What makes anyone thing the universe "began to exist?" For all we know it's like the negative integers ..., -3, -2, -1. Every element has a predecesso...
I'm stating William Lane Craig's argument in order to characterize it as disingenuous and silly. Was that unclear in my post? "Premise one: "Whatever ...
Disclaimer, I haven't read the rest of the thread and I don't know where it's gotten to by now. I did happen to look at William Lane Craig's cosmologi...
I think it might be helpful to distinguish the issue of whether existence is a predicate, with the issue of how philosophers handle fiction. That latt...
?x?S (x ? S) That would be the formal way, since x ? S is a predicate. Technically that is a convenient abuse of notation. Everyone writes it that way...
I do not believe the existential (or universal) quantifiers may stand alone. Rather there must be a unary predicate P so that you can write ?xP(x). If...
Ok. But now that I've explained it to you, your understanding should be excellent :-) It's true that there are logics where time is modeled, for examp...
Yes I think I see your point. If we think of it as a process, as in the execution of a computer program, then we are just flipping states back and for...
Logical implication is not causation. They're two completely different things. Have you ever seen the truth table for implication? I am wondering, do ...
A contradiction in sentential (aka propositional) logic, a contradiction is the statement "P ^ not-P" for some proposition P. There is no requirement ...
No. The assumption that we can form such a set leads to a contradiction, showing that unrestricted comprehension can not be allowed. Please read the W...
Yes exactly. Our intuition is that a tiny change in the input conditions will smooth out over time and make no difference to the future evolution of t...
If you quote you should quote literally. If you are paraphrasing someone, you should not make it look like you're quoting them. A stylistic nitpick, t...
A more precise statement can be made. It is that under a deterministic iterated system, points (or states) that start out very close together may end ...
Your erudition seems to have overtaken your common sense and your manners. You are incapable of explaining, only insulting. I'm using individual quote...
In the Zalamea paper on Peirce's continuum, Zalamea says on page 8: "As we shall later see, this synthetical view of the continuum will be fully recov...
Your full quote earlier was: There is only one way to read this. * For any value of N whatsoever, 2^N > N. * Therefore, a power set always has more me...
It's a bad argument. Suppose I like to juggle, and the local government forbids juggling. I say, "I have a right to juggle, especially in the privacy ...
That does not follow. It must be proved. That's Cantor's theorem. Well worth looking at since it's a beautiful little proof that gives us an endless h...
Well when you put it THAT way it's totally CLEAR. LOL. I see that Peirce has some jargon associated with him. From Googling around I think being triad...
Biology, that's interesting. I thought sign relations were some kind of postmodern talk I don't know anything about other than that Searle thinks Derr...
This is actually a great mathematical question. If you assume the Axiom of Choice (AC), then all sets have a well-defined cardinality that is the smal...
I started reading the Zalamea paper, Googled around, and found a pdf of his awesome book Synthetic Philosophy of Contemporary Mathematics. I'm enthral...
You can take my word for it that .999... = 1 is a theorem of nonstandard analysis. But actually you don't need to take my word, I provided a proof abo...
As it happens, .999... = 1 is a theorem even in nonstandard analysis. This is easily shown. The hyperreals are a model of the first-order theory of th...
My problem! LOL. I haven't read anything after this morning. No harm no foul. For what it's worth, I've often wondered about the relation between the ...
Your characterization of me is quite unfair. One, to lump me in with Tom, whose erroneious and confused mathematical misunderstandings I've refuted an...
I agree with that. Calling real numbers locations seems to avoid a lot of the philosophical issues about the nature of points. I've started reading th...
Good point. No pun intended. The answer is in the concept of "occupies a place." If we view the real numbers as specifying locations on a line, and we...
A point is that which has no part. Euclid was right about that. You can't subdivide a point and a point has no sides. It's sophistry to claim otherwis...
Can you explain (so that a philosophical simpleton like me could understand it) how mathematics has failed to successfully deal with continuity? Moder...
What do you mean by "bigger?" Bearing in mind that there are countable models of the reals? https://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skole...
You are each using different definitions. This is the fallacy of ambiguity. Surely we need not argue about this any more. I have humbly offered the wo...
I'll certainly take that to heart :-) Can you (or anyone) supply some of relevant Bergson and Pierce links that would shed light on the relation betwe...
Please locate that quote of mine, I can't find it and don't remember saying it. I probably said reordered and definitely well-ordered, but not disorde...
We can well-order the reals. https://en.wikipedia.org/wiki/Well-order#Reals I mention this because it's a counterexample to the intuition that a set c...
I don't know if it's a "substantial" difference. It's certainly a difference. The rationals are foozlable and the reals aren't. Even in countable mode...
The reals in their usual order are a continuum. They can be reordered to be discrete. Counterintuitive but set-theoretically true. Order is important ...
Which has absolutely nothing to do with the question of whether a given set is foozlable -- able to be bijected to the natural numbers. I don't want t...
I went back through this thread from the beginning. Finally on page 11, this quote is the first mention of mathematical countability. The above quote ...
You can certainly well-order an uncountable set. You need the Axiom of Choice to well-order the real numbers, but you do not need Choice to show the e...
This is not true. A set is defined as countable if it can be put into bijection with the natural numbers. By this definition we can then show that the...
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