Tuesday, April 30, 2024

On Abyss Wagers, 3

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!   


Monday, April 29, 2024

On Abyss Wagers, 1 and 2

On Abyss Wagers


I.                 Introduction


This essay describes a class of philosophical conundrums akin to “Pascal’s Wager”. For each of these “abyss wagers”, it is rational to bet against various negative scenarios, on the grounds that if any of these scenarios are true, then all bets are off; therefore the wagers have no downside.

The abyss wagers here described include: Pascal’s Wager, Smith’s Wager, the Dissenter’s Wager, Gödel’s Wager, Teller’s Wager, and the Android’s Wager. For instance, in Gödel’s Wager, the negative scenario is the inconsistency of arithmetic. According to Gödel, if the axioms of arithmetic are consistent then those axioms cannot prove their own consistency. Here I argue that it is rational to wager that arithmetic makes sense; for if it does not then all bets are irrelevant. Therefore betting on arithmetic (and logic and reason) is a bet that you cannot lose.


II. The Abyss


Blaise Pascal, the Jansenist who helped discover the theory of probability, proposed a famous Wager; is one to believe that God exists, or not? His reasoning was that if God does not exist, then it does not matter if one believes or not; but if God does in fact exist, then it would be far better to believe; and therefore belief is the better wager.

          This gambler’s theology is undermined by its hidden assumptions, for there is more than one way to believe. Consider George Smith’s Wager:

          If there is a theistic god, either he is just, or he is not. If he is just, he will not punish honest disbelief. But, if he is not just, there is no guarantee he won’t punish one unjustly, regardless of one’s belief or disbelief. Therefore, there is no downside to honest disbelief in any theistic God.

          Here is a political version of these wagers. The government is just, or it is not. If it is just, then it will not punish honest dissent. But if it is not just, then there is no guarantee that it won’t punish you unjustly, whether or not you dissent. Therefore there is no downside to dissent.  The Dissenter’s Wager!

I mentioned Smith’s Wager and the Dissenter’s Wager to my wife Sherri, and she scoffed. “No downside to dissent? Au contraire! It might draw the attention of the government, and the nail that sticks out gets hammered down!” I admitted that her logic has force; and it applies back to Smith’s Wager. There are plenty of reluctant theists, believing just in case.

So Smith and Dissenter Wagers are flawed; the chaotic breakdown case still allows for enough difference for not all bets to be off. The unjust god, and the tyrannical government, don’t oppress everyone equally - at least at first. In the beginning, they withhold enough threat and make enough distinctions to give cowards a refuge; but power corrupts intellect as well as empathy, so eventually they overreach, the people have nothing to lose, and the desperate logic of the Wager takes hold.


Friday, April 26, 2024

The Secret of Jewish Success

The Secret of Jewish Success



Once upon a time, on Long Island, three ladies were playing bridge.

Mrs. Smythe looked over her cards and remarked, “My son is a major-league football coach.”

Mrs. Abercrombie said, “Very good, my dear. But my son is a police chief.”

Mrs. Fitch said, “Ladies, ladies, let’s not quarrel! And besides, my son is a banker.”

She laid down her cards. The other women rolled their eyes and pushed over their bets. It wasn’t fair, but what can you do?


Meanwhile, on the other end of Long Island, three other ladies were playing Mah-Jonng.

Mrs. Shapiro looked over her tiles and remarked, “My son is an Ivy-league college professor.”

Mrs. Goldstein said, “Very good, my dear. But my son is a judge.”

Mrs. Cohen said, “Ladies, ladies, let’s not quarrel! And besides, my son is a doctor.”

She laid down her tiles. The other women rolled their eyes and pushed over their bets. It wasn’t fair, but what can you do?



Moral: Success is relative.