Proving Too Much

41 Proving Too Much

Kimberly Baltzer‐Jaray

Yes; but you must wager. It is not optional. You are embarked. Which will you choose then? Let us see. Since you must choose, let us see which interests you least. You have two things to lose, the true and the good; and two things to stake, your reason and your will, your knowledge and your happiness; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose. This is one point settled. But your happiness? Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.

Blaise Pascal, Pensées, #272

Quoted above is what is infamously known as Pascal’s wager, an argument that was intended to demonstrate that it is in one’s own best interest to behave as if God exists even if it cannot be absolutely proven: if He doesn’t exist, no harm done in believing He does; however, if He does exist, then you either have eternal bliss for being good or eternal damnation for being sinful. Pascal’s argument is pragmatic in nature as it states that the benefits of believing that God exists (even when there isn’t any proof for it) outweigh those of not believing; the possibility of eternal punishment in hell outweighs any advantage had in believing God doesn’t exist. However pragmatic it may seem, Pascal’s wager contains the fallacy of proving too much, and that calls into question its logic. This fallacy has been committed when an argument can be used to also prove something false or leads to contradictory conclusions. An argument that proves too much demonstrates a lack of soundness, since sound arguments can only establish true conclusions, and thus when an argument can be used to prove false conclusions, it becomes evident that there is a flaw in its reasoning. For example, a critic can construct a rival wager for an almighty demon, a spaghetti monster, or even Bigfoot by attaching comparable rewards and punishments to belief in that being. The problem is that the wager alone does not tell us which reward scheme to accept. It also advocates that you force yourself to believe in something you don’t take to be true, and even if it is somehow possible to force yourself to do this, what the wager demands amounts to living a lie (living in sin). Won’t that get you into trouble? Is it really better in the eyes of God that you lie to yourself and pretend you believe in Him rather than to live truthfully not believing? The contradictions just pile up.

There are a few forms this fallacy can take on such as when an argument leads to multiple contradictory conclusions. Pascal’s wager, once again, fits the bill. If the wager successfully proves we should believe in a benevolent god, then we can also use it to prove the benefit of believing in a sadistic god, or a god that contradicts the existence of all other gods. Another form of this fallacy occurs when an argument leads to a conclusion known to be absolutely false. Great examples are any of Zeno’s paradoxes of motion, whereby a person, object, or creature must cross an infinite number of points to get to a destination: if Homer wishes to walk to the end of the pathway, before he can get there he must get halfway, but before he can get halfway he must get a quarter of the way, but before he can get a quarter of the way he must get one‐eighth of the way, and so on. These paradoxes challenge the reality of motion and change, despite the evidence of our senses. A conflict with observation is not itself a logical contradiction, but it gives us reason to examine the premises and the reasoning. The problem found in the paradoxes of motion is that we have been tricked into thinking about space and time in the wrong way: Hans Reichenbach, for example, proposed that the paradox arises because space and time are considered as separate entities rather than a single space‐time continuum. Nick Huggett accuses Zeno of committing the fallacy of begging the question. Accounts such as those of Reichenbach, Huggett, Aquinas, or Aristotle try to locate the problem. A conclusion that conflicts with what we know sends us back to inspect both the premises and the steps of the argument.

Proving too much is a diagnostic tool rather than one unique mistake in reasoning. If an argument yields a false conclusion, it cannot be sound; either a premise is false or the inference fails. A counterexample helps reveal the problem, but an unfamiliar or strange conclusion is not enough on its own.

The source connects its discussion of Pascal’s wager with possible objections involving false dilemma (Chapter 81), appeal to emotion (chapters 13 and 14), inappropriate appeal to authority (Chapter 32), and genetic fallacy (Chapter 29). Each objection needs its own argument.

To check soundness, examine whether the premises are true and whether the conclusion follows from them. Then test the same reasoning on another case: does it support a conclusion you have independent reason to reject, or prescriptions that cannot all be followed? Identify the premise or inference responsible rather than dismissing the result merely because it sounds ridiculous.