Evidential Roles and Degrees of Truth

In many ways, maximally strong consistent precise propositions in this framework are approximations of possible worlds in an intensional framework.

There is a striking resemblance between this formalism and approaches to vague­ness based on fuzzy logic. Propositions, according to the fuzzy logician, are not simply true or false: there are many truth values between the two, which we can represent on a scale including all the real numbers between 0 and 1, with 0 representing outright falsehoods and 1 representing truths. A borderline proposition, on this view, has a truth value somewhere strictly between 1 and 0. A proposition, then, determines a mapping from possible worlds to numbers in the interval [0,1]: the mapping that takes a world w, to the truth value of that proposition at w.

These theorists typically work with a non-classical logic, due to the way in which the truth values at a world interact with the connectives. However, some theorists retain classical logic and consequently exhibit some strong parallels with the view I've been defending here. Edgington [39], for example, espouses a view in which the truth values behave like probability functions (see also Kamp [76], Lewis [89], and Williams [152], for versions and developments of the view in a supervaluationist setting). Given the analogies, one might wonder if the view I have defended here is just a version of the fuzzy view defended by Edgington.

Rational degrees of belief and degrees of truth might seem like different concepts on the surface: the former seem subjective and the latter objective.

Edgington, however, thinks that there are other important differences between truth values (which she calls ‘verities') and degrees of belief. In Edgington [39] she writes:

Some philosophers (e.g. Williamson 1994) hold that vagueness is a species of epistemic uncertainty: there is a precise line which divides the red from the non-red, etc., but it is epistemically inaccessible to us. Were this true, verity would be a kind of credence: the credence that a person with no relevant ignorance other than about the precise line, would give to a statement like ‘that’s red’. If a is redder than b, but neither is clearly (certainly) red, then one must, if rational, be more confident that a is red than that b is: a is more likely to be above the mystery line than b is.

The view I am defending is not epistemicism, but it agrees with the epistemicist in respects important to this discussion. According to Edgington degrees of truth and credences play different roles. Credences inform a rational person’s actions, whereas degrees of truth do not. In support of this she notes the distinction between the following kinds of justifications:

I prefer A to B by a long way. Therefore I prefer A with certainty to A or B happening with equal uncertainty, i.e. probability 2, and I should prefer A or B happening with equal uncertainty to B with certainty.

I prefer A to B by a long way. Therefore I prefer A with truth value 1 to A or B each with equal intermediate truth value, 2, and I should prefer A or B with equal truth value to B with truth value 1.

The former principle is a valid principle in most decision theories, yet Edgington gives an example, in which whether A or B is borderline figures in my preferences, to demonstrate that the second is not a universally correct principle of decision making: I might have a definite preference for drinks that are definitely tea, or definitely coffee, but strongly dislike things that are borderline between the two.

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I    am indebted to Robbie Williams for pressing me on this objection.

Other than Edgington’s argument above (which I find convincing), I think there are two further points to be made.

The second point I want to make involves an analogy with chances. Note the similarity between the following two claims

For each proposition, p there is a function, E, such that for each maximally strong consistent precise proposition w, and rational prior credence function Cr, Cr(p | w) = E(w).

For each proposition, p there is a function, F, such that for each maximally strong consistent piece of admissible evidence at t, w, and rational prior credence function Cr, Cr(p | w) = F(w).

In both cases there is a special partition of the space of propositions such that every rational prior agrees with every other prior conditional on any element of that partition. The former principle is a consequence of our theory of propositions, the latter a consequence of the principal principle (see Lewis [91]). In the latter case F(w) simply represents the chance that p at time t. In whatever sense E plays the truth role for the proposition p (relative to the partition of maximally specific precise propositions) so do chances (relative to the partition of worlds with the same admissible evidence at t). Since we are not at all tempted to call chances truth values on the basis of truth norms alone, I think that we should not be tempted to call credences truth values.