Dummett on Frege
What gives us reason to believe that a referring term refers?
I'm commenting on Dummett's Frege: Philosophy of Mathematics pages around 239 and the final part of the reading from Dummett's Frege: Philosophy of Language 496–500 and 508–511, approximately.
Suppose we have somehow given a method (for example, contextual definition) to determine for any sentence in which a name occurs whether that sentence is true or false? Is that sufficient for introducing the name into the language? If so, since names denote objects, that would suffice for specifying the denotation of a name. Intuitively, even if the proposed contextual definition of number worked, it would have done so without telling us the denotation of '2,' which is what we might think would be required to specify the denotation of '2.'
The
Grundlagen was written before
Uber Sinn und Bedeutung, and Frege did not yet have a two factor semantic theory. What is translated 'meaning' in Dummett's rendering of the
Grundlagen is usually
bedeutung, but that doesn't make it reference in the later Fregean sense to which we are accustomed. In fact, Frege seems to think in the Grundlagen that a sentence cannot express a proposition unless its components are meaningful, and that means having a bedeutung. Thus, Dummett proposes that to get clear about whether a method of determining truth values yields reference, what we need to do is look at Frege's account of contextual definition with an eye to seeing which claims are best taken to be about sense and which best taken to be about reference. What Frege says does not provide an answer to our unease.
Why doesn't Frege see the problem, since every first-year graduate student who reads the work does see the problem? I think what Wilson says about Frege is helpful here: his examples come from mathematics and are a reasonable reflection procedures mathematicians actually accept as securing reference.
So, after having secured the sense (let's suppose fixing truth values does secure the sense) what more do we need to know to know whether a name refers? One answer is to just find the truth value of the relevant sentence. 'Pegasus exists' is false, but '2 exists' is true, since, for example, it follows from '_there is_ a number between 1 and 3' and 'any number between 1 and 3 is 2." The question is one raised in language, we know the truth values of the relevant sentences, and that is the end of the story. (Note that that sounds a lot like Quine. There is no substantial fact about existence separable from the truth of suitable sentences.) At one point Dummett seems to endorse this view.
Why is there any discomfort in the first place? In the case of medium-sized dry goods, there is a way in which we know whether or not a name refers that is quite different from just specifying the truth values of sentences in which the name occurs. There are particular "recognition sentences" that play a role in determining whether names that purport to be names of medium-sized dry goods do in fact denote, sentences like "That is Lucy's goldfish." That makes it look like ostension plays a role in determining whether or not names refer, and that seems related to doubts about abstract objects because it seems that nothing can be ostended unless it is causally efficacious.
Dummett isn't sure he wants to buy into a story like this because, on the one hand, there are causally efficacious things that can't be ostended in any direct way (a distant galaxy, sounds, smells, countries). I wonder why he doesn't mention, for example, electrons. On the other hand, we do ostend words, letters, and moves in chess (types). He is suggesting, I take it, that any way of extending the notion of ostension to handle all the concrete cases will let in some of the abstract ones, that this doesn't give us a way to draw the line.
He takes the following to be a particularly hard case: colors are concrete, but shapes are abstract, and it is very hard to see any difference in what we do in ostending them. Why does he take colors to be concrete and shapes to be abstract? First of all, shapes are one of Frege's examples of contextually defined objects, and so we know why they are abstract. How do you tell 'the shape of a = the shape of b'? By determining whether the outline (which is kind of geometrical line) determined by a is similar to that determined by b. Shapes have no role in assessing the truth value. In contrast, how do you determine whether 'the color of a = the color of b' is true? I have no idea, but whatever you do, it involves the colors as occurrent qualities, they are not eliminable.
In Frege: Philosophy of Mathematics, 239, Dummett says "The notion of reference, as applied to singular terms, is operative within a semantic theory, rather than semantically idle, just in case the identification of its referent is conceived as an ingredient in the process of determining the truth-value of a sentence in which it occurs." He continues, "Hence the context principle, if it is to warrant an ascription of reference to a term, robustly understood, must include a further condition if it is to be valid. It is not enough that truth-conditions should have been assigned, in some manner or other, to all sentences containing the term: it is necessary also that they should have been specified in such a way as to admit a suitable notion of identifying the referent of the term as playing a role in the determination of the truth-value of a sentence containing it."
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ShaughanLavine - 30 Sep 2006