In 1936, Alan Turing solved a deep mathematical problem and, along the way, he invented modern computer science! His idea of a 'Universal Computing Machine' - a Turing Machine - is central to Computer Science. The problem Turing solved in 1936 was whether logic is decidable: whether any algorithm can tell us whether a logical sentence is valid or not. Turing proved that we can't: first-order logic is undecidable, one of the most important results in the history of logic
00:00 - Intro
01:07 - On Computable Numbers
01:21 - The Decision Problem
02:25 - Paradoxes in maths
03:41 - Algorithms
04:12 - Proving non-existence is hard!
07:06 - Turing’s strategy
07:38 - The Halting Problem
09:41 - The Halting machine argument
11:43 - The Impossible Machine
12:21 - Reduction
12:58 - Back to the Decision Problem
If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: markjago.net
My book What Truth Is: bit.ly/JagoTruth
Most of my publications are available freely here: philpapers.org/s/Mark%20Jago
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