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Applications of Formal Philosophy pp 221–241Cite as

Counterpossibles, Impossible Worlds, and the Notion of Similarity

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Part of the book series: Logic, Argumentation & Reasoning ((LARI,volume 14))

Abstract

The subject of this paper is a world-semantic analysis of counterpossibles, i.e., counterfactuals with impossible antecedents. We focus on the notion of similarity between worlds, which determines truth-value of counterfactuals. There are two commonly accepted assumptions about this notion. According to the first one, every possible world is more similar to the actual world than any impossible world. According to the second one, the trivial world (world where everything is true) is the most dissimilar to the actual world. Considering the notion of similarity we argue for a negative thesis and a positive thesis. The negative thesis is that both of these assumptions are false, and as such should not be taken as a “guide” to our understanding of similarity. The positive thesis is an alternative interpretation of the notion of similarity. The interpretation is based on an analogy of the inference to the best explanation and on the assumption that similarity is a ternary relation satisfied by the actual world, a non-actual world and a given factor of similarity. Similarity understood in this manner is a notion which requires an indication of a rule which supports the truth of the antecedent and explains its connection with the consequent.

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Notes

  1. 1.

    By standard analysis we mean theories delivered by Robert Stalnaker [24] and David Lewis [11].

  2. 2.

    [3, 4, 8, 14, 15, 22, 25,26,27].

  3. 3.

    For a comprehensive analysis of ontological status of impossible worlds see [2, 16].

  4. 4.

    Earlier versions of this material were presented in Bratislava (Slovak Academy of Science) at “Issues on the Impossible Worlds” in May 2014, in Warsaw (University of Warsaw) at “Philosopher’s Rally” in July 2014, in Ghent (Centre of Logic and Philosophy of Science) at “Entia et Nomina” in July 2014, and in New York at Graham Priest’s graduate student seminar in November 2014 (CUNY Graduate Center). I am grateful to the participants of these meetings for their helpful comments and discussions. I would like to thank to the anonymous reviewers for this volume for their comments concerning the earlier versions of the paper.

    This material is based on work supported by the Polish National Center of Science under Grant No. 2012/05/N/HS1/02794. Thanks to the Polish-U.S. Fulbright Commission I had the opportunity to develop the ideas presented here during my stay at CUNY Graduate Center.

  5. 5.

    Although the above example assumes that the metaphysics of Monadology and intuitionistic logic are incorrect, one can easily change examples.

  6. 6.

    It is worth to notice that indexical use of “possible” and ‘impossible” allows to avoid the risk of believing that the actual world is one of impossible worlds. After all, only a possible world could be actual.

  7. 7.

    See also [15].

  8. 8.

    See also [6, 10]: 87–9. It should be stressed that it does not mean that any true conditional results in a true implication.

  9. 9.

    This result is consistent with those theories of impossible worlds, which are based on paraconsistent logic ([14, 18, 22]). Nevertheless, one can modify the example in such a way that the acceptence of DTW will imply the claim that ECQ is false in the actual world according to classical logic. Regardless to what we believe to be the true logic of the actual world, one should not believe that according to classical logic ECQ is false.

  10. 10.

    See also [9].

  11. 11.

    See [12, 13, 17].

  12. 12.

    See, among others, [5, 13, 23].

  13. 13.

    By “consistent” we do not mean that there are no contradictions in them, but rather that they act according to certain regularities that in these worlds are supposed to be true. In this sense even a paraconsistent world might be taken to be consistent if it acts accordingly with the laws of paraconsistent logic.

  14. 14.

    Similarities between S-B and our account allow to ask whether we can avoid this problem. We will go back to this in the next section.

  15. 15.

    Being an “interesting” notion of logical consequence is an important condition, since it allows counting the trivial world as impossible as well. Even though it is closed under logical consequence, it is surely not a possible world.

  16. 16.

    “Absurd world” is a different name for what we called “trivial world”.

  17. 17.

    For an argument against the analysis of counterpossibles with logically impossible antecedents in terms of the American-style impossible worlds see [3].

  18. 18.

    Of course we do not want to claim that Russells arguments ended the discussion about the na’ive set theory or Theory of Objects.

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Authors and Affiliations

  1. Institute of Philosophy, University of Warsaw, Warsaw, Poland

    Maciej Sendłak

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  1. Maciej Sendłak
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Correspondence to Maciej Sendłak .

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  1. Institute of Philosophy, Sociology and Journalism, University of Gdansk, Poland and , Centre for Logic and Philosophy of Science, Ghent University,, Ghent, Belgium

    Rafał Urbaniak

  2. Dalhousie University , Halifax, Nova Scotia, Canada

    Gillman Payette

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Sendłak, M. (2017). Counterpossibles, Impossible Worlds, and the Notion of Similarity. In: Urbaniak, R., Payette, G. (eds) Applications of Formal Philosophy. Logic, Argumentation & Reasoning, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-58507-9_11

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