The quantitative problem of old evidence is the problem of how to measure the degree to which e confirms h for agent A at time t when A regards e as justified at t. Existing attempts to solve this problem have applied the e-difference approach, which compares A's probability for h at t with what probability A would assign h if A did not regard e as justified at t. The quantitative problem has been widely regarded as unsolvable primarily on (...) the grounds that the e-difference approach suffers from intractable problems. Various philosophers have proposed that 'Bayesianism' should be rejected as a research strategy in confirmation theory in part because of the unsolvability of this problem. I develop a version of the e-difference approach which overcomes these problems and possesses various advantages (but also certain limitations). I develop an alternative 'theistic' approach which handles many cases that my development of the e-difference approach does not handle. I conclude with an assessment of the significance of the quantitative problem for Bayesianism and argue that this problem is misunderstood in so far as it is regarded as unsolvable, and in so far as it is regarded as a problem only for Bayesians. (shrink)

Proponents of the Fine-Tuning Argument frequently assume that the narrowness of the life-friendly range of fundamental physical constants implies a low probability for the origin of the universe ‘by chance’. We cast this argument in a more rigorous form than is customary and conclude that the narrow intervals do not yield a probability at all because the resulting measure function is non-normalizable. We then consider various attempts to circumvent this problem and argue that they fail.

This paper offers an answer to Glymour's ‘old evidence’ problem for Bayesian confirmation theory, and assesses some of the objections, in particular those recently aired by Chihara, that have been brought against that answer. The paper argues that these objections are easily dissolved, and goes on to show how the answer it proposes yields an intuitively satisfactory analysis of a problem recently discussed by Maher. Garber's, Niiniluoto's and others’ quite different answer to Glymour's problem is considered and rejected, and the (...) paper concludes with some brief reflections on the prediction/accommodation issue. (shrink)

Instead of simply defending a denial of God's existence Le Poidevin presents instead a way of interpreting religious discourse which allows us to make sense of the role of religion in our spiritual and moral lives.

Where there are infinitely many possible [equiprobable] basic states of the world, a standard probability function must assign zero probability to each state—since any finite probability would sum to over one. This generates problems for any decision theory that appeals to expected utility or related notions. For it leads to the view that a situation in which one wins a million dollars if any of a thousand of the equally probable states is realized has an expected value of zero (since (...) each such state has probability zero). But such a situation dominates the situation in which one wins nothing no matter what (which also has an expected value of zero), and so surely is more desirable. I formulate and defend some principles for evaluating options where standard probability functions cannot strictly represent probability—and in particular for where there is an infinitely spread, uniform distribution of probability. The principles appeal to standard probability functions, but overcome at least some of their limitations in such cases. (shrink)

The universe appears fine-tuned for life. Bayesian confirmation theory is utilized to examine two competing explanations for this fine-tuning, namely design (theism) and the existence of many universes, in comparison with the ’null’ hypothesis that just one universe exists as a brute fact. Some authors have invoked the so-called ’inverse gambler’s fallacy’ to argue that the many-universes hypothesis does not explain the fine-tuning of ’this’ universe, but flaws in this argument are exposed. Nevertheless, the hypothesis of design, being simpler, is (...) arguably of higher prior probability and, therefore, to be preferred. The hypothesis of the single brute-fact universe is disconfirmed. (shrink)

This Element analyzes the various forms that design arguments for the existence of God can take, but the main focus is on two such arguments. The first concerns the complex adaptive features that organisms have. Creationists who advance this argument contend that evolution by natural selection cannot be the right explanation. The second design argument - the argument from fine-tuning - begins with the fact that life could not exist in our universe if the constants found in the laws of (...) physics had values that differed more than a little from their actual values. Since probability is the main analytical tool used, the book provides a primer on probability theory. (shrink)

The argument from fine tuning is supposed to establish the existence of God from the fact that the evolution of carbon-based life requires the laws of physics and the boundary conditions of the universe to be more or less as they are. We demonstrate that this argument fails. In particular, we focus on problems associated with the role probabilities play in the argument. We show that, even granting the fine tuning of the universe, it does not follow that the universe (...) is improbable, thus no explanation of the fine tuning, theistic or otherwise, is required. (shrink)

Recent discoveries in physics, cosmology and biochemistry have captured the public imagination and made the Design Argument - the theory that God created the world according to a specific plan - the object of renewed scientific and philosophical interest. This accessible but serious introduction to the design problem brings together new perspectives from prominent scientists and philosophers including Paul Davies, Richard Swinburne, Sir Martin Rees, Michael Behe, Elliot Sober and Peter van Inwagen.

In this volume, the sixth in Blackwell's Great Debates in Philosophy series, Smart and Haldane discuss the case for and against religious belief. The debate is unusual in beginning with the negative side. After a short jointly authored introduction, there is a fairly extended presentation of the atheist position by Smart. Haldane then offers an equally extended defense of theism. The authors respond to one another in the same order, and the book concludes with a brief co-authored treatment of antirealism, (...) which both reject. The discussion is broad-ranging, in part reflecting the size of the topic. It addresses the existence of God and the problem of evil, along with related issues having to do with God's nature and his involvement with the world: necessary being, eternity versus sempiternity, the relation between divine sovereignty and human freedom, and the possibility of miracles. But there is also discussion of subjects having to do with revealed religion, such as the reliability of scripture, and the roles of faith and reason in the life of the believer. The fact that the book commences with the case for atheism also contributes to its scope, since without a specific version of theism on which to focus, Smart has to aim broadly. The result is that topics that might otherwise have been ignored—moral arguments, and Pascal's wager, to cite two—are at least broached, though not pursued. (shrink)