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April 20th, 2012, 6:31 pm
April 21st, 2012, 1:02 pm
So, its being a tautology is irrelevant to whether or not such objects exist.
April 23rd, 2012, 8:03 pm
The equation 2 + 2 = 5 or for that matter any mathematical “tautology”.I'm not sure what you mean by this.
April 23rd, 2012, 8:20 pm
Pris it’s purely a semantic matter.What does your statement 3+2 = 5 mean if the terms 3, 2, and 5 do not exist? Would they not exist at least by virtue of their definitions?
April 24th, 2012, 12:35 pm
April 24th, 2012, 4:39 pm
It asks why waste a lot of words that can be interpreted to mean nearly anythingAnd what does saying that explain?
April 26th, 2012, 1:40 pm
No pris, only that it might stimulate some thinking in that direction. Profound I’m not, but Intuition strongly suggests that much of the apparent disagreement amongst us lies in that directionin the hope people will take that for profundity?
Brad does that mean that if there were no Universe numbers wouldn’t existWell I think if mathematical objects exist, they cannot be mental objects, since that would be to say they are dependent on thought
Aha! Bel my very favorite participant has nailed it. In other words, she is saying, as I understand her, and I concede I could be mistaken, as I have long maintained with virtually no support whatever, that nothing is entirely anything while everything is partly something elseEach and every concept is true to some degree.Truth is quantifiable.
Einstein could not have better expressed it nor in fewer well-chosen words. Bel I sometimes wish I were single once more, much younger, and you lived nearbyPersonally I feel that if something exists in space and time it is more true than any abstraction from the tangible world of things .
April 26th, 2012, 4:06 pm
I presume you mean entirely false. What if the fetus contains an extra set of dormant leg cells; how many legs does a woman have who is pregnant with twinshumans have six legs.
Yes but only if you maintain a distinct dividing line between paradoxical and notthe statement itself is paradoxical
I’ll have to take your word for it, I’m not a mathematician, my reactions purely spontaneousYour problem here is that you are using a property of finite sets on infinite sets.
Forgive me Pris but it’s hard to express some of these intuitional insights. It might prove for instance that an infinite Universe is impossible, calling into question the entire concept of infinity—but I'm not sure what you meant about the legitimacy of infinite universes.
April 26th, 2012, 4:48 pm
I imagine a race of six-legged humanoids in a distant galaxy who don’t consider us “human” so you still have to attach conditions. Lawsuits have been conducted and won on the basis of such apparent absurditiesjust change it to all humans have six legs.
Good one Pris, I must remember itI'm not prone to argue.
April 26th, 2012, 5:22 pm
Let me reiterate that six-legged Marty who considers himself human but doesn’t consider us so sees the statement as true. So you have to specify at least that what you mean by “human” excludes, say, anything not earthbound. You will have to continue adding conditions until what you’re saying is, “ 'All humans have six legs' is false” provided that which I callI call human has fewer than six legs” which is of course a tautologyThe statement [all humans have six legs] is false if there is a single human who doesn't have six legs.
April 26th, 2012, 7:21 pm
April 26th, 2012, 8:28 pm
seems to be that no definite statements can be made about anything
Pris while I don’t know any of them personally their existence is almost a certainty while surely some of them are six-footedNo, I don't. It may be true that my circle of acquaintances is not quite as extensive as yours, which seems to extend to alien life forms,
May 3rd, 2012, 3:20 pm
Well put Eric, according to the general principle that nothing is entirely anything while everything is partly something else so there’s no distinct dividing line between the abstract and the concrete. Thus we have a rock at one extreme and God at the other with The Catholic Church and Costco somewhere betweenExistence of the abstract is intermittent depending entirely upon apprehension by a living person.