Worst. Apologetic. Ever.

Phritz and I have been having a... spirited... discussion about Pascal's Wager. Phritz's inanity aside, Pascal's Wager has the distinction of being the worst apologetic argument ever employed. It is literally invalid, unsound, and ridiculous at every point; as such, it is at least instructive as an example of what not to do in philosophy. (It's controversial whether or not Pascal himself intended the Wager as an apologetic argument; I'll leave the assignment of blame to better scholars than myself. It is manifestly the case, however, that many Christians and Muslims (and even agnostics) employ Pascal's Wager as an apologetic argument.)

To recap, Pascal's Wager sets up a probabilistic decision matrix on two dimensions: The existence or non-existence of God, and the presence or absence of belief:

	God exists	God does not exist
Believe in God	Infinite reward	Zero cost
Diselieve in God	Infinite penalty	Zero reward

If there is a non-zero probability (Pascal himself puts the probability at 50%) that God exists, then the choice to believe in God dominates the choice not to believe.

Let's enumerate all the ways that this argument is bullshit through and through: Every assumption is unjustified and controversial.

First of all, the Wager demands an ontological commitment to objective probability; The Wager makes no sense at all expressed in terms of epistemic probability. It's entirely unclear, however, whether—despite its manifest utility—objective probability is at all physical.

Consider the case where I choose a poker hand of five random cards from a standard deck but don't look at them. In a linguistic sense, I can talk usefully about the probability of those five cards being a royal flush. But physically (unless we are willing to abandon all our notions of objective reality) those cards have exactly one definite content: The "objective" physical probability of the hand being a royal flush is either 1 or 0. We are merely expressing our epistemic ignorance—as we have not looked at the cards, we don't know their content—in terms of objective probability as a valuable shortcut. We must view any argument that relies exclusively on objective probability as inherently suspect.

The second general probabilistic difficulty is Pascal's assumption that the probability that God exists is not infinitesimal. But this assumption is completely unjustified, even if we assume arguendo that the probability is non-zero. If the probability were infinitesimal, then we can draw no conclusions about the resulting value, because simple multiplication of an infinity by an infinitesimal is undefined. Again, since Pascal predicates infinite reward, it seems legitimate consider also infinitesimal probability.

The two possibilities that Pascal enumerates are much too restrictive: We must consider not only the case that God exists, but several other conditionals:

1. God exists and
2. God rewards belief and
3. God rewards the particular belief the believer adopts

Given the Christian context of the argument as well as the consistent Christian deprecation of "heresy", it seems entirely legitimate to discuss correct vs. incorrect belief. An honest decision matrix would embed all of these assumptions, each with its own probability:

	God exists			God does not exist
	RB		~RB
	RA	RC
BC	+∞	+∞	0	0
~BC	+∞	-∞	0	0
~B	-∞	-∞	0	0

RB: God rewards belief; RA: God rewards all belief and punishes only disbelief; RC: God rewards only correct belief and punishes incorrect belief as well as disbelief; BC: The believer believes, and believes correctly; ~ means "not".


We can turn then to the supposed "choice": Whether to believe or disbelieve. But belief itself is not a choice. I can choose to say things, to act in particular ways, but one cannot choose what to actually believe: Belief must be coerced, either by reality's evidence, one's intrinsic nature, torture or (if you go for that sort of thing) divine inspiration. I can't choose to believe in a God: It is simply a fact of my consciousness, over which I have no power of will, that I believe that no God exists. Furthermore, even if belief were a matter of choice, it seems difficult to understand how one could "choose" to believe correctly.

Not only are the rows and columns of the decision matrix unjustified in Pascal's formulation, the assignment of all of the costs and benefits are also unjustified. What does an "infinite" reward mean? An "infinite" punishment? These concepts are not directly comprehensible. To apprehend any infinity in a meaningful sense, one's mind must become infinite. But our minds are finite: There are only a finite (albeit quite large) number of states any finite mind is capable of: After some finite time, all possible states of reward or punishment would be exhausted.

And, furthermore, the assumption that God would reward or punish infinitely (even if that were coherent) is unjustified. We must add yet another category of columns—God rewards/punishes finitely vs. infinitely—each with its own individual probability.

Likewise, the assumption that belief or disbelief has zero cost is likewise unjustified. What sort of God would create an infinite reward for an action that had no cost whatsoever, a belief that had no ethical or moral dimension at all? Clearly belief in God, to be other than entirely vacuous, must have some cost, even if it were finite. And a non-zero cost renders the decision matrix invalid under an infinitesimal probability of God existing (or rewarding only correct belief).

In a sense, all conditionals are "true": If God exists and if God rewards belief and punishes disbelief and if God rewards any sort of belief and punishes only disbelief and if the probability that God exists is not infinitesimal and if God rewards belief infinitely or belief entails zero cost... if all of these things, then yes, it is a good bet to believe in God.

Of course, one could say with an equal amount of "truth" that if the Moon were made of green cheese and if we could convince a billion Chinese that cheese was tasty, and if we could get to the moon by flapping our arms then it would be a good bet to invest in my lunar cheese mining stock.

If you buy Pascal's wager, email me and I'll send you a prospectus.