Path: csiph.com!eternal-september.org!feeder.eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail From: Keith Thompson Newsgroups: comp.theory Subject: Re: Simply defining =?utf-8?Q?G=C3=B6del?= Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Date: Sun, 26 Jul 2020 15:46:06 -0700 Organization: None to speak of Lines: 23 Message-ID: <87pn8hdhe9.fsf@nosuchdomain.example.com> References: <871rl8dyg1.fsf@bsb.me.uk> <87lfjfovhm.fsf@bsb.me.uk> <87zh7tok63.fsf@bsb.me.uk> <6MednYs8F9v7qYvCnZ2dnUU7-R3NnZ2d@giganews.com> <87lfjcmg9p.fsf@bsb.me.uk> <87tuxzkswv.fsf@bsb.me.uk> <87zh7ojzp8.fsf@bsb.me.uk> <877dusjsda.fsf@bsb.me.uk> <87zh7mgiux.fsf@bsb.me.uk> Mime-Version: 1.0 Content-Type: text/plain Injection-Info: reader02.eternal-september.org; posting-host="95ffb9788c7ede4782e1c216eeef2669"; logging-data="26873"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18dBKdDG4uLvCdr+1Oj5Su5" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/26.3 (gnu/linux) Cancel-Lock: sha1:lnA+lBB3TICTb7S/MjvdQyara1c= sha1:E4874mhQrHDSse0Sbxhr9H6xtSo= Xref: csiph.com comp.theory:21952 olcott writes: [...] > That a set is a subset of itself is incoherent. [...] > I disagree that the empty set has any subsets. [...] Are you familiar with the term "proper subset"? A is a proper subset of B if A is a subset of B and A is not B. If a set could not be a subset of itself, there would be no need for the term "proper subset". Every set is a subset of itself. The empty set is not an exception to this. (The word "proper" is not a moral judgement. Proper subsets and improper subsets are both subsets.) https://en.wikipedia.org/wiki/Subset -- Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com Working, but not speaking, for Philips Healthcare void Void(void) { Void(); } /* The recursive call of the void */