Physical obligation, Modus Tollendo Tollens, and the Stoic criterion
Abstract
The literature in the field of cognitive science reports that people only apply Modus Tollendo Tollens in some cases. A representative case in which individuals apply that logical schema is when the conditional premise consists of a physical obligation. In this paper, I try to show that a non-axiomatic logic can make inferences of Modus Tollendo Tollens just in the cases like that. The key is that the conditional is coherent with the Stoic criterion. That allows considering the negation of the consequent and the negation of the antecedent as clauses in a same implication statement with the highest frequency.References
Braine, M. D. S. & O’Brien, D. P. (1998). The Theory of Mental-Propositional Logic: Description and Illustration. M. D. S. Braine & D. P. O’Brien (eds.), Mental Logic. Lawrence Erlbaum Associates, Inc., Publishers: 79-89.
Byrne, R. M. J. (2005). The Rational Imagination: How People Create Alternatives to Reality. The Massachusetts Institute of Technology Press.
Byrne, R. M. J. & Johnson-Laird, P. N. (2009). ‘If’ and the Problems of Conditional Reasoning. Trends in Cognitive Science, 13(7): 282-287. https://doi.org/10.1016/j.tics.2009.04.003.
Cicero (1991). De Fato (On Fate). Ed. & trans. R. W. Sharples. Liverpool University Press.
Cramer, M., Hölldobler, S., & Ragni, M. (2021). When are Humans Reasoning with Modus Tollens? Proceedings of the Annual Meeting of the Cognitive Science Society, 43(43): 2337-2343. https://escholarship.org/uc/item/9x33q50g
Diogenes Laertius (1964). Vitae Philosophorum. Ed. H. S. Long. The Clarendon Press.
Gould, J. B. (1970). The Philosophy of Chrysippus. State University of New York Press.
Johnson-Laird, P. N. & Byrne, R. M. J. (2002). Conditionals: A Theory of Meaning, Pragmatics, and Inference. Psychological Review, 109(4): 646-678. https://doi.org/10.1037//0033-295X.109.4.646.
Lenzen, W. (2019). Leibniz’s Laws of Consistency and the Philosophical Foundations of Connexive Logic. Logic and Logical Philosophy, 28(3) 537-551. http://dx.doi.org/10.12775/LLP.2019.004.
López-Astorga, M. (2015). Chrysippus’ Indemonstrables and Mental Logic. Croatian Journal of Philosophy, 15(43): 1-15. https://doi.org/10.5840/croatjphil20151511.
(2025). Modus Tollendo Tollens with Obligation Conditionals: Towards a Deontic Inheritance Logic Respecting the Stoic Criterion. Schole, 19(1): 77-94. https://hrcak.srce.hr/file/246470.
Sedley, D. (1984). The Negated Conjunction in Stoicism. Elenchos, 5: 311-316.
Sextus Empiricus (1933). Pyrrhoniae Hypotyposes (Outlines of Pyrrhonism). Trans. R. G. Bury. Harvard University Press (Loeb Classical Library).
Wang, P. (2006). Rigid Flexibility: The Logic of Intelligence. Springer. https://doi.org/10.1007/1-4020-5045-3.
(2011). The Assumptions on Knowledge and Resources in Models of Rationality. International Journal of Machine Consciousness, 3(1): 193-218. https://doi.org/10.1142/S1793843011000686.
(2013). Non-Axiomatic Logic: A Model of Intelligent Reasoning. World Scientific. https://doi.org/10.1142/8665.
(2023). The Role of Copulas in Reasoning. Temple AGI Team. Temple University: 1-12. https://cis.temple.edu/tagit/publications/TAGIT-TR-17.pdf.
