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Choose Your Paradox – the downside of the Axiom of Choice
And He took the five loaves and the two fish, and looking up to heaven, He blessed and broke and gave the loaves to the disciples; and the disciples gave to the multitudes. So they all ate and were filled, and … Continue reading
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This Post is Meaningless – the Liar Paradox
The Liar Paradox is simple enough to explain – is the following statement true or false? This statement is false. If it’s true then it’s false, but if it’s false then it’s true … nothing works. In my notsohumble opinion, … Continue reading
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Grammar, Go, and the Unconscious – the Power of Facts and Rules.
In the last post there was plenty about Gödel but not much about Grammar and Gothegame. Time to pay my debt! Basically I said that Gödel’s results proved that no fixed set of facts and rules can on their own form … Continue reading
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Gödel, Grammar, Go – the Limits of Rules and Facts
More than eighty five years ago Kurt Gödel proved, roughly speaking, that no fixed set of a formal facts (like 23+14=37) and rules (like x+y = y+x) can establish the truth or falsity of every theorem about arithmetic over the counting … Continue reading
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Logic without Bound Variables
I’ve already described the relatively simple Monadic Hybrid Calculus that allows you to say simple things formally without bound variables. For example, sG may mean “Socrates is Greek”, [G]M “all Greeks are Mortal”, and the conclusion “Socrates is Mortal”, sM. … Continue reading
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My Video Career
A while back I decided that it would easy and useful to video record some lectures. Little did I know!
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AlKhwarizmi SchmalKhwarizmi
I like true/false exam questions and through my career have thought up hundreds of them. Every now and then, for comic relief and to inflate the grades, I include some that are ridiculously easy. However, I’ve never found one that … Continue reading
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