Am I a crank?
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From: Lester Zick on 1 Sep 2006 13:59 On Thu, 31 Aug 2006 16:53:04 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <0kfef21lbrjan4tjb6rq43vvt3etr8jajf(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Thu, 31 Aug 2006 12:57:46 -0600, Virgil <virgil(a)comcast.net> wrote: >> > >> >He is right, in the sense that definitions are requests to let one thing >> >represent another, and while one can refuse a request, it is silly to >> >call a request either true or false. >> >> So now it's silly to call axioms and definitions in modern math and >> theorems based on them true? > >Calling an axiom true is not silly, but an axiom is not provably true >unless the proof derives some assumptions made about what is true. Okay. So what does that mean? >Calling a definition true is silly because true or false are not >possible attributes of definitions. So axioms don't define anything? >Theorems are statements have a proof based on the axiom system in which >they are theorems. Note that every theorem by definition requires an >axiom system and a proof that it follows from those axioms( and "proof" >means logically valid proof). So once more axioms don't define anything? ~v~~
From: Lester Zick on 1 Sep 2006 14:01 On Thu, 31 Aug 2006 20:51:13 -0400, "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote: >Lester Zick <dontbother(a)nowhere.net> writes: > >> So is Virgil right or wrong that definitions in modern math can be >> neither true nor false? > >Of course they cannot be true or false. Definitions are stipulations; >that is, they specify how a term will be understood hereafter. So axioms don't stipulate how a term will be understood in the hereafter? >Clearly, definitions are not truth-bearing statements. And clearly stipulations as to how a term will be understood are not truth bearing statements either. They're just a little bit pregnant. ~v~~
From: Lester Zick on 1 Sep 2006 14:06 On Fri, 01 Sep 2006 09:39:56 +0300, Aatu Koskensilta <aatu.koskensilta(a)xortec.fi> wrote: >Lester Zick wrote: >> I didn't ask what common approaches are, Moe, and I don't care what >> common approaches are. I asked what the difference is between >> definitions and propositions. > >You've already been given the answer: propositions are statements that >express that something is that way or this way, and are true or false >according to whether that something really is that way or this way. >Definitions, on the other hand, are stipulations: "let's call something >something". You might object to a stipulation, crying "no, let's not do >that!", but not with a "no, that's not true!". In other words I've been given the bald assertion that definitions are statements which are neither true nor false and I've been given the bald assertion that propositions are statements which are true or false but I've been given no explanation as to why one statement is one and another statement the other except neomathematikers can demonstrate one statement and cannot demonstrate the other and are too lazy or stupid to do anything about the situation. ~v~~
From: Lester Zick on 1 Sep 2006 14:07 On Thu, 31 Aug 2006 17:03:57 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <bofef29jedcu2em78lm1euh0cphvqur009(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Thu, 31 Aug 2006 13:00:40 -0600, Virgil <virgil(a)comcast.net> wrote: >> >> >In article <ub6ef21d9o1m22bbhok6d0knbu12v0dt5d(a)4ax.com>, >> > Lester Zick <dontbother(a)nowhere.net> wrote: >> > >> > >> >> So how exactly do definitions differ from propositions? >> > >> >Definitions are requests to let one thing represent another, whereas >> >propositions are declarations that something is true. >> >> So propositions can be true based on definitions which are not true? >> Hmm, curiouser and curioser. > >Not quite. > >If a proposition containing definienda remains true when every >definiendum appearing in it is replaced by its definiens, only then >need it be true, but by then it is entirely independent of any >definitions. Which means what exactly? ~v~~
From: Lester Zick on 1 Sep 2006 14:17
On Thu, 31 Aug 2006 19:20:15 EDT, fernando revilla <frej0002(a)ficus.pntic.mec.es> wrote: >DontBother(a)nowhere.net wrote: > >> So how exactly do definitions differ from >> propositions? > >In the posts of Jack Markan I can't recall posts of Jack Markan on the subject. > and Virgil, you have the >answer. No, what I have from Virgil at least is the bald assertion that there are certain kinds of statements called definitions which are not subject to proof and certain kinds of statements called theorems which are subject to proof but no indications whatsoever of the difference between the two which renders one demonstrable and the other not except that neomathematikers are too lazy or stupid to be taxed with demonstrations of truth in the case of definitions but nevertheless want to enter them in the record and use them as if they were true. > If you give a name to something with sense, >you have a definition. And what if you give a name to something with no sense? > Nobody say " a horse carriage or >motor carriage that may be hired for short journeys" >usually we say " cab ", that is a definition, an agreement >( time is gold ! ). Propositions are not agreements. Both definitions and propositions are however statements. ~v~~ |