# What is the most profound insight ever conceived by armchair conceptual analysis?

A rigorous, set-theoretic definition of truth and meaning, due entirely to yours truly.

A ‘truth’ is a true proposition, a proposition being what is affirmed, denied, believed, disbelieved, etc., examples being *snow is white*, *grass is green*, and the like.

What is a proposition?

A proposition is a class of properties---of characteristics, in other words---and for a proposition to be true is for the members of the corresponding property-set to be instantiated.

Let k be the smallest set containing the following three properties.

P1. The property of being identical with John P2. The property of smoking, and

P3. The property of being a thing x such that x is identical with John and such that x smokes.

John smokes if, and only if, these three properties are jointly instantiated. In other words, if they are instantiated, then John smokes; and if John smokes they are instantiated.

Therefore, the proposition *John smokes *is to be identified with k and that proposition’s being

*true *is to be identified with those three properties’ being jointly instantiated.

To be sure, if P3 is instantatiated, then so are P1 and P2; so it might seem that *John smokes *could be identified with P3, and its being true with P3’s being instantiated, it being unnecessary to identify that proposition with k, since k contains P1 and P2.

But there are two conditions that a viable theory of truth must satisfy. First, it must account for any given proposition’s truth-conditions. In other words, for any given proposition T, if T is true under such and such circumstances, then a viable theory of truth must account for that fact; and if T is false under thus and such circumstances, a viable theory of truth must account for that fact as well.

At the same time, a viable theory of truth must *also *do justice to the internal, structural properties of propositions. It must account for their *decompositional *properties, in other words. It is a datum that *John smokes *has a discrete part corresponding to John, a second discrete part corresponding to *smokes*, and a third part, this being an improper part, corresponding to the fusion of the two.

Our theory is consistent with these facts about the decomposition of *John Smokes. *In general, our theory, unlike the other theory considered, is consistent with the decompositional properties of propositions.