III. Gödel’s Wager
Now consider what I call Gödel’s Wager. Gödel’s Second Incompleteness Theorem** states that an arithmetical deduction system is consistent, if and only if it cannot prove its consistency. Either it has a proof of consistency, which is false, or it is consistent but it cannot prove it.
So if arithmetic is consistent (and with it, logic and reason) then we cannot be sure that it’s consistent! Yet we use arithmetic anyhow; an act of faith.
And why not? Either arithmetic makes sense or it does not; and you may use it, or not. If you cannot prove that arithmetic makes sense, then any decision about using it is by definition a wager. I submit that wagering on arithmetic, logic and reason has no downside.
For if you wager on arithmetic, but arithmetic makes no sense, then neither does anything else; for how do you account, when the count itself is of no account? So there would be nothing to win or lose, and you would lose nothing.
Whereas if you wager on arithmetic, and it does make sense, then you make sense too; an enormous practical and spiritual blessing.
Therefore if you wager on arithmetic (and logic and reason) then at worse you lose nothing, and otherwise you win to great blessings. No downside, a huge upside. Therefore bet on arithmetic, logic and reason!
The above argument echoes Pascal’s Wager. Gödel, meet Pascal!