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Ockhamism without Thin Red Lines

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Abstract

This paper investigates the logic of Ockhamism, a view according to which future contingents are either true or false. Several attempts have been made to give rigorous shape to this view by defining a suitable formal semantics, but arguably none of them is fully satisfactory. The paper draws attention to some problems that beset such attempts, and suggests that these problems are different symptoms of the same initial confusion, in that they stem from the unjustified assumption that the actual course of events must be represented in the semantics as a distinguished history, the Thin Red Line.

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Notes

  1. Øhrstrøm presents Ockham’s doctrine and its historical context in Øhrstrøm and Hasle (2011, pp. 6–10). Note that, although the view considered is reminiscent of Ockham’s doctrine, this does not make it the only view that deserves to be called Ockhamism. The term ‘Ockhamism’ may be used in different ways, and this paper is not intended to question the legitimacy of any of them. For example, Ockhamism may be defined without reference to actuality, as the thesis that future contingents have truth-values, or that there are true future contingents. Here it is assumed, like in Øhrstrøm (2009) and in Malpass and Wawer (2012), that something like (O) is essential to any view faithful to Ockham’s thought.

  2. Here ‘necessity’ is understood in the historical sense, that is, as a synonym of ‘settledness’. Accordingly, ‘determinate truth’ might also be called ‘settled truth’.

  3. The origin of the line of reasoning considered is Aristotle’s discussion of future contingents in De interpretatione 9. Iacona (2013) provides a more thorough explanation of the divergence between Ockhamism and the Aristotelian tradition, pp. 31–34.

  4. Iacona (2013) dispels some misunderstandings that may lead to think that Ockhamism is incompatible with indeterminism in some important sense, pp. 39–44. Further objections to Ockhamism are discussed in Rosenkranz (2012).

  5. The notion of branching time structure goes back to Kripke, see Prior (1967, pp. 27–29).

  6. A definition of truth at a moment-history pair along these lines is provided in Prior (1967, pp. 126–127).

  7. This assumption is stated explicitly in Øhrstrøm (2009, pp. 25–26), and in Malpass and Wawer (2012, p. 124). The expression ‘Thin Red Line’ is introduced by Belnap and Green (1994, pp. 379–381).

  8. This option is considered in Belnap and Green (1994, p. 379), in Perloff et al. (2001, pp. 162–163), and in MacFarlane (2003, p. 325).

  9. Belnap and Green (1994, p. 379). See also Perloff et al. (2001, pp. 162–163).

  10. The supervaluational TRL is presented in Malpass and Wawer (2012). Standard supervaluationism is outlined in Thomason (1970).

  11. See Malpass and Wawer (2012, pp. 131–133).

  12. Malpass and Wawer (2012, p. 129).

  13. Or at least, this is what Belnap and Green seem to grant in (1994) when they use examples such as (4).

  14. The distinction between primary and secondary sense of ‘actual’ is drawn in Lewis (1983, p. 19).

  15. The indexical account of actuality is the account suggested in Lewis (1973).

  16. García-Carpintero considers a definition along these lines in (2012, p. 11).

  17. Malpass and Wawer are well aware of this, see (2012, p. 128).

  18. Braüner, Hasle and Øhrstrøm propose a semantics of this kind in (1998) and in (2000). A different version, suggested by McKim and Davis (1976), is that in which the value of the function for \(m\) is a linearly ordered set of moments that starts with \(m\), rather than a whole history. Perloff et al. (2001) considers both options, pp. 165–168.

  19. This is essentially the problem raised in Malpass and Wawer (1994, p. 380), and in Perloff et al. (2001, pp. 166–167), with some differences of formulation due to Definitions 1 and 6. The assumption that an Ockhamist should preserve (P) depends on the understanding of Ockhamism adopted in this paper, so it does not rule out that a formal semantics inspired by the ideas of Ockham, such as that proposed by Braüner, Hasle and Øhrstrøm, can coherently reject (P).

  20. This proposal is defended in Øhrstrøm (2009, pp. 29–30), and is already present in Braüner et al. (2000, pp. 204–205).

  21. Independently of this issue, Øhrstrøm’s proposal has some unorthodox consequences, as explained in (2009, p. 30).

  22. Obviously, the semantics need not specify which world is the actual world insofar as the language does not contain an actuality operator such as \(@_1\), that is, an actuality operator whose definition involves reference to a distinguished world.

  23. Interestingly, the thought that Priorian semantics suits Ockhamism lies at the origin of Priorian semantics, as it is shown by the fact that Prior himself called ‘Ockhamist’ that semantics in Prior (1967, pp. 126–127).

  24. Thomason (1970, pp. 270–271). Thomason finds both interpretations objectionable, although he recognizes that his arguments do not provide a final refutation of Priorian semantics, see fn. 9.

  25. Perloff et al. (2001, p. 232).

  26. Malpass and Wawer (2012, p. 122).

  27. Similarly, the objection that Malpass and Wawer raise later in the same section against contextual pluralism, according to which future contingents do not express a complete content, does not essentially concern Priorian semantics.

  28. Lewis (1986) provides some considerations against branching, pp. 206–209. Iacona (2013) includes a discussion of the claim that indeterminism entails branching, pp. 41–44.

  29. Evans (1985) is a locus classicus of the early philosophical resistance to tense logic. King (2003) is a recent linguistically oriented defence of the representation in terms of quantification over times.

  30. Iacona (forthcoming) suggests one way to substantiate the rejection of A1 and A2, in that it outlines a formal apparatus for Ockhamism that is based on the simplest quantified modal logic.

  31. An earlier version of this paper was given as a talk at the University of Leeds in May 2012. I thank those who attended the talk for their insightful questions and comments, especially John Divers and Ross Cameron. I’m also grateful to Pablo Rychter and Jordi Valor for the discussions we had on a first draft of the paper, and to two anonymous referees for the helpful revisions they suggested.

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  1. University of Turin, Turin, Italy

    Andrea Iacona

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Iacona, A. Ockhamism without Thin Red Lines. Synthese 191, 2633–2652 (2014). https://doi.org/10.1007/s11229-014-0405-6

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