(Is it Wednesday already? Oh well, better late than never....)
I've argued that, if (as I think) the truth predicate/operator is just a device used to assert things (just as the falsehood predicate/operator is just a device used to assert their negations), it can pretty clearly only be meaningfully applied when there is something there to be asserted--thus, it can only be meaningfully applied to claims about something other than truth. Thus, for example, in a Yablo-like series of sentences where each sentence ascribes truth to the next sentence in the series,
T1: T2 is true.
T2: T3 is true.
T3: T4 is true.
....and so on forever, all the sentences in the infinite series are literally as devoid of meaning as strings of nonsense syllables, or 'Colorless green ideas sleep furiously.' If, on the other hand, sentence T1000000 is "Snow is white," the rest of the sentences inherit their meanings (and, thus, truth-values) from that.
A semantic property pretty clearly *unlike* truth in this respect is meaningfulness itself. If the meaningfulness predicate only applied to meaningful sentences, it wouldn't fulfill its sole communicative function of separating out the meaningful sentences from the meaningless ones. This is important when we consider (18), which, by analogy to the Liar, we can call The Babbler:
(18) Sentence (18) is meaningless.
If (18) is true, it's both true and meaningless, therefore both meaningful and meaningless, and, of course, if it's meaningless, it's both true and meaningless, therefore both meaningful and meaningless. As such, on pain of contradiction, (18) had better just be false.
Fortunately, in light of the above, we have a good principled reason to think that this is indeed the case. If the function of the meaningfulness predicate is to separate out the meaningful from the meaningless sentences, it has to apply to all sentences. Therefore, it's meaningful to say of any sentence that it's meaningful or meaningless, regardless of the nature of the sentence we're talking about. As such, if all a sentence does is assert a view about the meaningfulness of some sentence, even itself, there's no reason for it not to be meaningful. Thus, (18) is false and (19):
(19) Sentence (19) is meaningful.
...is true.
One important principle, underlying the whole business of revenge-paradoxology, is worth calling attention to here, since I've been implicitly using it a lot. Given these sorts of examples, or, better yet, cased like (20) and (21):
(20) This sentence has seven words in it.
(21) This sentence has twenty words in it.
....where it would be clearly absurd to assert about sentence (20), for example, that is seven words long, without granting that sentence (21) is true, we have what we can call the Meaningfulness of Self-Reference Principle: "If Sentence X has property Y, and Sentence X *states* that Sentence X has property Y, then Sentence X is true (and thus, of course, meaningful)."
With all that in mind, and the demonstrations in Parts II and III that it clearly is possible to engage in apparent reasoning about even the most clearly meaningless sentences--meaning that it's not a problem for meaninglessness solutions to the Liar that it's "clearly possible to reason about it, and we all know what does and doesn't follow from it"--let's turn to the apparently troubling revenge paradox for my view that I ended with last time:
(17) Sentence (17) is one that one would have to ultimately label as "false" if one treated it as being meaningful and went through the motions of "reasoning" about it without making the sort of mistake we would regard in normal contexts as a mistake in reasoning.
So, playing along with the game of treating it as meaningful for a moment, an obvious first question is this:
Does (17) take a stand on the question of its own meaningfulness? In other words, does it (a) say of itself that it's meaningful, (b) say of itself that it's meaningless, or (c) remain neutral on that topic?
The wording strongly suggests that (a) would be the wrong gloss--talk of treating it 'as meaningful' and 'going through the motions' strongly suggests that the point is to, at the very least, keep open the possibility that it's meaningless, if not to actively assert it. That said, if (a) is right--it's taking a stand on its own meaningfulness in the directing of asserting it--then to say that, if one went through the motions of reasoning about it, one would make something we would regard in other contexts--i.e. really reasoning about meaningful things--as a mistake, is to say that, if one reasoned about it and failed to come to the conclusion that it was false, one would be making a real, full-fledged mistake in reasoning--a factual mistake, landing us with the wrong answer. In other words, given (a), (17) is just a normal if un-usually phrased Liar sentence, the normal meaninglesness solution applies to it, and the Principle of the Meaningfulness of Self-Reference is not violated if we simultanneously say of it that, although meaningless, going through the motions seems to get us the result that it's false (and true), given that what it's saying is that this isn't a matter of going through the motions in an empty context, because it really is false. (It can be neutral about its own falsehood, given that it asserts its own meaningfulness and thus converts the neutral-sounding language about apparent mistakes into, in effect, the positive claim that one would be making a substantive mistake and getting the wrong result.)
If (b) is the case, then we have a disguised conjunction of two claims: (i) a claim about its alleged meaninglessness, and (ii) a claim about whether any possible analysis of it that (1) took it as meaningful and (2) failed to include any mistakes unrelated to the meaningfulness question would therefore (3) diagnose (17) as false. There's a lot to untangle here, but suffice to say that if it is meaningless, then the true 'first conjunct' asserting as much doesn't make the whole thing meaningful, for reasons examined when we looked at (2), above, and if it's not meaningless, the falsity of the first conjunct guarantees the falsity of the whole thing without fear of contradiction. Really, though, I think the most natural reading is (c), and that's where the real problem seems to be.
If (c) is, then, the case, as should be clear by now, (17) really amounts to a disguised disjunction between the claim that (i*) reasoning about (17) and failing to come to the conclusion that it's false would be a *factual* mistake, and (ii*) that 'reasoning' about (17) leads us to the apparent conclusion that it is false, but only because we're indulging a nonsensical category mistake. In other words, given (c), what we end up with is a disguised version of sentence (2), above:
(2) The sentence marked (2) is either false or meaningless.
...which we already dealt with in Part I. Since I enjoy the circularity of ending by directing back to the first post in the series, I think I'll just leave off there and throw open the floor to questions, comments and devastating objections.
Subscribe to:
Post Comments (Atom)
21 comments:
If (18) is true, it's both true and meaningless, therefore both meaningful and meaningless
After reading this series, I'd like to hear you express a really precise definition of "meaningful". I'm not positive you're using the word consistently.
(17) Sentence (17) is one that one would have to ultimately label as "false" if one treated it as being meaningful and went through the motions of "reasoning" about it without making the sort of mistake we would regard in normal contexts as a mistake in reasoning.
Likewise for "normal contexts".
If you're trying to make your logical system consistent, you probably don't want "all true prepositions are meaningful" as an axiom. That leads directly to self-contradiction, as you point out.
It's an easy bullet to bite: "'This sentence is true', even if true, is still meaningless." It's a set of symbols without a referrent, and you can't derive anything interesting from it (though you can do all sorts of trivial derivations, e.g. "'This sentence is true' is true").
To be clear, I don't disagree with your conclusion that (17) works out to "this sentence is false or meaningless" and that such a paradox, no matter how vengeful, sill lacks meaning. I just don't see how the intermediate bit about (18) and (19) makes sense.
And I meant "propositions". Argh.
L33tminion,
"....you probably don't want 'all true prepositions are meaningful' as an axiom. That leads directly to self-contradiction, as you point out."
How?
I don't think I pointed out, in so far as I'm pretty sure I don't believe it. Should I?
You say:
If (18) is true, it's both true and meaningless, therefore both meaningful and meaningless
Later you say:
then Sentence X is true (and thus, of course, meaningful)
If you don't believe that all true propositions are meaningful, why do those follow?
(Or are you just limiting that to "sentences that say true things about themselves are meaningful"?)
"If you don't believe that all true propositions are meaningful, why do those follow?"
But I do believe all true propositions are meaningful (just as, of course, all false propositions are meaningful). That's as conceptually obvious as anything about truth can be--you have to be saying something to be saying something true! (Or false, of course.)
But you seemed to be suggesting I thought the opposite:
"....you probably don't want 'all true prepositions are meaningful' as an axiom. That leads directly to self-contradiction, as you point out."
So, for the record, no, I don't believe that the claim that 'all true propositions are meaningful' leads to self-contradiction. See Part I for my line about how to handle cases that, on the surface, might seem to show this--e.g. "This sentence is either false or meaningless."
Hmmm, okay, I see your argument now. But I still don't see how that connects to (18) and (19), especially when you consider versions of (2) without an explicit "or".
Consider this argument:
A: "This sentence is not true" is meaningless
B: Doesn't that mean it's true?
A: No.
With (18), the argument goes something like:
A: "This sentence is meaningless" is meaningless.
B: Doesn't that mean it's true?
A: Yes.
B: Isn't that a contradiction?
A: Yes, so I guess it's actually false (and meaningful).
But it could just as well go:
A: "This sentence is meaningless" is meaningless.
B: Doesn't that mean it's true?
A: No.
Why do you take the former route with (18) instead of the latter?
"Consider this argument:
A: "This sentence is not true" is meaningless
B: Doesn't that mean it's true?
A: No."
Right. It's a category mistake to apply truth talk to meaningless sentences (or coughs, or bits of burning candle wax), and no less of a category mistake when we're saying that they're untrue rather than that they're true. Given the (robustly disquotationalist) assumption that truth ascriptions must inherit the meaning of whatever statement they attribute truth to, it just follows that truth talk doesn't meaningfully apply to any items other than meaningful declarative statements. Fortunately for those robustly disquotationalist assumptions, this result exactly lines up with pre-philosophical common-sense--it seems nonsensical to say that a cup of coffee is untrue, in quite the same way as to say that it's true.
(Of course, if we switch from 'untrue' to 'not true', the sharp edge of counter-intuitiveness is blunted somewhat. I'd argue that's not because there's a real distinction there, but because we often use 'not true' in a loose, sloppy way, to mean something like 'we'd be making some sort of mistake if we said such-and-such was true' rather than in the strict sense of 'the negation of the sentence is true.')
"With (18), the argument goes something like:
A: "This sentence is meaningless" is meaningless.
B: Doesn't that mean it's true?
A: Yes.
B: Isn't that a contradiction?
A: Yes, so I guess it's actually false (and meaningful)."
Well, that assumes that the only reason to say that it's false is contradiction-avoidance. That's certainly one very important reason, but we can do better. Given the nature of the truth predicate (see above), it only meaningfully applies to meaningful sentences. With the meaningfulness predicate, however, the whole point is to be able to differentiate the meaningful sentences from the meaningless ones--we should, for the predicate to fill its sole communicative purpose, be able to use it to say of meaningless sentences that they're meaningless and meaningful sentences that they're meaningful (and if we ascribe meaningfulness to meaninglessness or meaninglessness to meaningfulness, that's a straightforward *factual* mistake if anything is, not any sort of category mistake), so *of course* meaningfulness talk meaningfully applies to *all* sentences, whether meaningful or meaningless. Given that principle, if Sentence A does nothing but ascribe meaningfulness (or meaninglessness) to Sentence B, Sentence A is *always* meaningful, regardless of whether or not Sentence B is meaningful. So why should it matter if A=B? Given all of that, it just follows that any sentence that (does nothing but) ascribe meaningfulness to itself will be true, and any sentence that (does nothing but) ascribe meaninglessness to itself will be false.
The fact that, given really basic, really standard intuitive assumptions about truth--like, if the referent of a sentence really is the way the sentence says it is, the sentence is true--the claim that "This sentence is meaningless" is meaningless generates a contradiction strikes me as another important reason
to reject the claim, since I don't think any contradictions are true, but the argument for the meaningfulness (and hence falsity) of "This sentence is meaningless" can be run perfectly well without reference to contradiction-avoidance.
"But it could just as well go:
A: "This sentence is meaningless" is meaningless.
B: Doesn't that mean it's true?
A: No."
In the sense that I could just as well abandon not only my own views about truth, but the overlapping consensus of all the views about truth that tend to sound at all plausible to me (i.e. the intersubstitutivity of P and T(P), the T-Schema...), then yes, that's something I could do. But I'd rather not.
That's mostly a satisfying answer, though I still suspect the only thing saving you from a further revenge paradox is an insufficiently precise definition of the word "meaningless".
OK, I'll bite: What do you think are the alternative possible notions of 'meaninglessness' are, such that one or more of them would, if sufficiently clarified, generate contradictions in conjunction with my views about the Liar? And do ordinary, pre-philosophical judgments about meaning (e.g. that "snow is white" means the same thing as "schnee ist weiss") suffer from the same imprecision?
(Of course, one could have all sorts of alternative philosophical *theories* of meaning, but it's not clear to me that this fact alone is sufficient for the sort of ambiguity about the meaning of meaninglessness that you're after. By analogy, much ink has been spilled about competing philosophical theories of possibility and necessity, but that doesn't mean that, when someone asserts that it's physically impossible for objects to accelerate to a speed faster than the speed of light, their claim can't be evaluated until we've sorted out all outstanding questions about modality.)
What do you think are the alternative possible notions of 'meaninglessness' are, such that one or more of them would, if sufficiently clarified, generate contradictions in conjunction with my views about the Liar?
I don't have a specific one at hand, but if I did, wouldn't you just assert that it's not the one you're using? The burden of clarifying your definitions lies on you.
Your process of determining that the Liar is meaningless seems to involve reasoning about it, but reasoning about meaningless sentences is not a meaningful thing to do. Are you asserting that sentences that have a particular set of properties when reasoned about "as if meaningful" are meaningless? What properties? How do those sentences differ from meaningless sentences without that property?
You say you mean "meaningless" in "precisely the ordinary mundane sense", but that's no help. Among other things, there's more than one definition of "meaningless".
Are you really asserting that a string of nonsense syllables is meaningless in the same way as a sentences that asserts something reasonable about a clear referent?
And do ordinary, pre-philosophical judgments about meaning (e.g. that "snow is white" means the same thing as "schnee ist weiss") suffer from the same imprecision?
Sure, but I'd want philosophical judgments about meaning to be more clear.
“I don't have a specific one at hand, but if I did, wouldn't you just assert that it's not the one you're using? The burden of clarifying your definitions lies on you.”
I don’t accept that. You’ve claimed that ‘meaninglessness’ is importantly ambiguous in some way that my argument relies on, but you haven’t told me what the ambiguity is. I see no reason to accept the assertion that ‘meaningless’ is ambiguous until I see some kind of argument for it.
“Your process of determining that the Liar is meaningless seems to involve reasoning about it, but reasoning about meaningless sentences is not a meaningful thing to do.”
Well, of course, there’s obviously some sense in which we can reason about meaningless sentences—e.g. reasoning about whether they are meaningful, reasoning about how many words they have in them and so on. If you mean, though, that we can’t meaningfully reason about what follows from meaningless sentences, since the idea of something ‘following’ from anything other than a meaningful sentence is nonsense, then (a) I agree, but (b) my argument for treating Liars as meaningless does not rely on anything that could even be remotely construed as ‘reasoning’ about Liars in that sense, except for, granted, (c) my arguments against other solutions on the basis of things like revenge paradoxes.
When it comes to (c), though, if the claim is that “it would be impossible to point out apparent mistakes people make while going through the motions of ‘reasoning’ about the ‘consequences’ of actually meaningless sentences”, that seems to be flatly wrong. For an example of how we could go about that process with an uncontroversially meaningless sentence, see Part III and the “Greenness Paradox.”
"Are you asserting that sentences that have a particular set of properties when reasoned about 'as if meaningful' are meaningless?"
No. I'm absolutely not saying that. I'm saying that meaninful sentences that use the truth-predicate/operator necessarily derive the whole of their meanings from the content of the 'true'-free sentences to which they (directly or indirectly) attribute truth. It's simply a consequence of this that sentences involving apparent use of the truth predicate/operator (e.g. "it's true that X", "'X' is true" and so on) where the intended ultimate referent is a non-'true'-free sentence (e.g. the self-referential sense of the phrase "This sentence") are meaningless. I don't see anything about that claim that involves any more reliance on some fuzzy notion of 'what we would regard as some property if it were meaningful' than the parallel (and much less controversial) claim that apparent uses of the greenness predicate (X is green) where the intended referent is "ideas" are meaningless, since color talk simply doesn't meaningfully apply to ideas.
"You say you mean "meaningless" in "precisely the ordinary mundane sense", but that's no help. Among other things, there's more than one definition of 'meaningless'."
If you mean "there's more than one in-depth philosophical theory of what meaninglessness is", that's certainly true, but, I think, irrelevant to the argument at hand), just as, if I hold up a red toy firetruck and say "this is red, so it has a color" I don't have to choose between the various competing philosophical theories of how to understand the notion of color. (Which is, in fact, an arena of philosophical controversy!)
If, on the other hand, you mean "there's hidden ambiguity in ordinary uses of the word 'meaningless' that could be relevant here", then see above. I have yet to see any reason given to back up that claim.
"Are you really asserting that a string of nonsense syllables is meaningless in the same way as a sentences that asserts something reasonable about a clear referent?"
No, but, obviously, I don't accept that Liars are sentences that assert something reasonable about a clear referent. When I said that I thought they were meaningless is precisely the ordinary way--i.e. precisely the same sense in which we'd refer to a string of nonsense syllables, or 'colorless green ideas sleep furiously' as meaningless--I meant it! I don't think Liars (or Truth-Tellers or any other bit of ungrounded truth talk) "assert" anything about anything. They're meaningless.
"And do ordinary, pre-philosophical judgments about meaning (e.g. that "snow is white" means the same thing as "schnee ist weiss") suffer from the same imprecision?"
Sure, but I'd want philosophical judgments about meaning to be more clear."
....and I don't accept that my claim about Liars is any more 'philosophical' than that, except in the sense that the 'snow is white'/'schnee ist weiss' case is uncontroversial (so one doesn't need to formulate philosophical arguments for it), whereas mine needs to be argued for. That said, there's nothing in the argument that relies on taking sides in philosophical debates about how precisely to understand 'meaningfulness'/'meaninglessness'.
If you accept that "snow is white" means the same thing as "schnee ist weiss" without a theory of meaning in your pocket, you've accepted that such is not necessary to justifiably accept a synonmy claim. If you'd go the step further and accept that English sentences ending in "is white" mean the same thing as German sentences with the same subject ending in "ist weiss", still without committing to an overall theory of meaning, you've accepted that such is not neceessary to justifiably accept a whole unified class of synonmy claims. What's the difference between that and accepting my claim that the truth predicate/operator is simply a meaning inheritance device, and that 'empty' attempts to use it are thus necessarily meaningless, without committing to an overall theory of meaning?
I see no reason to accept the assertion that ‘meaningless’ is ambiguous until I see some kind of argument for it.
Sure. There's a difference between a series of nonsense characters with no semantic content ("blorks gblork"), a grammatically-correct sentence where the words all have semantic content but the relations between the words don't ("green ideas sleep furiously"), and a sentence where the words have semantic content and the relationship between the words makes sense but the relationship (or lack thereof) between that sentence and other sentences renders it void of meaning ("this sentence is false", given that "false" is a reasonable thing for a sentence to be).
Those all are "meaningless", if your definition of "meaningless" is sufficiently broad. To assert that those are all meaningless "in exactly the same way" is wildly implausible at best, obviously false at worst.
my argument for treating Liars as meaningless does not rely on anything that could even be remotely construed as ‘reasoning’ about Liars in that sense, except for, granted, (c) my arguments against other solutions
Thanks for conceding that point.
I'm saying that meaninful sentences that use the truth-predicate/operator necessarily derive the whole of their meanings from the content of the 'true'-free sentences to which they (directly or indirectly) attribute truth.
Re-reading, I see that you're consistent about that in earlier posts in the series, but that doesn't apply to your argument that (17) is equivalent to (2). (2) has a truth-predicate, (17) talks about the result of an algorithm, it either spits that sentence into the "false" bin in bounded time or it doesn't. If we're avoiding contradictions, I'd assert that (17) is false (and meaningful), the assertion that it must be labeled false is false. For any formal, contradiction-free system, there are true statements about that system that the system can't prove. So that result isn't surprising.
if I hold up a red toy firetruck and say "this is red, so it has a color" I don't have to choose between the various competing philosophical theories of how to understand the notion of color.
To pull a Dennett: It doesn't prevent you from having a wrong understanding (one that is good enough most of the time yet leads to you being seriously confused in edge-cases).
(If paradoxes aren't an edge-case for boolean logic, I don't know what is.)
No, but, obviously, I don't accept that Liars are sentences that assert something reasonable about a clear referent.
The referent of "this sentence is false" is obviously the sentence "this sentence is false" and "false" is indeed something sentences can be (so that's reasonable in a way that "green ideas sleep furiously" is not). (Yes, I know your argument is that truth-predicates apply only to a subset of sentences, but since whether a sentence is in that class or not can't even be reliably determined by just looking at the sentence, it's a very different objection than "what would it even mean for an 'idea' to 'be green' or 'sleep'?".)
and I don't accept that my claim about Liars is any more 'philosophical' than that
The old "this is not a philosophical argument" philosophical argument? I thought you wanted to avoid contradictions!
If you'd go the step further and accept that English sentences ending in "is white" mean the same thing as German sentences with the same subject ending in "ist weiss", still without committing to an overall theory of meaning, you've accepted that such is not neceessary to justifiably accept a whole unified class of synonmy claims.
"Schnee ist kaukasisch"?
So no. Good enough until you run into ambiguities and edge cases is not necessarily good enough. Depends on the context.
"There's a difference between a series of nonsense characters with no semantic content ('blorks gblork'), a grammatically-correct sentence where the words all have semantic content but the relations between the words don't ('green ideas sleep furiously'), and a sentence where the words have semantic content and the relationship between the words makes sense but the relationship (or lack thereof) between that sentence and other sentences renders it void of meaning ('this sentence is false', given that 'false' is a reasonable thing for a sentence to be)."
Well, I'd argue that "the words all have semantic content but the relations between the words don't" is a pitch-perfect description of why Liars, Truth-Tellers and other bits of ungrounded truth talk are meaningless. For the sake of simplicity, instead of the Liar and 'colorless green ideas sleep furiously', stick with simpler cases, "This sentence is true" and "Ideas are green." In both cases, you have a clear intended referent (i.e. the same words used in other sentences would be referentially clear), but, when you put that together with the predicate, the result is devoid of any possible meaning. Color talk simply doesn't meaningfully apply to ideas, and truth talk doesn't meaningfully apply to anything except for 'true'-free sentences. You're trying to use an assertion-device ("is true") when there's nothing there to be asserted.
Of course, this isn't that different from "blorks geblork", except that "ideas" and "is green" have standard meanings (and "is true" has a standard conventional relationship to the meaning of whatever its applied to, although, I'd argue, it has no standard intrinsic meaning), whereas "blorks" and "geblork" aren't words woth amy stamdard meaning, so they can only have the stipulative meaning some speaker arbitrarily attaches to them. (It's still true that those words, in the context of other sentences, would mean something.)
So it looks like a fairly trivial difference to me, but even if it's not, all we've got is different explanations of *why* some sentence is meaningless, not different senses of meaninglessness. Two women can have divorced their husbands for entirely different and unrelated reasons, but that doesn't make the word "divorce" ambiguous.
So, again, when you say:
"To assert that those are all meaningless 'in exactly the same way' is wildly implausible at best, obviously false at worst."
....I'm utterly un-sold on that point, since I have yet to see any reason or argument of any kind for it. If it's a sheer appeal to intuition, all I can do is uncomfortably shrug my shoulders, since it's not an intuition I share.
"Thanks for conceding that point."
Sure thing, although it's a concession I've been loudly announcing and arguing about for the last four posts.
"The referent of 'this sentence is false' is obviously the sentence 'this sentence is false'..."
Sure, just like the intended referent of the sentence "ideas are green" is clearly ideas.
"...and 'false' is indeed something sentences can be..."
Nope. It's something that meaningful declarative sentences can be, and the whole bone of contention is whether the Liar (and other bits of ungrounded truth talk) is in that category.
The following might be a helpful way of thinking about it:
If you accept, say, correspondence or coherence or whatever, then "false" has a standard meaning across different sentences to which it might be applied, just like the predicate 'is red' has a standard meaning across different objects to which it is applied. If, on the other hand, the meaning-inheritance version of disquotationalism is right, then there is no such standard meaning--if I say that "'snow is white' is false", that just means "it's not the case that snow is white", and if I say that "'grass is green' is false," that just means that "it's not the case that grass is green." So the meaning of the phrase actually varies wildly from sentence to sentence in standard usage, just as the meaning of the colloquial phrase "What he said" does.
"To pull a Dennett: It doesn't prevent you from having a wrong understanding (one that is good enough most of the time yet leads to you being seriously confused in edge-cases)."
If by "pull a Dennett", you're talking about heterophenomenology, that's definitely my friend here! One of the basic points I've argued for at length, and that's central to my whole thesis, is that ordinary speakers can be mistaken about questions of meaningfulness/meaninglessness in the ordinary senses of those words. That seems to be the point doggedly denied by those semantic Cartesians who insist that anyone who claims that large numbers of competent speakers get the Liar's meaningfulness/meaninglessness status wrong must be using the word "meaningless" in some sense that's different from the mundane, ordinary sense that we apply that word to "borks geblork" or "colorless green ideas sleep furiously."
So, yes, meaningfulness/meaninglessness is something we can make mistakes about, just as color is something we can make mistakes about, and the content of our own experience is, and so on. You don't need to convince me of any of that!
....it is, however, irrelevant to the point at hand with the red fire truck. My only point there was, again, that one can rationally, justifiably make judgments about whether something falls into an ordinary, well-understood category ("red", "meaningless") without having to first take sides in a philosophical argument over which theory of how to understand that caregory is correct.
"(Yes, I know your argument is that truth-predicates apply only to a subset of sentences, but since whether a sentence is in that class or not can't even be reliably determined by just looking at the sentence, it's a very different objection than "'what would it even mean for an 'idea' to 'be green' or 'sleep'?'.)"
Yeah, predictably, I disagree with 100% of that. There are, pretty clearly, some sentences ending in 'is true' or 'is false' that you can just look at and tell that the intended referent is that very sentence, or some other sentence that isn't 'true'-free. The phrase "this sentence" might be ambiguous in some contexts, but if I use a disambiguating device like....
$ The sentence marked with a dollar sign is not true.
...then I could most certainly tell just by looking at.
And, in contexts like philosophical discussions, even ordinary uses like "This sentence" are transparently obviously intended to be self-referential at first glance.
OTOH, if I have reason to think someone is speaking in code or has a propensity to use eccentric stipulative definitions, I can't tell just at a glance that "Colorless green ideas sleep furiously" is meaningless--I need to ask follow-up questions.
I'll certainly grant you that contexts in which the intended referent of a sentence intended to be self-referential are less rare than contexts in which someone is suspected to be speaking in code or to have a propensity for filling his speech with eccentric stipulative definitions of common words, but I'm not sure how important that is in context.
"(If paradoxes aren't an edge-case for boolean logic, I don't know what is.)"
....only makes sense if you assume that the sentences in question have implications with consequences hard to accommodate in a classical framework. This is, granted, a standard assumption, but also one that rests on the implication that they imply anything at all, which in turn rests on the assumption that they mean anything at all, and, in context, begs the question.
"The old 'this is not a philosophical argument' philosophical argument?"
Nope. Re-read what I wrote.
I explicitly said that I was making a philosophical argument for the conclusion that Liars/Truth-Tellers/other bits of ungrounded truth talk are meaningless. (Although not an argument that relies on any philosophically controversial claims about what 'meaningfulness' or its negation amounts to.) I denied, however, that the conclusion itself was "philosophical" in some special way that ordinary judgments of meaninglessness aren't. To re-iterate, there's no special sense of "meaning" or "having a meaning" or "lacking a meaning" at play here, just the ordinary mundane one we use when we say that some German sentence means the same thing as some English sentence, or that both of them mean something, or that "blorks geblork" or "colorless green ideas sleep furiously" means nothing.
"So no. Good enough until you run into ambiguities and edge cases is not necessarily good enough. Depends on the context."
Maybe so, but I have yet to see a reason for even a prima facie reason for suspecting the presence of ambiguity here.
Two women can have divorced their husbands for entirely different and unrelated reasons, but that doesn't make the word "divorce" ambiguous.
It's more like one divorced her husband and one traveled back in time and killed his grandfather. And you're like, "The point is that they're both no longer married."
There are, pretty clearly, some sentences ending in 'is true' or 'is false' that you can just look at and tell that the intended referent is that very sentence, or some other sentence that isn't 'true'-free.
Well, that's not disagreement, I said you can't reliably tell. You construct cases above where you can't tell whether a sentence is meaningful without looking at a bunch of other sentences. Now that I think about it though, one probably could construct such sentences with a predicate like "is green" (it would be pointlessly convoluted, but whatever). So I withdraw that objection.
only makes sense if you assume that the sentences in question have implications with consequences hard to accommodate in a classical framework. This is, granted, a standard assumption, but also one that rests on the implication that they imply anything at all, which in turn rests on the assumption that they mean anything at all
I see your point. Though the constructibility of such sentences might imply something even if the sentences themselves don't.
I have yet to see a reason for even a prima facie reason for suspecting the presence of ambiguity here.
All that previous philosophical debate isn't evidence that something ambiguous is going on? Look, if I accept rules like "for all sentences S, T(S)->S" and I have a sentence like "L: T(~L)", I can derive "L->~L" and "~L->L". (That doesn't necessarily mean that rule of inference blows up the system, that would only be the case if this system also derives "L: T(~L)" from its axioms.)
Now obviously you reject that particular rule of inference (you say that the truth-predicate applies only to some sentences), but the point is that I can say things about what L would imply given a particular set of rules. It has this property semantic content within the context of that formal system, which is distinct from a sentence to which no rules of inference apply.
You can argue that sort of semantic content within arbitary formal systems doesn't constitute meaning, but that raises interesting questions about when/if the meaning of a sentence can have to do with that sentence implying something within the context of a formal system.
Also, you didn't answer my point about (17) and (2): Godel-strings (like 17) only reduce to Liar-paradoxes (like 2) if you assume the system of reasoning in question is complete and consistent. Which is probably a poor assumption, on account of that being provably impossible.
Post a Comment