This is evidently not the same as an implication A → B understood as a transformation of the proof conditions of A into those of B, because in the former case there is the additional information that, by hypothesis, A has been demonstrated.
The proof-of-concept that we present here, can be understood as a pioneer study towards a more direct analysis of spatial co-expression in the human brain.
However, against his own opinion, his work can better be understood as an attempt to define the logicality of constants and to structurally characterize them, than as a proof-theoretic semantics in the genuine sense.
Proof terms in \(\mathsf{LP}\) are nothing but BHK terms understood as classical proofs.
This complaint falls far short, as Quine well understood, of a proof that Carnap's appeal to analyticity was doomed.
It can be understood as applying a Popperian view to proof-theoretic semantics.
Furthermore, proofs are here understood as candidates of valid proofs, which means that the rules from which they are composed are not fixed.
According to scholars who take the form of the Proslogion as meditation seriously, that form makes it impossible to understand the argument as a "proof" for God's existence designed to convince an agnostic or atheist on a purely rational level.
Once individuation of proofs has been settled, we can distinguish between replaceable thinking and superfluous thinking, where these attributions are understood as relative to a given argument or proof.
The first was understood as analysis, providing a method of discovery, and the second as synthesis, providing a method of proof.
