Alexander R. Pruss

Consider the regularity thesis that each possible event has non-zero probability. Hájek challenges this in two ways: there can be nonmeasurable events that have no probability at all and on a large enough sample space, some probabilities will have to be zero. But arguments for the existence of nonmeasurable events depend on the axiom of choice. We shall show that the existence of anything like regular probabilities is by itself enough to imply a weak version of AC sufficient to prove the Banach–Tarski Paradox on the decomposition of a ball into two equally sized balls, and hence to show the existence of nonmeasurable events. This provides a powerful argument against unrestricted orthodox Bayesianism that works even without AC. A corollary of our formal result is that if every partial order extends to a total preorder while maintaining strict comparisons, then the Banach–Tarski Paradox holds. This yields an argument that incommensurability cannot be avoided in ambitious versions of decision theory

Suppose that one initiates a causal sequence leading to a basically evil state of affairs, but does not intend the evil effect, and the good effects of the action are proportionate to the bad. A state of affairs is a “basic evil” provided it is evil in virtue of itself and not in virtue of its connection with other states of affairs. The classic form of the Principle of Double Effect (PDE) can be taken to state that then the action that initiated the causal sequence is not wrong on account of the basically evil state of affairs it produces. The action might still be wrong for some other reason, say by violating a promise, or causing some other basically evil state of affairs, or being a..

We introduce three arguments for the thesis that time cannot exist prior to an original creation event. In the first argument, we seek to show that if time doesn’t depend upon creation, then time is infinite in the backwards direction, which is incompatible with arguments for a finite past. In the second and third arguments, we allow for the possibility of backwards-infinite time but argue that God could not have a sufficiently good reason to refrain from creating for infinitely many moments—either in a world void of created things or in the actual world prior to creation. Our end goal is to help clarify connections between time and divine action.

The pseudonymous author of this article argues that neither Kierkegaard nor Climacus in the Concluding Unscientific Postscript are claiming that Christian beliefs are nonsense or contradictory, but that it is contrary to universal epistemic norms to believe these beliefs or even to believe they can be believed. In an appendix for which the rest of the article is a preparation the author gives an interpretation of the pseudonymity and form-content contradiction and of how Kierkegaard in a sense agrees with all the assertions made in the Postscript. If Kierkegaard is right, this article could only have been written pseudonymously.