Still no faith required
Posted Aug 20, 2012 1:07 UTC (Mon) by man_ls
In reply to: Lack of faith is not a kind of faith
Parent article: Garzik: An Andre To Remember
Yes, you need axioms and rules. No, rules are not mysterious entities that require belief; they are a well understood part of the system. Logic and set theory are also sets of axioms and rules, and in that they are very similar to mathematics. Again, no belief or faith necessary: if you don't believe e.g. that "a and ¬a cannot be true at the same time" you can still be happy, just accepting that the conclusions of first-order logic cannot be carried out to the physical world.
as soon as you accept that the two in "I have two hands" is the same as the two that mathematicians use, you have indeed made a statement about the universe (and one that also requires faith!).
That is precisely why the "I have two hands" part is firmly planted in reality, and outside the realm of mathematics. I am forced to quote Einstein
as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
Not that I dislike quoting father Einstein, but citing the same quote twice in a week is excessive and has the danger of becoming old.
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