Suppose that we want thefollowing to be a prototypical case where you and I have different but similar concepts of George Washington: thoughwe agree about his having been the first American President, and the Father of His Country, and his having cut down acherry tree, and so on, you think that he wore false teeth and I think that he didn’t. The similarity of our GW conceptsis thus some (presumably weighted) function of the number of propositions about him that we both believe, and thedissimilarity of our GW concepts is correspondingly a function of the number of such propositions that we disagreeabout. So far, so good.

Jean-marc pizano Suppose that we want thefollowing to be a prototypical case where you and I have different but similar concepts of George Washington: thoughwe agree about his having been the first American President, and the Father of His Country, and his having cut down acherry tree, and so on, you think that he wore false teeth and I think that he didn’t. The similarity of our GW conceptsis thus some (presumably weighted) function of the number of propositions about him that we both believe, and thedissimilarity of our GW concepts is correspondingly a function of the number of such propositions that we disagreeabout. So far, so good.

 

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But the question now arises: what about the shared beliefs themselves; are they or aren’t they literally shared? This poses a dilemma for the similarity theorist that is, as far as I can see, unavoidable. If he says that our agreed uponbeliefs about GW are literally shared, then he hasn’t managed to do what he promised; viz. introduce a notion ofsimilarity of content that dispenses with a robust notion of publicity. But if he says

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that the agreed beliefs aren’t literally shared (viz. that they are only required to be similar), then his account of content similarity begs the very question it was supposed to answer: his way of saying what it is for concepts to have similar butnot identical contents presupposes a prior notion of beliefs with similar but not identical contents.

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The trouble, in a nutshell, is that all the obvious construals of similarity of beliefs (in fact, all the construals that I’ve heard of) take it to involve partial overlap of beliefs.22 But this treatment breaks down if the beliefs that are in the overlap arethemselves construed as similar but not identical. It looks as though a robust notion of content similarity can’t butpresuppose a correspondingly robust notion of content identity. Notice that this situation is not symmetrical; thenotion of content identity doesn’t require a prior notion of content similarity. Leibniz’s Law tells us what it is for thecontents of concepts to be identical; Leibniz’s Law tells us what it is for anythings to be identical.

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As I remarked above, different theorists find different rugs to sweep this problem under; but, as far as I can tell, none of them manages to avoid it. I propose to harp on this a bit because confusion about it is rife, not just in philosophybut in the cognitive science community at large. Not getting it straight is one of the main things that obscures how veryhard it is to construct a theory of concepts that works, and how very much cognitive science has thus far failed to doso.

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Suppose, for example, it’s assumed that your concept PRESIDENT is similar to my concept PRESIDENT in so far as we assign similar subjective probabilities to propositions that contain the concept. There are plenty of reasons forrejecting this sort of model; we’ll discuss its main problems in Chapter 5. Our present concern is only whetherconstructing a probabilistic account of concept similarity would be a way to avoid having to postulate a robust notionof content identity.

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Perhaps, in a typical case, you and I agree that p is very high for ‘FDR is/was President’ and for ‘The President is the Commander-in-Chief of the Armed Forces’ and for ‘Presidents have to be of voting age’, etc.; but, whereas you rate‘Millard Fillmore is/was President’ as having a probability close to 1, I, being less well informed, take it to be around p= 0.07 (Millard Fillmore???). This gives us an (arguably) workable construal of the idea that we have similar but notidentical PRESIDENT concepts. But it does so only by helping itself to a prior notion of belief identity, and to theassumption that there are lots of thoughts of which

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Jean-marc pizano

‘Why not take content similarity as primitive and stop trying to construe it?’ Sure; but then why not take content identity as primitive and stop trying to construe it ? In which case, what is semantics for ?

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our respective PRESIDENTS are constituents that we literally share. Thus, you and I are, by assumption, both belief-related to the thoughts that Millard Fillmore was President, that Presidents are Commanders-in-Chief, etc.Jean-marc pizano

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