Abstract
This paper presents structural similarities and historical connections between Prior’s rejection of the Barcan formula and his critique of Berkeley’s master argument for idealism in his 1955 paper “Berkeley in Logical Form”. Making use of Mackie’s paper “Self-Refutation—A Formal Analysis”, it concludes with some suggestions concerning what is at stake in the debate between Prior and Berkeley and in structurally similar debates such as whether to accept the Barcan formula.
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Notes
Prior (1967, p. 161) characterizes Kripke’s approach as involving “a deliberate impoverishment of the formal machinery”.
Where “now” rigidly refers to the original time of utterance. I say that Prior “suggests” this view, since he was not sympathetic, at least early on, to this use of “now”. See Prior (1968c/2003).
It is this feature of Q that leads Prior to reject the rule of necessitation and the interdefinability of \(\diamond \) and \(\Box \). Thus, if a does not exist necessarily, then, for Prior, while \(Fa\,v\sim Fa\) is a logical truth, and is incapable of being false, it is not necessarily true (since it is not statable in all worlds).
See, for example, (Prior 1962/2003, pp. 18–19) and (Prior 1968b/2003, pp. 220–221) for other places where Prior makes the same point.
“Roughly”, because statements in the future tense may be about objects that now exist.
Further, he argues for rejecting the rule of necessitation, not any rule of classical quantification, to avoid (BF).
In using variables in predicate (as well as sentential) positions, Prior does not thereby take himself to be committing himself to an ontology that includes properties (or propositions). (BLF) is one of the first, if not the first, of Prior’s publications in which he presents that view (see Prior’s Preface to the second edition of (Prior 1968a/2003, pp. 1–2).
Berkeley would presumably reply to this objection by appealing to his view of “notions”, according to which we can have “notions”, but not “ideas”, of minds (see, for example, Berkeley 1710/1965, pp. 72–98).
Albeit making use of an “actually” operator that Prior does not invoke (see in this connection note 2).
While Prior does not make the point in his BLF, he does make the point, with reference to Berkeley, in (Prior 1969/1976, p. 217).
He also distinguishes both of these from “pragmatic” self-refutation. This also involves instances of “\(Op\rightarrow \sim p\)”; however, in these cases, the operators replacing “O” are less fundamental than those where the self-refutation is “operational”. See (Mackie 1964, p. 197).
See Levine (2013), which contains a more detailed presentation of the argument in this section.
Recall Prior’s remark that “even if it be true that whatever exists at any time exists at all times, there is surely no inconsistency in denying it” (TM, 30).
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Levine, J. Prior, Berkeley, and the Barcan formula. Synthese 193, 3551–3565 (2016). https://doi.org/10.1007/s11229-015-0909-8
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DOI: https://doi.org/10.1007/s11229-015-0909-8