Yep.

Addition: He's right, since he is talking about formal languages. In English, which sentences can we not turn onto quotation-mark names?

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.

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.

This seems to be the only definition of truth that Tarski offers: — Michael

Yes, he defines truth for the object language in terms of satisfaction. He is correct in saying that a definition in terms of satisfaction may not work for English. Others have since developed on that notion.

That's besides the point.

You seem to be saying "Tarski didn't say that", and I agree. It is a follow-on argument.

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.

And my reply is that for Tarski, that is correct. But it has been used as such since his work.

And I refer to you the previous argument:

"p" is true ≡ p

...there can be no doubt that the meaning of p is held constant; that p is used on the right and mentioned on the left. (p cannot mean something other than it means.) So there is no need for satisfaction, or any other theory of meaning. — Banno

To which you replied

the totality of possible substitutions for the symbol 'x' is here restricted to quotation-mark names.

to which I replied

In English, which sentences can we not turn onto quotation-mark names? — Banno

And that is where I think we are up to.

For me to give a decent response I'd have to do a lot more reading, and give it a lot more thought. At this point though, I'm inclined to be more Wittgensteinian in my view.

Well, that's what we are here for - to muddle through.

Looking out from my stoa, Family resemblance, Gödel incompleteness and the deranged epitaphs, and Banno's game, all seem to be indicative of much the same aspect of language. That it is open.

"The cat is on the mat" is true ≡ The cat is on the mat

The thing represented by the sentence on the right is a fact. — bongo fury


I dunno, Bong. You seem to me to just be repeating an argument I've already addressed a couple of times.

And it seems that others (@Michael) have tried to make the same point to you.

The thing represented by the sentence on the right is a fact. — bongo fury


It's clear that the thing on the right is not the name of a fact. Names do not have truth values.

AND again,

I. "Snow is white" is not a fact, because facts are things in the world, and so while "snow is white" represents a fact, it is not a fact. — Banno

Bongo can defend himself, but he did not say that the thing on the right is the name of a fact.

Anyhow, you appear to be saying that names are not facts because facts have truth values whereas names do not. But it is propositions, not facts, that have truth values. I don't see why facts must be propositional, other than you stipulating they must.

Also, you contradicted this when you said:

facts are things in the world — Banno

Things in the world have names and they are facts.

I don't know what to do with that. Names are not propositions.

I didn't say names are true. I said things in the world have names and they are facts.

...and they are facts. — Luke

What are facts? Names? Things in the world? Both? I still do not know what to do here.

Facts are things in the world - as you said. We use names to refer to things in the world; to distinguish them from other things.

Facts are things in the world - as you said. — Luke

Yes, things like that snow is white.

We use names to refer to individuals.

That's why in first order logic we use a,b,c... for individuals and f,g,h... for predicates and then put these together to make f(a), g(a), h(a,b) and so on...

a,b,c... are names. f(a), g(a), h(a,b) are propositions or statements or sentences - you choose - and so not names.

If f(a), g(a), h(a,b)... happen to be true, then they are facts.

Like that snow is white.

The commonality seems to be correspondence between saying and seeing, or actuality, however it is conceived.

Why can't an individual be a fact? Isn't snow a thing in the world and, therefore, a fact of the world?

As I mentioned earlier, one definition of "fact" given in many dictionaries is "something that really exists".

In English, which sentences can we not turn onto quotation-mark names? — Banno

It's not that we can't turn sentences into quotation-mark names, it's that such a proposed definition only applies to quotation-mark names, which is insufficient. The correct definition should apply to all true sentences. Again, from his 1933 paper, continuing immediately from the prior quote:

In-order to remove this restriction we must have recourse to the well-known fact that to every true sentence (and generally speaking to every sentence) there corresponds a quotation-mark name which denotes just that sentence. With this fact in mind we could try to generalize the formulation (5), for example, in the following way:

(6) for all x, x is a true sentence if and only if, for a certain p, x is identical with 'p' and p.

At first sight we should perhaps be inclined to regard (6) as a correct semantical definition of 'true sentence', which realizes in a precise way the intention of the formulation (1) and therefore to accept it as a satisfactory solution of our problem. Nevertheless the matter is not quite so simple. As soon as we begin to analyse the significance of the quotation-mark names which occur in (5) and (6) we encounter a series of difficulties and dangers.

I suggest you read that section of the paper rather than have me quote it piecemeal to you.

And my reply is that for Tarski, that is correct. But it has been used as such since his work. — Banno

Then you should probably mention that in your exegesis as it currently reads as if this was Tarski's position and so is misrepresentative.

I have the paper before me. But your point continues to escape me.

Let me have a go at paraphrasing what is going on here, with an eye towards our at the least agreeing on that. Tarski has
"Snow is white" is true IFF snow is white.
He is pointing out that one cannot substitute p for (snow is white) in order to obtain

"p" is true IFF p

because the quote marks make the context intensional; 'snow is white' and that snow is white have different extensions. Substitution cannot occur salva veritate. And so on.

Bowdlerising the argument, suppose we call "Snow is white", Fred.

Then we can write

Fred is true IFF snow is white

And perform a universal generalisation to get

U(x) Fred is true IFF x

...which is not what we want.

Do we agree that this is what is going on?

Tarski gets past this for formal languages by developing the mechanism of satisfaction, so that he has extensionally transparent terms on both sides of the equivalence.

Are we happy so far?

But your point continues to escape me. — Banno

My point is only to show you what Tarski said, which is that, to quote him again:

(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.

And later:

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.

He quite literally says that the T-schema isn’t a definition of truth and that a definition of truth for our everyday language is impossible. Maybe you and other authors disagree with him, but I’m not here to defend Tarski’s position, only to present it.

The only contribution of my own that I’ve added is that the sentence “this sentence has thirty one letters” appears to be an exception to the rule that “p” is true iff p, and so this disquotational account of truth is deficient. Tarski does pre-empt this, saying in Truth and Proof that, of his formalized language, "demonstrative pronouns and adverbs such as 'this' and 'here' should not occur in the vocabulary of the language", but I'm unsure how other authors who adopt the disquotational account for everyday language resolve the issue.

And in fact earlier you seemed to agree with me on this, saying "it always was [ 'p' is true iff q ]. Putting p on both sides is a special case", showing that "'p' is true iff p" isn't the definition of truth but something which (most of the time, at least) follows from whatever the actual definition is.

He quite literally says that the T-schema isn’t a definition of truth and that a definition of truth for our everyday language is impossible. Maybe you and other authors disagree with him, but I’m not here to defend Tarski’s position, only to present it. — Michael

Ok. Do you think I have claimed he said otherwise?

I'm now puzzled as to why we are having this conversation.

What could a truthful account of an event be if not an accurate portrayal of what happened? — Janus

This is precisely where the problem is, unwarranted attempts such as yours, to reduce the meaning of "a truthful account" to "an accurate portrayal of what happened". We all know, that "to tell the truth" means to state what one honestly believes. Therefore, we should also know, and adhere to the epistemic principle, that "a truthful account" means one's honest opinion. Now if we look at what "one's honest opinion" means, and what "an accurate portrayal of what happened" means, we see a huge gap between these two.

So if we simply assume that "a truthful account" means "an accurate portrayal of what happened" when it could equally mean "one's honest opinion" we have made a very serious mistake which could badly mislead us. And of course, as explained above, the problem is with the assumption that "a truthful account" means "an accurate portrayal of what happened". That one's honest opinion is an accurate portrayal of what happened is something which needs to be justified.

At this point, justification enters the scheme, allowing us to move from "one's honest opinion" to the conclusion of "an accurate portrayal of what happened". But we clearly ought not make this move without justification. Since there is in principle, such a huge gap between those two (ones honest opinion, and an accurate portrayal of what happened), we cannot move from one to the other without justification. To do so would be an irrational leap of faith.

Taking your radical skeptical line we could never know. I could have witnessed the same event someone is giving an account of, and so be in a position to judge whether the account were truthful or not, but according to your line of reasoning, my memory might be faulty, which means I could never be in a position to judge the truthfulness of any account of anything. — Janus

This is not "radical skepticism" in any way shape or form. It is a simple reflection on the reality of things. Different people have different descriptions of the same event, very often conflicting. That is commonplace, everyday, and not a statement of radical skepticism. Therefore every "truthful account" ought to be justified before we act on it. Have you never observed the proceedings of a court of law where people are sworn to tell the truth? These are not the proceedings of some sort of radical skepticism, these are the day to day proceedings of people who are working to determine the Truth.

Notice, I say "Truth" here with a capitalized T. That is because this is supposed to be some sort of Divine Truth, independent of human opinion, which we think we might be able to get at, through the process of justifying human truths (honest opinions). However, we of course, being only human, will never achieve that Divine Truth, that perfect, absolutely accurate portrayal of what happened. So, all this talk about "truth" in that sense, what I call "Truth" here (the perfect portrayal), is just pie in the sky nonsense for us lowly human beings.

But the point is we must understand what it would mean to be able to judge whether some account were truthful or not, in order to be skeptical about our ability to do so. — Janus

As explained above, this is the purpose of "justification". To properly judge the accounts of other people requires an understanding of justification. These accounts may contain honest mistakes as well as dishonesty, and uncovering these two requires different investigative skills. That is why we cannot simply assume an account is an honest, or truthful account.

Yes, although the circularity perhaps only reflects the fact that definitions are unnecessary. The game asks for judgements, but not reasons.......But, as such, they all fail the sorites test, which requires some perfectly absolute intolerance, as well as tolerance.. — bongo fury

Truth rests on meaning - and meaning rests on definition

The Sorites Paradox asks that when on the removal of a single grain a heap becomes a non-heap.

In the dictionary, a "heap" is defined as a "large number of". "Large" is defined as "considerable". "Considerable" is defined as "large". In this case, circular. Does this mean that definitions are unnecessary? Society has determined that it is not necessary that a "heap" be defined within a single grain, as it has, or example, with the metre length, recorded on a bar of platinum - iridium in the Bureau International des Poids et Mesures.

The Sorites Paradox is only a paradox because it requires a definition that does not exist. It would be like asking if the proposition "a xyxxy swims in the sea" is true or false before the meaning of "xyxxy" had been defined.

The Sorites Paradox requires the definition "a heap has at least X grains and at most Y grains" without defining the meaning of X and Y.

In Tarski's terms, the proposition " a heap has at least X grains and at most Y grains" is in the object language. The truth or falsity of the proposition may only be proven in the metalanguage, whereby a heap has at least X grains and at most Y grains. Yet the meaning of X and Y has never been defined. Truth can never be proven in the metalanguage until meaning has been defined in the object language.

The Sorites Paradox shows that it is not the case that definitions are unnecessary, rather, that it is only a paradox because it is requiring a definition that doesn't yet exist.

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

Another consideration; what if we drop the use of the word "false" and replace it with some substantial notion of falsity?

1. This sentence does not correspond to a fact

We can then say:

2. "This sentence does not correspond to a fact" does not correspond to a fact

Is (2) a contradiction that entails that (1) does correspond to a fact? Perhaps you might say that it corresponds to the fact that it doesn't correspond to a fact? But it would seem that that reasoning would have to be said of every sentence that doesn't correspond to a fact, and so falsity itself would be self-defeating according to the correspondence theory of truth. Or if (2) isn't a contradiction then the liar paradox is solved: liar-like sentences do not correspond to a fact. Rather than being contradictions they're redundant, as (2) appears to show.

(And in fact the above applies to the stronger "this sentence is not true" form of the paradox).

Or if we don't like the correspondence theory of truth:

3. "This sentence does not cohere with some specified set of sentences" does not cohere with some specified set of sentences
4. "This sentence has not been proved" has not been proved
5. "This sentence does not warrant assertion" does not warrant assertion
etc.

Another consideration; what if we drop the use of the word "false" and replace it with some substantial notion of falsity? — Michael

It's best not to oppose false with true. This is because a true and honest statement may be demonstrated to be unjustifiable (false). So "false" is best presented as unjustifiable, which is not the same as untrue (dishonest).

and meaning rests on definition — RussellA

I think the heap puzzle is a clear enough counterexample to that general assertion.

Meaning rests on, or is, usage: some of it agreed, some controversial. Whether 10 grains constitutes a heap is controversial. But a million grains is an obvious case. And obvious cases and obvious non-cases are sufficient to guide usage, for many words. We don't need a dictionary or manual.

The Sorites Paradox is only a paradox because it requires a definition that does not exist. — RussellA

If by definition you now mean threshold or cut-off point, then yes, and I agree. But then it's "only" a paradox because ordinary usage is perfectly meaningful without such definition.

Are scrawlings on a page or vibrations in the air true? — hypericin

Some of them are sentences, and some of those are true, yes. Meaning, some them are what we choose to point the word "sentence" at, and some of those are what we choose to also point the word "true" at.

Absurd, this is an obvious category error. They are symbols, only their interpretations can be true or false. — hypericin

What are interpretations? I would say: sentences that help us construe symbols as pointing at things. What would you say?

What are interpretations? I would say: sentences that help us construe symbols as pointing at things. What would you say? — bongo fury

Interpretations are the meanings we construe from sentences. Meaning is what the sentence points to, not the sentence itself. It is the signified, not the signifier.

Meaning is not something in the world either, it is something in the head (otherwise, how can we make sense of abstractions, lies, or fictions?).

We can express meanings with sentences in one language or another, with body language, with pictures.

Sentence, meaning, worldly referent are all not identical, do you agree?

Meaning is not something in the world either, it is something in the head (otherwise, how can we make sense of abstractions, lies, or fictions?) — hypericin

Hilary Putnam famously claimed that ‘meanings just ain’t in the head’. He meant by this that what our language concepts refer to in the world determines their meaning. He illustrated this with his twin earth experiment.

https://www.quora.com/What-did-Hillary-Putnam-mean-by-meanings-just-aint-in-the-head

Meaning is not something in the world either, — hypericin

Agreed.

it is something in the head — hypericin

It is invented, or pretended, by people using their heads, but that doesn't locate it in the head.

(otherwise, how can we make sense of abstractions, lies, or fictions?). — hypericin

See the link above.

Sentence, meaning, worldly referent are all not identical, do you agree? — hypericin

The second is our pretended connection between the first and third.

He illustrated this with his twin earth experiment. — Joshs

I'd come across this at some point before, I found it very unconvincing, then and now.

I would say that Putnam is conflating meaning and referent.

The meaning of "the water is cold" is the same on Earth and Twin Earth. We can see this by the fact that it would translate to the same sentences in other languages on both planets.

It just so happens that the worldly referent on Twin Earth is different.