The End of an Era - That of The Natural Numbers
in [Math]
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From: William Hughes on 4 May 2010 09:22 On May 4, 9:30 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > William Hughes wrote: > > On May 4, 2:21 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > > <snip> > > >>> It is interesting to note that while you have been presented with > >>> many putative "intuitions" given which the truth or falsehood > >>> of (1) is knowable (you have accepted none and explicitly rejected > >>> one), you have not presented a single "intuition" under which the > >>> truth or falsehood of (1) is not knowable. > >> That's correct: I have not - yet. That doesn't mean I'm not going to. > > > I'm not holding my breath. > > If you don't have a good faith on that then that's your issue and > isn't my concern. [Btw, the post about imprecision in reasoning and > the recent T post are part of the explanation. So in effect I've been > doing the explanation, whether or not you're listening to.] Can give an intuition without using multiple long posts? Forget about Observation 1. Just give an example of an intuition Any intuition will do. - William Hughes
From: Nam Nguyen on 4 May 2010 22:36 William Hughes wrote: > On May 4, 9:30 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> William Hughes wrote: >>> On May 4, 2:21 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>> <snip> >>>>> It is interesting to note that while you have been presented with >>>>> many putative "intuitions" given which the truth or falsehood >>>>> of (1) is knowable (you have accepted none and explicitly rejected >>>>> one), you have not presented a single "intuition" under which the >>>>> truth or falsehood of (1) is not knowable. >>>> That's correct: I have not - yet. That doesn't mean I'm not going to. >>> I'm not holding my breath. >> If you don't have a good faith on that then that's your issue and >> isn't my concern. [Btw, the post about imprecision in reasoning and >> the recent T post are part of the explanation. So in effect I've been >> doing the explanation, whether or not you're listening to.] > > Can give an intuition without using multiple > long posts? Forget about Observation 1. > Just give an example of an intuition > Any intuition will do. OK. If you just want a short description intuition about (1) then here it is. Intuitively, to see _either_ cGC or ~cGC as true or false, you have to do the same impossible thing: transverse the entire set of natural numbers to figure it out, hence (again intuitively) it's impossible to know the truth value of cGC, hence of (1). [In contrast, intuitively it's not impossible to see ~GC as true since a counter example is still a distinct possibility. So in principle, we can't say it's impossible to know the truth value of GC, though *IF* GC is genuinely true then intuitively it's impossible to know so.] And that is as short as I could put it.
From: William Hughes on 4 May 2010 23:24 On May 4, 11:36 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > *IF* GC is genuinely true > then intuitively it's impossible to know so. I see this one of "all intuitions" but If GC is genuinely true then intuitively this can be shown by induction is not. - William Hughes
From: Nam Nguyen on 4 May 2010 23:56 William Hughes wrote: > On May 4, 11:36 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > >> *IF* GC is genuinely true >> then intuitively it's impossible to know so. > > I see this one of "all intuitions" but > > If GC is genuinely true then intuitively > this can be shown by induction > > is not. Not sure I understand what you've said here. Are you saying we can show GC true if it's true?
From: Nam Nguyen on 5 May 2010 00:00
Nam Nguyen wrote: > William Hughes wrote: >> On May 4, 11:36 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> >> >>> *IF* GC is genuinely true >>> then intuitively it's impossible to know so. >> >> I see this one of "all intuitions" but >> >> If GC is genuinely true then intuitively >> this can be shown by induction >> >> is not. > > Not sure I understand what you've said here. Are you saying > we can show GC true if it's true? Also, are you making a statement in saying: >> If GC is genuinely true then intuitively >> this can be shown by induction ? (I didn't say that. Right?) |