'When Are Relations Neither True Nor False?
in [Math]
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From: Marshall on 11 Apr 2010 16:39 On Apr 11, 8:25 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Marshall <marshall.spi...(a)gmail.com> writes: > > I don't see any reason to pay much attention to anyone's > > intuition, my own included. > > This is a sober attitude. I am mostly a sober person, in that I am drunk less than half the time. > > "Intuition" is just a fancy word for "hunch." > > "Intuition" can mean pretty much anything, from a vague hunch to > something very specific, as in e.g. Kant's thought. Indeed so, which is exactly what makes it a poor choice when used in contexts such as this newsgroup. Marshall
From: Nam Nguyen on 11 Apr 2010 17:08 Alan Smaill wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> David Bernier wrote: > >>> Do you see problems with starting with a false premise, not(P) ? >> Yes. I'd break "the Principle of Symmetry": if we could start with not(P), >> we could start with P. > > And so you could, so that's not a problem. > > But what would you prove? > It was a typo, I meant "It'd the Principle of Symmetry". Would you still have any question then?
From: Nam Nguyen on 11 Apr 2010 17:09 Nam Nguyen wrote: > Alan Smaill wrote: >> Nam Nguyen <namducnguyen(a)shaw.ca> writes: >> >>> David Bernier wrote: >> >>>> Do you see problems with starting with a false premise, not(P) ? >>> Yes. I'd break "the Principle of Symmetry": if we could start with >>> not(P), >>> we could start with P. >> >> And so you could, so that's not a problem. >> >> But what would you prove? >> > > It was a typo, I meant "It'd the Principle of Symmetry". > Would you still have any question then? I meant "It'd break the Principle of Symmetry".
From: Nam Nguyen on 11 Apr 2010 17:46 Marshall wrote: > On Apr 11, 8:25 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: >> Marshall <marshall.spi...(a)gmail.com> writes: >>> I don't see any reason to pay much attention to anyone's >>> intuition, my own included. >> This is a sober attitude. > > I am mostly a sober person, in that I am drunk less > than half the time. > > >>> "Intuition" is just a fancy word for "hunch." >> "Intuition" can mean pretty much anything, from a vague hunch to >> something very specific, as in e.g. Kant's thought. > > Indeed so, which is exactly what makes it a poor choice > when used in contexts such as this newsgroup. Then, it also looks like a poor choice of using the _intuition_ about the naturals as a foundation of reasoning, as the school of thought AK, TF seem to have subscribed to, would suggest.
From: Alan Smaill on 11 Apr 2010 18:09
Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Nam Nguyen wrote: >> Alan Smaill wrote: >>> Nam Nguyen <namducnguyen(a)shaw.ca> writes: >>> >>>> David Bernier wrote: >>> >>>>> Do you see problems with starting with a false premise, not(P) ? >>>> Yes. I'd break "the Principle of Symmetry": if we could start with >>>> not(P), >>>> we could start with P. >>> >>> And so you could, so that's not a problem. >>> >>> But what would you prove? >>> >> >> It was a typo, I meant "It'd the Principle of Symmetry". >> Would you still have any question then? > > I meant "It'd break the Principle of Symmetry". How? You *can* start by supposing P; and if you can derive a contradiction, you get a proof on "not P". What's the symmetry that's broken, according to you? -- Alan Smaill |