Several of the blog entries here have been about the Quine-Carnap debate over the status of analytic truth. Generally, I don't feel the force of Quine's arguments as they are usually presented, either because his interpretation of Carnap is unfair or inaccurate, or the arguments just aren't that persuasive. Multiple commentators on the Quine-Carnap debate have suggested that the two are 'talking past each other,' at least to some degree. So, I am constantly trying to find a way to make Quine's view make sense to me, AND simultaneously really disagree with Carnap. This seems like installment 19 or so in that endeavor.
Carnap and Quine agree that language can be studied at various levels of abstraction. Using Carnap's taxonomy, we start at the level of pragmatics, where we study how individual speakers use expressions under particular circumstances. This level contains the most detail: speakers, their circumstances, plus the meanings of the words for particular speakers under particular circumstances. At the next, more abstract level, we have semantics, which abstracts away from particular speakers and particular circumstances. And at the highest level, we have syntax, which abstracts away the meanings of words, leaving just the symbols, the way they are put together, and which strings follow from others.
In each transition from pragmatics to semantics to syntax, some information about language is omitted/ discarded. (Like the move from Euclidean geometry to neutral geometry, which drops the parallel postulate.) Now, we can conceive of Quine's indeterminacy of meaning thesis (the radical translation thought experiment) as critiquing Carnap in the following way: Carnap is importing or introducing new information at the semantic level, because the semantic facts Carnap includes in a semantically-characterized language [a "semantic system"] cannot be 'read off' even the information contained at the pragmatic level. The analogy in the geometry case shows why this is clearly an unacceptable maneuver. It would be: thinking that there exists some claim that could be proved in neutral geometry (= Euclid's first four postulates only) but couldn't be proved in Euclidean geometry.
This may not be Quine's actual worry; his concern may stem from the fact that applied semantics (or whatever branch of language study) underdetermines pure semantics (or whatever). However, Carnap is perfectly happy to accept that claim: Creath says this is why Carnap's copy of Word and Object Ch.2 (Indeterminacy of Translation) has no marginalia. [But how does the geometry analogy fare here? Would Carnap admit that applied geometry underdetermines pure geometry? My guess is yes; and that that's not so bad...
8 comments:
Hi Greg,
You say:
In each transition from pragmatics to semantics to syntax, some information about language is omitted/ discarded. (Like the move from Euclidean geometry to neutral geometry, which drops the parallel postulate.)
But I don't think that the analogy is right. Neutral geometry is more rich geometry than the Euclidean, and Euclidean is a special case of a neutral geometry, when you abstract from it the possibilities for parallel postulate not to hold.
So the move from pragmatics to semantics to syntax, seems to me would be like move from neutral geometry to Euclidean geometry.
Also not sure what you mean by applied geometry underdetermining pure one... If seems to me it determines it fully, when we abstract in specific way (namely possibilities other than parallel postulate).
BTW, I had a post on almost the same issue (though not mentioning Carnap and Quine, I didn't even know that this might be the disagreement between them! Also, I imagine more concrete as being up, and more abstract down, while you seem to imagine it the other way around.) I'm very interested to hear what you think.
Also not sure what you mean by applied geometry underdetermining pure one... If seems to me it determines it fully, when we abstract in specific way (namely possibilities other than parallel postulate).
I interpreted Greg's statement as saying that applied geometry underdetermines pure geometry because we have a choice in which postulates to drop --- it's not clear (at least in language, according to Quine; I don't know about geometry) why some postulates should be dropped rather than others.
But I don't think that the analogy is right. Neutral geometry is more rich geometry than the Euclidean, and Euclidean is a special case of a neutral geometry, when you abstract from it the possibilities for parallel postulate not to hold.
Not sure what you mean by 'richer' here. Do you mean that it applies to a greater variety of cases? On the other hand, one could say that Euclidean geometry is 'richer' because you can prove more things with it. Analogously, the more 'concrete' levels of language are richer because you can say more things with them. Many of these things will turn out to be 'the same' when interpreted at a more abstract level, so at the abstract level it seems that one has less to say (although, analogously, what one has to say there would apply to a greater variety of cases).
Hi Ponder,
Yes, not just that it applies to greater variety of cases, but the cases of the Euclidean geometry are special cases of the neutral geometry.
There is nothing that can be proven in the Euclidean geometry that also can't be proven in the neutral geometry as a special case.
Or so to say, the neutral geometry doesn't abstract from parallel postulate of the Euclidean geometry, but the Euclidean geometry abstracts from possibilities in which the parallel postulate doesn't hold.
Tanasije,
Or so to say, the neutral geometry doesn't abstract from parallel postulate of the Euclidean geometry, but the Euclidean geometry abstracts from possibilities in which the parallel postulate doesn't hold.
I find this a strange use of the phrase 'abstracts from'. In general I would use 'abstracts from' to describe a process of moving to greater generality. So neutral geometry abstracts from Euclidean geometry.
There is nothing that can be proven in the Euclidean geometry that also can't be proven in the neutral geometry as a special case.
But in order to prove it in neutral geometry as a 'special case', you have to assume the parallel postulate. All you can say in neutral geometry is 'If [parallel postulate], then [theorems of Euclidean geometry].' Which doesn't amount to actually proving [theorems of Euclidean geometry] unless you also add that the parallel postulate holds, in which case you'd be using Euclidean geometry.
I can see what you're getting at, that the theorems of Euclidean geometry remain as possibilities within neutral geometry, but they still can't be proved within it.
Ponder,
1.One doesn't have to assume that parallel postulate holds in all cases, in order to prove the Euclidean theorems in the neutral geometry. One can prove how for those cases within the neutral geometry in which the parallel postulate holds, such and such truths will hold.
Imagine a right-angle-geometry, in which every triangle is right angle. Pythagorean theorem holds for every triangle there. In the Euclidean geometry Pythagorean theorem still hold, but just so it happens that there are also different triangles in the Euclidean geometry, and we have law of cosines there, of which Pythagorean theorem is a special case (Pythagorean theorem still holds there, just that it is not for all triangles). So, it is not the case that imagined right-angle-geometry is more rich than Euclidean. It abstracts from the possibilities for triangles to be otherwise than right-triangles, and is poorer.
2. I actually tried to explain how I use 'abstraction' in the first post on my blog. Here.
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