He's right, since he is talking about formal languages. — Banno
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.
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 = xn and pn, the symbols 'x1', 'x2', ... , 'xn' being replaced by structural descriptive names of all the sentences of the language investigated and 'p1', 'p2', ... , 'pn' by the corresponding translation of these sentences into the metalanguage.
This seems to be the only definition of truth that Tarski offers: — Michael
That's besides the point. — Banno
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.
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∞"
"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
the totality of possible substitutions for the symbol 'x' is here restricted to quotation-mark names.
In English, which sentences can we not turn onto quotation-mark names? — Banno
"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
facts are things in the world — Banno
Facts are things in the world - as you said. — Luke
In English, which sentences can we not turn onto quotation-mark names? — Banno
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.
And my reply is that for Tarski, that is correct. But it has been used as such since his work. — Banno
And perform a universal generalisation to getFred is true IFF snow is white
U(x) Fred is true IFF x
But your point continues to escape me. — Banno
(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.
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. — Michael
What could a truthful account of an event be if not an accurate portrayal of what happened? — Janus
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
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
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
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? — Michael
and meaning rests on definition — RussellA
The Sorites Paradox is only a paradox because it requires a definition that does not exist. — RussellA
Are scrawlings on a page or vibrations in the air true? — hypericin
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? — bongo fury
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
Meaning is not something in the world either, — hypericin
it is something in the head — hypericin
(otherwise, how can we make sense of abstractions, lies, or fictions?). — hypericin
Sentence, meaning, worldly referent are all not identical, do you agree? — hypericin
He illustrated this with his twin earth experiment. — Joshs
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