Wright (Wabash ’97) has as his topic “alethic pluralism” as an “inflationary” approach to truth. The use of ‘alethic’ here amounts to ‘concerning truth’, and an “inflationary” approach treats truth as a substantive property (so it is opposed to the “deflationary” approaches, like Ramsey’s, that treat a truth predicate primarily as a device for disquotation). In this first part of the paper, Wright presents the motivation for this sort of theory of truth, notes a problem for it, and introduces a solution that has been suggested for that problem. (The remainder of the paper, which we will discuss on Fri., develops a criticism of that solution.)
• The first section is Wright’s introduction. Pay attention to his list of ten examples because he will refer to them periodically throughout the paper. And note the suggestion that traditional inflationary theories (of the sort we have seen in James, Joachim, and Russell) might each be appropriate for truth in different domains of discourse.
• Section 2 introduces alethic pluralism as a solution to a problem noted at the end of §2.1 and notes a difficulty with it. Think about the distinction made between strong and weak pluralism in §2.2, but don’t worry if it isn’t entirely clear because Wright will call it into question at several points later. (The formula (11) can be read to say “There is a collection consisting of the propositions (1)-(10) all of whose member are true,” so it applies the same truth predicate to all of the ten examples.)
• Finally, §3 introduces the suggestion that a “functionalist” approach will solve the difficulty noted in §2.3. Functionalism began as an approach to the relation between the mind and body which holds, roughly, that mental properties provide a functional description of neurophysiology. Although mental properties cannot be given definitions in terms of physiology (and thus cannot be “reduced” to it), they need not be seen as referring to a separate mental substance but instead as indicating functions that can be realized physically but cannot be identified with any single physical realization. The same is true of the functional descriptions of tools (a hammer, even a particular kind of hammer, can be realized in many different materials and shapes) and computer programs (where the hardware and even underlying system operations can vary widely). This is the idea of “multiple realizability” that Wright speaks of.
The formulas (14) and (15) are derived from an idea of Frank Ramsey about capturing the role of special theoretical terms in scientific theories. The relation R in (14) is supposed to express what a theory says about a group of familiar terms (the Os) and a group of new ones (the Ts). The right side of the ↔ (i.e., ‘if and only if’) in (15) is intended to say that there are some properties x1, …, xn that stand in the relation R to the Os and that the sentence (σ) has these properties. (There is actually a typo in what is printed, so the Ts were not, as they should have been, replaced by the xs.)