Practice or practical? Maybe there's space for practical theory, instead of relying on things that don't exist. Why do we distinguish practice from theory? Seems like a fallacy there. On Apr 20, 2013 10:51 PM, "David Barbour" <[email protected]> wrote:
> only in practice > > > On Sat, Apr 20, 2013 at 8:23 PM, John Carlson <[email protected]> wrote: > >> Take my word for it, theory comes down to Monday Night Football on ESPN. >> On Apr 20, 2013 10:13 PM, "John Carlson" <[email protected]> wrote: >> >>> I think that concepts in some sense transcend the universe. Are there >>> more digits in pi than there are atoms in the universe? I guess we are >>> asking if there are transcendental volumes which are bigger or more complex >>> than the universe. If the universe contains the transcendental as symbols >>> then how many transcendental symbols are there? I think you still run into >>> Russell's Paradox. >>> On Apr 20, 2013 9:15 PM, "Simon Forman" <[email protected]> wrote: >>> >>>> On 4/20/13, John Carlson <[email protected]> wrote: >>>> > Do you need one symbol for the number infinity and another for >>>> denoting >>>> > that a set is inifinite? Or do you just reason about the size of the >>>> set? >>>> > Is there a difference between a set that is countably infinite and >>>> one that >>>> > isn't countable? I barely know Russell's paradox... you're ahead of >>>> me. >>>> >>>> Well, for what it's worth, quoting from Meguire's 2007 "Boundary >>>> Algebra: A Simple Notation for Boolean Algebra and the Truth >>>> Functors": >>>> >>>> "Let U be the universal set, a,b∈U, and ∅ be the null set. Then the >>>> columns headed by “Sets” show how the algebra of sets and the pa are >>>> equivalent. >>>> >>>> Table 4-2. The 10 Nontrivial Binary Connectives (Functors). >>>> >>>> Name Logic Sets BA >>>> >>>> Alternation a∨b a∪b ab >>>> Conditional a→b a⊆b (a)b >>>> Converse a←b a⊇b a(b) >>>> Conjunction a∧b a∩b ((a)(b)) >>>> ___ >>>> NOR a↓b a∪b (ab) >>>> ___ >>>> Sheffer stroke a|b a∩b (a)(b) >>>> >>>> Biconditional a↔b a⊆b⊆a (((a)b)(a(b))) -or- ((a)(b))(ab) >>>> >>>> (Apologies if the Unicode characters got mangled!) >>>> >>>> Check out http://www.markability.net/sets.htm also. >>>> >>>> >>>> I don't know much about set theory but I think the "Universal" set >>>> stands for the set of everything, no? >>>> >>>> Cheers, >>>> ~Simon >>>> >>>> >>>> >>>> >>>> >>>> "The history of mankind for the last four centuries is rather like that >>>> of >>>> an imprisoned sleeper, stirring clumsily and uneasily while the prison >>>> that >>>> restrains and shelters him catches fire, not waking but incorporating >>>> the >>>> crackling and warmth of the fire with ancient and incongruous dreams, >>>> than >>>> like that of a man consciously awake to danger and opportunity." >>>> --H. P. Wells, "A Short History of the World" >>>> _______________________________________________ >>>> fonc mailing list >>>> [email protected] >>>> http://vpri.org/mailman/listinfo/fonc >>>> >>> >> _______________________________________________ >> fonc mailing list >> [email protected] >> http://vpri.org/mailman/listinfo/fonc >> >> > > _______________________________________________ > fonc mailing list > [email protected] > http://vpri.org/mailman/listinfo/fonc > >
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