that case the sentence would no longer refer to the subject matter, but only to its mode of
designation.To deal with the evident difference in the cognitive value of sentence pairs such
as ‘ ’ and ‘ ’ where a and b are designations of the same object, Frege
proposes a distinction between the sense (Sinn) of a term and its reference
(Bedeutung). He illustrates this distinction with an equilateral triangle and the
intersection point of its medians, a, b, and c (Figure 4). This point can be
described as the point of the intersection of a and b, of b and c, of a and c, or of
a, b, and c. These descriptions have different senses, but the same reference.
- Equilateral triangle with three medians.
In any universe of discourse, there are, moreover, expressions that have a sense
but no reference. Anyone can think up examples, such as, ‘the longest English
sentence’, ‘the bachelor’s wife’, or ‘a spacecraft travelling at three times the
speed of light’.
Logicians and philosophers in the Aristotelian traditions accepted Frege’s tenet,
which links identity with the theory of the meaning of signs. To avoid confusion,
the reference, or extensional meaning, of an expression must be distinguished
from its sense, or intensional meaning. One important consequence of this line of
thought was a reinterpretation of Leibniz’s Law. That synonymous expressions
should be interchangeable in all contexts was henceforth understood as holding