The principle of indifference

In several previous posts I have applied the principle of indifference, albeit I did not call it by that name.

• In the post The eerie silence I wrote this:

The probability of the existence of extraterrestrial intelligence is 50%. As we know nothing, this is equivalent to throwing a coin, and if it comes up heads, we say that we are alone; if tails, that we have company.

• In the post Relativism in science? I said this:

If we have no reason to assume that a theory is true or false, its probability should be close to 0.5... Theories about which we have no information, for or against, with a probability between 0.4 and 0.6. I will cite the existence of extraterrestrial intelligence, the possibility of building strong artificial intelligence, or the various theories of the multiverse.

The Pascal wager and the Smith wager

Blaise Pascal

Blas Pascal (1623-1662) is known for his activity in mathematics (he devised the triangle of Pascal), physics (he proved the principle of Pascal, invented the hydraulic press and experimented with atmospheric pressure) and especially for his Pensées (Thoughts) one of which contains the first known example of the use of game theory, whose theoretical development had to wait until the twentieth century. This example is the famous Pascal wager, which he expressed thus:

Dieu est ou il n’est pas. Mais de quel côté pencherons‑nous?... Pesons le gain et la perte en prenant croix que Dieu est. Estimons ces deux cas: si vous gagnez, vous gagnez tout, si vous perdez, vous ne perdez rien. Gagez donc qu’il est sans hésiter. 

Whose English translation is:

God exists or He does not exist. Which side shall we take?... Let us weigh the gain and loss, assuming that God exists. Let us consider both cases: if you win, you win everything; if you lose, you lose nothing. So you must wager, without doubt, for His existence.