The End of an Era - That of The Natural Numbers
in [Math]
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From: Jesse F. Hughes on 4 Jun 2010 10:54 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Jesse F. Hughes wrote: >> One last, pointless attempt to show Nam that his reading of Shoenfield >> is butt-wrong. >> >> It will not work. >> >> But here we go anyway. >> >> Let's apply the definitions found on p.19 to >> >> ~(Ex)(x = x) >> >> in the case where |M| = {}. That is not really a structure in >> Shoenfield's definition (a point which *still* eludes you, though it >> is explicit on p. 18), but no matter. We must, of course, assume that >> our language L has no constants and hence no closed terms. >> >> M(~(Ex)(x = x)) = T iff M((Ex)(x = x)) = F. >> >> Now, I know you don't realize Shoenfield says this, but he does. He >> says M(~B) = H_~(M(B)), but >> >> H_~(T) = F and >> H_~(F) = T. >> >> That's defined on p. 12. The *same* definition applies on p. 19. >> >> So, let's check M((Ex)(x = x)). >> >> M((Ex)(x = x)) = T iff M((x = x)_x[i]) = T for some i in L(M). >> >> L(M)is the language obtained from L by adding all the names of >> individuals of M, while i is a name in L(M). But M is empty, so there >> are *no* names in L(M). Hence, >> >> M((Ex)(x = x)) = F >> >> and thus >> >> M(~(Ex)(x = x)) = T. >> >> *That's* a simple application of Shoenfield's rules. > > How is all this relevant when the case I've been talking about > is the the degenerated case where U is empty? Where is your U above? U and |M| are the same darn thing. |M| is the support of the structure, also called the universe. U is empty in everything that I did above. > I really think your guys have a serious problem of hearing what > people technically _did or did not_ say, hypothesize, and conclude! > (So to speak, you guys are "barking at the wrong tree" and still > aren't aware of the it!). Er, right. Sure. Well, I had a go at it, but there's no stopping someone who is willfully ignorant. -- Jesse F. Hughes "It is a brilliant proof you, you math haters!!!" -- James S. Harris
From: Marshall on 4 Jun 2010 11:19 On Jun 4, 7:54 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > > Well, I had a go at it, but there's no stopping someone who is > willfully ignorant. On comp.databases.theory, we call such people "invincibly ignorant." Has a nice ring to it. Marshall
From: Aatu Koskensilta on 4 Jun 2010 11:46 herbzet <herbzet(a)gmail.com> writes: > 4) So, on what view is the syllogism valid or invalid, if there are no > men? Beats me. The syllogism seems valid to me in any case -- were > the premises true, so would the conclusion be. This is essentially just a matter of what convention to adopt. With any formalism there will always be questions of how and to what extent it models these and those arguments in informal reasoning. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Daryl McCullough on 4 Jun 2010 11:52 In article <87ljau98q0.fsf(a)dialatheia.truth.invalid>, Aatu Koskensilta says... > >Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> Look it isn't that difficult. My argument is: >> >> H implies C >> >> what you guys are "arguing" is: >> >> H' implies C >> >> Attack my H but don't attack my C with H' ! > >What's at issue is not any argument you've presented, but rather your >baffling and bizarre claim that every formula is true in a model with >empty domain. I think he said that every formula is *false* in a model with empty domain. Not that that makes much difference. -- Daryl McCullough Ithaca, NY
From: Jesse F. Hughes on 4 Jun 2010 11:29
Aatu Koskensilta <aatu.koskensilta(a)uta.fi> writes: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> Look it isn't that difficult. My argument is: >> >> H implies C >> >> what you guys are "arguing" is: >> >> H' implies C >> >> Attack my H but don't attack my C with H' ! > > What's at issue is not any argument you've presented, but rather your > baffling and bizarre claim that every formula is true in a model with > empty domain. No, it's the equally baffling and bizarre claim that every formula is *false* in a model with empty domain. -- "Your knowledge is the power that promote good thought, how then can you have good thought without powerful knowledge or how can you have powerful knowledge without learning or how can you learn without a teacher and how can a teacher teach if he or she has not learned the subject." --CA Alternative High School |