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Frege's Puzzles; Sense vs. Reference 1 Teaching Assistants Brenden MURPHY
office h: 12:001:00pm
Paterson 330A Mark TOVEY
office h: 2 Identity It’s a relation (a = b), but:
1. between objects?
2. between signs (i.e. names of objects)? 3 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. 4 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”.
5 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”. All we would know is that an object is identical with itself.
6 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).
7 Formulating Frege’s Problem
Terminology: n = a referring expression [e.g. “Tully”] r(n) = r is the referent of n [e.g. Tully(“Tully”)] 8 Sα = a sentence containing the singular term α [e.g. “Tully smokes” is a sentence containing the singular term “Tully”]
Sα/β = a sentence obtained by replacing the occurrences of α with occurrences of β [e.g. “Jane smokes” can be obtained by replacing occurrences of “Tully” with occurrence of “Jane” in “Tully smokes”] 9 Substitution Principle (Begriffsschrift):
If Sα is about r(α ), then if r(α ) = r(β ), Sα and Sα /β 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]
10 2 Assumptions
1. Substitution principle
2. Identity relates objects 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.
11 Solution: reject either (1) or (2), i.e. either the substitution principle or the view that identity relates objects. 12 Solution 1: Early Frege (Begriffsshrift 1879)
Rejection of assumption 2: Identity is not a relation between objects (it’s a relation between signs). 13 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.
14 Substitution of coreferential singular terms preserves truth value but not cognitive value.
In substituting terms with the same sense cognitive value is preserved . 15 Frege’s Puzzles 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?
16 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. 17 Proper Names 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.
18 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. 19 Sense vs. Reference Sense determines reference
r(n) = r(s)n)) [e.g. the referent of “Tully” is the referent of the sense of “Tully”] 20 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) 21 Frege’s Semantics Three worlds
2. World of senses/thoughts
22 1. sign proper name predicate sentence ↓ ↓ ↓ ↓ 2. sense/thought sense sense thought ↓ ↓ ↓ ↓
3. referent object concept Truth Value → object falling under the concept
23 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.
24 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. 25 Oratio Obliqua 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 (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’?
26 Frege’s Solution (i) “Hesperus” and “Phosphorus” express different senses;
(ii) Senses are the constituents of thoughts (Gedanke), 27 (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. The moral is that the names “Hesperus” and “Phosphorus” cannot be substituted salva veritate in oratio obliqua constructions.
28 Ordinary Senses vs. Indirect Senses 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. E.g.: “Hesperus” in (1) and “Phosphorus” in (3) do not refer to Venus, but to their ordinary sense, which differ.
29 (1) gets represented as: (1a) BEL (Sue, <MP(Hesperus), MP(being a star)>) while (3) as:
(1b) BEL (Sue, < MP(Phosphorus), MP(being a star)>)
30 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. 31 Moral:
Coreferring expressions / terms / names cannot be substituted salva veitate in oblique / oratio obliqua / intensional contexts. 32 ...
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- Winter '08