Quote:
Originally posted by punkworld
Ehm, no?
- The statement "purely formal mathematics applies to OUR physical universe incredibly well. almost by design" seems to consider purely formal mathematics as something independant of us. However, mankind created mathematics, and did that so as to describe our physical universe. So ofcourse it seems to apply perfectly to our physical universe, we made it as the best method we could find for describing our universe.
- The statement "purely formal mathematics (possibly) applies to ALL concievable universes incredibly well. almost by design." Well duh. We are a part of this universe, and our mental world is created completely in relation with this universe. Thus, it would be hard, if not impossible, for us to create in our heads a universe which is not based on the universe we know.
- The statement "purely formal mathematics does/may exist WITHOUT our physical universe, and without our minds and/or the way our bbrains might be wired." simply doesn't make sense when looking at the previous points. There is no good reason why it would have objective existence, and, furthermore, it would raise more new problems than it would solve. For instance, where would we situate this objective mathematics?
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the argument only works if you agree that purely formal mathematics does infact exist outside of our minds. many people far, far smarter than me (Einstein is an example) look at this premise over and over. and what it's possible truth may indicate.
"simply doesn't make sense when looking at the previous points. There is no good reason why it would have objective existence, and, furthermore, it would raise more new problems than it would solve. For instance, where would we situate this objective mathematics?"
no one is trying to solve problems here (at least i'm not). because it brings up more problems than it solves, has abosolutely nothing to do with it's validity.
again, most will agree with the first point. the second point, you more or less brush over. the third, you don't agree with(?). if you can fathom that purely formal mathematical theories exist without the human mind, or our particular universe, then we are talking about something potentially very profound.
however, if formal math is simply a reflection of the 'wiring' of our brains, then certainly, it may be more or less trivial
