I just had a weird thought
in [Logic]
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From: Charlie-Boo on 12 May 2010 03:14 On May 11, 2:50 pm, John Jones <jonescard...(a)btinternet.com> wrote: > taffer wrote: > > I just had a weird thought. It actually left me confused about what is > > mathematical, and what is physical. The statement was: > > > "Every finite set can be generated by adding one element at a time, > > starting from nothing". > > > This seems to be true. But then (and this is what confused me) I > > wondered, is that a mathematical statement? If so, would there not be > > a formal mathematical theorem expressing the statement? Or if it's a > > definition, a formal mathematical definition? Or maybe it's not a > > mathematical statement after all? > > What mystifies me is how you, and other mathematicians, seem to think > that adding one element at a time is one thing, and a new set is another > thing AND that they are both the same thing. That's a general problem with equality: We need two arguments to the relation but insist there is only one thing involved. Long ago I pointed out that the problem is that equality is more general than that. Any two things are equal at some level of abstraction and above, and not equal at all lower levels. For example, 1=1 and anything X satisfies X=X etc. at the higher levels, but 1 and 1 differ in their location and number of molecules required to construct the symbols etc. at the lower levels of abstraction. (This is part of a general Theory of Abstraction which generates cool ideas like UP + DOWN = siblings to generate more good stuff e.g. you like a store so you find out what category it is in (in the yellow pages) and look at other stores in that category to generate more neat stores.) C-B
From: Charlie-Boo on 12 May 2010 03:19 On May 11, 5:39 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Charlie-Boo <shymath...(a)gmail.com> writes: > > Since TRUE(x) and EQ(I,J) are axioms in computer programming, r.e. = > > partially solvable, although people define them to be the same thing. > > No they don't. Really? You have an example of someone speaking of "partially solvable" and "recursively enumerable" as well, as being distinct? I would be interested in that. To understand the difference once has to formalize part of Computer Science that is never seen in print. C-B > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Daryl McCullough on 12 May 2010 08:56 Jesse F. Hughes says... >It is *amazing* how many stories you tell that involve someone else >complimenting and admiring you! Hey, there are people who admire me, too. But they prefer to remain anonymous. -- Daryl McCullough Ithaca, NY
From: Marshall on 12 May 2010 10:20 On May 11, 7:07 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Marshall <marshall.spi...(a)gmail.com> writes: > > You can verify > this for yourself at Facebook, which abomination I was pressganged into > joining some time ago, but take perverse joy in leaving my page in in a > state of utter dereliction, this joy not at all unlike the immense > pleasure I derive from devising convoluted sentences that more-or-less > naturally allow for duplicated prepositions which at first sight seem an > error, but turn out to be, on closer reflection, a matter of grammatical > necessity, or at least plausibly not altogether inexcusable. I sent you a friend request. Marshall
From: Frederick Williams on 12 May 2010 10:57
"Jesse F. Hughes" wrote: > > Charlie-Boo <shymathguy(a)gmail.com> writes: > > > > Ask Gerald Sax who kept correcting him during his Mathematical Logic > > [...] > > > > It is *amazing* how many stories you tell that involve someone else > complimenting and admiring you! You know what? This makes me wish I > was more like you! > > You must be the best person in all Cambridge! Even I know that Sacks is spelt Sacks and I've never met him. (I think his friends call him Ger..) -- I can't go on, I'll go on. |