Abstract
Consider the following argument, where ‘\(\langle p\rangle\)’ abbreviates ‘the proposition that p’:
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(1)
It is possible that Socrates does not exist.
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(2)
Necessarily, if Socrates does not exist, then \(\langle \text {Socrates does not exist}\rangle\) is true.
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(3)
Necessarily, if \(\langle \text {Socrates does not exist}\rangle\) is true, then \(\langle \text {Socrates does not exist}\rangle\) exists.
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(4)
Necessarily, if \(\langle \text {Socrates does not exist}\rangle\) exists, then Socrates exists.
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(5)
Therefore, it is possible that Socrates exists and does not exist.
How can one respond to this argument? Fine (1985) thinks that the argument involves an equivocation concerning the notion of truth for propositions: if we stand inside a possible world to evaluate the truth, in this ‘inner’ sense (3) holds but (2) fails; but if we stand outside, in this ‘outer’ sense (2) holds but (3) fails. In this paper we argue that such an equivocation response is obscure, ad hoc, and unmotivated.
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Notes
A reviewer suggested that the left-hand side of the biconditional, ‘\(\langle p\rangle\) is possible’, can be replaced with ‘Possibly, p’. The replacement is indeed cogent and avoids possible confusions. Yet, part of the issue is about the modal and the ontological status of propositions. Despite its intelligibility, the replacement may not make enough contribution to the issue, since it is not concerned with propositions at all.
See Williamson (2016).
Williamson (2002) argues that necessarily everything necessarily exists, and thus Socrates necessarily exists. Yet, Socrates is merely contingently concrete, i.e. he fails to be concrete after his physical body perishes. This provides a possibility for Socrates to exist in a non-concrete way. Even so, Williamson would not hold that there are two notions of existence.
The idea is that once we can clearly define the two notions, some of the charges can be lifted. Thus, the following is an attempt to define Fine’s distinction in terms of Adams’s distinction: \(\langle\text{p}\rangle\) is true in Fine’s inner sense in w iff \(\langle\text{p}\rangle\) is true in w (in Adams’s sense ), and \(\langle\text{p}\rangle\) is true in Fine’s outer sense in w iff \(\langle\text{p}\rangle\) is true at w (in Adams’s sense).
Adams (1981), p.22
For Adams, a set of propositions, say S, is consistent iff all propositions which are members of S can be true together. And a set of propositions S is maximal iff for every proposition \(\langle \text {p}\rangle\), either S contains \(\langle \text {p}\rangle\) or its negation as its member. Of course, (non-qualitative) propositions about contingent existents or non-existent lead to some complexities. See the discussion below.
Adams (1981), p.23
The expression ‘follow truth-functionally from’ may incur some possible confusion. The intended meaning of this expression is simply semantic entailment. We thank a reviewer for pointing this out.
We thank an anonymous reviewer for the suggestion to clarify the issue.
Provided that they both have eventually distinguished two kinds of possibilities, their natural response to the puzzle would be that the argument is unsound and commits the fallacy of equivocation since the modal operators involved are different. Yet, we shall argue that the better response, for those who follow the course of Turner (2005) and Stalnaker (2012), is the straightforward response.
Stalnaker (2012), p. 46.
References
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Acknowledgements
Thanks to two anonymous referees, Hsiang-Yun Chen, Kok Yong Lee, and audiences at the 2017 Joint Session of the Aristotelian Society and the Mind Association, the 2019 Taiwan Philosophical Association Annual Conference and the 2020 Taiwan Metaphysics Colloquium.
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Lin, HC., Deng, DM. Inside and Outside a Possible World. Philosophia 50, 1265–1275 (2022). https://doi.org/10.1007/s11406-021-00464-x
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DOI: https://doi.org/10.1007/s11406-021-00464-x