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| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) |
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| Newsgroups | comp.theory |
| References | (1 earlier) <87sgdgr0nj.fsf@nosuchdomain.example.com> <2Y6dnX93V_vr-obCnZ2dnUU7-VnNnZ2d@giganews.com> <87imecjxm4.fsf@bsb.me.uk> <VNSdnY4F1-y0H4bCnZ2dnUU7-IvNnZ2d@giganews.com> <rfg1tr$val$1@dont-email.me> |
| From | olcott <NoOne@NoWhere.com> |
| Date | 2020-07-25 23:04 -0500 |
| Message-ID | <Jt-dnYx36fMnnYDCnZ2dnUU7-LfNnZ2d@giganews.com> (permalink) |
On 7/24/2020 8:29 PM, André G. Isaak wrote: > On 2020-07-24 18:51, olcott wrote: >> On 7/24/2020 6:34 PM, Ben Bacarisse wrote: >>> olcott <NoOne@NoWhere.com> writes: >>> >>>> Then "p ⇒ q" is a fricking God damned liar thus proving that symbolic >>>> logic is broken. >>> >>> This again. >>> >>> p ⇒ q means ¬p ∨ q. If you forget the arrow and the word "implies" and >>> just write ¬p ∨ q instead, you won't get upset. You can't get rid of it >>> because ¬p ∨ q is just one of the 16 ways in which truth values can be >>> combined. If it does not express what you want, that's because you >>> picked the wrong connective to express the relationship. >>> >> >> p = "I will go to the store" >> q = "I will buy eggs at the store" >> >> p q ¬p ∨ q >> (a) T T T >> (b) T F F >> (c) F T T >> (d) F F T >> >> (a) I will either not go to the store or buy eggs while I am there T >> (b) I will either not go to the store or buy eggs while I am there F >> (c) I will either not go to the store or buy eggs while I am there T >> (d) I will either not go to the store or buy eggs while I am there T >> >> This is a quite backasswards way to say If I go to the store I will >> buy some eggs while I am there. > > Note that your p ⇒ q does not translate to "If I go to the store I will > buy some eggs while I am there'. To the extent that it translates to an > English sentence it would be "If I will go to the store, then I will buy > eggs at the store". There's no 'while I am there' anywhere in that > statement. > > You need to *stop* trying to think of logical connectives in terms of > natural language. Logic is not a theory of natural language, and its > connectives don't correspond to natural language constructions. More > importantly, logic doesn't *claim* that logical connectives correspond > exactly to natural language connectives. Every introductory logic text > will emphasize this within the first chapter or two. > > None of the connectives ∧, ∨, →, or ¬ correspond to natural language > and, or, if...then, or not. That is because in natural language, every > single one of these connectives is ambiguous. I am not going to the store translates to what: I might go to the store? All of the logical connectives correspond to their English counter-parts perfectly. (Except for the one that lies: "⇒"). That some people do not say what they mean or mean what they say is neither the fault of natural language nor it limimitation. > In logic, each of these is > precisely defined to have exactly one meaning. > > I suggest you simply stop thinking of ∧, ∨, →, and ¬ as 'and', 'or', > 'if..then' and 'not' and instead just think of them as 'caret', > 'turned-caret', 'right arrow', and 'broken dash'. > > André > We really need a way to say if p then q if not p then no one knows about q. To formalize natural language we need a correct underlying infrastructure. That logic does not have the English IF-THEN makes some key elementary ideas inexpressible in logic. -- Copyright 2020 Pete Olcott
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Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-24 17:26 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) David Kleinecke <dkleinecke@gmail.com> - 2020-07-24 15:45 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-24 17:53 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Kaz Kylheku <793-849-0957@kylheku.com> - 2020-07-24 23:55 +0000
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-24 15:47 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-24 17:57 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-24 16:19 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-24 19:20 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-24 18:29 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-25 23:14 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) André G. Isaak <agisaak@gm.invalid> - 2020-07-25 23:13 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-25 00:34 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-24 19:51 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) André G. Isaak <agisaak@gm.invalid> - 2020-07-24 19:29 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-25 23:04 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) André G. Isaak <agisaak@gm.invalid> - 2020-07-25 23:05 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-25 02:39 +0100
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