## The Liberal Paradox

As it turns out, it is not logically consistent to both support personal freedom, and efficiency. Ethics is a complicated topic.

Ron Gross' blog 2007-2015

Posts tagged ‘Logic’

As it turns out, it is not logically consistent to both support personal freedom, and efficiency. Ethics is a complicated topic.

Well, personally I am agnostic/atheist, but I’ve heard from several people that believe in God, that they believe “he exists” more than they believe that 1≠2.

Please put aside for one moment the exact meaning of the sentence “God exists”. All knowledge is, to an extent, subjective. I know that 1≠2 because it is a mathematical theorem, but also is a theorem that Zorn’s Lemma is provable from the Axiom of Choice – my level of confidence in these two theorems being true is rather different.

I claim that anyone (if he understands logic), even if he believes that “God exists”, should place more confidence in the statement “1≠2” than in his belief in God *. Why? Let’s assume 1=2, and prove God does not exists:

- Assume 1=2, and suppose by negation that God exists
- 1≠2 (from standard arithmetic axioms and inference rules)
- If God exists, then 1=2 and 1≠2 (from 1 and 2)
- Therefore, God does not exist (from 3, by Proof by Contradiction)

Q.E.D

So, one can prove from 1=2 that God exists, but I doubt you’ll find a proof that 1=2 from the assumption God exists. So believing 1=2 requires more faith, and provides more information, than believing God exists (because it implies God exists, but the other way around does not hold).

* Of course, there is at least one flaw in the above argument. Can you find it?

Recommended for hardcore logicians only (or just people who like to think).

Löb’s Theorem apparently states that "if it is provable that ‘if X is provable, then X’, then X itself is provable". The cartoon helps you (just a bit) to avoid getting trapped in an endless loop of logic.

There’s also a bonus exercise at the end, quite refreshing.

Just thought to tell everyone that the 2008 Turing Award will be given to two guys that invented Model Checking, that has a __very loose__ connection to my own master thesis. How loose? Both relate to Temporal Logic, that’s it.