Showing papers by "Neil Tennant published in 1993"
TL;DR: Proofs are normalizable when they can be brought into normal form by a finite sequence of applications of reduction procedures, designed to get rid of unnecessary prolixity.
Abstract: The basic idea behind that account is that we need to distinguish straightforward inconsistency, or self-contradiction, of a set of assumptions, from paradoxicality. Both involve proofs of absurdity (1). But the proofs of absurdity in connection with straightforward contradictions are normalizable, whereas those in connection with paradoxes are not. Proofs are normalizable when they can be brought into normal form by a finite sequence of applications of reduction procedures. These reduction procedures are designed to get rid of unnecessary prolixity. Such prolixity can arise, most importantly, by applying an introduction rule for a logical operator and then immediately applying the corresponding elimination rule. The result is a sentence occurrence within the proof standing as the conclusion of an application of the introduction rule and as the major premiss of an application of the corresponding elimination rule. Reductions get rid of such 'maximal' sentence occurrences, which stand as unwanted 'knuckles' in the proof. The reduction procedures for the logical operators are designed to eliminate such unnecessary detours within proofs.1
213 citations
TL;DR: There is a widespread and perhaps uncritically accepted assumption on the part of SETI researchers and popularizers that the authors could tell what an ETI might be trying to tell us, and if this assumption is abandoned, a lot follows.
Abstract: There is a widespread and perhaps uncritically accepted assumption on the part of SETI researchers and popularizers that we could tell what an ETI might be trying to tell us. We raise difficulties for this assumption. If the assumption is abandoned, a lot follows. We might even be able to argue, in a novel way, that SETI will be utterly futile.
5 citations