According to the OED, the earliest attestation of truth value in English is in Russell (1903), where it occurs in a discussion of Frege's theory of judgment:
There are, we are told..., three elements in judgment: (1) the recognition of truth, (2) the Gedanke, (3) the truth-value (Wahrheitswerth). (p. 502)
As Russell indicates, truth value is a direct translation of Frege's German term Wahrheitswerth. Here is the passage in Frege (1891) where he introduces this term:
Ich sage nun: »der Werth unserer Function ist ein Wahrheitswerth« und unterscheide den Wahrheitswerth des Wahren von dem des Falschen. Den einen nenne ich kurz das Wahre, den andern das Falsche. Hiernach bedeutet z.B. »2² = 4« das Wahre ebenso, wie etwa »2²« 4 bedeutet. Und es bedeutet »2² = 1« das Falsche. (p. 13)
(Now I say: "The value of our function is a truth value" and distinguish the truth value of what is true from that of what is false. The one I call briefly the True, the other the False. From this, for example, "2² = 4" means the True, just about as "2²" means 4. And "2² = 1" means the False.)
Note: Frege uses an archaic spelling, and Russell follows him in this. The more standard spelling in modern German would be Wahrheitswert, with no H at the end.
References
- Frege, G. (1891). Function und Begriff. Hermann Pohle.
- Russell, B. (1903). The Principles of Mathematics. Cambridge University Press.
