Thanks. It’s taken me awhile to get it just right 
1 Like
That pretty well nails it. It can also describe some of the rational but false presuppositions that arguments justified by ‘rationality’ are built on.
I’m afraid to ask what those arguments are… So much of it amounts to ideology, that tendency of the mind to fill in the blanks. I understand this has been documented with patients who are hypnotized.
1 Like
I see what you mean. Do you think “an” infinite number helps at all over “the” infinite number or, worse, the number infinity. Better yet let’s just say one or more and leave it at that.
1 Like
Hmmmm. I see the problem. Infinity of things is a fact.
Possibly for sets of things but I’m not sure that the number of universe expansions from singularities is infinite. Definitely possible … or impossible. But definitely indeterminable.
But I don’t accept the primacy of things. I lack the perspective that would be required to make that determination. I don’t have one bloody (does that really count as a curse word?) clue what is really going on. Fortunately I’m not required to steer or repair anything.
Yes, a brute one, by declaration.
The number is infinite, but not an infinite number 
infinity isn’t numerable. And I’m not keen on singularities as they seem to just concentrate general relativity whereas gravity and quantum effects would dominate I believe.
1 Like
4 Likes
See if you can find a picture of a guy snapping his fingers, with the intention to prove all those people wrong who said he can’t snap his fingers for the infinite time.
1 Like
Snaps are things, and an infinitude of them cannot exist (and we are not talking about the snapper’s longevity ; - ).
Infinity of things is a fact.
Or not.
1 Like
In heaven, hell or any possible universe given the fastest snapper among us, they don’t stand a chance.
1 Like
This survey on the OT by Walton is one of the finest most succinct expositions I’ve ever heard on the subject.
It hard to imagine how the skeptic could hear it, and not wonder “What if?”
This non-philosophical skeptic, unlike the true philosophical skeptic here, has been hearing such for nearly 60 years and is waiting for anyone in range to be philosophically perceptive enough to remove the plank of fallacy from their eye.
The speck can be any number of things, the plank is just one thing, and that’s hatred.
Treating other people like they don’t exist. Not feeling any grief for their suffering and sin.
Interesting is that person in the gospel who saw people as trees.
We should design the infinite waiting room for you to loiter in while you’re waiting on all the rest of us, Klax.
It depends. Since not all infinities are equal - some prevail over others. It’s all about which ones are approaching infinity faster (which calculus students should recognize as L’Hopital’s Rule.)
I like the “Hilbert’s Hotel” example for conceptualizing one of the “lesser” infinities (the countable sort… which … are all identical?) At least I think that’s one conclusion the hotel can help people visualize.
Hilbert’s Hotel has an infinite number of rooms, numbered 1, 2, 3, … and on to infinity. But here’s the kicker: every one of the rooms is occupied! So the ‘no-vacancy’ sign is lit up in front of the hotel. No new guests can be admitted. So then - what to do when a new guest shows up hoping for a room! The clever manager has it all well in hand. He sends out a general message to the infinity of existing occupants to all vacate their rooms and move into the next room up. So the occupants of rm 1 move to rm 2, rm 2 moves to rm 3, and so forth all the way up to infinity. Nobody is left without a room, and yet now room 1 is empty and the new guest moves in! So … are there more people in the hotel now than there were before? Well - no. There was a countable infinity there before, and there still is now. So infinity + 1 is still just the same as infinity. And in fact any arbitrary number of new guests can always be admitted in exactly the same way.
[And in fact, if the manager wanted to just open up a new infinity of rooms all in one stroke so as to minimize all the moving, he could do that too! Simply have all the guests vacate their room number ‘n’ and move into ‘2n’. So Rm 1 occupants move to 2. 2 moves to 4, 3 moves to 6; and once again, nobody goes without a room. But after it’s all done, now rooms 1, 3, 5, and all the odd numbered rooms out to infinity are now vacant! So even 2 x infinity fails to be bigger than infinity, since they both still have a one-to-one correspondence, and therefore are both equally countable.] […of course, this necessitates some having to move inconveniently far, since the occupant of Rm # 1000000 has to schlep her stuff all the way down the hall to rm # 2000000.]
1 Like
Ever notice that Hilbert’s Hotel cannot exist in any possible universe? This is probably why the counterintuitive examples work or don’t work. Or work and don’t work.
Infinity is a value, a non-numerical value. Infinite numbers are like an old married bachelor in a fancy new suit.
You’re right - that infinity is not a real number. For that reason.
And yet, as a concept, it remains mathematically useful. And makes for interesting mind games, like the hotel example. But mostly I brought it up as just an interesting mind game here.
BUT - when one infinity is pitted against another, there can be and are very real ‘winners’ and ‘losers’. I.e. Infinity divided by infinity is sometimes … infinity (top one wins); or zero (bottom one wins); or any finite number you might wish, like 5 (both infinities cancel each other but in a definite ratio).
And that does have implications for reality and understanding probabilities and how stuff works.
1 Like
There are no doubt meaningful differences with infinite relations.
To repeat what I’ve said before:
I understand how the natural and real numbers cannot be put in corresponding relationships. I also get a sense of wonder, as if we are touching on a basic premise of reality when X can be considered as a discrete value representing 4 dimensions, and yet it is ‘smaller’ than the reals between 0 and 0.000001.
(X<---->non-X) > (X, X+1, X+2…)
1 Like
What are the implications for understanding Hilbert’s Hotel cannot be built in any possible universe?