Am I a crank?
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From: fernando revilla on 1 Sep 2006 05:52 Han deBruijn wrote : > Have no idea. But I'm sure that 10 / 5 = 2 can be > derived from them. Han de Bruijn Let us see, 10/5= 2 iff 2*5=10 ( by definition of the quotient ). Now 2*5=5+5 ( by definition of the product ). Now 5+5=10 is synthetic a priory and has to do with the pure intuition of time. Surely there are mathematicians who think that global formalism goes further mathematical truth, but that is another question. Fenando.
From: Han de Bruijn on 1 Sep 2006 10:21 Jesse F. Hughes wrote: > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > >>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. > > I thought you "checked this with the axioms of arithmetic". How could > you do that if you have no idea what the axioms are? Oh, come on, Jesse! I checked this with arithmetic. Arithmetic is based upon axioms. So I checked it with the axioms of arithmetic. No ? Han de Bruijn
From: Han de Bruijn on 1 Sep 2006 10:22 Dik T. Winter wrote: > In article <e9d42$44f7dda1$82a1e228$28200(a)news1.tudelft.nl> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > > 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. > > And you said you had checked it with the axioms of arithmetic? So > you were talking nonsense when you wrote that? See my response to Jesse F. Hughes. Han de Bruijn
From: Jesse F. Hughes on 1 Sep 2006 11:53 Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > Jesse F. Hughes wrote: > >> I thought you "checked this with the axioms of arithmetic". How >> could you do that if you have no idea what the axioms are? > > Oh, come on, Jesse! I checked this with arithmetic. Arithmetic is based > upon axioms. So I checked it with the axioms of arithmetic. No ? No. -- "[Criticizing JSH's mathematics will result in] one of the worst debacles in the history of the world. It is foretold in most mythologies and religions. And yes, you are the ones, the cursed ones, who destroy the world." --James S. Harris reads from the Aztec Book of the Damned Mathematicians
From: MoeBlee on 1 Sep 2006 13:06
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. By 'alias' of a sequence of logical propositions', I guess you mean that it is an open formula. Open formulas are neither true nor false in a model, but rather are satsified or not satisfied in the model. Of course, an open formula is valid (satisfied by every model) iff a universal closure of that open formula is true in all models, but that is not the same as saying that the open formula is true or false. Anyway, neither 'x is an even odd' nor 'let x be an even odd' are definitions. The first one is just an open formula, and the second one is either a universal or existential instantiation. (Also, other posters are claiming that definitions are imperatives. If that isn't stipulated in a syntax, then I don't see it at work in first order predicate logic, not even in a meta-theory. Even if one could formulate the notion of imperatives in such contexts, I don't see what it would add while it does unnecessarily complicatie things. The Lesniewski approach already provides a fine explication of definitions, and it is completely formalizable in the meta-theory.) MoeBlee |