To put the doubts plainly, just what features, visible from outside, differentiate it from a pseudo-science, with pseudo-experts and pseudo-knowledge? In the case of modal logic as metaphysics, such features have been grouped under two heads. First, there is the role of formalization and formal proof. The latter comprises both proof in a formal system for the formal object-language and proof by normal mathematical standards in a natural language as a metalanguage for the formal language. The first general feature is as easy to recognize as the role of mathematics in physics. It enables us to discriminate by uncontroversial technical means the theorems from the non-theorems of a proposed modal logic. Second, there is the role of pre-theoretic modal knowledge, accessible to almost any reasonable, intelligent person. That second general feature enables us to subject some theorems of the proposed logic on the metaphysical interpretation to independent test. Together, the two features differentiate modal logic as metaphysics from any pseudo-science.
Of course, a sceptic who doubts that there is modal knowledge will not be impressed by the second feature, just as a sceptic who doubts that is logical or mathematical knowledge will not be impressed by the first feature, and a sceptic who doubts that there is knowledge of the external world will not be impressed by the pretensions of natural science. But it is not the business of science to answer the determined sceptic. Such a character, always ready to raise the stakes by widening the area of doubt, is beyond the reach of good sense, and must be left to find his own way out of the corner into which he has painted himself...Like any other scientific enquiry, metaphysics as modal logic is rooted in our pre-scientific cognitive capacities.--Williamson, Modal Logic as Metaphysics, 427-8.
I made the mistake to glance ahead at the "Methodological Afterword," partially quoted above. Williamson's book is fascinating and difficult, and, I suspect, will shape discussions for decades to come. Later in the year, I hope to offer some remarks on the historical and substantive arguments. But here I'll write as a philosopher with an ongoing interest in evidential arguments in the sciences.
Williamson relies on a false, even dangerous, somewhat Kuhnian Image Of Science [hereafter IOS] to argue his case. This IOS entails (i) that once "mature," (426) "reasonable" insiders, who use an esoteric, "technical" langauge, do not have to answer certain objections. (Recall this post on the economist Stigler and his use of Kuhn.) These insiders are (ii) said to have "good sense" and "educated instinct" (428). Of course, such fine sense is "irreducible to knowledge of explicit rules." (428) So, that (iii) ultimately the claims of the science of modal logic as metaphysics are not transparent or to be checked by (potentially unreasonable) outsiders (whose objections do not have to be answered anyway (recall (i)). It is a fascinating fact of contemporary formal philosophy, that paradoxically, the philosophical method that is (legitimately) most associated with transparency and clarity rest here on non explicit foundations! (Recall my recent post on the abuses of formal philosophy.)
On Williamson's IOS (iv) science is ultimately an "abductive" enterprise (423ff), and his purported science (v) appeals to explanatory "strength, simplicitly, and elegance, partly on the fit between their consequences and what is independently known." (423) What is independently known turns out to be "pre-theoretic modal knowledge," which (vi) is rooted "our pre-scientific cognitive capacities." Finally, critics are told (vii) to play by Williamson's rules and develop an "alternative" that "does better by the same abductive methodology" (429, this is the last sentence of the book).
To put it in a slogan: Williamson's book should have been named, "The Science of Modal Logic as Metaphysics."+
As it happens, I agree with Williamson that it is not science's responsibility to answer the determined sceptic. Ever since Kant (with nods to Descartes and other predecessors), that's a task for philosophy. Within philosophy this task is (recall) not taken up by General Philosophy of Science (GPOS), which, in practice, relies on a kind of a Quasi-Transcendental Assumption (QTA): if anything counts as knowledge it is fallible science, especially physics (chemistry, biology, whatever), so let's now articulate how this is possible or, more formally, justified (and develop, say, norms appropriate to this). Within philosophy, this task of answering the sceptic is left to epistemology and, when we're dealing with formal languages, the philosophers of mathematics and logic. (Of course, sceptics about value are answered in meta-ethics/aesthetics; etc.) So, one consequence of Williamson's stance, if adopted, is the narrowing of philosophy; some questions are simply taken off the table because, well, Williamson says so. Of course, if modal logic as metaphysics were really a science, then Williamson ought to petition the division of "Mathematical, Physical and Life Sciences" at Oxford for inclusion with confidence.* That way, philosophers can continue to debate the epistemological foundations of modal logic as metaphysics.
It is, however, convenient for his case that Williamson misrepresents the skeptic here. When I am a skeptic about, say, the purported knowledge claims about economics (as I am a few days a week), I am most definitely not skeptical about the social reality that economists purport to describe. (Of course, the situation can be tricky because of the peformative and reflexive character of some economics-y knowledge claims, but you get the point.) So, one can be a skeptic about modal logic as metaphysics without denying that there is such a thing as necessity or possibility. One's skepticism can be more localized; for example, one can embrace neutral quantification (e.g., Routley, Azzouni, Nolan, etc.). When one embraces neutral quantification one need not turn into an external world sceptic or a sceptic about the existence of necessity.
To the best of my knowledge, neutral quantification is not argued against in the book. A position like neutral quantification is gestured at and dismissed in a footnote (146). Williamson responds to an objection by claiming "in what other science is the uninformativeness of a theory considered a virtue." (n. 77) But this is an unsatisfying response. Consider a physicists or an economists who deploy mathematical techniques that do not allow for, say, discontinuous phenomena. Even if the predictions based on these (and further theory) are very impressive, there will be a legitimate, nagging concern that will only be eliminated once more neutral mathematics is deployed. Because Williamson focuses almost exclusively on abductive success in his IOS, he misses this humdrum fact of scientific practice. Given that modal logics as metaphysics purports to be about what is one doesn't want to load the dice in virtue of the adoption of a certain formal language. So, Williamson's favored approach is in a crucial way very unlike "the role of mathematics in physics."
Could one be a partial skeptic about some of Williamson's other claims?
Let me close with a gesture toward another source of scepticism here. I have already noted that Williamson relies on a pre-theoretic knowledge that is non-explicit (recall (ii-iii; vi-vi)). A naturalist may well wish to see some evidence from psychology and X-PHI that Williamson's claims withstand scrutiny if only for species like us. But let's leave that aside. A key feature of science is a kind of stress-testing of its evidential input; this is done by careful measurement with carefully calibrated instruments relying on the science of metrology. Data is carefully analyzed by way of statistics. Measures, instruments, data, even the concepts deployed are, as it were, continuously stress-tested and only then black-boxed (although always open for review). By contrast, Williamson insists that we can black-box the pre-theoretic bit that is the core evidential input of modal logic as metaphysics. This gives Williamson's whole approach a kind of confirmatory bias. To the best of my knowledge this is an original move in the history of science. I do not doubt that it is possible to generate consensus on such slender, evidential grounds; that's because I have read what anthropologists have written about modern witchraft.
*Some such combinations are not unprecedented: formal semantics with linguistics; symbolic logics with artificial intelligence and computer science; decision theory with economics; etc.