On Sense and Reference

# On Sense and Reference - On Sense and Meaning r Equality1...

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On Sense and Meaning Equality1 gives rise to challenging questions which are not altogether 25 easy to answer. Is it a relation? A relation between objects, or between names or signs ofobjects? In my Begr\$sschriftz I assumed the latter. The reasons which seem to favour this are the following: a= a and a= b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labelled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori. 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 re-identification of a small planet or a comet is not always a I matter of course. Now if we 26 were to regard equality as a relation between that which the names 'a' and 'b' designate, it would seem that a= b could not differ from a = a (i.e. provided a= b is true). A relation would thereby be expressed of a ' thing to itself, and indeed one in which each thing stands to itself but r (1 to no other thing. What we apparently want to state by a = b is that the .signs or names 'a' and 'b' designate the same - . thing, ~ so that those signs themselves wouId be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only in so far as they named or designated something. It would be . mediated by the connection of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use - -- , any arbitrarily producible event or object as a sign for something. In 'that case the sentence a = b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper , knowledge by its meansj;~ut in many cases this is just what we want to do. If the sign 'a' is distinguished from the sign 'b' only as an object (here, by means of its shape), not as a sign (i.e. not by the manner in 'I use this word in the sense of identity and understand 'a= b' to have the sense of 'a is the same as b' or 'a and b coincide'. '[The reference is to Frege's Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (Halle, 1879); English translation, Conceptual Notation (London, 1972).] Zeitschrift.fiir Philosophie und philosophische Kritik 100 (1892), pp. 25-50 (Tr. Max Black)

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, 158 Sense and Meaning I \$\ - which it designates something), the cognitive value of a = a becomes essentially equal to that of a = b, provided a = b is true. A difference can . arise only if the difference between the signs corresponds to a difference c, 'L in the mode of presentation of the thing designated. Let a, b, c be The .\ :, '-. . 1 I % v lines connecting the vertices -of a triangle with the midpoints of the s : 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.
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