Gödel’s Wager

Gödel’s Wager

          For arithmetic to make sense, it must be consistent; otherwise it means nothing. The same goes for logic and reason in general. But according to Gödel’s Second Incompleteness Theorem, 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. How do you account, when the count itself is of no account? All bets would be off; there’d be nothing to win or lose; so you’d 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 great blessings. No downside, a huge upside. Therefore bet on arithmetic, logic and reason!

          The above argument echoes Pascal’s Wager. Gödel, meet Pascal!