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Path: ...!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: Richard Damon <richard@damon-family.org> Newsgroups: sci.logic,comp.theory Subject: Re: Truthmaker Maximalism and undecidable decision problems Date: Sun, 9 Jun 2024 14:29:25 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <v44sa5$3egpa$10@i2pn2.org> References: <v44i60$3jnc8$1@dont-email.me> <v44o5t$3l9t2$1@dont-email.me> <v44r29$3egpa$5@i2pn2.org> <v44rd0$3m841$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 9 Jun 2024 18:29:25 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="3621674"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: <v44rd0$3m841$2@dont-email.me> X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US Bytes: 4058 Lines: 76 On 6/9/24 2:13 PM, olcott wrote: > On 6/9/2024 1:08 PM, Richard Damon wrote: >> On 6/9/24 1:18 PM, olcott wrote: >>> On 6/9/2024 10:36 AM, olcott wrote: >>>> *This has direct application to undecidable decision problems* >>>> >>>> When we ask the question: What is a truthmaker? The generic answer is >>>> whatever makes an expression of language true <is> its truthmaker. This >>>> entails that if there is nothing in the universe that makes >>>> expression X >>>> true then X lacks a truthmaker and is untrue. >>>> >>>> X may be untrue because X is false. In that case ~X has a truthmaker. >>>> Now we have the means to unequivocally define truth-bearer. X is a >>>> truth-bearer iff (if and only if) X or ~X has a truthmaker. >>>> >>>> I have been working in this same area as a non-academician for a few >>>> years. I have only focused on expressions of language that are {true on >>>> the basis of their meaning}. >>>> >>> >>> Now that truthmaker and truthbearer are fully anchored it is easy to see >>> that self-contradictory expressions are simply not truthbearers. >>> >>> “This sentence is not true” can't be true because that would make it >>> untrue and it can't be false because that would make it true. >>> >>> Within the the definition of truthmaker specified above: “this sentence >>> has no truthmaker” is simply not a truthbearer. It can't be true within >>> the above specified definition of truthmaker because this would make it >>> false. It can't be false because that makes >>> it true. >>> >>> >> >> Unless the system is inconsistent, in which case they can be. >> >> Note, > > When I specify the ultimate foundation of all truth then this > does apply to truth in logic, truth in math and truth in science. Nope. Not for Formal system, which have a specific definition of its truth-makers, unless you let your definition become trivial for Formal logic where a "truth-makers" is what has been defined to be the "truth-makers" for the system. > > *Three laws of logic apply to all propositions* > ¬(p ∧ ¬p) Law of non-contradiction > (p ∨ ¬p) Law of excluded middle > p = p Law of identity Nope, only for systems that accept those requirements. There are (typically non-binary) systems that do not include one or both of the first two "laws". I am not sure about the third, while I can't think of a system that doesn't have the law of identity, I am not sure it is absoultely required. (after a bit of research) In Schrödinger logic https://en.wikipedia.org/wiki/Schrödinger_logic the law of identity is greatly restricted, because the statement x = y is not a well-formed formula in many cases, so it might not be true that x = x > > Inconsistent systems cannot be truthmakers > in those cases where they derive inconsistency. > Illogical. "inconsistent SYSTEMS" are not the same sort of thing as a "truth-maker" as the first is a system of logic, and the second is a statement expressed in such a system.