Tully = Tully
Cicero = Cicero
Hesperus = Hesperus
Cassius Clay = Cassius Clay
Cicero = Tully
In Sense and Reference, Frege argues that identity is a relation between the
signs of objects.
This is because if “a = b” is only about the objects, then that means it has no new
information than “a = a,” which as a tautology is a trivial identity.
However, “a = b” is not a trivial identity.
Hence, “a = b” is not simply about the objects.
Thus, in saying “Cicero = Tully” it must be that it's something about the names
which makes it different from “Tully = Tully.”
If the sole linguistic function of names is to pick out the thing that they name
(Mill's Thesis) then there should be no essential cognitive difference between a =
b and a = a, and we're back with something like the worry we had before.
The latter, as we've said, is trivial, and expresses no real knowledge, whereas the
former can be used to express something important.
Again, one always know the truth of a = a. However, we do not necessarily know
that a = b.
Frege's answer: all naming expressions have what he calls a sense as well
as a reference.
This is against Mill's Thesis, which argued that the sole