Path: csiph.com!eternal-september.org!feeder.eternal-september.org!.POSTED!not-for-mail From: Alexis Newsgroups: comp.theory,comp.lang.c++,comp.lang.c,comp.ai.philosophy Subject: Re: I corrected the very subtle error in the halting problem Followup-To: comp.theory Date: Sun, 28 Sep 2025 12:52:10 +1000 Organization: A noiseless patient Spider Lines: 24 Message-ID: <87seg71e79.fsf@gmail.com> References: <10b3hmc$avbp$1@dont-email.me> <10b3j44$bfb6$1@raubtier-asyl.eternal-september.org> <10b481v$i8bv$2@dont-email.me> <10b6cbr$13cvv$1@raubtier-asyl.eternal-september.org> <10b6d30$13h5r$3@dont-email.me> <10b6h4c$13hh3$4@dont-email.me> <10b6hqn$164mh$1@dont-email.me> <20250926121612.571@kylheku.com> <10b6qp0$18q7n$1@dont-email.me> <20250926130112.166@kylheku.com> MIME-Version: 1.0 Content-Type: text/plain Injection-Date: Sun, 28 Sep 2025 02:52:17 +0000 (UTC) Injection-Info: dont-email.me; posting-host="0bc136cf82140407253df4e6e97f99b1"; logging-data="2226315"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/rpE8HJ5Lys9ckPil+p30sV6XdICL0KUg=" User-Agent: Gnus/5.13 (Gnus v5.13) Cancel-Lock: sha1:4iqanWaoi6SDKeua5CYlb3vbDks= sha1:w1xXVSv1RnXF79LMEAeSmvx/FjU= Xref: csiph.com comp.theory:130724 comp.lang.c++:122788 comp.lang.c:394414 comp.ai.philosophy:31952 Kaz Kylheku <643-408-1753@kylheku.com> writes: > A contradiction is a piece of foreign material in a formal system. It > is nonsensical to bring it in, and assert it as a truth; it makes no > sense to do so. Once you do, it creates contagion. As an aside, the field of paraconsistent logic, which excludes the PoE, tries to study and develop 'inconsistency-tolerant' formal systems: https://en.wikipedia.org/wiki/Paraconsistent_logic > The entailment relations of paraconsistent logics are propositionally > weaker than classical logic; that is, they deem fewer propositional > inferences valid. The point is that a paraconsistent logic can never > be a propositional extension of classical logic, that is, > propositionally validate every entailment that classical logic > does. In some sense, then, paraconsistent logic is more conservative > or cautious than classical logic. It is due to such conservativeness > that paraconsistent languages can be more expressive than their > classical counterparts including the hierarchy of metalanguages due to > Alfred Tarski and others. Alexis.