This is a lesson in Philosophy of Language discussing Frege's seminal points with examples and illustrations for deepening and clarification.

1. Theory of Sense and Reference
Gottlob Frege

2. Frege’s puzzle:
“The Puzzle About Identity”
How can ‘a=a’ convey anything different
from ‘a=b’?
What treatment of identity statements
will explain the difference?
Frege’s two view of identity:
(1) Identity is a relation between objects
(2) Identity is a relation between names
(or signs) of objects

3. Frege favors #2 (identity is a relation
between names (or signs). Why?
 E.g. :
‘a=a’ (Hesperus=Hesperus) known a priori
‘a=b’ (Hesperus=Phosphorus) cannot be
known a priori
The difference between two such statement is
a difference in their cognitive value. The
difference is unaccountable if identity is a
relation between objects since both
statements alike would only record the fact
that some thing is the same as itself.
It seems that something is learned from an
identity statement because it is learned
through the difference of the two names,
hence, what the statement really tells us
about is a relation between names.

4. Or isn’t the view of identity as a
relation between signs no better than
the view of it as a relation between
objects? Why?
 If we take identity statements to speak merely
about names, then the cognitive difference
between the statements that Hesperus=Hesperus
and that Hesperus=Phosphorus would not be
apparent.
 We do not wish to show just the difference of
names, but the meaning.
 Any sign can be used and this could not convey
the sort of knowledge expressed in
Hesperus=Phosphorus.

5. ‘a=b’ is both informative and true
 Informative: the difference
between ‘a’ and ‘b’ in respect
of how they present the
objects that they name—a
difference in their mode of
presentation; thus, a certain
object may be presented in
different ways according to
such a difference can explain
the difference in cognitive
value; ‘a’ and ‘b’ differ in
sense
 True: ‘a=b’ where ‘a’ and ‘b’

6. The Problem having the informative
aspect solely: incorrect picture of the
whole
 Blind men and the Elephant

8. The Problem with looking at the
‘truth’ aspect solely: lack of depth
and richness of reality
 “A bachelor is
unmarried.”
 No new learning,
no other aspect
seen, no
richness in
perspective

9. Do you agree with Frege that ‘Hesperus is
Phoshorus’ conveys proper knowledge
which is not covered by saying that
the names ‘Hesperus’ and ‘Phosphorus’
refer to the same thing?
 ‘metalinguistic account’:
identity as a relation between
names
 We talk about the Hesperus
not about the name Hesperus
when we say it is the same as
Phosphorus
 Hesperus=Phosphorus is true
only if we talk about the same
thing and that the name refers

10.  Sign: name, combination of words, letter
 Reference: that to which the sign refers
 Sense: the mode of presentation
“point of intersection of a
and b” and “the point of
intersection between b and
c”
>sign: different
>reference: the same
>sense: different

11. “Proper Name”
 By ‘sign’ and ‘name’ : any designation
representing a proper name which thus has as its
reference a definite object
 Can also consist of several words or other signs
 For brevity, every such designation will be called
proper name
 the sense of a proper name is grasped by
everybody who is sufficiently familiar with the
language or totality of designations to which it
belong
e.g. “Aristotle”
Senses: “the pupil of Plato”
“the teacher of Alexander the Great”

12. Regular connexion between a sign,
its sense and its reference
 To the sign there
corresponds a definite
sense and to that in
turn a definite reference
(an object)
 while to a given
reference (an object)
there does not belong
only a single sign
 The same sense has
different expression in
different languages or
even in the same

13. Exception to this regular
connexion
1.To a sense, there may
not be a corresponding
reference:
e.g. “the celestial body
most distant from the
Earth”
“the least rapidly
convergent series”
2. “signs of signs”: when
words of another are
quoted

14. Frege vs. Locke
Reference/sense Idea
Reference is an object perceivable
by the senses
An internal image arising from the
memories of sense impressions
which I have had and acts, both
internal and external which I have
performed
Not saturated with feelings Saturated with feelings;
The clarity of its separate parts
remains the same
The clarity of its separate parts
varies and oscillates
Sign’s sense: common property of
many; not part of a mode of the
individual mind (mankind has a
common store of thoughts passed
from one generation to another)
Subjective: different persons will
have a variety of differences in the
idea associated with the same
sense
Two persons can grasp the same
sense.
Si duo idem faciunt, non est idem (If
two persons picture the same thing,
each still has its own idea.)

15. Frege’s analogy of sense vs. idea:
“observing the Moon through a telescope”
Reference: Moon
Sense: real image projected by
the object glass in the interior of
the telescope (optimal image is
dependent upon the standpoint
of the observation but it is still
objective)
Idea or experience: the retinal
image of the observer (diverse
shapes of the observer’s eyes
will cause his own retinal
image)

16. 3 levels of difference between
words/expression or sentences:
1. Difference in ideas (different persons will have
different ideas given a particular word; will also
cover “coloring and shading”)
2. Difference in sense but not reference
3. Difference in reference
Conclusion:
A proper name (word, sign, sign combination,
expression) expresses its sense, stands for or
designates its reference. By means of a sign
we express its sense and designate its
reference.

17. Assignment:
1. Compare and Contrast Mill and
Frege’s treatment of Proper Names
2. Read Wittgenstein’s Philosophical
Investigations
Mill Frege