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Worries about the nature of mathematical entities and our access to them prompts the antecedent puzzle of the nature of identity itself. Frege's genius was to grasp that this puzzle could be understood in terms of the language of identity itself. Equality gives rise to challenging questions which are not altogether easy to answer. Is it a relation? A relation between objects, or between names or signs of objects?

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In my Begriffsschrift I assumed the latter. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even today the identification of a small planet or a comet is not always a matter of course. A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing. But this relation would hold between the names or signs only in so far as they named or designated something.

Character, proper names, and Frege’s Puzzle | Martone | Filosofia Unisinos

It would be mediated by the connexion of each of the two signs with the same designated thing. But this is arbitrary.

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Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. But in many cases this is just what we want to do. If the sign 'a' is distinguished from the sign 'b' only as object here, by means of its shape , not as sign i. A difference can arise only if the difference between the signs corresponds to a difference in the mode of presentation of that which is designated.

Let a, b, c be the lines connecting the vertices of a triangle with the midpoints of the opposite sides. The point of intersection of a and b is then the same as the point of intersection of b and c. So we have different designations for the same point, and these names 'point of intersection of a and b,' 'point of intersection of b and c' likewise indicate the mode of presentation; and hence the statement contains actual knowledge.

Frege's puzzles

In antiquity it was not understood that the star that sometimes appeared in the early evening sky just above the horizon, Hesperus, was the same star, Phosphorus, that sometimes appeared early in the morning. Hesperus and Phosphorus were simply the planet Venus, as it turned out.

The meaning of a term is give by its reference. That is, it is enough to understand the meaning of a term to grasp what the term designates. A term's reference exhausts its meaning. The meaning of a sentence is a function of the meanings of its parts. For example, it suffices to understand the sentence, 'Hesperus is bright', that one understand the term 'Hesperus' and the predicate 'is bright'.

If any two statements have the same meaning, then they convey the same information inasmuch as they are synonymous. That is, statements which mean the same thing have the same cognitive value, as Frege puts it, because they express the same basic proposition.

Thus, taken individually, 1 , 2 , and 3 seem true as best we can tell, yet they are just as clearly inconsistent with one another, so they cannot all be true. Something has got to give. Consider, to use another example, that the surprise Mary Jane lacks upon being informed that Spiderman is Spiderman is abundant when she learns that Spiderman is Peter Parker. Yet we would be at least as surprised by her divergent reactions if the names 'Spiderman' and 'Peter Parker' contributed no more than the individual they co-designate to the meanings of statements in which they occur.

The natural--though not uncontested--conclusion to draw is that 'Spiderman' and 'Peter Parker' have distinct cognitive significance for Mary Jane, a distinction rooted, no doubt, in the very different ways Peter Parker has presented to her at different times, wearing different garb, while taking very different social roles. One puzzle is how to explain the distinct cognitive significance co-referring names might have, since it seems, at least in the case of Mary Jane, that 'Spiderman' and 'Peter Parker' contribute more than just an individual to the meanings of the claims she makes using them.

Frege's famous solution to this puzzle is reject A above and distinguish the reference 'Peter Parker' has from the sense it expresses: 'The mild-mannered, somewhat geeky college student and long-time friend of Mary Jane' might more clearly express the sense of 'Peter Parker' if the sense expressed by 'Peter Parker' captures how Peter Parker has presented himself to Mary Jane as Peter Parker, whereas 'the red-suited web-slinging super-hero and love-interest of Mary Jane' might more clearly express the sense of 'Spiderman'.

Thus the senses expressed by different names might diverge even when those names designate the same individual. One way to understand senses is that they do much of the theoretical work for names and probably other expressions that propositions do for sentences. For instance, one argument is that differences in knowledge concerning e.

Gottlob Frege

The key Fregean principle which they reject is that cognitive differences such as that between 1 and 2 are to be explained by a difference in semantic content p. According to Sainsbury and Tye, concepts have an introductory use which is their origin, and different concepts have different introductory uses.

This is, they argue, analogous to the individuation of words pp. Words are not individuated by their semantic content, because if two words are true synonyms i. Thus, 1 and 2 are distinct thoughts pp. Sainsbury and Tye in agreement with e. Thus, 1 and 2 have the same content as opposed to a Fregean view , but since concepts are individuated by their origin 1 and 2 are nonetheless different thoughts. This explains why, for example, the same person can believe 1 but not believe 2.

Sainsbury and Tye hence reject the Fregean principle that the cognitive difference between 1 and 2 must be explained by a difference of content. The Fregean data which need to be explained are the cognitive differences between identity statements containing distinct co-referential expressions. This includes the fact that the same person can believe 1 but not believe 2. Frege says, for instance p. The theory of sense and reference is taken by Frege to explain this cognitive difference p. Following their analogy with words see pp.

For Sainsbury and Tye, this should be analogous to the Frege cases. I learn that two words which I believed to have different meanings actually have the same semantic content. However, Lois 6 There may be no true synonyms in actuality, because every word may have at least some slight variation in meaning.

However, they are at least possible in principle. Similarly, when the Babylonians discovered 2 they discovered something about the world, about the astronomical body in the sky. When I reflect upon not accepting 4 at an earlier point in time, I realize that I made a mistake about words, but that in a sense I believed 4 all along. We might say that 2 and similar Frege sentences are ontologically informative, and this feature is left unexplained by the Originalist story. They argue, for instance, that thinking 1 involves tokening the same concept twice but that thinking 2 involves tokening a new concept on the other side of the identity, and so will require more cognitive effort p.

Thanks to Alex Grzankowski for pointing this out. They also express agreement with the spirit of the Fodor solution from LOT 2 on page 73 footnote 16 and page I agree with the latter point as far as it goes; in fact, I take it to be relatively uncontroversial. There is plenty of evidence that synonymous words can be processed differently, or even that the same word can be process differently when preceded by different sentences ambiguous words, for example.

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Where I disagree is with the claim that these sorts of differences in cognitive processing can explain the difference in informativeness between thoughts such as 1 and 2. Discovering that Hesperus is Phosphorous feels like discovering something about the external world, rather than discovering something about cognition. For example, by using multiple object tracking displays I may discover that I can only visually track four objects at a time Pylyshyn In this way I discover something about human cognition, about cognitive processing.

However, Sainsbury and Tye continue, that just puts all identity statements in the same category as mathematical truths and other necessary truths. We can talk about mathematical discoveries or the discovery that water is H2O, but these are all cognitive discoveries and not possibility-eliminating ones. Frege rejects the supposition because he thinks that content is a combination of sense and reference. If one accepts the supposition, then one needs a new explanation. Sainsbury and Tye simply take an odd view about concept individuation and tack on an implausible view concerning discovery.

Water is H2O was a scientific discovery of a fact about our world. The problem with the Sainsbury and Tye view is that discovering Hesperus is Phosphorous is for them learning something new about our concepts or about our cognition when intuitively it is learning something about the external world, and this has nothing to do with the metaphysical necessity of identity statements.

All identity statements are necessary and so none of them can be possibility-eliminating. However, what is interesting is that some identity statements viz. Even Kripke —the definitive dismantling of descriptivism—notes that there is an epistemic sense in which e. This is the crucial difference which Frege sought an explanation for. If the analogy with words were correct, then we can see how such a difference would affect cognitive processing, but this fails to explain the cognitive difference in question, such as how it is possible that one may believe one but not the other.

If it were simply a matter of finding some difference between 1 and 2 , then we could simply individuate words and concepts by their spelling in English, for example. A plausible solution to the puzzle must explain the cognitive difference which Frege was interested in. As an illustration, Originalism appears subject to a problem which McKay raises for a similar view pp. He tells both B and C that Hesperus is visible in the evening. B reports to D that Hesperus is visible in the evening, but C for whatever reason tells D that Hesperus is not visible in the evening.

D believes both B and C and assumes that they must be talking about two different astronomical objects which happen to share the same name.