• MindForged
    474
    What they both have in common is that the full sentence appears truth-apt (since it has a subject and a predicate) until, of course, the content of the sentence is analyzed and the subject is found to not support the predication. It's a category mistake (as Michael earlier noted).

    I agree that your example is a category mistake, but that's because it's trying to predicate truth on an object which cannot bear it, whereas sentences (such as what the Liar refers to) are arguably truth-bearers, so your analogy seems flawed.

    Then we are using "grounded" in a different way. I mean that the subject is resolved and supports the predication, whatever it may be. In this case, the subject doesn't support the grounded predication and so the sentence isn't truth-apt. (BTW, this was essentially Gilbert Ryle's solution to the liar-style sentences rather than Kripke's.)

    Then this does appear to be a rejection of self-reference (I'm not familiar with Ryle's attempt at resolving it). But it seems spurious since it's treating truth and falsity predicates differently than other predicates. No one denies that "This sentence has five words" or "This sentence is in English" by saying the predicates cannot be supported. These seem to be sentences, and if sentences are the correct objects to bear truth I'm not sure how Ryle's solution addresses that. There's also Quine's formulation (which lacks the demonstrative "this") which I think was a response to Strawson:

    "yields a falsehood when proceeded by its negation" yield a falsehood when proceeded by its negation.

    Self-reference is generally fine. For example, "this sentence has ten words". The truth or falsity of this doesn't depend on the subject being truth-apt, only that its words can be counted. That is a valid predication and so the sentence is truth-apt.

    But the point I was making was that both sentences are constructed the same, the only difference is their respective predicates. The subject of each sentence makes reference to a sentence (themselves) and applies some predicate to them. The predicate "has X words" is allowed, what distinguishes that from "is false"?

    If you agree the sentence is ungrounded, that entails that it is true, which contradicts being ungrounded.
    — MindForged

    It doesn't entail that since the sentence doesn't support truth predication (because, in turn, the subject of the sentence doesn't support grounded predication). But you're treating it as if it does.

    But why doesn't it support it? And also, "grounded" isn't a truth-predicate. Prior you said that ungrounded sentences are meaningless, yes? "This sentence is ungrounded" is not applying a truth-predicate to itself, it merely asserts (as the solution purports) that it's ungrounded (which means it's true). And since it doesn't make reference to a truth-predicate it seems like that objection is flawed.
  • Andrew M
    469
    whereas sentences (such as what the Liar refers to) are arguably truth-bearersMindForged

    Here is Ryle's argument which I think explains the issue well:

    The same inattention to grammar is the source of such paradoxes as 'the Liar ', 'the Class of Classes ...' and 'Impredicability'. When we ordinarily say 'That statement is false ', what we say promises a namely-rider, e.g. '... namely that to-day is Tuesday'. When we say 'The current statement is false' we are pretending either that no namely-rider is to be asked for or that the namely-rider is '... namely that the present statement is false'. If no namely-rider is to be asked for, then 'The current statement' does not refer to any statement. It is like saying 'He is asthmatic' while disallowing the question 'Who?' If, alternatively, it is pretended that there is indeed the namely-rider, '... namely that the current statement is false', the promise is met by an echo of that promise. If unpacked, our pretended assertion would run 'The current statement {namely, that the current statement [namely that the current statement (namely that the current statement ...'. The brackets are never closed; no verb is ever reached; no statement of which we can even ask whether it is true or false is ever adduced. — Gilbert Ryle, Heterologicality

    Thus the liar sentence is not truth-apt. It doesn't actually assert anything.

    "This sentence is ungrounded" is not applying a truth-predicate to itself, it merely asserts (as the solution purports) that it's ungrounded (which means it's true).MindForged

    The ungrounded sentence has the infinite recursion problem as well and so also doesn't actually assert anything. As with the liar sentence, it's a category mistake to say that it is true (or false).
  • MindForged
    474
    The same inattention to grammar is the source of such paradoxes as 'the Liar ', 'the Class of Classes ...' and 'Impredicability' (Ryle)
    [..]
    Thus the liar sentence is not truth-apt. It doesn't actually assert anything

    So the issue is with impredication (what I earlier called self-predication), which is how I construed this resolution earlier. I don't think this works for a number of reasons. The sentence "The tallest person in this room" is just as impredicative as the Liar, as its subject depends on a set of which it is itself a member. Or even just take my earlier example, "This sentence is an English sentence." Ryle's solution makes that sentence a nonsense sentence, since we run into his so-called "name-rider problem":

    "This sentence is an English sentence."
    What sentence?
    "The current sentence {The current sentence [The current sentence...

    This is just as is impredicative as the Liar (the only difference is the predicate they put onto themselves), and so as with Russell's version of type theory, this renders scores of seemingly comprehensible sentences into nonsense. And I suspect this is why Ryle's solution isn't mentioned very often nowadays since it eliminates self-reference entirely.
  • Andrew M
    469
    So the issue is with impredication (what I earlier called self-predication),MindForged

    The issue as I see it is not impredication, but whether the sentences in question have a truth-apt use.

    "This sentence is an English sentence" would ordinarily be unpacked as, "The sentence 'This sentence is an English sentence' is an English sentence". The inner sentence is not being used as an expression but is only being mentioned. If it were used as an expression, then infinite recursion would result.

    Now consider a similar unpacking for the liar sentence, "The sentence 'This sentence is false' is false". For the outer 'false' to be predicable of the inner sentence, the inner sentence must be an expression. But since it is only being mentioned, it doesn't support truth predication. So it's a category mistake. Whether a category mistake or an infinite recursion, no truth-apt use is available for the liar sentence.
  • MindForged
    474
    The issue as I see it is not impredication, but whether the sentences in question have a truth-apt use.

    But your quote of Ryle said that the issue was the use of impredicative definitions:
    The same inattention to grammar is the source of such paradoxes as 'the Liar ', 'the Class of Classes ...' and 'Impredicability'. — Gilbert Ryle

    A far as I can tell, Ryle's argument is that the sin of the Liars family of paradoxes is that they make use of impredicative definitions, they are part of the thing they are defining, and that by doing this you can never get down to a truth-apt sentence because it the subject expands indefinitely.

    "This sentence is an English sentence" would ordinarily be unpacked as, "The sentence 'This sentence is an English sentence' is an English sentence". The inner sentence is not being used as an expression but is only being mentioned. If it were used as an expression, then infinite recursion would result.

    That's not how Ryle's analyzed the Liar though. His claim is that the impredication never gets anywhere, and so when run against "This sentence is an English sentence", it would, when you ask for the "namely-rider" come out (as per your Ryle's quote): "Namely, the current sentence{namely, the current sentence etc. That supposedly unbridgeable gap to the verb is, on Ryle's account the problem and impredication is his diagnosis of the cause.

    Now consider a similar unpacking for the liar sentence, "The sentence 'This sentence is false' is false". For the outer 'false' to be predicable of the inner sentence, the inner sentence must be an expression. But since it is only being mentioned, it doesn't support truth predication. So it's a category mistake. Whether a category mistake or an infinite recursion, no truth-apt use is available for the liar sentence.

    That's not Ryle's analysis then, at least not from what you quoted (Ryle's said that the sentence cannot even get to the verb, so the inner sentence would expand indefinitely when you try to identify the subject). Your analysis here doesn't make sense to me. Try this: "The sentence 'Snow is white is true' is true". The inner sentence is clearly true, we can predicate truth there. If "snow is white" is true, we can validly assert that "The sentence 'snow is white is true' is a true sentence". The outer sentence is just the metalanguage to the object language of the inner sentence. Ironically enough, doing this in natural language allows for Liar sentences to be validly formed (as per Tarski), because you used English as both the metalanguage and the object language.
  • Andrew M
    469
    A far as I can tell, Ryle's argument is that the sin of the Liars family of paradoxes is that they make use of impredicative definitions, they are part of the thing they are defining, and that by doing this you can never get down to a truth-apt sentence because it the subject expands indefinitely.MindForged

    Ryle is arguing against cyclic expressions (fillings of their own namely-riders), but he is not arguing against mentions of the referring expression (where quotation-marks have to be employed). As he says in the same paper:

    Many of the Paradoxes have to do with such things as statements about statements and epithets of epithets. So quotation-marks have to be employed. But the mishandling which generates the apparent antinomies consists not in mishandling quotation-marks but in treating referring expressions as fillings of their own namely-riders. — Gilbert Ryle, Heterologicality

    His claim is that the impredication never gets anywhere, and so when run against "This sentence is an English sentence", it would, when you ask for the "namely-rider" come out (as per your Ryle's quote): "Namely, the current sentence{namely, the current sentence etc.MindForged

    Yes, an infinite expansion results if the subject is always a truth-evaluable expression (as is indicated with the nested brackets). But that's not how we ordinarily use that sentence. Instead the referring expression is only mentioned (which I unpacked and indicated with quotation-marks in my previous post), not used as an expression. That's the use-mention distinction.

    As explained in my previous post, that specific use would result in a category mistake for the liar sentence, since a mention of the referring expression would not be truth predicable.

    Try this: "The sentence 'Snow is white is true' is true". The inner sentence is clearly true, we can predicate truth there. If "snow is white" is true, we can validly assert that "The sentence 'snow is white is true' is a true sentence"MindForged

    That's fine. There's nothing wrong with nested expressions. The problems only arise with cyclic expressions.
  • MindForged
    474
    Ryle is arguing against cyclic expressions (fillings of their own namely-riders), but he is not arguing against mentions of the referring expression (where quotation-marks have to be employed). As he says in the same paper:

    The Liar isn't cyclic though. The subject of "This sentence is false" is the same as the subject of "This sentence is an English sentence".

    Yes, an infinite expansion results if the subject is always a truth-evaluable expression (as is indicated with the nested brackets). But that's not how we ordinarily use that sentence. Instead the referring expression is only mentioned (which I unpacked and indicated with quotation-marks in my previous post), not used as an expression. That's the use-mention distinction.
    As explained in my previous post, that specific use would result in a category mistake for the liar sentence, since a mention of the referring expression would not be truth predicable.

    I don't follow you here. Both expressions have the same subject (the very sentence itself), so if the expansion occurs on one I can't see what feature doesn't cause it in the other. You say it's a use-mention error, but how so? Your rendering of the Liar came out as:

    "The sentence 'This sentence is false' is false"
    And then you concluded that
    For the outer 'false' to be predicable of the inner sentence, the inner sentence must be an expression. But since it is only being mentioned, it doesn't support truth predication.

    But this applies exactly the same to the "The sentence 'This sentence is an English sentence' is an English sentence". The inner sentence is only being mentioned, so is it a category mistake? I don't think it is. This is not a use-mention issue, the inner sentence is capable of being true even if it's only being mentioned. "2+2=4" is true, for example. Your rendering of the Liar is fine for my purposes though. If "This sentence is false" is a false sentence, then it is also a true sentence and that's the contradiction!

    That's fine. There's nothing wrong with nested expressions. The problems only arise with cyclic expressions.

    I don't follow you here. The sentence is structured no differently. What makes one a nested sentence while the other commits a use-mention error?
  • Luke
    122

    I don't really understand your "revenge paradox".

    As I understand it, the paradox of the Liar Paradox is that IF "This sentence is false" is true then it's false, and if false then it's true.

    But this is not the same for "This sentence is meaningless", which if true is meaningless, and if false is meaningful. I don't see a paradox here. It is false.
  • MindForged
    474
    Well to be fair I goofed a bit. The Revenge Paradox is actually "This sentence is not true", which covers the meaningless case I gave, since "meaningless" falls under "not true".

    But to take the meaningless case, it's simple why it's a Liar sentence for the same reason as the above (although I need to change it a bit since I think you're right). If "This sentence is either false or meaningless" is true, the sentence is both meaningless and true or true and false, which are contradictions. After all, presumably the point of labeling the Liar "meaningless" is to deny the Liar a truth-value so one can escape the situation where picking one truth-value gets you the other one too. But that means that it both lacks a truth-value (because it's meaningless) and is true (has a truth-value). Otherwise it's both true and false again. And if that sentence is itself meaningless, it's true and meaningless.
  • Andrew M
    469
    This is not a use-mention issue, the inner sentence is capable of being true even if it's only being mentioned.MindForged

    This is the key issue. My claim is that a sentence is only capable of being true or false if it is used (i.e., expressed).

    Consider the sentence, "'Snow' has four letters and is cold". Snow is mentioned, but that mention is not something that can be cold, only the snow itself is. So the "is cold" predication is a category mistake (specifically, a use-mention error). However we could apply an interpretive rule and say that in such circumstances, the "is cold" predication disquotes the mention and so is really saying that snow is cold. This would unpack as, "'Snow' has four letters and snow is cold". Such a rule would tolerate the above sentence and allow it to be truth-apt.

    Now compare that with "'2+2=4' has three numbers in it and is true". My claim is that the mention of '2+2=4' is not something that can be true, but the expression (or use) of '2+2=4' is. If so, then the truth-predication disquotes the mentioned expression and uses it. This would unpack as, "'2+2=4' has three numbers in it and 2+2=4".

    Since "This sentence is an English sentence" doesn't contain a truth-predicate, the referring expression is only mentioned, not used (i.e., only the surface aspects of the sentence are referred to). Whereas in the liar sentence, the truth-predication disquotes the mention and uses the referring expression. Thus it is cyclic.
  • MindForged
    474
    Consider the sentence, "'Snow' has four letters and is cold". Snow is mentioned, but that mention is not something that can be cold, only the snow itself is. So the "is cold" predication is a category mistake (specifically, a use-mention error). However we could apply an interpretive rule and say that in such circumstances, the "is cold" predication disquotes the mention and so is really saying that snow is cold. This would unpack as, "'Snow' has four letters and snow is cold". Such a rule would tolerate the above sentence and allow it to be truth-apt.

    That's not really the sort of sentence I used. I didn't say the Liar was " 'This sentence' is false". "This sentence" cannot have the property of truth. But I think it's worse for your approach if you apply that interpretive rule. Then the expression just becomes the Liar sentence because the falsity-predicate disquotes the phrase "this sentence" and transforms it into " 'This sentence' is false is false and this sentence is false." That's just a conjunction of Liar Paradoxes.

    Now compare that with "'2+2=4' has three numbers in it and is true". My claim is that the mention of '2+2=4' is not something that can be true, but the expression (or use) of '2+2=4' is. If so, then the truth-predication disquotes the mentioned expression and uses it. This would unpack as, "'2+2=4' has three numbers in it and 2+2=4".

    I know that's the contention but you haven't explained why truth and falsity predicates are subject to a different set of rules than other predicates which can apply to quoted sentences. We both agree the expression that is quoted can be attributed truth. The difference seems to be (correct me if I'm wrong) that you think the following quote cannot be predicated truth while I think it can:

    " '2+2=4' is true"

    On your view, does this work? Can you predicate truth of a mentioned expression? I think you can, provided the mentioned expression is the sort of thing that can bear truth. Some mentions are truth-y, the expression mentioned just has to have the right kind of structure. The Liar has that structure. This solution is the same sort of solution Kripke tried and I don't think it works.

    Since "This sentence is an English sentence" doesn't contain a truth-predicate, the referring expression is only mentioned, not used (i.e., only the surface aspects of the sentence are referred to). Whereas in the liar sentence, the truth-predication disquotes the mention and uses the referring expression. Thus it is cyclic.

    OK, I think this runs into an issue I mentioned earlier to another user (assuming that user wasn't you, too lazy to check). Take the following:

    This sentence is true.

    Now that's an odd sentence, but it doesn't even have the appearance of a paradox, unlike the Liar. Under the rule you mentioned, it comes out as

    "The sentence 'This sentence is true' is true and this sentence is true"

    Well, that conjunction is obviously true under this interpretive rule, both conjuncts come out as true because the mentioned sentence is transformed into a use of the quoted expression. But that means that impredicative truth assignment cannot be sufficient to say the Liar is a category mistake. And note, Ryle specifically calls out impredication as the issue here (just look at the passage you quoted, he names "Impredicability").
  • Andrew M
    469
    I know that's the contention but you haven't explained why truth and falsity predicates are subject to a different set of rules than other predicates which can apply to quoted sentences.MindForged

    There needs to be a way to convert a mention to a use and using the subject-predicate form is an efficient way to do that.

    " '2+2=4' is true"

    On your view, does this work?
    MindForged

    Yes. To say "'2+2=4' is true" is to say "2+2=4". That is, truth predication of a mentioned expression uses the expression. So it's the inverse of quoting.

    This sentence is true.MindForged

    The truth-teller sentence cycles for the same reason as the liar sentence. Here's the iterative unpacking (the => is just an arrow to indicate the transformation steps):

    "This sentence is true" => "'This sentence is true' is true" => "This sentence is true" (truth predication rule). So we have a cycle.

    Compare with unpacking the liar sentence:

    "This sentence is false" => "'This sentence is false' is false" => "Not ('This sentence is false' is true)" => "Not (This sentence is false)" => "Not ('This sentence is false' is false)" => "'This sentence is false' is true)" => "This sentence is false". So we also have a cycle.

    And compare with the English sentence:

    "This sentence is an English sentence" => "'This sentence is an English sentence' is an English sentence" => true. So it's truth-apt.
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