Sunday, December 23, 2012

Your basic 'naive set theory' exercises.

Lately, I have been seeing much of Mathematics as Philosophy, and this new attitude, although hard to describe, has been a major factor in yet another totally new level of understanding what I have studied in the past, am studying, and will be studying.

If you wish to see the philosophical roots of each and every set theory exercise you have ever been given, to the point that, while reading the philosophical paper, which contains not one formula, you keep going 'oh, this was in fact turned into an exercise' and 'this one' and 'that one' all while realizing the very painful thinness to which the whole idea was reduced before it was given to you, if you wish to read a whole chapter explaining the philosophy behind similarity, yes, the same one that is thinned down and taught in you linear algebra book, I suggest the not at all easy, but very rewarding read 'Introduction to Mathematical Philosophy by Bertrand Russell'.

I have read most of it, and now finally I see where the ideas of transfinite of Cantor that are the basis of standard analysis come from, and I see where I disagree with them, (with the help of Wittgenstein), and I can finally zoom out and see both perspectives, (me being on the non-standard, and finitist side), and I can now 'go along with' standard analysis some more steps, maybe even very large strides (which despite my previous many reading about the 'foundational problem' I was not yet ripe enough to do), knowing what I am doing, what is being fed to me, how to translate into the finitist perspective, and in general where the whole differences are leading. Finally, after days of sleepless reading, and dozens months of doubt, a bit of peace of mind.

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