M. Losonsky
Davidson, "Truth and Meaning"
Argument to Show that Meaning Cannot be Reference
Explanation of symbols and terms in Davidson's argument
Read "x" as "the class of objects x such that"
Read " " as "and"
Two sentences are logically equivalent just in case they always have the same truth-value; so in all
circumstances, if one is true, so is the other one and vice versa.
The Argument in full dress:
1) The meaning of a singular term is wholly determined by its reference.
2) Sentences are complex singular terms.
3) Logically equivalent singular terms have the same reference.
4) A complex singular term does not change its reference if a singular term it contains is replaced with another
co-referential singular term.
5) Consider any two sentences R and S with the same truth-value.
6) These two sentences are logically equivalent:
(a) R
(b) The class of all objects x such that x is self-identical and R is identical to the class of all selfidentical
objects.
7) Hence (by premises 2 and 3), 6a and 6b have the same reference.
8) These two sentences are also logically equivalent.
(a) S
(b) The class of all objects x such that x is self-identical and S is identical to the class of all selfidentical
objects.
9) Hence (by premises 2 and 3), 8a and 8b have the same reference.
10) If R and S have the same truth-value, then these two terms have the same reference:
(a) the class of all objects x such that x is self-identical and R
(b) the class of all objects x such that x is self-identical and S
11) Hence (by 5 and 10), 10a and 10b have the same reference.
12) Hence (by 4 and 11), 6b and 8b have the same reference.
13) Hence (by 7, 9 and 12), R and S have the same reference.
14) Hence (by 1 and 13), R and S have the same meaning.
15) But 14 is absurd.
16) So (1) or (2) must be false.