Logical truth is a phrase used in three senses, rendering it almost useless.
1. The harmony of a thought with itself. Most usually so defined, but seldom so employed. So far as this definition is distinct, it makes logical truth a synonym for logical possibility; but, no doubt, more is intended. (Hamilton, Lects. on Logic, xxvii.)
2. The conformity of a thought to the laws of logic; in particular, in a concept, consistency; in an inference, validity; in a proposition, agreement with assumptions. This would better be called mathematical truth, since mathematics is the only science which aims at nothing more. (Kant, Krit. d. reinen Vernunft, 1st ed., 294.)
3. More properly, the conformity of a proposition with the reality, so far as the proposition asserts anything about the reality. Opposed, on the one hand, to metaphysical truth, which is an affection of the ens, and, on the other hand, to ethical truth, which is telling what a witness believes to be true. (Burgersdicius, Inst. Met., chap. xviii.)