent is a fact, there are times, like with (b), where it isn't. A rigorous account of the T-schema should cover both cases.

So, "p" is true iff p. What sort of thing is p? It is not always a fact. Maybe an answer to that will tell us what sort of thing a fact is.

It doesn't excuse the equivocating between a string of words and alleged things or situations that aren't strings of words. — bongo fury

I think the issue is that facts aren’t always things, e.g material objects. It is a fact that unicorns don’t exist, but the non-existence of unicorns isn’t a thing that exists. Is there a distinction between the fact that unicorns don’t exist and the sentence “unicorns don’t exist” being true?

Exactly. According to correspondence theory in this kind of context. — bongo fury

Not necessarily. “1 + 1 = 2” is true iff 1 + 1 = 2. 1 + 1 = 2 because this is what follows from the axioms of mathematics. The T-schema works with a coherence theory, too.

Something worth considering is that "snow is green" is true iff snow is green, but it is not a fact that snow is green. So what does "snow is green" refer to if not a fact? A fiction? Or does it make sense to talk about non-obtaining facts?

Perhaps it isn't quite right to say that the consequent of the T-schema is/refers to a fact.

No, the thing on the right of the T-schema is a string of words. — bongo fury

That string of words refers to a fact.

When we say "Joe Biden is President" we're not saying that the string of words "Joe Biden" is President; we're saying that the man referred to by the string of words "Joe Biden" is President.

This discussion was merged into Life Sucks: (General Anti-Life Discussion)

So the snow being white is a fact but the white snow isn't a fact. Or it is? I don't understand why it matters. Is the word "fact" important? This just seems to be an issue of grammar.

We even criticised Boris Johson for the same reason when he was partying at downing street — javi2541997

We criticized him because he was breaking the law.

I'll put it to the team.

It was suggested when the forum first started that we notify users each time a discussion or comment is moderated but we decided against that. More comments get moderated than most people are aware of so it would be a lot of extra work.

But if you ask us either by PM or the feedback section we answer.

I moved it because it didn’t seem to be philosophy. Not sure what it is.

It doesn't need to be "the mind-independent material world" and cohering with "some specified set of sentences" is not enough; simply being in accordance with what is experienced will do. — Janus

I was just pointing out that the T-schema is rather empty as-is. Tarski didn't even offer it as a definition of truth:

Thus, if the definition of truth is to conform to our conception, it must imply the following equivalence:

The sentence "snow is white" is true if, and only if, snow is white.

Note that he's not saying that "p" is true iff p is the definition of truth, he's saying that it's something that must be implied by the definition of truth. His actual definition was later:

Hence we arrive at a definition of truth and falsehood simply by saying that a sentence is true if it is satisfied by all objects, and false otherwise.

But as Goodman suggests, any number of theories on truth can imply the T-schema.

This discussion was merged into "What is truth? said jesting Pilate; and would not stay for an answer."

I don't see that. for me, the words on the right of "iff" in '"Snow is white" is true iff snow is white' point to the grounding fact of snow being white (or not). — Janus

That "grounding fact" might be that the sentence "snow is white" coheres with some specified set of sentences, à la coherence theory.

a. "snow is white" is true iff snow is white
b. snow is white iff "show is white" coheres with some specified set of sentences
c. Therefore, "snow is white" is true iff "show is white" coheres with some specified set of sentences

The T-schema of (a) works with any number of more substantive views of truth. (b) can be thought of a theory of meaning that adds to the rather empty theory of truth given by (a).

Alternatively:

a. "snow is white" is true iff snow is white
b. snow is white iff the mind-independent material world is a certain way
c. Therefore, "snow is white" is true iff the mind-independent material world is a certain way

That would be closer to the traditional correspondence theory.

I would say knowledge entails certainty. — Andrew M

Then knowledge requires certainty. If we are not certain that John is a bachelor then we do not know that John is a bachelor.

The argument I offered was premised on the notion that we can know things even if we are not certain, and so I accept that a rejection of that premise allows one to reject the conclusion.

Whether or not we'd want to reject that premise is another matter, but I see that you are willing.

A related question, then, is what it takes for us to be certain that something is true. My initial view is that we can only be certain that something is true if that thing is necessarily true, and so I can only be certain that John is a bachelor if it is necessarily true that John is a bachelor, although perhaps that's a matter for another discussion.

But what you've been chasing in this thread is me knowing aliens exist even though they might not. — Srap Tasmaner

Because I understand "aliens might not exist" as "I am not certain that aliens exist" as opposed to just "I do not know that aliens exist". So the argument would be:

I know that aliens exist
Aliens might not exist (≔ I am not certain that aliens exist)
Therefore, I know that aliens exist and aliens might not exist

Why do we say that we might be wrong? Because the evidence available to us has not proved our belief. Even if we want to say that something like 80% certainty is sufficient for our belief to count as knowledge, it seems strange to say that we could be wrong when we have 79% certainty but can't be wrong when we have 80% certainty simply because that's the – somewhat arbitrary – point at which our belief counts as knowledge (if it happens to be true).

I think the "can't be wrong" is only true when our belief is proved (i.e. it is 100% certain).