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Formal Methods and the History of Philosophy

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Introduction to Formal Philosophy

Part of the book series: Springer Undergraduate Texts in Philosophy ((SUTP))

Abstract

Although not (yet) entirely mainstream, uses of formal methods for the study of the history of philosophy, the history of logic in particular, represent an important trend in recent philosophical historiography. In this chapter, I discuss what can (and cannot) be achieved by the application of formal methods to the history of philosophy, addressing both motivations and potential pitfalls. The first section focuses on methodological aspects, and the second section presents three case studies of historical theories which have been investigated with formal tools: Aristotle’s syllogistic, Anselm’s ontological argument, and medieval theories of supposition.

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Notes

  1. 1.

    More recently, computational methods have been gaining quite a lot of traction for research in history of philosophy, under the umbrella of ‘digital humanities’. These are exciting developments that may well change substantially how historians of philosophy approach their topics, but for now they are still at early stages. While these can be broadly understood as formal methods, in this piece I do not discuss them any further for reasons of space.

  2. 2.

    In fact, I have argued elsewhere ([11], chap. 3) that it is a mistake to think about formalizations in general merely as taking portions of ‘natural language’ as their starting point and translating them into a formal language.

  3. 3.

    Shapiro [30].

  4. 4.

    See [13].

  5. 5.

    For an example of formal analysis actually revealing something new about a historical theory, see [8] on Bradwardine’s solution to the Liar paradox.

  6. 6.

    See ([29], 37–39).

  7. 7.

    Polish notation is based on prefixing operators. ‘C’ stands for implication and ‘K’ for conjunction, so this expression roughly means ‘Abc & Aab ➔ Aac’.

  8. 8.

    See for example [1] for some interesting meta-theoretical results, and [18] for a formal analysis of Buridan’s modal syllogism.

  9. 9.

    See [34] for a concise presentation of the argument.

  10. 10.

    ([24], 509)

  11. 11.

    See also [22], and [4] for an overview focusing specifically on the scholarship on Ockham.

  12. 12.

    See [26] for an overview from a contemporary perspective.

  13. 13.

    See (Ockham [36], chap. 70) and ([17], chaps. 4.3.5 and 4.3.6) for some of the original formulations of these definitions.

  14. 14.

    [27] is a particularly ambitious and impressive recent example of applications of modern formal tools borrowed from logic and linguistic to medieval logical theories.

  15. 15.

    There is not much literature specifically on the application of formal methods for the study of the history of philosophy, but the interested reader can consult in particular [12, 15, 33].

References

There is not much literature specifically on the application of formal methods for the study of the history of philosophy, but the interested reader can consult in particular [12, 15, 33].

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  1. Department of Philosophy, Vrije Universiteit, Amsterdam, The Netherlands

    Catarina Dutilh Novaes

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Correspondence to Catarina Dutilh Novaes .

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  1. Division of Philosophy, Royal Institute of Technology (KTH), Stockholm, Sweden

    Sven Ove Hansson

  2. Center for Information and Bubble Studies, University of Copenhagen, Copenhagen, Denmark

    Vincent F. Hendricks

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Dutilh Novaes, C. (2018). Formal Methods and the History of Philosophy. In: Hansson, S., Hendricks, V. (eds) Introduction to Formal Philosophy. Springer Undergraduate Texts in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-77434-3_3

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