Am I a crank?
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From: Randy Poe on 1 Sep 2006 15:21 Lester Zick wrote: > On Fri, 01 Sep 2006 09:49:03 +0300, Aatu Koskensilta > <aatu.koskensilta(a)xortec.fi> wrote: > > >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'". > > Is a stipulation a statement? Is a definition a statement? Is a > theorem a statement? Then my question remains as to what the > difference is between or among statements such that one can be true or > false and others not? Obviously the answer is that there is no such > difference. "Obviously"? Consider the example given above. It constitutes a definition of the phrase "John Doe" within the context of some legal process (let's say a trial). Are you prepared to declare that statement as true or false? Compare that to: "The defendant's name is John Doe." Do you agree that the defendant has a name, and that there are only two possibilities, that the name is John Doe or that it is not? Is it really "obvious" to you that "Let's call the defendant John Doe" must be either true or false? - Randy
From: Virgil on 1 Sep 2006 15:23 In article <vcugf2ht4c900qhea350gp8lc1vk7mvk5d(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > On Thu, 31 Aug 2006 20:51:38 EDT, fernando revilla > <frej0002(a)ficus.pntic.mec.es> wrote: > > >> 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. > > Nor is it an explanation why one kind of statement is demonstrable and > the other not. There are many who have been able to figure out which is which without help. Zick is apparently not one of them, but needs to be spoon fed about even the most miniscule details.
From: MoeBlee on 1 Sep 2006 15:24 Lester Zick wrote: > It really doesn't matter the form of the statement or > abstruse reformulations. They all entail predicate combinations and > predicate interrelations which are either true, false, or ambiguous. But that does not entail that there aren't distinctions among such statements. For example, some are atomic, some are compound, etc. And one of the distinctions I menioned is that certain statements uphold the criteria of eliminability and non-creativity and others don't. Those that uphold those criteria are those that are correctly formed definitions. Those that do not uphold the criteria are either not definitions or not correctly formed definitions. MoeBlee
From: Virgil on 1 Sep 2006 15:28 In article <mgugf2t1k9l25c2i7hcf6ojsq9umcjo0oh(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > On Thu, 31 Aug 2006 17:50:38 -0600, Virgil <virgil(a)comcast.net> wrote: > >> Just as you have nothing to do with any real mathematics. > > > >I have a good deal more to do with real mathematics than Zick has > >evidenced that he has to do with it. > > So you claim. If you stacked all your undemonstrated claims end to end > they still wouldn't reach a conclusion. Zick, on the other hand, leaps to conclusions on no evidence at all. > > >Zick speaks from virtually total ignorance and an apparently total > >unwillingness to learn anything more. > > Well more likely just a little reluctance to fall into line with the > rest of the stormtroopers. "Stormtroopers"? Zick has a remarkably biased view of what goes on in the world of mathematics if he thinks that mathematicians can be induced to march around in lockstep.
From: Virgil on 1 Sep 2006 15:43
In article <1lugf2hnqivjk9jpitvd0k062hhihq77hb(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > On Thu, 31 Aug 2006 23:08:10 GMT, "Dik T. Winter" <Dik.Winter(a)cwi.nl> > wrote: > > >In article <1g6ef29j95erganm4b51kteh5ab6d7pcdf(a)4ax.com> Lester Zick > ><dontbother(a)nowhere.net> writes: > >... > > > >Zick claims that mathematicians claim their axioms to be true. > > > >What evidence does he have of this claim? > > > >Like most of his claims here, none! > > > > > > Actually Zick claims that modern mathematikers claim their axioms are > > > not true. > > > >Mathematicians do not claim axioms to be either true or false. They are > >non-provable basic assumptions. And when reasoning within a certain set > >of axioms they are assumed to be true. > > Okay. So how exactly can they be assumed true if their axioms are not > assumed true? In an axiom system anything deducible from those axioms, including the axioms themselves, is deemed "true in that system", but not necessarily true outside it. > > The problem is that they're routinely assumed true Only with in some system of axioms, but not outside that system. > and referred to as true without regard to assumptions of truth for > their axioms. Very much with regard for these assumptions. > So are definitions. Definitions are generally only useful within certain axioms systems. There is no use in defining a triangle if there is not going to be anything geometrical involved. But there is nothing tha would prevent one from making useless definitins in any axiom system. > All that is really demonstrated of > theorems is the absence of logical inconsistency between them and > their axioms and not truth. Precisely. But that allows theorems of the form "if these axioms are all true then that proposition is also true", which is the form all mathematical theorems take. |