Logically I would state that the reason why aleph-null makes no sense is because like both aleph-null and the numbers on the list are infinity, then to say that aleph-null is in any way different from the numbers on the list is to state that the numbers on the list have an ending. This is because for them to actually be different is for both numbers to end in a difference. Such statement may sound illogical at first glance because no matter what number appears it will always be different, however the point is that if we think about it aleph-null is still impossible to fully become different. — Emmanuele
That does not follow. For one to be larger than the other all that need be true is that one set has a greater cardinality. What this will mean is that when you try to place them in a one-to-one correspondence with each other, it fails to be possible to do so. After all, sets that can be mapped together in this way are the same size. What Cantor showed was that it's impossible to map the naturals with the reals on pain of contradiction, it turned out the reals were larger not that the naturals had an end (in the sense of a final member). That's what makes them different, despite being infinite. They're different levels of infinity. — MindForged
Incorrect, their argument was that some were not "qualities" as you deemed them because they are part of reality. Pointing out that some aren't (as that user already admitted) is very much besides the point when they already admitted so. — MindForged
How is that not an argument? Ease of use is a perfectly legitimate reason to do prefer something. — MindForged
Also, try to do set a circle equal to 4 degrees and see how the math works out for you. — MindForged
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.