1. 1 2 Frege's Puzzles; Sense vs. Reference

2. 2 Teaching Assistants Brenden MURPHY Brenden MURPHY bjmurphy@connect.carleton.ca office h:12:00-1:00pm Paterson 330A Mark TOVEY Mark TOVEY mtovey@connect.carleton.ca office h:

3. 3 Identity It’s a relation (a = b), but: It’s a relation (a = b), but: 1. between objects? 2.between signs (i.e. names of objects)?

4. 4 If it’s a relation between objects then: If it’s a relation between objects then: “a = b” doesn’t differ from “a = a” We would say that an object is identical to itself.

5. 5 If it’s a relation between signs then: If it’s a relation between signs then: given that signs are arbitrary we would lose contact with what the signs stand for (“the subject matter”) and, again, “a = b” would not differ from “a = a”. It would amount of saying that the word “a” is identical to the word “b”.

6. 6 Cognitive Value “a = b” and “a = a” (e.g.: “Superman is Superman” vs. “Superman is Clark Kent”) differ in cognitive value. “a = b” and “a = a” (e.g.: “Superman is Superman” vs. “Superman is Clark Kent”) differ in cognitive value. If “a = b” merely concerns the objects a and b, its cognitive content would not differ from the one of “a = a”. If “a = b” merely concerns the objects a and b, its cognitive content would not differ from the one of “a = a”. All we would know is that an object is identical with itself.

7. 7 If “a = b” merely concerns the signs “a” and “b”, its cognitive content would not differ from the one of “a = a”. If “a = b” merely concerns the signs “a” and “b”, its cognitive content would not differ from the one of “a = a”. All we would know is that signs “a” and “b” are identical. It seems that identity is neither a relation between objects, nor a relation between signs (nouns/names). It seems that identity is neither a relation between objects, nor a relation between signs (nouns/names).

8. 8 Formulating Frege’s Problem Terminology: n = a referring expression [e.g. “Tully”] n = a referring expression [e.g. “Tully”] r(n) = r is the referent of n [e.g. Tully(“Tully”)] r(n) = r is the referent of n [e.g. Tully(“Tully”)]

9. 9 S  = a sentence containing the singular term  [e.g. “Tully smokes” is a sentence containing the singular term “Tully”] S  = a sentence containing the singular term  [e.g. “Tully smokes” is a sentence containing the singular term “Tully”] S  /  = a sentence obtained by replacing the occurrences of  with occurrences of  [e.g. “Jane smokes” can be obtained by replacing occurrences of “Tully” with occurrence of “Jane” in “Tully smokes”] S  /  = a sentence obtained by replacing the occurrences of  with occurrences of  [e.g. “Jane smokes” can be obtained by replacing occurrences of “Tully” with occurrence of “Jane” in “Tully smokes”]

10. 10 Substitution Principle (Begriffsschrift): Substitution Principle (Begriffsschrift): If S  is about r(  ), then if r(  ) = r(  ), S  and S  /  have the same cognitive value. [if “Tully smokes” is about the referent of “Tully” then, if the referent of “Tully” = the referent of “Cicero”, “Tully smokes” and “Cicero smokes” have the same cognitive value]

11. 11 2 Assumptions 2 Assumptions 1. Substitution principle 2. Identity relates objects These two assumptions generate the following paradox: These two assumptions generate the following paradox: “a = b” differs in cognitive value from “a = a”, yet, according to the substitution principle they do not differ.

12. 12 Solution: Solution: reject either (1) or (2), i.e. either the substitution principle or the view that identity relates objects.

13. 13 Solution 1: Early Frege (Begriffsshrift 1879) Solution 1: Early Frege (Begriffsshrift 1879) Rejection of assumption 2: Identity is not a relation between objects (it’s a relation between signs).

14. 14 Solution 2: Later Frege Solution 2: Later Frege (“Über Sinn und Bedeutung “ / “Sense and Reference” 1892) The sense/reference solution. Rejection of assumption 1, i.e. the substitution principle.

15. 15 Substitution of coreferential singular terms preserves truth value but not cognitive value. Substitution of coreferential singular terms preserves truth value but not cognitive value. In substituting terms with the same sense cognitive value is preserved.

16. 16 Frege’s Puzzles Cognitive value Cognitive value “Hesperus = Hesperus” is trivial and non- informative, whereas “Hesperus = Phosphorus” is informative. So, the cognitive value of these sentences ought to differ. Where does the difference come in?

17. 17 Frege’s solution Frege’s solution “Hesperus” and “Phosphorus” express two distinct senses (Sinne), I.e. the modes of presentations of the referent (Bedeutung), i.e. Venus, associated with both terms are different.

18. 18 Proper Names A proper name expresses a sense and refers to an object. A proper name expresses a sense and refers to an object. The sense of a proper name, say “Tully”, is the mode of presentation of the object, Tully, it stands for. Intuitively, a sense is that property of a linguistic expression in virtue of which it is understood (grasped) by a competent speaker. The sense of a proper name, say “Tully”, is the mode of presentation of the object, Tully, it stands for. Intuitively, a sense is that property of a linguistic expression in virtue of which it is understood (grasped) by a competent speaker.

19. 19 Sense and thought Sense and thought The sense of a sentence (thought) is determined by the senses of its constituents. Different senses make different contributions to a thought.

20. 20 Sense vs. Reference Sense determines reference Sense determines reference r(n) = r(s)n)) [e.g. the referent of “Tully” is the referent of the sense of “Tully”]

21. 21 Reference is a function Reference is a function Any two terms having the same sense refer to the same object, i.e. If s(n) = s(m), then r(n) = r(m)

22. 22 Frege’s Semantics Three worlds Three worlds 1. Language 2. World of senses/thoughts 3. Reality

23. 23 1.sign proper name predicate sentence         2. sense/thought sense sense thought         3. referent object concept Truth Value  object falling under the concept  object falling under the concept

24. 24 A is a linguistic expression which: A proper names is a linguistic expression which: (i) expresses a sense and (ii) stands for/refers to/designates an object. An object is the ontological reflection of a name. An object is the ontological reflection of a name.

25. 25 Sentences are compound proper names whose referents are either the Truth or the False which are objects. Sentences are compound proper names whose referents are either the Truth or the False which are objects. The Bedeutung of a sentence (the truth value) is determined by the Bedeutung of its constituents, just as the sense of a sentence (the thought expressed) is determined by the senses of its constituents. The Bedeutung of a sentence (the truth value) is determined by the Bedeutung of its constituents, just as the sense of a sentence (the thought expressed) is determined by the senses of its constituents.

26. 26 Oratio Obliqua Oratio obliqua vs oratio recta; i.e indirect discourse vs direct discourse; intensional contexts vs extensional context Oratio obliqua vs oratio recta; i.e indirect discourse vs direct discourse; intensional contexts vs extensional context (1) Sue believes that Hesperus is a star (1) Sue believes that Hesperus is a star (2) Hesperus = Phosphorus (2) Hesperus = Phosphorus So: (3) Sue believes that Phosphorus is a star How to block this inference, i.e. the substitution salva veritate of ‘Hesperus’ and ‘Phosphorus’? How to block this inference, i.e. the substitution salva veritate of ‘Hesperus’ and ‘Phosphorus’?

27. 27 Frege’s Solution (i) “Hesperus” and “Phosphorus” express different senses; (i) “Hesperus” and “Phosphorus” express different senses; (ii) Senses are the constituents of thoughts (Gedanke), (ii) Senses are the constituents of thoughts (Gedanke),

28. 28 (iii) an attitude ascription relates a subject with a thought; (iii) an attitude ascription relates a subject with a thought; So: (iv) (1) and (3) do not relate Sue with the same thought and, therefore, may differ in truth value. So: (iv) (1) and (3) do not relate Sue with the same thought and, therefore, may differ in truth value. The moral is that the names “Hesperus” and “Phosphorus” cannot be substituted salva veritate in oratio obliqua constructions. The moral is that the names “Hesperus” and “Phosphorus” cannot be substituted salva veritate in oratio obliqua constructions.

29. 29 Ordinary Senses vs. Indirect Senses The ordinary sense is what is referred to, via an indirect sense, by embedded expressions. The ordinary sense is what is referred to, via an indirect sense, by embedded expressions. Since embedded expressions switch reference, Frege gives up semantic innocence. Since embedded expressions switch reference, Frege gives up semantic innocence. E.g.: “Hesperus” in (1) and “Phosphorus” in (3) do not refer to Venus, but to their ordinary sense, which differ.

30. 30 (1) gets represented as: (1) gets represented as: (1a) BEL (Sue, ) while (3) as: (1b) BEL (Sue, )

31. 31 MP(Hespeus) differs from MP(Phosphorus) MP(Hespeus) differs from MP(Phosphorus) Thus as (1a) and (3a) show, (1) and (3) do not relate Sue with the same thought. Thus, they may well differ in truth value.

32. 32 Moral: Moral: Coreferring expressions / terms / names cannot be substituted salva veitate in oblique / oratio obliqua / intensional contexts.