Can a sentence without a truth-value ever be approximately true?

I am curious to hear people's thoughts on the question in the title. There has been a lot of philosophical work done on the idea that a sentence can be strictly speaking false, yet nonetheless approximately true (or 'truthlike' or 'verisimilar'). For example: I am 5'11", but if someone said 'Greg is 6 feet tall,' we want to say that that claim is approximately true or something like that. But what if the claim was (strictly speaking) neither true nor false? (Readers may insert their own favorite truth-valueless sentence here.)

I ask because, as I mentioned in an earlier post, I'm toying with the idea that the Pessimistic Induction over the history of science plus something like Kuhnian incommensurability (esp. untranslatability) will lead us not to the conclusion that current science is likely to be false, but rather is likely to lack a truth-value. For if we cannot translate the claims of a pre-revolutionary language into the post-revolutionary one, then the pre-revolutionary language (from our current point of view) is truth-valueless, not false.

I ask the question in the title because one common realist response to the Pessimistic induction is: "Well, yes, our current scientific theories are probably not exactly true, but they are approximately true." If truth-valueless sentences cannot be approximately true, then this response is not available to the realist.

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APA wrap-up: Kyle Stanford's "New Induction"

My time at the APA last weekend was pretty good: I learned a few new things, met some new people I've been wanting to meet, and got to catch up with a couple old friends. Particularly helpful/ enlightening presentations included Angela Potochnick on how the context of inquiry shapes explanation, Ken Waters (plus commenters Jay Odenbaugh and Michael Strevens) on causes that make a difference (not, I learned, to be confused with the conception of causes as 'difference-makers'), and the Author-Meets-Critics session on Kyle Stanford's Exceeding Our Grasp.

Stanford's basic claim is that current scientific theories are underdetermined -- not because we can generate empircially equivalent rivals to our currently accepted theories, but rather because at many, many times in the past, the scientific community has been unable to conceive of good alternatives to the then-current theory. The evidence that such alternatives exist is the fact that they are proposed and accepted centuries later: thus, Newton's mechanics did not consider special relativity as an alternative hypothesis; Newton's, when he proposed his gravitation theory, did not consider the general theory of relativity as an alternative; no classical physicists before 1900 considered quantum mechanics as an alternative explanation of the data, and so on. This is what Stanford calls the "New Induction" over the history of science.

The idea, as just presented, strikes me as a promising line to take. But there is one aspect of Stanford's presentation of the problem that I don't understand. Fiona Cowie asked (in part) about this in the question and answer session, but I still didn't follow the answer. Stanford says that (e.g.) in 1700, the special theory of relativity and Newtonian mechanics were "(roughly) equally well-confirmed". Similarly for the other cases: the future theory is supposedly just as confirmed as the old one -- even in the past.

I don't understand why Stanford says this for two reasons: (1) He doesn't need the theories to be equally well-confirmed for his point to hold (viz., scientists aren't even conceiving of a hypothesis that will later be accepted as superior), and (2) it seems false to me, on any reasonable (i.e., not hardcore hypothetico-deductive)notion of confirmation. In 1700, it is true that special relativity and Newtonian mechanics agreed on all the consequences that could then be observed. But someone who, in 1700, said "Newton is approximately right, yet when something goes really, really fast its length will contract and its local time will dilate from the point of view of slower-moving observers" -- there is NO evidence at all for postulating that further bit of theory. And it's the same with GTR (what evidence would there've been for gravitation being a 10-component tensor instead of a scalar?) and especially QM (what evidence was there for thinking a body cannot have a determinate position and momentum simultaneously?). In 1700, these now-accepted alternatives were consistent with the data, but they were not equally well-confirmed.

Note: a very similar line of objection is pushed at the end of P.D. Magnus's "What's New about the New Induction?" (Synthese, 2006), though he develops it slightly differently, I think. (As I understand him, P.D. claims that in 1700, STR, GTR and QM would look like 'gruesome' hypotheses.)

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Off to the Pacfic APA

I'll be at the APA in San Francisco from this Wednesday til Saturday afternoon; I'm be commenting on a paper by Barry Ward on the paradox of confirmation (a.k.a. the Ravens paradox).

So if you're there, and you want to catch up/ chat/ harrass me etc., please track me down.



semantic pathology spotted in the wild

Perhaps the most famous instance of a sentence that exhibits semantic pathology is the Liar: 'This sentence is false'; if the 'this' strikes you as problematic --

(1) (1) is false.

But there are many other types of semantic pathology, such as the 'heterological' paradox and the so-called 'truth-teller': 'This sentence is true.' My colleague James Woodbridge is doing a lot of interesting research in this area; check out his work if you are interested.

This is not a serious post about semantic pathology, but rather just a field report. I sometimes wonder whether these examples like the truth-teller are all that important, since it's hard to imagine circumstances under which speakers might utter it. But I think I may have found a couple of instances of something akin to the truth-teller "in the wild":

(i) A couple of weeks ago, I went to see Spamalot, the musical adaptation of Monty Python and the Holy Grail. One of the songs contained (something close to) the following line: "This is the song that goes like this."

(ii) In the instructions for the Pennsylvania state tax forms, I found (something like) the following:

"You are eligible for the Tax Forgiveness credit if you meet the following requirements:

1. ...
2. ...
3. You meet the eligibility requirements for the Tax Forgiveness Credit.
4. ..."