'When Are Relations Neither True Nor False?
in [Math]
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From: Newberry on 27 Feb 2010 00:32 On Feb 25, 4:28 am, Frederick Williams <frederick.willia...(a)tesco.net> wrote: > Newberry wrote: > > > How can you arrive at the conclusion that something is true other than > > by a proof? > > If you ever come across a paper of Tarski's called Truth and Proof you > should read it: Scientific American, late sixties. If you want a > precise reference I'll find one for you. I wonder if you can answer it in your own words. > > BTW, there cannot be any intuition or probability that ZFC > > or PA are consistent. > > Oh come, come, how do you know what people can intuit? Needless to say, I meant that if PA were the model of people's thought processes then they could not have any intuition that PA is consistent. > > Why did Dedekind frame Peano's axioms in just the way he did? Because > they squared with his intuitions.
From: Don Stockbauer on 27 Feb 2010 04:45 "Darlene, I want to have relations with you." "Are they true or false?" "Forget it. Let's post to sci.math/sci.logic instead."
From: Jesse F. Hughes on 27 Feb 2010 07:40 Newberry <newberryxy(a)gmail.com> writes: > For what I know ordinary mathematics may well go on by using "there > are no counterexamples to GC less than 27." But if you want to do > any work in the foundations of mathematics you need higher > precision. So you say, yet curiously folks who *do* work in the foundations of mathematics do *not* seem to share your view. Honestly, this is a Quixotic battle you're waging, as far as I can tell. Good luck with it. -- Jesse F. Hughes "You're ketchup, so I'll put you on meatloaf!" -- Quincy P. Hughes, age five, tries his hand at insults
From: Aatu Koskensilta on 27 Feb 2010 09:56 Newberry <newberryxy(a)gmail.com> writes: > For what I know ordinary mathematics may well go on by using "there > are no counterexamples to GC less than 27." But if you want to do any > work in the foundations of mathematics you need higher precision. In ordinary mathematical language and reasoning there is no distinction between "there are no counterexamples to GC less than 27" and "it's not true that there are counterexamples to GC less than 27" and thus nothing to be highly precise about. We can of course introduce whatever ideas and semantics we want on which such a distinction can be understood, but in the wider scheme of things such novelties have any interest only in so far as we can relate them in some informative manner to our actual mathematical experience and reasoning. To take another example, consider Priest's suggestion that there are true arithmetical contradictions, of the form "there is a natural n such that P(n) and not-P(n)" with P a decidable predicate. He also defines a non-standard semantics (essentially, just a bit of standard mathematics) on which we can make sense of this. However, absent some account of how this semantics relates to our actual mathematical reasoning about naturals, the idea, that number theorists might one day solve, say, the Goldbach conjecture by showing that there is an even natural greater than two that can't be expressed as the sum of two primes but can be expressed as the sum of two primes, remains baffling and entirely vacuous. The same is true of your various musings and logical fiddling. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Newberry on 27 Feb 2010 12:37
On Feb 27, 4:40 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > Newberry <newberr...(a)gmail.com> writes: > > For what I know ordinary mathematics may well go on by using "there > > are no counterexamples to GC less than 27." But if you want to do > > any work in the foundations of mathematics you need higher > > precision. > > So you say, yet curiously folks who *do* work in the foundations of > mathematics do *not* seem to share your view. > > Honestly, this is a Quixotic battle you're waging, as far as I can > tell. Good luck with it. Do you have anything to say about the substance? |