Tableaux for an alethic-epistemic logic and its conditional versions
Abstract
Although modal logic has significantly developed since the possible worlds semantics invention, today, it is recognized that a modal logic that uses only one type of modality is very restricted. In this article, I aim to provide the semantics and tableaux systems for some alethic-epistemic-doxastic logics. The basic system (T/T/KD*) is used to discuss the validity of some principles and some of Spinoza’s ideas on modal thinking, for he believed that the possibility and contingency ideas are defects of our cognition. Next, the system’s extensions based on are used to discuss the validity of the doxastic, epistemic, and alethic closure principles by means of the distinction between absolute and relative knowledge. Finally, the system is extended to develop a pair of conditional epistemic-doxastic logics to evaluate some skeptical statements.Downloads
References
Beziau, Jean-Yves (2017) "Possibility, Contingency and the Hexagon of Modalities." South American Journal of Logic, vol. 3, núm. 2, pp. 273-290.
Benedetti, Mario. (1969) Gracias por el fuego. México, Punto de lectura.
Blanché, Robert. (1953) "Sur l'opposition des concepts." Theoria, vol. 19, núm. 3, pp. 89-130.
Carnap, Rudolph. (1956) Meaning and necessity: a study in semantics and modal logic. Estados Unidos, University of Chicago Press.
Chellas, Brian F. (1975) "Basic conditional logic." Journal of philosophical logic, vol. 4, núm. 2, pp. 133-153.
Costa-Leite, Alexandre (2016) “Interplays of knowledge and non-contingency”. Logic and Logical Philosophy vol. 25, núm. 4, pp. 521-534.
Dretske, Fred (1970) “Epistemic operators”. Journal of Philosophy, vol. 67, núm. 24, pp. 1007-1023.
Egan, Andy y Weatherson, Brian (2011) Epistemic modality. Estados Unidos, Oxford University Press.
Feldman, Richard (2003) Epistemology. Estados Unidos, Pearson Education.
Gómez Caminero Parejo, Emilio Francisco (2011) Tablas semánticas para lógica epistémi-ca, tesis doctoral, Departamento de Filosofía y Lógica y Filosofía de la ciencia, Universidad de Sevilla.
Herrera González, José Rafael (2005) “Conocimiento e incertidumbre. Una aproximación desde la lógica de las modalidades epistémicas”, Contextos, vol. 23, núm. 45, pp.227-257.
Hughes, George Edward y Cresswell, Max J. (1973) Introducción a la lógica modal. Espa-ña, Tecnos.
Ichikawa, Jonathan Jenkins y Steup, Matthias. (2018) “The Analysis of Knowledge” en Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy [https://plato.stanford.edu/entries/knowledge-analysis/], consultado: 2 de junio de 2021.
Jarrett, Charles. (1978) “The Logical Structure of Spinoza’s “Ethics”, Part I”. Synthese, pp. 15-65.
Lewis, Clarence Irving (1918) A survey of symbolic logic. Estados Unidos, University of California Press.
Lewis, David (1973) Counterfactuals. Estados Unidos, Basil Blackwell.
Menzel, Christopher (2017) “Possible Worlds”, en Edward N. Zalta (ed.), The Stanford En-cyclopedia of Philosophy [https://plato.stanford.edu/entries/possible-worlds/], consultado: 2 de junio de 2021.
Meyer, John Jules Charles (2003) “Modal epistemic and doxastic logic”, en D. M. Gabay y F. Guenther (eds.), Handbook of philosophical logic, Alemania, Springer, pp. 1-38.
Miller, Jon. A (2001) “Spinoza’s Possibilities”, The Review of Metaphysics, vol. 54, pp. 779-814.
Montgomery, Hugh y Routley, Richard. (1966) “Contingency and non-contingency bases for normal modal logics”. Logique et analyse, vol. 9, núm. 36, pp. 318-328.
Newlands, Samuel (2018) “Spinoza's Modal Metaphysics”, en Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy [https://plato.stanford.edu/entries/spinoza-modal/], consultado: 2 de junio de 2021.
Pacuit, Eric (2017) Neighborhood semantics for modal logic. Estados Unidos, Springer.
Papineau, David (2020) “Naturalism”, en Edward N. Zalta (ed.), The Stanford Encyclope-dia of Philosophy [https://plato.stanford.edu/entries/naturalism/], consultado: 2 de junio de 2021.
Priest, Graham (2008) An introduction to non-classical logic: From if to is. Reino Unido, Cambridge University Press.
Read, Stephen (1994) Thinking about logic: An introduction to the
philosophy of logic. Reino Unido, Oxford University Press.
Schmidt, Andreas (2009) “Substance Monism and Identity Theory in Spinoza”, en Don Garret (ed.), The Cambridge Campanian to Spinoza’s Ethics, Reino Unido, Cambridge University Press, pp. 79-98.
Scott, Dana (1970) “Advice on modal logic”, en Karel Lambert (ed.), Philosophical Prob-lems in Logic. Some recent developments, Holanda, D. Reidel Publiching Company, pp. 143-173.
Sharples, Robert W. (2009) Estoicos, epicúreos y escépticos. Introducción a la filosofía helenística. México, Universidad Nacional Autónoma de México, Instituto de Investigaciones Filosóficas.
Smets, Sonja y Velázquez Quesada, Fernando (2019) “Philosophical Aspects of Multi-Modal Logic”, en Edawrd N. Zalta, The Stanford Encyclopedia of Philosophy [https://plato.stanford.edu/entries/phil-multimodallogic/], consultado 2 de junio de 2021.
Spinoza, Baruch (1988) Correspondencia. España, Alianza, 1988.
Spinoza, Baruch(2000) Ética demostrada según el orden geométrico. España, Trotta, 2000.
Spinoza, Baruch (2014) Tratado de la reforma del entendimiento. Principios de la filosofía de René Descartes. Pensamientos metafísicos. España, Alianza.
Thomason, Richmond H. (2002) “Combinations of tense and modality”, en D. M. Gabay y F. Guenther (eds.), Handbook of philosophical logic, vol. 7, Alemania, Springer, pp. 205-234.
Von Wright, George H. (1983) Philosophical Papers of Georg Henrik Von Wright, vol 3, Estados Unidos, Basil Blackwell.
