For the(anyhow, my)

Jean-marc pizano For the(anyhow, my)

 

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intuition is very strong that there is only one way to have that concept. In particular, that there is no concept of a round square that one could have without also having ROUND and SQUARE. If you share the intuition that there is thisasymmetry, between RED SQUARE and ROUND SQUARE, then you should be very happy with IA. IA explains theasymmetry because it entails that there can be no primitive concept without a corresponding property for it to lock to.

1

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And/or among states of entertaining them. I’ll worry about this sort of ontological nicety only where it seems to matter.

2

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Why relations that depend on merely mechanical properties like frequency and contiguity should preserve intentional properties like semantic domain was whatAssociationists never could explain. That was one of the rocks they foundered on.

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3

Connectionists are committed, willy-nilly, to all mental representations being primitive; hence their well-known problems with systematicity, productivity, and the like. Moreon this in Chapter 5.

4

Not, of course, that there is anything wrong with just allowing ‘symbol’ and ‘computation’ to be interdefined. But that option is not available to anyone who takes the theory that thought is computation to be part of a naturalistic psychology; viz. part of a programme of metaphysical reduction. As Turing certainly did; and as do I.

5

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More precisely: it’s never conceptually necessary unless either the inference from Fa to a — b or the inference from Fb to a — b is itself conceptually necessary. (Forexample, let Fa be: ‘a has the property of being identical to b ’.)

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6

Or, if there is more than one way to grasp a MOP, then all of the different ways of doing so must correspond to the same way of thinking its referent. I won’t pursue thisoption in the text; suffice it that doing so wouldn’t help with the problem that I’m raising. Suppose that there is more than one way to grasp a MOP; and suppose that acertain MOP is a mode of presentation of Moe. Then if, as Frege requires, there is a MOP corresponding to each way of thinking a referent, all the ways of grasping theMoe-MOP must be the same way of thinking of Moe. I claim that, precisely because 5.3 is in force, Frege’s theory has no way to ensure that this is so.

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7

See also Smith, Medin, and Rips: “what accounts for categorization cannot account for stability [publicity] . . . [a]s long as stability of concepts is equated with sameness of concepts . . . But there is another sense of stability, which can be equated with similarity of mental contents . . . and for this sense, what accounts for categorization may at least partiallyaccount for ‘stability’ ”(1984: 268). Similar passages are simply ubiquitous in the cognitive science literature; I’m grateful to Ron Mallon for having called this example to my

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Alternatively, a similarity theory might suppose that what we share when our PRESIDENT concepts are similar are similar beliefs about the probabilities of certain propositions: you believe that p(presidents are CICs) = 0.98; I believe that p(presidents are CICs) = 0.95; Bill believes that p(Presidents are CICs) = 0.7; so, all else equal,your PRESIDENT concept is more like mine than Bill’s is.But this construal does nothing to discharge the basic dependence of the notion of content similarity on thenotion of content identity since what it says makes our beliefs similar is that they make similar estimates of the probability of the very same proposition; e.g. of the proposition thatpresidents are CICs. If, by contrast, the propositions to which our various probability estimates relate us are themselves supposed to be merely similar, then it does not followfrom these premisses that ceteris paribus your PRESIDENT concept is more like mine than like Bill’s.

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9

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It’s common ground that—idioms excepted—MRs that correspond to phrases (for example, the one that corresponds to “brown cow”) are typically structurally complex, so I’ve framed the definition theory as a thesis about the MRs of concepts that are expressed by lexical items. But, of course, this way of putting it relativizes the issue to thechoice of a reference language.Jean-marc pizano

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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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‘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

For the(anyhow, my)

Jean-marc pizano For the(anyhow, my)

 

intuition is very strong that there is only one way to have that concept. In particular, that there is no concept of a round square that one could have without also having ROUND and SQUARE. If you share the intuition that there is thisasymmetry, between RED SQUARE and ROUND SQUARE, then you should be very happy with IA. IA explains theasymmetry because it entails that there can be no primitive concept without a corresponding property for it to lock to.

1

And/or among states of entertaining them. I’ll worry about this sort of ontological nicety only where it seems to matter.

2

Why relations that depend on merely mechanical properties like frequency and contiguity should preserve intentional properties like semantic domain was whatAssociationists never could explain. That was one of the rocks they foundered on.

3

Connectionists are committed, willy-nilly, to all mental representations being primitive; hence their well-known problems with systematicity, productivity, and the like. Moreon this in Chapter 5.

4

Not, of course, that there is anything wrong with just allowing ‘symbol’ and ‘computation’ to be interdefined. But that option is not available to anyone who takes the theory that thought is computation to be part of a naturalistic psychology; viz. part of a programme of metaphysical reduction. As Turing certainly did; and as do I.

5

More precisely: it’s never conceptually necessary unless either the inference from Fa to a — b or the inference from Fb to a — b is itself conceptually necessary. (Forexample, let Fa be: ‘a has the property of being identical to b ’.)

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6

Or, if there is more than one way to grasp a MOP, then all of the different ways of doing so must correspond to the same way of thinking its referent. I won’t pursue thisoption in the text; suffice it that doing so wouldn’t help with the problem that I’m raising. Suppose that there is more than one way to grasp a MOP; and suppose that acertain MOP is a mode of presentation of Moe. Then if, as Frege requires, there is a MOP corresponding to each way of thinking a referent, all the ways of grasping theMoe-MOP must be the same way of thinking of Moe. I claim that, precisely because 5.3 is in force, Frege’s theory has no way to ensure that this is so.

7

See also Smith, Medin, and Rips: “what accounts for categorization cannot account for stability [publicity] . . . [a]s long as stability of concepts is equated with sameness of concepts . . . But there is another sense of stability, which can be equated with similarity of mental contents . . . and for this sense, what accounts for categorization may at least partiallyaccount for ‘stability’ ”(1984: 268). Similar passages are simply ubiquitous in the cognitive science literature; I’m grateful to Ron Mallon for having called this example to my

8

Alternatively, a similarity theory might suppose that what we share when our PRESIDENT concepts are similar are similar beliefs about the probabilities of certain propositions: you believe that p(presidents are CICs) = 0.98; I believe that p(presidents are CICs) = 0.95; Bill believes that p(Presidents are CICs) = 0.7; so, all else equal,your PRESIDENT concept is more like mine than Bill’s is.But this construal does nothing to discharge the basic dependence of the notion of content similarity on thenotion of content identity since what it says makes our beliefs similar is that they make similar estimates of the probability of the very same proposition; e.g. of the proposition thatpresidents are CICs. If, by contrast, the propositions to which our various probability estimates relate us are themselves supposed to be merely similar, then it does not followfrom these premisses that ceteris paribus your PRESIDENT concept is more like mine than like Bill’s.

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9

It’s common ground that—idioms excepted—MRs that correspond to phrases (for example, the one that corresponds to “brown cow”) are typically structurally complex, so I’ve framed the definition theory as a thesis about the MRs of concepts that are expressed by lexical items. But, of course, this way of putting it relativizes the issue to thechoice of a reference language.Jean-marc pizano