Am I a crank?
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From: Virgil on 1 Sep 2006 14:40 In article <2dtgf2havu47vvhrhsv4u9qqtvperloon3(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > 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 ... If Zick wishes, for some odd purpose of his own, to assign truth values to definitions or to refuse to recognize the truth values of the propositions in some exam system, no one is preventing him, but what he will be doing is not part of standard mathematics nor compatible with standard logic. But Zick has already shown his distain for both.
From: Lester Zick on 1 Sep 2006 14:43 On Fri, 01 Sep 2006 09:55:52 +0300, Aatu Koskensilta <aatu.koskensilta(a)xortec.fi> wrote: >Han de Bruijn wrote: >> Virgil wrote: >> >>> Let's see Zick empirically establish the axiom of infinity, then. >> >> Nobody can. Therefore it does not correspond to (part of an) implicit >> definition of some real world thing. Therefore it will do no harm if >> we throw it out. > > When we run over libraries, persuaded of these principles, what havoc > must we make? If we take in our hand any volume; of divinity or school > metaphysics, for instance; let us ask, /Does it contain any abstract > reasoning concerning quantity or number/? No. /Does it contain any > experimental reasoning concerning matter of fact and existence/? No. > Commit it then to the flames: for it can contain nothing but sophistry > and illusion. Well obviously truthless definitions can safely be committed. If not to the flames then to exactly to those bibliographic reliquaries where none will be chance to read them anyway. ~v~~
From: Virgil on 1 Sep 2006 14:44 In article <7ltgf2tarf5puaeiesb3v9ka7rldm2uvlr(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > 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? For which words can Zick not find definitions? In the Google search window, enter the word 'define' followed by the word you need looked up and then do a search.
From: Lester Zick on 1 Sep 2006 14:46 On 1 Sep 2006 04:32:57 -0700, schoenfeld.one(a)gmail.com wrote: > >Jesse F. Hughes wrote: >> schoenfeld.one(a)gmail.com writes: >> >> > Definitions can be false too (i.e. "Let x be an even odd"). >> >> That is not what one usually means when he says "mathematical >> definition". A mathematical definition is a stipulation that a >> particular phrase means such-and-such. >> >> Like: A /group/ is a set S together with a distinguished element e and >> an operation *:S x S -> S such that blah blah blah >> >> But what you're doing is different. You are specifying that a >> variable should be interpreted as a certain kind of number, namely an >> even odd. Even though there is no such thing as an even odd, however, >> this is not false. How could it be false? It's an imperative, >> telling the reader to do something (namely, assume that x names an >> even odd). > >It is false as it contradicts itself. The statement 'x is an even odd' >is an alias for a sequence of (first order) logical propositions >containing at least one contradiction. It's not polite to tease the animals.There's a reason they're animals. >> If I tell you to find integers a, b such that a/b = sqrt(2), I haven't >> said something false. I've given you a command that is impossible to >> fulfill, but it isn't false. Imperatives don't have truth values. >> >> I'm not sure that "Let x be an even odd," is impossible to do in the >> same sense that finding a rational equal to sqrt(2) is impossible. I >> think that this imperative just means: Assume that x satisfies certain >> conditions. And as far as I can see, I can assume impossible facts >> willy nilly. > > >> -- >> Jesse F. Hughes >> >> Jesse: Quincy, you should trust me more. >> Quincy (age 4): Baba, I never trust you. And I've got good reasons. ~v~~
From: MoeBlee on 1 Sep 2006 14:48
Lester Zick wrote: > .All that is really demonstrated of theorems > is the absence of logical inconsistency between them and their axioms > and not truth. No, I told you a long time ago that a proof of a theorem is a proof that the theorem is entailed by the axioms, not just that the theorem is consistent with the axioms (and entailment entails consistency as long as the axioms are consistent). That you still don't understand the difference between entailment and consistency indicates again your lack of understanding even the most basic matters of logic. MoeBlee |