Williamson on Fine on Prior on the reduction of possibilist discourse

Abstract

I attempt to meet some criticisms that Williamson makes of my attempt to carry out Prior's project of reducing possibility discourse to actualist discourse.

Keyword:

• Modality

Notes

1. I should like to thank the audiences at the 2014 Prior conference in Oxford and at the 2014 meeting of the Bucharest Society of Analytic Philosophy for helpful comments. I have also benefitted from conversations with Walter Dean and from conversations with and written comments from Peter Fritz and Jeremy Goodman.

2. This is part of my general stance on ontological questions (Fine 2009). However, the formulation in this case might be regarded as over-simple for at least two reasons. One is that the actualist might wish to make a modal claim, to say that necessarily only actual objects are real; another is that a philosopher might believe that only actual objects are real, not because he is an actualist, but because he is a Pythagorean, let us say, and believes that only numbers are real and that all numbers are necessarily actual. But I take it that such subtleties in the formulation of the dispute are not here at issue.

3. I provide a defense of my own view in chapter 9 of Fine (2005a), especially §9.

4. At one point (23), Williamson asks ‘And why should the alternative to the view that everything does the harder thing [being actual] be a view on which everything could do the harder thing [be possibly actual]?’ A good question, to which the answer is that this is not the only alternative. One might think, for example, that there are sets of incompossible objects which could not even be possibly actual and, indeed, such a view would naturally follow from a position which took all urelements to be possibly actual and yet took some of the urelements to be incompossible.

5. I also believe that there is no intelligible notion of unrestricted quantification (Fine 2006). But I do not press the point here, since I agree with Williamson (MLM, 15) that we can get at ‘the point’ behind the N/C dispute without appeal to the notion.

6. Additionally, if one thinks, as I do, that a wooden chair, say, is necessarily wooden and hence necessarily concrete then the appeal to concreteness is doomed from the start.

7. But I should note that, strictly speaking, the reduction applies recursively to all formulas and that care should be taken to avoid clash of variables.

8. In the more general case, the outer quantifiers may also range over impossible objects – over sets of incompossibles, for example.

9. This is not quite Williamson’s proposal on 353 of MLM, but the differences are incidental to the purpose at hand. There is also a subtlety concerning empty pluralities which I have, for convenience, ignored.

10. Fritz and Goodman (2014) point out that an especially severe form of this difficulty arises with the quantifier ‘most.’

11. The study of parallel processing or ‘process algebra’ has become a significant branch of computer science in its own right (see Boeten 2005 for a brief survey). I might also note that the case of substitution shows that Williamson’s putative tests for independence (idempotence and commutativity, 358) are clearly off the mark.

12. The theory of classes advocated in Fine (2005b) is one such example.

13. This is a place where appropriate adjustments will need to be made under the N/C construal of the debate.

14. A similar approach to Sider’s is considered in Fine (1977a), 147 and developed in §3 of Fine (2002). My own approach also avoids the problems raised by Leuenberger (2006) and extended in the formal appendix to Fritz and Goodman (2014).

15. A symbolism of this sort is familiar from dynamic programming logic (Harel 1984), another well-developed branch of computer science.

16. This claim makes most sense if we take it to be essential to an act of killing that it be an act of killing.

17. If only the identity, and not also the distinctness, of individuals is an aspect of logical form, then we should add the supposition ΠxΠy(¬x = y → /¬x = y/) (suppose, of any two distinct possible objects, that they are distinct).

18. As Jeremy Goodman has pointed out to me, the contingentist also does not think that the Barcan Formula holds for metaphysical necessity and so this may be a respect in which there is a significant difference between the A/P and N/C formulations of the debate.