This article analyzes and compares several approaches of formalizing the notion of evidence in the context of general-purpose reasoning system. In each of these approaches, the notion of evidence is defined, and the evidence-based degree of belief is represented by a binary value, a number (such as a probability), or two numbers (such as an interval). The binary approaches provide simple ways to represent conclusive evidence, but cannot properly handle inconclusive evidence. The one-number approaches naturally represent inconclusive evidence as a degree of belief, but lack the information needed to revise this degree. It is argued that for systems opening to new evidence, each belief should at least have two numbers attached to indicate its evidential support. A few such approaches are discussed, including the approach used in NARS, which is designed according to the considerations of general-purpose intelligent systems, and provides novel solutions to several traditional problems on evidence.

Does evolutionary theory have implications about the existence of supernatural entities? This question concerns the logical relationships that hold between the theory of evolution and different bits of metaphysics. There is a distinct question that I also want to address; it is epistemological in character. Does the evidence we have for evolutionary theory also provide evidence concerning the existence of supernatural entities? An affirmative answer to the logical question would entail an affirmative answer to the epistemological question if the principle in confirmation theory that Hempel (1965, p. 31) called the special consequence condition were true: The special consequence condition: If an observation report confirms a hypothesis H, then it also confirms every consequence of H. According to this principle, if evolutionary theory has metaphysical implications, then whatever confirms evolutionary theory also must confirm those metaphysical implications. But the special consequence is false. Here‟s a simple example that illustrates why. You are playing poker and would dearly like to know whether the card you are about to be dealt will be the Jack of Hearts. The dealer is a bit careless and so you catch a glimpse of the card on top of the deck before it is dealt to you. You see that it is red. The fact that it is red confirms the hypothesis that the card is the Jack of Hearts, and the hypothesis that it is the Jack of Hearts entails that the card will be a Jack. However, the fact that the card is red does not confirm the hypothesis that the card will be a Jack. 2 Bayesians gloss these facts by understanding confirmation in terms of probability raising: The Bayesian theory of confirmation: O confirms H if and only if Pr(H│O)> Pr(H). The general reason why Bayesianism is incompatible with the special consequence

Abstract: After describing the difference between methodological and metaphysical naturalism, I distinguish three theistic positions – creationism, deism, and the view that evolutionary theory is true but incomplete because God‟s interventions in nature sometimes supplement the causes that the theory describes. I argue that evolutionary theory is compatible with the third of these positions as well as with the second. I do so by clarifying what biologists mean by saying that mutations are undirected. I then consider three defenses of methodological naturalism ─ that science, by definition, is an enterprise in which claims about supernatural deities are excluded, that claims about the supernatural are untestable, and that including such claims in scientific theories would bring science to a stop. After criticizing these arguments, I provide a more modest defense of methodological naturalism. “ … any confusion between the ideas suggested by science and science itself must be carefully avoided. ” – Jacques Monod, Chance and Necessity, p. xiii.

This question is a test case for Naturalismp, which is the thesis that philosophical theories and scientific theories should be evaluated by the same criteria. In this paper, I describe the justifications that attach to two types of parsimony argument in science. In the first, parsimony is a surrogate for likelihood. In the second, parsimony is relevant to estimating how accurately a model will predict new data when fitted to old. I then consider how these two justifications apply to parsimony arguments in philosophy concerning theism and atheism, the mind/body problem, ethical realism, the question of whether mental properties are causally efficacious, and nominalism versus Platonism about numbers. For many philosophers, the word “naturalism ” immediately conjures up a metaphysical and a methodological thesis. Both concern objects that are “in nature, ” meaning things that exist in space and time; the contrast is with the supernatural entities that might be thought to exist “outside ” of space and time: 1 Metaphysical Naturalism: The only things that exist are things in nature. Methodological Naturalisms: Science should not postulate the existence of things that are outside of nature. I put an “s ” subscript on the second naturalism to mark the fact that it gives advice to science. These two naturalisms are the ones that get trotted out in discussions of evolutionary theory versus creationism. Evolutionists often say that their theory obeys the strictures of methodological naturalism but is silent on the metaphysical question. They further contend that creationism rejects both these naturalisms; here they are helped by creationists themselves, who often express their belief in a supernatural deity and argue that methodological naturalisms is a shackle from which science needs to break free. Although it is worth inquiring further into this interpretation of both evolutionary theory and creationism, 2 that is not my topic 1 The words “inside ” and “outside ” are used metaphorically here. A more literal formulation is that metaphysical naturalism says that all existing things have spatio-temporal location; supernatural entities, if they exist, do not.