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Unformatted text preview: PROBABILITY CAPTURES THE LOGIC OF SCIENTIFIC CONFIRMATION 1. Introduction Confirmation is a word in ordinary language and, like many such words, its meaning is vague and perhaps also ambiguous. So if we think of a logic of confirmation as a specification of precise rules that govern the word confirmation in ordinary language, there can be no logic of confirmation. There can, however, be a different kind of logic of con- firmation. This can be developed using the philosophical methodology known as explication (Carnap, 1950, ch. 1). In this methodology, we are given an unclear concept of ordinary language (called the explican- dum ) and our task is to find a precise concept (called the explicatum ) that is similar to the explicandum and is theoretically fruitful and simple. Since the choice of an explicatum involves several desiderata, which different people may interpret and weight differently, there is not one right explication; different people may choose different explicata without either having made a mistake. Nevertheless, we can cite reasons that motivate us to choose one explicatum over another. In this paper I will define a predicate C which is intended to be an explicatum for confirmation. I will establish a variety of results about C dealing with verified consequences, reasoning by analogy, universal generalizations, Nicods condition, the ravens paradox, and projectability. We will find that these results correspond well with intuitive judgments about confirmation, thus showing that our expli- catum has the desired properties of being similar to its explicandum and theoretically fruitful. In this way we will develop parts of a logic of confirmation. The predicate C will be defined in terms of probability and in that sense we will conclude that probability captures the logic of scientific confirmation. 2. Explication of justified degree of belief I will begin by explicating the concept of the degree of belief in a hypothesis H that is justified by evidence E . A little more fully, the explicandum is the degree of belief in H that we would be justified in having if E was our total evidence. We have some opinions about pctl.tex; 3/05/2006; 16:13; p.1 2 this but they are usually vague and different people sometimes have different opinions. In order to explicate this concept, let us begin by choosing a for- malized language, like those studied in symbolic logic; we will call this language L . We will use the letters D , E , and H , with or without subscripts, to denote sentences of L . Let us also stipulate that L contains the usual truth-functional connectives for negation, for disjunction, . for conjunction, and for material implication....
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- Fall '06