Timeline for What practical applications does set theory have?
Current License: CC BY-SA 2.5
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| Jan 3, 2010 at 2:24 | comment | added | Zach Conn | As a direct answer to your question in the comment, however, I suspect that the most basic predispositions of human thought made the discovery and formalization of set theory and its role in supporting many mathematical theories somewhat inevitable. It's certainly an arguable point, but as I suggested in my answer I have often felt that the mental construct of grouping together similar objects is more basic even than counting, so it is not surprising to me that this pattern of thought should have come to underly nearly all of mathematics, even those areas wholly unconcerned with counting. | |
| Jan 3, 2010 at 2:21 | comment | added | Zach Conn | If I understand right, you are asking if it is possible that we could have obtained enough of our current understanding in order to produce all current technology without formalizing set theory. In a certain sense I don't think it's relevant to the precise question that was asked here. Set theory is helpful in elucidating many modern mathematical theories even if these theories could conceivably be formalized and understood otherwise. Whether it's useful is different from whether it's strictly necessary, and I think your comment is addressing the latter whereas this thread addresses the first. | |
| Jan 2, 2010 at 3:20 | comment | added | user2929 | OK, but say that this fundamental aspect of mathematics had never been discovered. I mean, we had been doing other kinds of math before we figured this out, right? So would we still be in the same place technologically if we had never figured out the basis of mathematical techniques that are already commonplace? | |
| Jan 1, 2010 at 8:42 | history | answered | Zach Conn | CC BY-SA 2.5 |