Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: sci.logic Subject: Re: A different perspective on undecidability --- incorrect question Date: Mon, 21 Oct 2024 21:04:14 -0500 Organization: A noiseless patient Spider Lines: 31 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Tue, 22 Oct 2024 04:04:14 +0200 (CEST) Injection-Info: dont-email.me; posting-host="0250fa4f333a237bb4a9bec06e6bd0e6"; logging-data="1245427"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19kY2cFbEIIaRxw7HFjFkqp" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:jgw4eIwp9XQzDFXTV0YKHJn5UJ8= Content-Language: en-US In-Reply-To: X-Antivirus: Norton (VPS 241021-4, 10/21/2024), Outbound message X-Antivirus-Status: Clean Bytes: 2266 On 10/16/2024 11:37 AM, Mikko wrote: > On 2024-10-16 14:27:09 +0000, olcott said: > >> The whole notion of undecidability is anchored in ignoring the fact that >> some expressions of language are simply not truth bearers. > > A formal theory is undecidable if there is no Turing machine that > determines whether a formula of that theory is a theorem of that > theory or not. Whether an expression is a truth bearer is not > relevant. Either there is a valid proof of that formula or there > is not. No third possibility. > After being continually interrupted by emergencies interrupting other emergencies... If the answer to the question: Is X a formula of theory Y cannot be determined to be yes or no then the question itself is somehow incorrect. An incorrect question is an expression of language that is not a truth bearer translated into question form. When "X a formula of theory Y" is neither true nor false then "X a formula of theory Y" is not a truth bearer. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer