Modal pluralism and higher-order logic (William McCarthy)

The Logic and Metaphysics Workshop will meet on November 28th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 7314) for a talk by William McCarthy (Columbia).

Title: Modal pluralism and higher-order logic

Abstract: Modal pluralism is the view that there are a variety of candidate interpretations of the predicate ‘could have been the case that’ which give intuitively different answers to paradigmatic metaphysical questions (‘intuitively’ because the phrase means subtly different things on the different interpretations). It is the modal analog of set-theoretic pluralism, according to which there are a variety of candidate interpretations of ‘is a member of’.  Of course, if there were a broadest kind of counterfactual possibility, then one could define every other kind as a restriction on it, as in the set-theoretic case.  It would then be privileged in the way that a broadest kind of set would be, if there were one.  Recently, several authors have purported to prove from higher-order logical principles that there is a broadest kind of possibility. In this talk we critically assess these arguments.  We argue that they rest on an assumption which any modal pluralist should reject: namely, monism about higher-order logic. The reasons to be a modal pluralist are also reasons to be a pluralist about higher-order quantification. But from the pluralist perspective on higher-order logic, the claim that there is a broadest kind of possibility is like the Continuum Hypothesis, according to the set-theoretic pluralist.  It is true on some interpretations of the relevant terminology, and false on others.  Consequently, the significance of the ‘proof’ that there is a broadest kind of possibility is deflated.  Time permitting, we will conclude with some upshots of higher-order pluralism for the methodology of metaphysics.

Note: This is joint work with Justin Clarke-Doane.

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