Content Inside :
Al-Farabi
* Applied logic to the study of language (Arabic)
* Developed a philosophical method to reconcile Islam and Aristotle’s logic
* Still believed that human reason was superior to revelation.
Muslim Theologians
* Both reason and revelation necessary.
* Debated for 300 years, which is superior?
* The 3 brothers: the good brother is in Paradise, the wicked brother is in Hell, and the one who died as a child is in a place less than Paradise. The third brother complains that by dying as a child he was not given the opportunity to worship God and enter Paradise. To this, God responds that dying early was better for him because God foresaw that he would have grown up to be wicked. To this the second brother asks why he was not made to die at a young age?
* Consensus emerged that revelation is superior.
Gödel
* By the beginning of the 1900s, the consensus of the mathematical community was that all of mathematical facts could be derived using logic.
* Gödel in an astonishing 1931 article showed that this was impossible.
* His argument is very similar to our argument that the perfect virus detector cannot exist: a simple yet devious mathematical fact which refers to itself in a way that asserts that it can’t be proved.
Some quotes …
In the nineteenth and early twentieth centuries, one of the big mathematical goals was to reduce all of number theory to a formal axiomatic system. Like Euclid’s Geometry, such a system would start off with a few simple axioms that are almost indisputable, and would provide a mechanical way of deriving theorems from those axioms. It was a very lofty goal. The idea was that this system would represent every statement you could possibly make about natural numbers. So if you made the statement “every even number greater than two is the sum of two primes,” you would be able to prove strictly and mechanically, from the axioms, that it is either true or false. For real, die-hard mathematicians, the words “true” and “false” would become shorthand for “provable” or “disprovable” within the system. Russell and Whitehead’s Principia Mathematica was the most famous attempt to find such a system, and seemed for a while to be the pinnacle of mathematical rigor.
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