Am I a crank?
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From: fernando revilla on 31 Aug 2006 16:51 > fernando revilla wrote: > > In the posts of Jack Markan and Virgil, you have > the > > answer. > > You have one or two answers there. There may be > others. > > MoeBlee Of course, this is not a thesis. Fenando.
From: Aatu Koskensilta on 1 Sep 2006 02:39 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!". -- Aatu Koskensilta (aatu.koskensilta(a)xortec.fi) "Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 1 Sep 2006 02:49 Lester Zick wrote: > On 31 Aug 2006 10:54:03 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > >> schoenfeld.one(a)gmail.com wrote: >>> Definitions can be false too (i.e. "Let x be an even odd"). >> That's not a definition. That's just a rendering of an open formula >> whose existential closure is not a member of such theories as PA. > > Which really clears things up for us, Moe. MoeBlee's answer might be considered somewhat more obfuscated than necessary. We can rephrase it without reference to all this formal stuff and simply say that "let x be an even odd" is not a definition, it's just a shorter version "let x be a natural number and further assume that x is both even and odd" which is neither a proposition nor a definition. It's probably the beginning of a - relatively boring! - proof in which it is established that there is no natural that is both even and odd. Definitions in mathematics often appear in the following forms "An X such that P will be called a Q" "By a X we mean a Y" "When P(X,Y) we often say that X glurbles Y" ... One might quibble and say that a definition of that kind might be false if in fact no one will call an X such that P a Q; or if, in fact, the devious author doesn't really mean a Y by X; or if "we" will not, in fact, often say that X glurbles Y when P(X,Y); and so forth. However, such objections ignore the role claims such as above have in mathematical language, acting as they do essentially as stipulations, analogously as one might say "let's call whoever it was who committed this heinous crime 'John Doe'". -- Aatu Koskensilta (aatu.koskensilta(a)xortec.fi) "Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 1 Sep 2006 02:55 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. -- Aatu Koskensilta (aatu.koskensilta(a)xortec.fi) "Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Han de Bruijn on 1 Sep 2006 03:13
Dik T. Winter wrote: > In article <1157052981.177594.80970(a)p79g2000cwp.googlegroups.com> > Han.deBruijn(a)DTO.TUDelft.NL writes: > ... > > Is that so? Lately, I found that if you have ten apples and five > > people, then you can give everybody two apples. I checked > > this with the axioms of arithmetic and found that 10 / 5 = 2. > > Interesting. What are the axioms of arithmetic? Have no idea. But I'm sure that 10 / 5 = 2 can be derived from them. Han de Bruijn |