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" <forman.si...@gmail.com> wrote:
> On 4/20/13, John Carlson <yottz...@gmail.com> 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 > fonc@vpri.org > http://vpri.org/mailman/listinfo/fonc >
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