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Perplexed comments on Unsolved Problems in Philosophy Part 1: The Liar's Paradox - Less Wrong
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Comments (130)
The issue where? Are you saying that this thread is about language, rather than truth? Or that my example, as written, is about language rather than (as intended) about truth?
I'm a bit surprised that anyone could conceive of a concept of truth independent of language. I've always considered truth as an attribute of sentences - linguistic objects. Perhaps I am missing your point.
As for your example, yes, I would say that it does point out something interesting, though already known, about the concept of color. That valid classification systems based on this criterion may disagree. This is also true of truth and logic. Some people say that the Liar statement is neither true nor false. Some people say that it is both true and false. Both can be correct, depending on what else they claim.
"Snow is white" is true if, and only if, snow is white - Tarski's material adequacy condition - only makes sense if there is a fact of the matter about whether or not snow is white independent of language.
Tarski left out some of the fine print. That "if and only if" works only under the prior assumption that "snow" designates snow, "white" designates white, and "is" designates the appropriate infix binary relation.
In other words, "Snow is white" is true only if we know that "Snow is white" is a sentence in the English language.
Not really. If "snow" designates grass, and "white" designates green, then "'snow is white' is true if and only if snow is white" is still correct. Same if "snow" designates the sky and "white" designates green.
I'm afraid I don't understand your point.
It should have read: "Same if "snow" designates the sky and "white" designates blue."
It was apparently a nitpick of your first paragraph, ignoring your second paragraph.
That can't be right. If he both misinterpreted 'prior assumption' and made a serious typo, his comment would not have been twice upvoted, would it?
If you can't take as a given that statements actually are in the language they appear to be in no statement can have any knowable truth value. If "snow" in the utterance is a word in the same language as the identically spelled word in the statement, and the same for "white" (and "is"), and the rest of the statement means exactly the same as it does in English then the statement is still correct. But if "white" might designate orange "true" might just as well designate bubblegum or "only" designate "to treat like a second cousin".
And further the grammar of English is being assumed... as well as the very concept of languages.
Let me see if I understand you. "Snow is white" is true if and only if "snow" means snow, "is" means is, "white" means white, and snow is white? Because that still only makes sense if there's a fact of the matter about whether or not snow is white. And as ata pointed out, it's also false.
Edit: Maybe Tarski's undefinability theorem applies here. It says that no powerful formal language can define truth in that language. So if, as you say, truth is an attribute of linguistic objects, you have to invoke a metalanguage in which truth is defined. Then you need a meta-meta-language, etc. Of course English is not a formal language, and there is no formal meta-language for English - we talk about the truth of English sentences in English - but that is my point, that it relies for certain things on non-linguistic definitions. When we start discussing sentences like "This sentence is false", there's a tendency to forget that English does not and cannot define the truth of all English sentences.
No, that is not what I said. I said that IF "snow" means snow, "is" means is, and "white" means white, THEN "Snow is white" is true iff snow is white.
I never denied that. But the fact has nothing to do with truth unless you bring language into the discussion. Only linguistic objects (such as sentences) can be true.
Somehow, I feel that we are talking past each other.
ETA:
And now I know we are talking past each other.
That makes a lot more sense, thanks.
I think we're getting somewhere. I thought that you were saying that whether or not a statement is true is a property of language. Tarski's saying that whether or not a sentence is true is determined by whether it corresponds to reality. You're saying that whether or not it corresponds to reality is determined by the meaning the language assigns to it.
I'm still not convinced that truth is to do with language, though. Consider a squirrel trying to get nuts out of a bird-feeder, say. The squirrel believes that the feeder contains nuts, that there's a small hole in the feeder, and that it can eat the nuts by suspending itself upside down from a branch to access the hole. The squirrel does actually possess those beliefs, in the sense that it has a state of mind which enables it to anticipate the given outcome from the given conditions. The beliefs are true, but I'm certain that the squirrel is not using a language to formulate those beliefs in.
That sounds right. I think if we describe a sentence as being "true" then we're really saying that it induces a possibly-nonverbal mental model of reality that is true (or very accurate), but we can say the same about mental models that were nonverbal to begin with.
Can you clarify more exactly what you mean by "valid?" Because my initial reaction is that of course, you can come up with many classification systems for any set of things. It's not yet clear to me what interesting thing we can take away about how people are using the classifications of "true" and "false", other than the fact that they don't work very well for classifying certain unusual statements.
It seems to me that we have seen people in this thread advocate two value logics, three value logics, and four value logics. You can have workable systems of logic with and without the law of the excluded middle, and with and without a law of contradiction. There are intuitionistic logics, relevance logics, classically consistent and paraconsistent logics. To say nothing of linear logic, modal logics, and ludics.
Follow the links to the SEP articles on dialethi and paraconsistency. And then follow the citations from there to learn that logic is pretty big and flexible field.
The latter, though the former might also be the case.
"Independent of language" as in independent of the conventions of English, or Chinese, or Python, or street signs, or dolphin calls or whatever, not removed everything that could bear it.
Well, arguing about words is not very interesting to me, nor is the insight that words are just conventions and to a large degree arbitrary.