The proof layer is the layer at which meanings are explained: The meaning of a proposition A is explained by telling what counts as a proof (object) for A. The distinction made between canonical and non-canonical proofs is a distinction at the propositional and not at the judgement al layer.
This may make a difference in particular for the explanation of implication, where, instead of only the information under what condition something counts as a proof of p, we now can also take into consideration that, by hypothesis, a concrete construction for p has been effected.
Believers and non-believers should be able to agree on what counts as a good proof in a given area even if they expect different results from such a proof.
That PT Cruiser is counted as a truck.
To count as a finitary consistency proof, the operation itself must be acceptable from the finitist standpoint, and the proofs required must use only finitarily acceptable principles.
They do not say the pileated case is airtight, but argue that the images can not be counted as proof of an ivory bill.
For Clarke Cooper, the executive director of Log Cabin Republicans, a group leading the fight for gay rights within the Republican Party, the mere presence of this volume counted as proof that the GOP is beginning to welcome gays into its fold.
Whether Gleevec will come to count as the proof of a new and powerful principle or, rather, as yet another broken promise remains to be seen.
If that doesn't count as proof beyond a reasonable doubt, it is hard to imagine what would.
As we shall see, however, relevant logic does provide us with a relevant notion of proof in terms of the real use of premises (see the section "Proof Theory" below), but it does not by itself tell us what counts as a true (and relevant) implication.
Do thermals count as a gadget?
