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日時：2016年11月11日(金) 18:00–19:30

場所：京都大学 文学部校舎１階 会議室

話者：Syraya Chin-Mu Yang(国立台湾大学)

言語：英語

題目：

Semantic Considerations on Contingentist Quantified Modal Logic

概要：

Timothy Williamson has defended necessitism, the thesis that necessarily

everything is necessarily something: ‘(NE) － □∀x□∃y x = y’. By contrast,

contingentism, a negation of necessitism, accepts the contingency of being

－ there are things which exist contingently. Williamson rightly remarks

that ‘common sense has no authority to decide between necessitism and

contingentism; it is a more theoretical dispute’. And so, he claims that

necessitism can be justified in a framework for quantificational, or

higher-order, modal logic, which originated from the proof theoretic work

of Ruth Barcan Marcus. Typically, the well-known Barcan Formula (BF) －

∀x□φ(x)→□∀x φ(x), and its converse (CBF) － □∀xφ(x) →∀x□φ(x), have been

taken as the characteristic formulas for the necessitist quantified modal

logic. In contrast, the contingentist’s quantified modal logics by and

large repudiate BF and CBF.

I will examine some intrinsic semantic problems with the contingentist’s

treatments in the framework of possible worlds semantics. Special attention

will be paid to the difficulties with variable domains. I show that

sticking to the legitimacy of the Being Constraints, the use of names as

rigid designators in modal contexts will render truth value gaps in

variable domains and by the same reasoning we may not have appropriate

assignments of free variables in de re modal contexts. However, I show that

this can be solved if we opt for a mid-way, i.e. equinumerous domains. We

will not appeal to constant domains, nor will we accept variable domains,

but simply assume that all domains have the same cardinality, though not

the same set of objects. A semantic treatment will be proposed so that both

BF and CBF can be validated, but the thesis of necessitism will no longer

hold.

A genuine threat will be noted, that is, the intended interpretation of de

re sentences may not express the imposed de re modality. Two options to

deal with this problem will be suggested. (i) The appeal to the rigidity of

names based on a substitutional interpretation of quantifiers in

alphabetical-expansion models However, when modal contexts are involved, we

may be forced to rephrase universal sentences in terms of a conjunction

with an infinite number of conjuncts and to re-interpret a formula with an

existence quantifier in terms of an infinitary conjunction. We then need an

infinitary language and take as the required underlying system a certain

version of infinitary logic. Alternatively, we may suspense with names and

put forth some special semantic treatment to express the rigidity of

variables. We would have a much more complicated, or even ad hoc,

semantics, and the price could be too high to pay.

Clearly, for the contingentist, the moral is: there is no loyal road to the

theorization of metaphysical modality in terms of quantified modal logic.

Perhaps, Williamson is right when he points out that the contingentist

‘must take a more instrumental attitude to the model theory’. (2014: 714).

Then why not accept the necessitist’s quantaified modal logic?