Saturday, February 24, 2007

Cause quotes are awesome

And quotes from Wittgenstein are really awesome. From Rhees's review of Anscombe's book on the Tractatus:
"In a remark written considerably later than the Tractatus Wittgenstein said 'No philosophical problem can be solved by a calculus.' He had no longer spoke quite as he had in the Tractatus, but he always thought that 'meta-languages' were an evasion. This was not because he did not feel that logic was important, but because he was convinced that it was."
Whatever one thinks of the use of a calculus, too often people make the knee jerk inference to the idea that formal tools are worthless, period.

12 comments:

N. N. said...

I've often thought that the problems, such as the liar paradox, which the notion of a meta-language is supposed to avoid are pseudo-problems and that the the notion of a meta-language is confused.

Concerning 'sentences' such as 'This sentence is false,' Wittgenstein replied 'Which sentence?' This question, it seems to me, dissolves the liar paradox.

Aidan said...

How does that dissolve the paradox? It still looks utterly paradoxical to me, even if Wittgenstein was confused as to which sentence was under discussion.

Aidan said...

Oh, and if the suggestion was just the familiar one that there isn't really a sentence here, why doesn't that fall prey to the standard strengthened Liar-paradox?

N. N. said...

Aidan,

By no means am I well versed in this topic, so correct me if I'm wrong, but I was under the impression that the strengthened liar was formulated to counter the solution by Kripke (et al.) to the liar paradox, viz., denying bivalence. How does it counter the move of denying that there is a sentence here? If there isn't a sentence, there isn't anything that can be 'not true.'

So, yes, as I understand Wittgenstein's quip, he is denying that there is a sentence here.

Aidan said...

There are a bunch of ways to strengthen the Liar (though you're right that the term "strengthened Liar" is often reserved for the sentence (or string of letters if you prefer) that ascribes non-truth (as opposed to falsity) to itself).

I'm sure there's a ton of literature on why the 'denying there's a sentence or proposition here' strategy doesn't get us very far which I'm not familiar with.

But in any case, W's response is utterly dissatisfying without a great deal of supplementation. We want a diagnosis of why certain pseudo-sentences in fact fail to be sentences, despite looking like sentences, behaving the way we'd expect w.r.t. the Boolean sentential operators, etc. It's self-referential, but then so are lots of other strings of letters which don't give rise to contradiction (nor since Yablo are we that convinced that self-reference is responsible for the paradox).

In fact, Kripke suggested that there's no mark of paradoxical strings - in some cases it depends on the empirical facts. As Kripke puts it (691), 'many, probably most of our ordinary assertions about truth and falsity are liable, if the empirical facts are extremely unfavorable, to exhibit paradoxical features'. Are we to believe that whether or not we have a sentence on our hands is similarly in flux depending on the empirical facts? In the absence of some principled criterion of sentence-hood which would vindicate such a strange thought, how are we to take that thought seriously?

These look like seriously hard, perhaps intractable challenges. Presumably a successful dissolution to a philosophical problem shouldn't leave us in such dire straits.

N. N. said...

Certainly a principled criterion of sentence-hood is a precondition for judgments about whether a particular string of words is a sentence. 'This sentence is false' (or 'not true') fails the criterion put forward in the Tractatus, i.e., it's not a picture of anything. Following Kenny, I happen to believe that the later Wittgenstein retains this criterion; but even if that's not so, there's something suspicious about the grammar of 'this sentence' as it's used in the 'liar paradox.'

The paradox is: if it's true, it's false, and vice versa. If it's true.... but what would make it true? It doesn't assert anything but it's own truth-value.

What about this: According to a deflationist take on truth, 'p is true' is equivalent to 'p.' Conversely, 'p is false' is equivalent to '~p.' In the string of words 'This sentence is false,' what corresponds to 'p'? 'This sentence'? What is the conceptual content of 'This sentence'?

Perhaps I'm lost here, but the whole business strikes me as odd.

Aidan said...

I'm not sure why you're getting so fixated on the 'This sentence' business - it seems quite peripheral to me:

S: S is not true.

And presumably even this doesn't exhaust the possibilities for getting away from the 'This sentence' locution; Goedel numbering or some such trick. So I'm just not clear on why we'd be interested in the 'conceptual content' of that particular expression.

I'm only not clear on how appeal to the Tractarian criterion helps respond to Kripke's point. Take some string of letters that will give rise to Liar-like paradox if the empirical facts are one way, but if the empirical facts turn out differently will just be a normal truth-evaluable empirical statement (see Kripke's J Phil '75 paper if you want examples). Kripke's point is that even if we have a criterion for sentence-hood, that won't cut the strings-that-give-rise-to-paradox/
strings-that-do-not-give-rise-to-paradox
contrast at the joints, since whether a string of words gives rise to paradox can depend on facts that have nothing to do with whether that string is a sentence or not (by whatever criterion you like).

Now, it might be claimed that W has at least dissolved the standard, non-empirical version of the Liar (assuming for now there aren't revenge problems lurking). But that surely a hollow victory; we've known for a very long time that there's a family of problems here which we'd like to know what to say in response to. The classic one-line Liar is just one member of that family.

"The paradox is: if it's true, it's false, and vice versa. If it's true.... but what would make it true? It doesn't assert anything but it's own truth-value."

Why think anything needs to make it true? One lesson people draw from the truth-teller and No-No paradoxes is that sometimes sentences don't need anything to make them true (Sorensen takes this line, for example). I'm not all that sympathetic to this line of response, but I don't see how one could dismiss it out of hand in good conscience. Again, I don't feel the problems here have been dissolved; Wittgenstein's remark just seems to raise more questions than it answers.

Aidan said...

"I'm only not clear" = I'm also not clear. Sorry.

N. N. said...

Aidan,

Is the Sorensen text you're refering to Vagueness and Contradiction? It's been sitting on my shelf for a few years now, but I've yet to read it. And is the Kripke 'Outline of a Theory of Truth'?

If so, I'll take a look at these, and see if I have anything intelligent (or intelligible) to reply.

Aidan said...

Yup, that's right. The relevant stuff from Kripke is towards the beginning. The relevant stuff in Sorensen is in the final chapter.

N. N. said...
This comment has been removed by the author.
N. N. said...

Interesting read. I'll have to ruminate on it for a while. Thanks for the references.