Supposition: A Problem for Bilateralism
DOI:
https://doi.org/10.18778/0138-0680.2023.07Keywords:
assertion, denial, negation, supposition, assumptions, speech actsAbstract
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.
References
E. Anscombe, P. T. Geach (eds.), Descartes. Philosophical Writings., Nelson and Sons, London (1954).
M. Dummett, Frege. Philosophy of Language, 2nd ed., Duckworth, London (1981).
M. Dummett, The Source of the Concept of Truth, [in:] The Seas of Language, Clarendon, Oxford (1993), pp. 188–201, DOI: https://doi.org/10.1093/0198236212.003.0008 DOI: https://doi.org/10.1093/0198236212.003.0008
N. Francez, Bilateralism in Proof-Theoretic Semantics, Journal of Philosophical Logic, vol. 43 (2014), pp. 239–259, DOI: https://doi.org/10.1007/s10992-012-9261-3 DOI: https://doi.org/10.1007/s10992-012-9261-3
G. Frege, Begriffsschrift. Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Louis Nebert, Halle (1879).
G. Frege, Funktion und Begriff, Vortrag, gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medicin und Naturwissenschaften, Jena (1891). DOI: https://doi.org/10.1111/j.1438-8677.1891.tb05760.x
G. Frege, Über Sinn und Bedeutung, Zeitschrift für Philosophie und philosophische Kritik, vol. 100 (1892), pp. 26–50.
G. Frege, Grundgesetze der Arithmetik. Begriffsschriftlich abgeleitet. II. Band., Hermann Pohle, Jena (1903).
G. Frege, Über die Grundlagen der Geometrie. II, Jahresberichte der Deutschen Mathematiker-Vereinigung, vol. 15 (1906), pp. 377–403.
G. Frege, Der Gedanke. Eine logische Untersuchung, Beiträge zur Philosophie des deutschen Idealismus, vol. 1 (1918), pp. 58–77. DOI: https://doi.org/10.1515/bgsl.1918.1918.43.219
G. Frege, Die Verneinung. Eine logische Untersuchung, Beiträge zur Philosophie des deutschen Idealismus, vol. 1 (1918), pp. 143–157.
G. Frege, Gedankengefüge. Eine logische Untersuchung, Beiträge zur Philosophie des deutschen Idealismus, vol. 3 (1918), pp. 36–51.
P. Geach, Assertion, [in:] Logic Matters, Blackwell, Oxford (1972), pp. 254–269.
P. Geach, M. Black (eds.), Translations from the Philosophical Writings of Gottlob Frege, Blackwell, Oxford (1952).
G. Gentzen, Untersuchungen über das logische Schließen, Mathematische Zeitschrift, vol. 39 (1934), pp. 176–210, 405–431, DOI: https://doi.org/10.1007/BF01201353,10.1007/BF01201363 DOI: https://doi.org/10.1007/BF01201363
G. Gentzen, The Collected Papers of Gerhard Gentzen, North Holland, Amsterdam (1969).
M. Green, The Status of Supposition, Noûs, vol. 34(3) (2000), pp. 376–399, DOI: https://doi.org/10.1111/0029-4624.00216 DOI: https://doi.org/10.1111/0029-4624.00216
R. Hare, The Language of Morals, Clarendon, Oxford (1952), DOI: https://doi.org/10.1093/0198810776.001.0001 DOI: https://doi.org/10.1093/0198810776.001.0001
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: https://doi.org/10.1215/00294527-2798700 DOI: https://doi.org/10.1215/00294527-2798700
L. Humberstone, The Revival of Rejective Negation, Journal of Philosophical Logic, vol. 29 (2000), pp. 331–381, DOI: https://doi.org/10.1023/A:1004747920321 DOI: https://doi.org/10.1023/A:1004747920321
Ignatius of Loyola, Personal Writings, Penguin, London (2005).
L. Incurvati, P. Smith, Is ‘no’ a force-indicator? Sometimes, possibly, Analysis, vol. 72(2) (2012), pp. 225–231, DOI: https://doi.org/10.1093/analys/ans048 DOI: https://doi.org/10.1093/analys/ans048
S. Jaśkowski, On the Rules of Suppositions in Formal Logic, Studia Logica, vol. 1 (1934), pp. 5–32.
B. Jespersen, Two Tales of the Turnstile, Journal of Applied Logics, vol. 8(2) (2021), pp. 511–530.
J. Kearns, Propositional Logic of Supposition and Assertion, Notre Dame Journal of Formal Logic, vol. 38(3) (1997), pp. 325–349, DOI: https://doi.org/10.1305/ndjfl/1039700742 DOI: https://doi.org/10.1305/ndjfl/1039700742
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: https://doi.org/10.15496/publikation-18676
N. Kürbis, Proof and Falsity. A Logical Investigation, Cambridge University Press (2019), DOI: https://doi.org/10.1017/9781108686792 DOI: https://doi.org/10.1017/9781108686792
N. Kürbis, Normalisation for Bilateral Classical Logic with some Philosophical Remarks, The Journal of Applied Logics, vol. 8(2) (2021), pp. 531–556.
N. Kürbis, Note on ‘Normalisation for Bilateral Classical Logic with some Philosophical Remarks’, Journal of Applied Logics, vol. 8(7) (2021), pp. 2259–2261.
H. Price, Sense, Assertion, Dummett and Denial, Mind, vol. 92 (1983), pp. 161–173, DOI: https://doi.org/10.1093/mind/XCII.366.161 DOI: https://doi.org/10.1093/mind/XCII.366.161
H. Reichenbach, Elements of Symbolic Logic, Macmillan, London (1966).
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.
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
I. Rumfitt, “Yes” and “No”, Mind, vol. 109 (2000), pp. 781–823, DOI: https://doi.org/10.1093/mind/109.436.781 DOI: https://doi.org/10.1093/mind/109.436.781
I. Rumfitt, Unilateralism Disarmed: A Reply to Dummett and Gibbard, Mind, vol. 111 (2002), pp. 305–312, DOI: https://doi.org/10.1093/mind/111.442.305 DOI: https://doi.org/10.1093/mind/111.442.305
J. Searle, Speech Acts. An Essay in the Philosophy of Language, Cambridge University Press (1969), DOI: https://doi.org/10.1017/CBO9781139173438 DOI: https://doi.org/10.1017/CBO9781139173438
T. Smiley, Rejection, Analysis, vol. 56 (1996), pp. 1–9, DOI: https://doi.org/10.1093/analys/56.1.1 DOI: https://doi.org/10.1093/analys/56.1.1
E. Stenius, Mood and Language-Game, Synthese, vol. 17(3) (1967), pp. 254–274, DOI: https://doi.org/10.1007/bf00485030 DOI: https://doi.org/10.1007/BF00485030
Teresa of Avila, The Life of Saint Teresa of Avila by Herself, Penguin, London (1988).
M. Textor, Frege on Judging as Acknowledging the Truth, Mind, vol. 119(475) (2010), pp. 615–655, DOI: https://doi.org/10.1093/mind/fzq041 DOI: https://doi.org/10.1093/mind/fzq041
M. Textor, Is ‘no’ a force indicator? No!, Analysis, vol. 71(3) (2011), pp. 448–456, DOI: https://doi.org/10.1093/analys/anr050 DOI: https://doi.org/10.1093/analys/anr050
M. van der Schaar, Frege on Judgement and the Judging Agent, Mind, vol. 127(505) (2018), pp. 225–250, DOI: https://doi.org/10.1093/mind/fzw059 DOI: https://doi.org/10.1093/mind/fzw059
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). DOI: https://doi.org/10.4324/9781315103587-5
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