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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Newsgroups | comp.theory |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) |
| Date | 2020-07-25 23:05 -0600 |
| Organization | Christians and Atheists United Against Creeping Agnosticism |
| Message-ID | <rfj2v9$kqv$1@dont-email.me> (permalink) |
| References | (2 earlier) <2Y6dnX93V_vr-obCnZ2dnUU7-VnNnZ2d@giganews.com> <87imecjxm4.fsf@bsb.me.uk> <VNSdnY4F1-y0H4bCnZ2dnUU7-IvNnZ2d@giganews.com> <rfg1tr$val$1@dont-email.me> <Jt-dnYx36fMnnYDCnZ2dnUU7-LfNnZ2d@giganews.com> |
On 2020-07-25 22:04, olcott wrote: > 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? I didn't say they never translate to a logical connective. I said they have multiple meanings. > All of the logical connectives correspond to their English counter-parts > perfectly. (Except for the one that lies: "⇒"). "One and one is two" is well-formed English. It certainly doesn't correspond to ∧ "Would you like tea or coffee?" usually assumes an exclusive rather than inclusive or. "Would you like cream or sugar" usually assumes an inclusive or. Logical ∨ is unambiguously inclusive. "If you are under 21 then we cannot legally serve you alcohol" corresponds to material implication just fine. If...then also has other usages which do not. > 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. Someone might. But truth-functional logic does not. > To formalize natural language we need a correct underlying infrastructure. Right. And FOL was never designed with that goal in mind. People have certainly worked on formalizing natural language, but they design theories specifically aimed at that goal. > That logic does not have the English IF-THEN makes some key elementary > ideas inexpressible in logic. What ideas can and cannot be expressed in logic depends entirely on which logic you are talking about. Criticizing a logic for being unable to express ideas which it was never intended to express makes about as much sense as criticizing Peano Arithmetic for its inability to deal with complex numbers or Armenian poetry. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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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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