Immune Logics ain't that Immune

Jeremiah Joven Joaquin

doi:10.12775/LLP.2022.029

Autor

Jeremiah Joven Joaquin Department of Philosophy, De La Salle University, Manila https://orcid.org/0000-0002-8621-6413

DOI:

https://doi.org/10.12775/LLP.2022.029

Słowa kluczowe

defining logical operations, immune logics, infectious logics, material conditionals

Abstrakt

Da Ré and Szmuc argue that while there is a symmetry between ‘infectious’ and ‘immune’ logics, this symmetry fails w.r.t. extending an algebra with an immune or an infectious element. In this paper, I show that the symmetry also fails w.r.t. defining a new logical operation from a given set of primitive (Boolean) operations. I use the case of the material conditional to illustrate this point.

Bibliografia

Belikov, A., 2021, “Peirce’s triadic logic and its (overlooked) connexive expansion”, Logic and Logical Philosophy, 30 (3): 535–559. DOI: http://dx.doi.org/10.12775/LLP.2021.007

Bochvar, M., and D. A. Bergmann, 1981, “On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus”, History and Philosophy of Logic, 2 (1–2): 87–112.

Cooper, W. S., 1968, “The propositional logic of ordinary discourse”, Inquiry, 11 (1–4): 295–320.

Da Ré, B., and D. Szmuc, 2021, “Immune logics”, The Australasian Journal of Logic, 18 (1): 29–52. DOI: http://dx.doi.org/10.26686/ajl.v18i1.6582

Fisch, M., and A. Turquette, 1966, “Peirce’s triadic logic”, Transactions of the Charles S. Peirce Society, 2 (2): 71–85.

Humberstone, L., 2011, The Connectives, MIT Press, Boston, Mass. DOI: http://dx.doi.org/10.7551/mitpress/9055.001.0001

Joaquin, J. J., 2022, “Infectious and transparent emotivism”, Journal of Applied Non-Classical Logics, 32 (1): 1–10. DOI: http://dx.doi.org/10.1080/11663081.2021.2016242