• MindForged
    554
    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.
  • Emmanuele
    7
    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

    I get the point. The ending member is different in a one to one correspondance from T (numbers on the list) to N (aleph). I would just like to believe that from R to N (naturals) the last member is different because that's how they are defined by themselves. If we make a number out of the difference of a specific number is to state that the former was a number at all, even in regards to the cardinality of a set.

    I would like to believe that this up here is sufficient to say that aleph as a set was to just be math dribble. And the last member of the set T never existed in order for it to be different. So the definition of the set aleph is not satisfied.
  • Metaphysician Undercover
    4.8k
    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

    I can see that one, or both of us, misunderstands what Ikolos was saying. I can restate what I was saying though. I said that qualities can be quantified, but it is a mistake to attempt to qualify quantities. Both qualities and quantities are "part of reality", so this reference is just a diversion. The issue is what the mind is doing when it attempts to quantify a quality, or qualify a quantity.

    Ikolos replaced "quality" with "relation", and I had to insist that relation is a quality rather than a quantity, because Ikolos wanted to argue that a relation is a quantity, without the required mental act which quantifies that quality.

    How is that not an argument? Ease of use is a perfectly legitimate reason to do prefer something.MindForged

    As I said, there are many other numbers which offer equal, or greater ease of use, so there is no basis for your argument.

    Also, try to do set a circle equal to 4 degrees and see how the math works out for you.MindForged

    If a circle were 4 degrees, I see that an acute angle would be less than one degree, and an obtuse angle would be greater than one degree. Forty five would be half a degree, and one eighty would be two degrees. Looks very easy to me. I'm no mathematician so I might be missing something. Where would the mathematical problem be, which would make 360 degrees mathematically easier than 4 degrees?
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