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

“We are always already thrown into concrete factual circumstances, facing possibilities that we need to come to grips with. By choosing some we exclude others, thus making them no longer possible. What we are thrown into is the past and present, and the possibilities loom ahead of us, though we may try to turn our back on them. The future is the home of the possibilities while the present and past define the circumstances in which we make our choices, circumstances we can no longer affect.” Or so we might say, and there is something right about this way of talking. Our basic conception of ourselves as agents is radically temporally asymmetric. And so we adopt asymmetric metaphors for time: we talk of time having a direction, as flowing from the future, through the present, to the past, closing possibilities that once were open; or perhaps we think of time as a measure of our own movement from the past to the future. Such metaphors are of very limited value. To think of time as having a direction spatializes time; to think of time as flowing or of ourselves as moving in time is to invite the question of how fast it is flowing or how fast we are moving (at one second per second, perhaps, one might quip, thereby inviting the question of why it cannot flow at two seconds per second instead).             Although the metaphors are flawed, we need to come to grips with an inextricable asymmetry between past and future in them. As agents, we deliberate about the future, while the past we can only bewail or rejoice over. We know the future not only through theoretical knowledge, but also through the intentional knowledge that the agent has of the effects she intends to produce. We think a life that started in years of sorrow but ended in great joy is preferable to one that started with a great joy and ended in years of sorrow..

It is widely accepted that divine creation of human beings is compatible with evolutionary theory, except perhaps in regard of the human soul, and that neo-Darwinian evolutionary theory provides an explanation of speciation and of complex features of organisms that undercuts Paley-style teleological arguments, whether or not the evolutionary mechanisms are truly random or deterministic. I will argue that a plausible understanding of the doctrine of creation of human beings is either logically or rationally incompatible with full evolutionary theory, even if one does not take souls into account. Consequently, a theist needs to move to a weaker version either of the creation doctrine or of evolutionary theory, or both.

Our new cosmological argument for the existence of God weakens the usual Principle of Sufficient Reason premise that every contingent true proposition has an explanation to a weaker principle (WPSR) that every such proposition could have an explanation. Almeida and Judisch have criticized the premises of our argument for leading to a contradiction. We show that their argument fails, but along the way we are led to clarify the nature of the conclusion of our argument. Moreover, we discuss an argument against us based on a principle of alternate explanation incompatible with our WPSR, and show that his argument fails.

McGrew, McGrew and Vestrup (MMV) have argued that the fine-tuning anthropic principle argument for the existence of God fails because no probabilities can be assigned to the likelihood that physical constants fall in some finite interval. In particular, the fine-tuning argument that, say, some constant must lie in the range (1.000,1.001) in order for intelligent life to be possible is no better than a seemingly absurd coarse-tuning argument based on the need for that constant to lie in the range (0.001, 10000000). The author of this piece defends the coarse tuning argument as a rational piece of reasoning, and, further, argues that the countable additivity assumption in the MMV paper can be dropped in favor of finite additivity

Patrick Toner has argued that eternalism, the doctrine that all times are ontologically on par, conflicts with the Catholic view of judgment as based on the state of the soul at death. For, he holds, it is arbitrary that judgment should be based on what happened at some particular time, unless, as presentism holds, that time is the only that really exists. I shall argue that his argument fails because the eternalist can say that judgment is simultaneous with the state of soul that is being judged, and there is nothing arbitrary about judging something at t on the basis of its state at the same time t.

As Mark Murphy has recently shown, standard justifications of universal divine authority are insufficient. [1] By “divine authority” I shall mean the doctrine that obedience is morally owed to God by all. God would not give us a command that we did not have a reason to act in accordance with, Murphy argues, but it does not follow that we would be obliged, much less morally obliged, to have the fact of God’s having commanded the action be among our practical reasons for the action. We might, for instance, think that what God has commanded us is prudentially the best policy for us or that it is the best possible evidence for what is on independent grounds morally obligatory.

Some, notably Peter van Inwagen, in order to avoid problems with free will and omniscience, replace the condition that an omniscient being knows all true propositions with a version of the apparently weaker condition that an omniscient being knows all knowable true propositions. I shall show that the apparently weaker condition, when conjoined with uncontroversial claims and the logical closure of an omniscient being's knowledge, still yields the claim that an omniscient being knows all true propositions.

Adhering to the traditional concept of omniscience lands Gale in the incoherence Grim’s Cantorian arguments reveal in talk of “all propositions.” By constructing variants and extensions of Grim’s arguments, I explain why various ways out of the incoherence are unacceptable, why theists would do better to adopt a certain revisionary concept of omniscience, and why the Cantorian troubles are so deep as to be troubles as well for Gale’s Weak PSR. I conclude with some brief reflections on method, suggesting that we pursue the full implications of Gale’s own revisionary remarks and replace his method of analytic argumentation with non-analytic revisionary theory-construction.

          Despite the fact that the strength of argument is clearly on the pro-life side—nobody except a handful of academics would question the grave wrongness of abortion were pregnancy never inconvenient—somehow ordinary intelligent people, like our students, often remain unconvinced. There are many reasons for this, of course. For instance, a number of students have had their children aborted while many know others who have had abortions, and one does not want to condemn oneself or oneÂ’s friends. I am a philosopher, however, and so I will be interested in intellectual reasons, even though these subjective psychological ones are almost surely more important. Specifically, I will be interested in the fact that the ordinary person subscribes to a number of erroneous big-picture ethical beliefs, each of which, to a different degree, does something to block access to the pro-life arguments. I will not talk about all such erroneous beliefs and I would be grateful in the discussion for more examples.           I will talk about eight errors I have identified, largely through teaching. For each one, I will identify the error, show how it impacts the pro-life message and explain why it is tempting to most of us —there is, after all, something right about five of the errors. For each of these errors is one that we might ourselves be tempted by on occasion. I will then suggest some ways of refuting the error. In some cases, the mere identification of the error should do the trick, as these erroneous beliefs are often not explicitly identified by our interlocutors. My suggested refutations will not always be phrased in the way in which I would phrase them for didactic effectiveness: in this talk, I am mainly trying to convey ideas.

Let S be the set of all entities that exist (or have existed). Define the relation <= on S by saying that x<=y if and only y is a cause of x. By verbal fiat we will define x to be a cause of x for all x in S (if we do not accept this definition, our assumptions will be slightly different; however, it is clear that the existence of x is necessary and sufficient for the existence of x, and that the existence of x is never strictly temporally posterior to that of x, so calling x a cause of itself is not such a bad idea.) Then, <= is transitive, and moreover if x<=y and y<=x, then x=y (i.e., there are no circles of causation). Hence, <= defines a partial ordering on S.