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About the article
Published Online: 2014-01-07
Published in Print: 2014-04-01
For example, in conversation with Carl Hoefer he argued for the position that while there are no probabilities in nature, there are necessities.
Some examples of the creed, where E is the ultimate evidence proposition and where is to be read as “the rational credence in A, where one’s evidence is exhausted by E”, are Lewis’ (1980) Reformulated Principle: , where is the ultimate evidence that is true at world w and time t and is the chance at t and w function. Hall’s (1994) Principle: Meacham’s (2010) Principle: , where is the E-grounded or E-entailed chance function.Williamson’s (2010) Principle: If E entails , then .
This is so for no other reason than that I think I can see how a reduction to ultimate belief can be achieved, whereas I cannot see how to demonstrate the convergence required for the reduction of these probabilities to belief at the convergent limit of updating.
For the sake of simplicity I ignore the inertial frame relativity of simultaneity. It can be accommodated in what is to follow by taking the frame of the state to be the inertial frame of the person making the physical probability ascription, or it can just be left as an arbitrarily chosen Cauchy surface.
With only a slight, and obvious, alteration to the reduction schema for physical probability ascriptions, one can also give a similar analysis for claims like “The objective chance of A is in .”
This is not true of projectivist positions on lawhood; those where there is no objectivity to the extension of the term “natural law” over and above our intersubjective agreement – however this is obtained – on what is to count as a natural law. Typically, such intersubjective agreement will be a fleeting thing, so the extension of “natural law” will change over time and perhaps even across social context. For such a position, the law sentence will be sensitive to all aspects of the context in which it is used. This causes no problems for van Fraassen’s reduction– one simply retains as the argument of N, where t is a rigid designator of a time and a designates that actual-at-w′’s individual’s counterpart at w′. What is incompatible with van Fraassen’s reduction is his later (van Fraassen 1989) claim that there are no natural laws. Fortunately, I see no reason why an empiricist need be forced to such an extreme.
Where context makes it plain that is a proposition, I follow van Fraassen in omitting the square brackets.
On the basis of these commonly agreed distinctions, I tend to side with those who assert that of these three attitudes, only de dicto belief qualifies as a propositional attitude.
There are cogent arguments for the reducibility of r-belief to d-belief—Kaplan (1968) himself even attempted such a reduction explicitly – and I am sympathetic to that program; however, it is harder to sustain the view that all belief can be reduced to d-belief once one has recognised the legitimacy of belief de se. Lewis (1979) argues convincingly when introducing s-belief that though d-belief is reducible to s-belief, the converse is not the case.