Supposition: A Problem for Bilateralism

Kürbis, Nils

Bulletin of the Section of Logic, Tome 52 (2023) no. 3, pp. 301-327.

Résumé

In bilateral logic formulas are signed by + and –, indicating the speech acts assertion and denial. I argue that making an assumption is also speech act. Speech acts cannot be embedded within other speech acts. Hence we cannot make sense of the notion of making an assumption in bilateral logic. Attempts to solve this problem are considered and rejected.

Détail

Keywords: assertion, denial, negation, supposition, assumptions, speech acts

Bibliographie

[1] E. Anscombe, P. T. Geach (eds.), Descartes. Philosophical Writings., Nelson and Sons, London (1954).

[2] M. Dummett, Frege. Philosophy of Language, 2nd ed., Duckworth, London (1981).

[3] M. Dummett, The Source of the Concept of Truth, [in:] The Seas of Language, Clarendon, Oxford (1993), pp. 188–201 | DOI

[4] N. Francez, Bilateralism in Proof-Theoretic Semantics, Journal of Philosophical Logic, vol. 43 (2014), pp. 239–259 | DOI

[5] G. Frege, Begriffsschrift. Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Louis Nebert, Halle (1879).

[6] G. Frege, Funktion und Begriff, Vortrag, gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medicin und Naturwissenschaften, Jena (1891).

[7] G. Frege, Über Sinn und Bedeutung, Zeitschrift für Philosophie und philosophische Kritik, vol. 100 (1892), pp. 26–50.

[8] G. Frege, Grundgesetze der Arithmetik. Begriffsschriftlich abgeleitet. II. Band., Hermann Pohle, Jena (1903).

[9] G. Frege, Über die Grundlagen der Geometrie. II, Jahresberichte der Deutschen Mathematiker-Vereinigung, vol. 15 (1906), pp. 377–403.

[10] G. Frege, Der Gedanke. Eine logische Untersuchung, Beiträge zur Philosophie des deutschen Idealismus, vol. 1 (1918), pp. 58–77.

[11] G. Frege, Die Verneinung. Eine logische Untersuchung, Beiträge zur Philosophie des deutschen Idealismus, vol. 1 (1918), pp. 143–157.

[12] G. Frege, Gedankengefüge. Eine logische Untersuchung, Beiträge zur Philosophie des deutschen Idealismus, vol. 3 (1918), pp. 36–51.

[13] P. Geach, Assertion, [in:] Logic Matters, Blackwell, Oxford (1972), pp. 254–269.

[14] P. Geach, M. Black (eds.), Translations from the Philosophical Writings of Gottlob Frege, Blackwell, Oxford (1952).

[15] G. Gentzen, Untersuchungen über das logische Schließen, Mathematische Zeitschrift, vol. 39 (1934), pp. 176–210, 405–431 | DOI

[16] G. Gentzen, The Collected Papers of Gerhard Gentzen, North Holland, Amsterdam (1969).

[17] M. Green, The Status of Supposition, Noûs, vol. 34(3) (2000), pp. 376–399 | DOI

[18] R. Hare, The Language of Morals, Clarendon, Oxford (1952) | DOI

[19] O. T. Hjortland, Speech acts, categoricity, and the meanings of logical connectives, Notre Dame Journal of Formal Logic, vol. 55(4) (2014), pp. 445–467 | DOI

[20] L. Humberstone, The Revival of Rejective Negation, Journal of Philosophical Logic, vol. 29 (2000), pp. 331–381 | DOI

[21] Ignatius of Loyola, Personal Writings, Penguin, London (2005).

[22] L. Incurvati, P. Smith, Is ‘no’ a force-indicator? Sometimes, possibly, Analysis, vol. 72(2) (2012), pp. 225–231 | DOI

[23] S. Jaśkowski, On the Rules of Suppositions in Formal Logic, Studia Logica, vol. 1 (1934), pp. 5–32.

[24] B. Jespersen, Two Tales of the Turnstile, Journal of Applied Logics, vol. 8(2) (2021), pp. 511–530.

[25] J. Kearns, Propositional Logic of Supposition and Assertion, Notre Dame Journal of Formal Logic, vol. 38(3) (1997), pp. 325–349 | DOI

[26] N. Kürbis, Intuitionist Bilateralism: Negations, Implications and some Observations and Problems about Hypotheses, [in:] J. Fichot, T. Piecha (eds.), Beyond Logic. Proceedings of the Conference held in Cerisy-la-Salle, 22–27 May 2017 (2017), pp. 429–438 | DOI

[27] N. Kürbis, Proof and Falsity. A Logical Investigation, Cambridge University Press (2019) | DOI

[28] N. Kürbis, Normalisation for Bilateral Classical Logic with some Philosophical Remarks, The Journal of Applied Logics, vol. 8(2) (2021), pp. 531–556.

[29] N. Kürbis, Note on ‘Normalisation for Bilateral Classical Logic with some Philosophical Remarks’, Journal of Applied Logics, vol. 8(7) (2021), pp. 2259–2261.

[30] H. Price, Sense, Assertion, Dummett and Denial, Mind, vol. 92 (1983), pp. 161–173 | DOI

[31] H. Reichenbach, Elements of Symbolic Logic, Macmillan, London (1966).

[32] G. Restall, Multiple Conclusions, [in:] P. Hájek, L. Valdés-Villanueva, D. Westerståhl (eds.), Logic, Methodology and Philosophy of Science: Proceedings of the Twelfth International Congress, King’s College Publications, London (2005), pp. 189–205.

[33] G. Restall, Speech acts & the quest for a natural account of classical proof (2021), URL: https://consequently.org/papers/speech-acts-for-classical-natural-deduction.pdf

[34] I. Rumfitt, “Yes” and “No”, Mind, vol. 109 (2000), pp. 781–823 | DOI

[35] I. Rumfitt, Unilateralism Disarmed: A Reply to Dummett and Gibbard, Mind, vol. 111 (2002), pp. 305–312 | DOI

[36] J. Searle, Speech Acts. An Essay in the Philosophy of Language, Cambridge University Press (1969) | DOI

[37] T. Smiley, Rejection, Analysis, vol. 56 (1996), pp. 1–9 | DOI

[38] E. Stenius, Mood and Language-Game, Synthese, vol. 17(3) (1967), pp. 254–274 | DOI

[39] Teresa of Avila, The Life of Saint Teresa of Avila by Herself, Penguin, London (1988).

[40] M. Textor, Frege on Judging as Acknowledging the Truth, Mind, vol. 119(475) (2010), pp. 615–655 | DOI

[41] M. Textor, Is ‘no’ a force indicator? No!, Analysis, vol. 71(3) (2011), pp. 448–456 | DOI

[42] M. van der Schaar, Frege on Judgement and the Judging Agent, Mind, vol. 127(505) (2018), pp. 225–250 | DOI

[43] B. Weiss, Let’s admit defeat! Assertion, Denial and Retraction, [in:] O. Beran, V. Kolman, L. Koreň (eds.), From Rules to Meanings: New Essays on Inferentialism, Routledge, London, New York (2018).