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Existence as a Property of Individuals

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Abstract

In this paper I aim to defend a version of the view that ‘exist’ expresses primarily a property of individual objects, a property that each of them has. In the first section, I will distinguish the three main types of rival conceptions concerning the semantic status of ‘exist’ that will define the subsequent discussion. In the second section it will be shown that the best explanation of our overall use of ‘exist’ in natural language requires the treatment of ‘exist’ as a predicate that can be applied to individual objects. The third section will be concerned with the problem of the semantic analysis of negative singular existential sentences that contain proper names. I will briefly defend a specific solution to this problem that makes use of a single-domain free logic. In the following sections, I will try to defend this view of existence in more detail. That is, I will deal with three different specific challenges that prima facie seem to speak against the proposed view and for some rival alternatives; and I will show how these challenges can be met.

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Notes

  1. In classical predicate logic, we can directly derive instances from universal generalizations. So for example ‘∀xFx’ implies ‘Fa’. This rule of universal instantiation is not valid in single-domain free logic. It requires the additional existential assumption ‘E!a’ to derive ‘Fa’ from ‘∀xFx’. In classical predicate logic, we can also derive existential generalizations from atomic sentences—for example ‘Fa’ implies ‘∃xFx’. This rule of existential generalisation is not valid in single-domain free logic. It requires the additional existential assumption ‘E!a’ to derive ‘∃xFx’ from ‘Fa’. These examples show why the existence predicate ‘E!’ is required for logical reasons and therefore has to be conceived as a logical predicate in single-domain free logic.

  2. C.f.: Burge (1974, 311–317); Sainsbury (2005, 64–75); Nolt (2010, §3.1).

  3. A non-logical atomic sentence is an atomic sentence that contains a non-logical predicate.

  4. C.f.: Nolt (2010, §3.1).

  5. C.f.: Malinowksi (1993, 80).

  6. C.f.: Malinowksi (1993, 55).

  7. The main differences between our two distinguished versions of single-domain free logic concern the truth-values of non-logical atomic sentences that contain constants without denotations like ‘Vulcan is a planet’ and specific quantifications that also contain constants without denotations like ‘No planet is larger than Vulcan’. In any other case, they provide equivalent truth- and falsity-conditions.

  8. Cf.: Priest (2008, 190–191); Nolt (2010, §3.2).

  9. C.f.: Priest (2008, 295–297).

  10. C.f.: Williamson (2002, 244–245).

  11. C.f.: Evans (1984, 345).

  12. We have to alter the truth-conditions for universal generalisations as follows: VI(∀xA) = T iff (D/DI=Ø and for every interpretation I* differing from I at most in what it assigns to t, VI*(A[t/x]) = T) or (D/DI≠ Ø and for every defined interpretation I* differing from I at most in what it assigns to t, VI*(A[t/x]) = T); otherwise VI(∀xA) = F.

  13. Thanks to an anonymous referee for pointing this out.

  14. A descriptive act of naming is an act of naming where an attributively used definite description is used to pick out the intended bearer of a name. Such an act is unsuccessful if there is no object that satisfies this description.

  15. Or: alternatively the logical form ‘E!!(H)’.

  16. C.f.: Priest (2009, 238).

  17. C.f.: Leslie (2012, 355–357).

  18. C.f.: Leslie (2012, 356).

  19. C.f.: Parsons (1982, 365–366).

  20. C.f.: Priest (2005, 13–14), (2008, 295–296).

  21. Quine is a famous proponent of this view; c.f.: Quine (1990, 26–28).

  22. C.f.: Moro (2006, 212; 216–222).

  23. C.f.: Sainsbury (2010, 50, 117, 118).

  24. Grice’s maxim of quality says: Try to make your contribution one that is true; so do not convey what you believe false or unjustified. C.f.: Grice (1989[1975], 27).

  25. C.f.: Stanley and Gendler Szabó (2000, 241–242).

  26. It has to be noticed that even for a defender of the classical version of the first-order discriminating property view of existence there is no straight-forward semantic way to account for the two different intuitive readings of (23) and (24), although (23) and (24) are not logical truths according to this view. Therefore, our third challenge is a problem that concerns any of our distinguished views on existence.

  27. C.f.: Heim und Kratzer (1998, 159–162).

  28. At first sight this Aristotelian framework might seem attractive for a defender of the second discussed variant of the classical version of a first-order discriminating property view of existence. Against this background ‘No unicorn exists’ is not only semantically equivalent with ‘Unicorns do not exist’, but this claim also logically entails ‘Some unicorns do not exist’. C.f.: Heim and Kratzer (1998, 160). So there is at least one alternative logical interpretation of the first mentioned argument in Sect. 5 to justify the truth of (14). However, the main obstacle of this framework is that it does not provide a plausible account of our overall use of quantifier expressions in natural language.

  29. In Horn (1997, 166–167) it is, for example, suggested that the distinction between universal generalisations with and those without existential import corresponds with a distinction between contingent and law-like generalisations.

  30. Grice’s maxim of quantity essentially says: Be as informative as required. C.f.: Grice (1989[1975], 26).

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Acknowledgments

I would like to thank Gail Leckie, Wilfried Keller, Peter Ridley, Mark Sainsbury, Peter Sutton, Thomas Spitzley and Timothy Williamson for interesting and helpful discussions. Specials thanks go to two anonymous referees of this journal for their detailed and very helpful comments. My research work on this paper was founded by the Alexander-von-Humboldt-Foundation.

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  1. Department of Philosophy, King’s College London, Strand, London, WC2R 2LS, UK

    Dolf Rami

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Rami, D. Existence as a Property of Individuals. Erkenn 79 (Suppl 3), 503–523 (2014). https://doi.org/10.1007/s10670-013-9505-9

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