Transcript 1. Frege's Puzzles and The Sense/Reference Distinction

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Frege's Puzzles; Sense
vs. Reference
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Teaching Assistants

Brenden MURPHY
[email protected]
office h: 12:00-1:00pm
Paterson 330A

Mark TOVEY
[email protected]
office h:
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Identity

It’s a relation (a = b), but:
1. between objects?
2. between signs (i.e. names of objects)?
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
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.
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
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”.
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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.
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
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).
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Formulating Frege’s Problem
Terminology:

n = a referring expression [e.g. “Tully”]

r(n) = r is the referent of n [e.g. Tully(“Tully”)]
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

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”]
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
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]
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
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.
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
Solution:
reject either (1) or (2),
i.e. either the substitution principle or the view
that identity relates objects.
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
Solution 1: Early Frege (Begriffsshrift 1879)
Rejection of assumption 2:
Identity is not a relation between objects (it’s a
relation between signs).
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
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.
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
Substitution of coreferential singular terms
preserves truth value but not cognitive value.
In substituting terms with the same sense
cognitive value is preserved .
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Frege’s Puzzles

Cognitive value
“Hesperus = Hesperus” is trivial and noninformative, whereas “Hesperus = Phosphorus”
is informative.
So, the cognitive value of these sentences
ought to differ. Where does the difference come
in?
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
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.
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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.
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
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.
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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”]
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
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)
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Frege’s Semantics

Three worlds
1. Language
2. World of senses/thoughts
3. Reality
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1. sign
proper name

2. sense/thought

3. referent

sense

object
predicate
sentence


sense
thought


concept
Truth Value
 object falling
under the concept
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
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.
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

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.
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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’?
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Frege’s Solution


(i) “Hesperus” and “Phosphorus” express
different senses;
(ii) Senses are the constituents of thoughts
(Gedanke),
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


(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.
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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.
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
(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)>)
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
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.
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
Moral:
Coreferring expressions / terms / names cannot
be substituted salva veitate in oblique / oratio
obliqua / intensional contexts.
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