Book Discussion of Christopher Norris' "Epistemology: Key Concepts in Philosophy"
Chapter 2: Realism, Reference and Possible Worlds - Section III.
A lingering question left from the last section-what IS the difference between the reality of David Lewis' possible worlds, and Thomas Kuhn's (via Quine) world-webs? Essentially, I think the answer is, that Lewis' thinks they are real without verification, whereas Kuhn thinks they're real 'due to' verification. That's why Lewis is a realist, and Kuhn is an anti-realist. In this section, Norris notes Dummett would reject Lewis' transworld necessary mathematical truths, and stuff like Goldbach's Conjecture, putting them in the "disputed class" (neither true nor false, as they cannot be verified/falsified)-"as distinct from merely undecidable according to our best, most advanced or sophisticated proof procedures." To the realist that seems unreasonable, but so does Lewis' "outlook of intransigent realism with regard to possible worlds and his suggestion that the case for mathematical realism stands or falls with that for the reality (as distinct from the logical conceivability) of any and every such world." And (if I read Norris correctly) Lewis' position is inferior to Kripke-Putnam's distinguishing between contingent and necessary truths, and analytic (transworld) necessity from a posteriori necessity-that such distinguishing is the only way "the realist [can] hope to produce the kind of argument that would challenge the case for anti-realism advanced by thinkers like Dummett…that treats every area of discourse as having no room for truth-apt statements whose objective truth-value transcends the limits of recognition or verification."
How do we know current "knowledge" is any better than past errors/incompleteness? Lewis' answer: "1) any talk of past errors presupposes our possession of other, more advanced or adequate truth-standards," 2) the recommendation that we remain epistemically humble presupposes we might be wrong according to "(what else?) objective criteria of scientific truth and falsehood." If it's all in our head, we're never wrong. If we can be wrong, the truth must be outside our head, waiting to be discovered. Norris mentions "convergent realism" - "science may be taken as converging on truth at the end of enquiry to the extent that its theories are increasingly borne out by the best evidence to hand." The anti-realist would like to remain humble and not go so far as saying "atoms actually exist"-would rather "treat atoms and such-like as useful posits for the sake of upholding some empirically adequate theory." Anti-realism, unlike realism, carries no ability to explain scientific progress, and Norris takes some time to speak of mathematics' importance in that progress, which Wigner acknowledges but considers to be "bordering on the mysterious and…there is no rational explanation for it." The Kripke-Putnam approach provides an explanation.
The rest of the section is spent prepping for the next section, which will avoid the problem of Lewis considering possible worlds to have the same ontology as our own (just not "actual"), and will introduce some ideas that are pertinent to "critical realism"-like the distinction between ontology (truth is outside head) and epistemology (knowledge requires verification).