The End of an Era - That of The Natural Numbers
in [Math]
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From: Marshall on 14 May 2010 21:24 On May 13, 11:06 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > They didn't want to call me as a "crank" so they > labeled me "philosophical" and somehow that might have stayed in > people's minds. For the record: you, Nam Nguyen, are a crank. Marshall
From: Jesse F. Hughes on 14 May 2010 21:51 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > For what it's worth, I actually didn't believe you intended to jump > on the bandwagon. They didn't want to call me as a "crank" so they > labeled me "philosophical" and somehow that might have stayed in > people's minds. Oh, goodness, no! You're ramblings are *not* philosophical. -- Jesse F. Hughes "Quincy, why should you not play with matches?" "Because... [pause] Aahhh! I'm on fire!!"
From: Nam Nguyen on 15 May 2010 01:17 Alan Smaill wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> Marshall wrote: >>> On May 13, 7:13 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>> ... the fact that nobody could have a single example of a _FOL_ >>>> absolute (formula) truth. >>> x=x >>> >> Is that formula true in the theory T = {(x=x) /\ ~(x=x)}? > > What does "true in a theory" mean? How about true in all models of a consistent theory (formal system). > > Please be precise. >
From: Nam Nguyen on 15 May 2010 01:37 Marshall wrote: > On May 13, 9:38 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> Marshall wrote: >>> On May 13, 8:01 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>> The thing escapes my understanding is why my opponents and the >>>> "standard theorists" never want to admit we only have an intuitive >>>> knowledge of the natural numbers. Why is that? >>> Because it's wrong. >>> 1+1=2 is not an intuition. >> S0 + S0 = SS0 is also true in arithmetic modulo 2. So do the naturals >> form the arithmetic modulo 2? > > This question is merely a diversion from the discussion of whether > "1+1=2" in an intuition or not, Be correct in arguing, Marshall. The discussion is why the "standard theorists" "never want to admit we only have an intuitive knowledge of the natural numbers", and you defended them in saying that 1+1=2 is not an intuitive knowledge. And I pointed out to you that if you can't make the distinction between 1+1=2 in modulo arithmetics and in the naturals then the knowledge of "1+1=2" is true in the naturals is only an intuitive knowledge (i.e. not a precise knowledge). (Pointing out is not a diversion!) > and furthermore is a question we > both know the answer to. My answer to that question is that "1+1=2" is true in the naturals is an intuition. Which is different from yours. So quit pretending you could force your incorrectness into people's reasoning. > It is a waste of your time and mine. What a mediocre, childish, and irrelevant saying!
From: Nam Nguyen on 15 May 2010 01:43
Marshall wrote: > On May 13, 9:30 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> Marshall wrote: >>> On May 13, 7:13 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>> ... the fact that nobody could have a single example of a _FOL_ >>>> absolute (formula) truth. >>> x=x >> Is that formula true in the theory T = {(x=x) /\ ~(x=x)}? > > The formula is true in every model of T. So an inconsistent system like T has a model? > In fact, the formula is true > in every model. Every model of what? > > The formula is provable in T. The formula is provable in every theory. Sure. Including inconsistent systems. But what does this observation have to do with my question above? |