Logic and Logical Philosophy
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Humble Connexivity
DOI: http://dx.doi.org/10.12775/LLP.2019.001
Abstract
In this paper, I review the motivation of connexive and strongly connexive logics, and I investigate the question why it is so hard to achieve those properties in a logic with a well motivated semantic theory. My answer is that strong connexivity, and even just weak connexivity, is too stringent a requirement. I introduce the notion of humble connexivity, which in essence is the idea to restrict the connexive requirements to possible antecedents. I show that this restriction can be well motivated, while it still leaves us with a set of requirements that are far from trivial. In fact, formalizing the idea of humble connexivity is not as straightforward as one might expect, and I offer three different proposals. I examine some well known logics to determine whether they are humbly connexive or not, and I end with a more wide-focused view on the logical landscape seen through the lens of humble connexivity.
formalizing the idea of humble connexivity is not as straightforward as one might expect, and
I offer three different proposals. I examine some well known logics to determine whether they
are humbly connexive or not, and I end with a more wide-focused view on the logical landscape
seen through the lens of humble connexivity.
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Carnap, R., Meaning and Necessity, Chicago University Press, 1947.
Estrada-González, L. and E. Ramírez-Cámara. “A comparison of connexive logics”, IfCoLog Journal of Logics and their Applications 3, 3 (2016): 341–355.
Kapsner, A., “Strong connexivity”, Thought: A Journal of Philosophy 1, 2 (2012): 141–145. DOI: http://dx.doi.org/10.1002/tht3.19
Kapsner, A., Logics and Falsifications, vol. 40 of Trends in Logic, Springer, 2014. DOI: http://dx.doi.org/10.1007/978-3-319-05206-9
Kapsner, A., and H. Omori, “Counterfactuals in Nelson logic”, chapter 34 in International Workshop on Logic, Rationality, and Interaction, Springer, 2017. DOI: http://dx.doi.org/10.1007/978-3-662-55665-8_34
Leahy, B., “Presuppositions and antipresuppositions in conditionals”, pages 257–274 in Proceedings of SALT 21, Springer, 2011. DOI: http://dx.doi.org/10.3765/salt.v21i0.2613
Lewis, D.K., Counterfactuals, Blackwell, 1973.
Makinson, D., “How meaningful are modal operators?”, Australasian Journal of Philosophy 44, 3 (1966): 331–337.
McCall, S., “Connexive implication”, in A.R. Anderson and N.D. Belnap (eds.), Entailment. The Logic of Relevance and Necessity. Volume 1, Princeton University Press, 1975.
Omori, H., and K. Sano, “Generalizing functional completeness in Belnap-Dunn Logic”, Studia Logica 103, 5 (2015). DOI: http://dx.doi.org/10.1007/s11225-014-9597-5
Priest. G., “Negation as cancellation and connexive logic”, Topoi, 18, 2 (1999): 141–148. DOI: http://dx.doi.org/10.1023/A:1006294205280
Routley, R., “Semantics for connexive logics. I”, Studia Logica 37, 4 (1978): 393–412. DOI: http://dx.doi.org/10.1007/BF02176171
Routley, R., R.K. Meyer, V. Plumwood, and R.T. Brady, Relevant Logics and Their Rivals: Part 1. The Basic Philosophical and Semantical Theory, 1982.
Stalnaker, R.C., “A theory of conditionals”, pages 41–55 in Ifs, Springer, 1968.
Vidal, M., “When conditional logic met connexive logic”, in C. Gardent and C. Retoré (eds.), IWCS 2017 – 12th International Conference on Computational Semantics.
Wansing, H., “Connexive modal logic”, pages 367–383 in R. Schmidt, I. Pratt-Hartmann, M. Reynolds, and H. Wansing (eds.), Advances in Modal Logic. Volume 5, King’s College Publications, 2005.
Wansing, H., “Connexive logic”, in E.N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Fall 2014 edition, 2014. Available at http://plato.stanford.edu/archives/fall2014/entries/logic-connexive/.
Wansing, H., H. Omori, and T.M. Ferguson, “The tenacity of connexive logic: Preface to the special issue”, IfCoLog Journal of Logics and their Applications (2016): 279.
Wansing, H., and D. Skurt, “Negation as cancellation, connexive logic, and qLPm”, Australasian Journal of Logic 15, 2 (2018): 476–488. DOI: http://dx.doi.org/10.26686/ajl.v15i2.4869
Williamson, T., Modal Logic as Metaphysics, Oxford University Press, 2013. DOI: http://dx.doi.org/10.1093/acprof:oso/9780199552078.001.0001
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