KOSLOW, Arnold, 2002. Laws, explanations and the reduction of possibilities. In: Real Metaphysics. Routledge. ISBN 978-0-203-16429-7.
> There is a good case to be made for the idea that explanations delimit or ‘narrow down’ a certain range of possibilities, if the concepts of possibility and the narrowing down or reducing of possibilities are understood in a way that differs from the standard candidates for them that can be found in the literature. So the task, as I see it, is to make the case for these new types of possibilities, and to describe the special way that sets of possibilities get narrowed down by laws and explanations. These possibilities (let’s call them natural possibilities) might easily be dismissed as no possibilities at all, but merely a case of speaking with the vulgar. Nevertheless, there is, I think, good reason to take these examples as seriously modal. Indeed, they represent a kind of modality that opens the way to a new account of the way in which scientific explanations and laws are related to possibilities.
The idea that laws and explanations reduce possibilities is an attractive one. Arnold Koslow’s chapter makes a case for this idea. The first thing that Koslow notes is that for laws and explanations to reduce possibilities, a new concept of possibilities and their reduction is needed. Koslow starts by describing a new set of possibilities (he calls them natural possibilities), which includes things as varied as the truth values of sentences, the members of sample spaces and the outcomes of tossing a die. Natural possibilities can be abstract (numbers, numerical equations, truth values), concrete (a particular act, such as eating a banana), object-like, property-like, structured, structureless, and so on. However varied these and other possibilities are, Koslow shows why they are all genuinely modal. He does this by introducing a mini-theory of natural possibilities. The modal character of a set of natural possibilities N is explained by means of the notion of a certain implication relation defined on the power set of N.
Koslow explains how laws and explanations reduce possibilities. After showing how laws reduce possibilities, Koslow notes that Mellor’s facticity condition on explanation, namely that A’s explaining B entails both A and B, entails that explanations that either are laws or involve laws as parts will reduce possibilities. But not all explanations are like that: some do not involve laws at all. Koslow notes that many models of explanation do not guarantee that explanations reduce possibilities but says that Mellor accepts certain constraints on explanations which yield the result that explanations in general reduce possibilities. The constraint in question is that A’s explaining B entails that the chance of B given A is greater than the chance of B given the absence of A.
Mellor replies that he does not assume this constraint on explanations. For him only causes are required to raise the chances of their effects, and many explanations are not causal. Nevertheless, Mellor argues, even these explanations reduce possibilities. To show this only the facticity of explanation is required.
Construction as Reduction
The language acquisition process is suggested to be a process of selection and cumulative reduction from the language of more experienced (i.e. older) individuals. The population structure ensures that the approximation of the language learner results in a common language that is stable under normal conditions. Language is described as a 'stasis' between constructive and eliminative reduction.
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JOHANSSON, Christer, 1996. Construction as reduction. Lund University, Dept. of Linguistics Working Papers. 1996. Vol. 45, p. 79–92.