[The following is the consequence of discussion with F.A. Muller, Lieven Decock, and Victor Gijsbers. They should be blamed for my mistakes.--ES]

A few weeks ago I complained that Ted Sider's approach to "knee-jerk realism" is dismissive toward views that do not share his (ahum) fundamental outlook (and I mused a bit about the sociology of knowledge that facilitates such dismissiveness). One worrisome consequence is that Sider fails to see objections to his view when they ought to be staring him in the face. Consider the following two passages from Ted Sider's *Writing the Book of the World*:

I hold that the fundamental is also determinate. "The fundamental is determinate" is not particularly clear, and improving the situation is difficult because there are so many different ways to understand what "determinacy" amounts to, but perhaps we can put it thus. First, no special-purpose vocabulary that is distinctive of indeterminacy...carves at the joints. Second, fundamental languages obey classical logic. The combination of these two claims is perhaps the best way to cash out the elusive dogma that vagueness and other forms of indeterminacy are not "in the world." (137)

The continuum hypothesis is sometimes said to be indeterminate. But suppose that mundane set-theoretic truths, such as the axiom of extensionality, are fundamental. Then by the combinatorial principle, the continuum hypothesis must be determinate, since it can be stated using only expressions that occur in mundane set-theoretic truths (namely, logical expressions and the predicate ∈). Thus we have a surprising result: the fundamentality of the mundane truths of set-theory requires the non-mundane continuum hypothesis to be determinate. (151)

Now, first, the "sometimes said to be," is an odd locution. After all, it was proven that if ZFC is consistent then the continuum hypothesis can neither be proven nor disproven in it (see here for a good intro). Second, in the context of Sider's program ("mundane set-theoretic truths"), abandoning ZFC is not on the table. Third, I know that *One's modus ponens* is *another's modus tollens, *but Sider has no "result" here--he ought to be facing up to the fact that there is a straightforward objection against his claim that the "fundamental languages"* obey *classical logic and mundane set theory*: *there is no reason to think the continuum hypothesis is determinate. To think otherwise is an act of faith (recall my observation about the odd religiosity of his so-called "knee-jerk realism"). So, I stand by my earlier claim that there is something troubling about an agenda-setting book that wishes away obvious problems with the program.

## Recent Comments