However, it can be difficult to determine if another's failure to have an intuition that p is epistemically significant, as they may have yet to really grasp or consider the precise proposition at issue.
In this case, it might seem that the ordinary language statement is sufficiently vague that there is likely no one precise or unambiguous proposition that represents the "correct analysis" of the proposition.
However, in a properly analyzed proposition, there is a clear isomorphism between the structure of the proposition and the structure of the fact that would make it true (PLA, 197); hence a precise and analyzed proposition is capable of being true in one and only one way (Vag, 219).
Another important application of the distinction between the constitutive and regulative uses of judgments concerns the precise semantic status of "empty" propositions (i.e., propositions lacking objective validity) that also have the same overall form as objectively valid synthetic a priori judgments.
While the mile seemed like a simple proposition (four precise laps around the quarter-mile track), the preparation was not.
Still, Alan is tall is not as close to the truth as the quite precise, but nevertheless clearly false proposition that Alan is exactly 178.5 cm tall.
The two phrases — the popular and the precise — transmit the same general proposition.
They were chatting about Wittgenstein's idea that every proposition had to have a precise place in the axiomatic order of rational language, independently of the various contexts in which it may be employed.
However, to prove the proposition, we need a more precise bound on (H_{k} x, y)), at least for large k.
In keeping with the incomplete nature of the Aristotelian treatment of hypothetical propositions, Boole did not give a precise description of possible forms for his secondary propositions.
