Alexander R. Pruss

A new cosmological argument

We present a valid deductive cosmological argument for the necessary existence of a powerful and intelligent creator of the actual universe. Whereas traditional cosmological arguments had to employ a strong version of the principle of sufficient reason that held that every fact actually has an explanation, our argument can make do with the weak version of Duns Scotus according to which every fact possibly has an explanation. As a result, our argument is less vulnerable to the charge of begging the question than are these traditional cosmological arguments.

The Hume-Edwards Principle and the Cosmological Argument

The Cosmological Argument for the existence of God claims that the universe is as a whole contingent and the only possible explanation for its existence is that it has been created by a necessary entity or entities, where a necessary being (or, alternatively, a self-explainer) would be one for which a sound ontological argument holds, even though finite humans might not be smart enough to find this ontological argument or to verify its premises. This paper will follow the tradition of Samuel Clarkes version of the Cosmological Argument.1 One famous attack against the Cosmological Argument has been to the effect that an infinite chain of contingent causes could also provide a sufficient explanation for the existence of the universe even if the chain had no first element. Were the universe such a chain, then every entity would be explained through the causal efficacy of some entity further down in the chain, and Hume has argued that this would provide a sufficient explanation of the universe as a whole (or of the universe considered as an individual). Humes argument is based on the principle that if each element of a collection is given a causal explanation, then the aggregate of all the elements has likewise been explained. Reacting doubtless to Clarkes argument, Hume wrote: Did I show you the particular causes of each individual in a collection of twenty particles of matter, I should think it very unreasonable, should

A two-sided estimate in the Hsu--Robbins--Erdös law of large numbers

Let X1, X2, ... be independent identically distributed random variables. Then, Hsu and Robbins (1947) together with Erdos (1949, 1950) have proved that , if and only if E[X21] 0.

Comparisons between tail probabilities of sums of independent symmetric random variables

Abstract We show how estimates for the tail probabilities of sums of independent identically distributed random variables can be used to estimate the tail probabilities of sums of non-identically distributed independent symmetric random variables which are majorized by a single distribution in the sense of Guts (1992) weak mean domination. As an application, we prove a weak one-sided extension of a law of large numbers of Chen (1978) to a non-identically distributed case and show how some of Guts (1992) extensions of Hsu-Robbins type laws of large numbers follow from previously known identically distributed cases. We also extend some theorems of Klesov (1993) to the case of weak mean domination. One intermediate result of independent interest is that if X 1 ,…, X n and Y 1 ,…, Y n are two collections of independent symmetric random variables such that P (| X k | ≥ λ ) ≤ P (| Y k | ≥ λ ) for every λ and k , then P (| Y 1 + … + Y n | ≥ λ ) ≤ 2 P (| X 1 + … + X n | ≥ λ ) for all λ.

CONJUNCTIONS, DISJUNCTIONS AND LEWISIAN SEMANTICS FOR COUNTERFACTUALS

AbstractConsider the reasonable axioms of subjunctive conditionals (1) if pq1 and pq2 at some world, then p (q1 & q2) at that world, and (2) if p1q and p2q at some world, then (p1 ∨ p2) q at that world, where pq is the subjunctive conditional. I show that a Lewis-style semantics for subjunctive conditionals satisfies these axioms if and only if one makes a certain technical assumption about the closeness relation, an assumption that is probably false. I will then show how Lewisian semantics can be modified so as to assure (1) and (2) even when the technical assumption fails, and in fact in one sense the semantics actually becomes simpler then.

The Cardinality Objection to David Lewis's Modal Realism

According to David Lewiss extreme modal realism, every waythat a world could be is a way that some concretely existingphysical world really is. But if the worlds are physicalentities, then there should be a set of all worlds, whereasI show that in fact the collection of all possible worlds is nota set. The latter conclusion remains true even outside of theLewisian framework.

A restricted Principle of Sufficient Reason and the cosmological argument

The Principle of Sufficient Reason (PSR) says that, necessarily, every contingently true proposition has an explanation. The PSR is the most controversial premise in the cosmological argument for the existence of God. It is likely that one reason why a number of philosophers reject the PSR is that they think there are conceptual counter-examples to it. For instance, they may think, with Peter van Inwagen, that the conjunction of all contingent propositions cannot have an explanation, or they may believe that quantum mechanical phenomena cannot be explained. It may, however, be that these philosophers would be open to accepting a restricted version of the PSR as long as it was not ad hoc. I present a natural restricted version of the PSR that avoids all conceptual counter-examples, and yet that is strong enough to ground a cosmological argument. The restricted PSR says that all explainable true propositions have explanations.

A general Hsu-Robbins-Erdős Type estimate of tail probabilities of sums of independent identically distributed random variables

AbstractLet X1,X2,... be a sequence of independent and identically distributed random variables, and put % MATHTYPE!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qeguuDJXwAKbacfiGae83uam1aaSbaaSqaaiab-5gaUbqabaacfaGc% cqGF9aqpcaWGybWaaSbaaSqaaiaaigdaaeqaaOGaey4kaSIaeyyXIC% TaeyyXICTaeyyXICTaey4kaSIaamiwamaaBaaaleaacqWFUbGBaeqa% aaaa!4B7C!

A new free-will defence

S_n = X_1 + \cdot \cdot \cdot + X_n