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The paper is dvoted to interdisciplinary research at the intersection of symbolic logic, mathematical ethics, and philosophical theology. By comparing definitions of relevant functions, a surprising analogy is discovered between the well-known Philo’s precise definition of implication in logic (classical one) and Augustine’s precise definition of God’s morally good reaction to human actions. The moral-value-table-representation of Augustinian doctrine is compared with moral-value-table-representations of Pelagius’ and Leo Tolstoy’s views of adequate moral-response-actions.
Aquinas, T. (1975). Summa contra Gentiles. Notre Dame: University of Notre Dame Press.
Aquinas, T. (1994a). The Summa Theologica. V. I. In Adler Mortimer (Ed.), Great Books of the Western World. V. 17. Aquinas: I. Chicago, Auckland, London, Madrid: Encyclopedia Britannica, Inc.
Aquinas, T. (1994b). The Summa Theologica. V. II. In Adler Mortimer (Ed.), Great Books of the Western World. V. 18. Aquinas: II. Chicago, Auckland, London, Madrid: Encyclopedia Britannica, Inc.
Augustine, A. (1963). The Trinity. Washington, D. C.: The Catholic University of America Press.
Augustine, A. (1994). The Confessions. The City of God, On Christian Doctrine. In Adler Mortimer (Ed.), Great Books of the Western World. V. 16: Augustine. Chicago, Auckland, London, Madrid: Encyclopedia Britannica, Inc.
Augustine, A. (2010). On Grace and Free Choice. In Augustine. On the Free Choice of the Will, On Grace and Free Choice, and Other Writings (pp. 141-184). Cambridge: The Univ. Press.
Beachy, F. J. (1977). The concept of Grace in the Radical Reformation. Nieuwkoop: De Graaf.
Béziau, J.-Y. (1999). What is paraconsistent logic? In Frontiers of paraconsistent logic (pp. 95-112). Baldock: Research Studies Press.
Béziau, J.-Y. (2015). The logical hexagon of analogy: Structuring the relations between difference, identity and similarity. In Katarzyna Gan-Krzywoszyńska, Małgorzata Leśniewska, Przemysław Krzywoszyński, Piotr Leśniewski (Eds.), Handbook of the First World Congress on Analogy, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico, November 4-6, 2015 (pp. 12-13). Poznań: Publishing House KONTEKST.
Béziau, J.-Y., & Costa, N. da. (2015). Is God paraconsistent? In Ricardo Sousa Silvestre and Jean-Yves Beziau (Eds.), Handbook of the 1st World Congress on Logic and Religion, João Pessoa, April 1-5, Brazil (p. 25). Federal University of Campina Grande, Federal University of Paraiba, Federal University of Rio de Janeiro, Brazilian Academy of Philosophy: João Pessoa:
Bobzien, S. (2015). Ancient Logic. In Edward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2016 Edition). Retrieved from https://plato.stanford.edu/archives/win2016/entries/logic-ancient/.
Bonner, G. (1963). St. Augustine of Hippo. Philadelphia: Westminster Press.
Bonner, G. (1987). God’s decree and man’s destiny: Studies on the thought of Augustine of Hippo. L.: Variorum Reprints.
Cassirer, E., Kristeller, P. O., & Randall, J. H. Jr. (1948). The Renaissance Philosophy of Man. Chicago: The University of Chicago Press.
Celenza, C. S. (2017). Marsilio Ficino. In Edward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. Retrieved from http://plato.stanford.edu/archives/fall2017/entries/ficino/.
Costa, N. C. A. da (1974). On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15, 497-510.
Costa, N. C. A. da, Krause, D., & Bueno, O. (2007). Paraconsistent logics and paraconsistency. In D. Jacquette (Ed.), Philosophy of Logic: Handbook of the Philosophy of Science (pp. 791-912). North-Holland.
Couenhoven, J. (2007). Augustine’s rejection of the free-will defense: An overview of the late Augustine’s theodicy. Religious Studies, 43(3), 279-298.
Dolan, J. P. (Ed.) (1964). The essential Erasmus. N. Y.: Mentor Books/New American Library.
Dougherty, M. V. (Ed.). (2008). Pico della Mirandola. New Essays. Cambridge: The University Press.
Epstein, R. L. (2001). Propositional logics: The semantic foundations of logic (2nd edition). Belmont, C. A.: Wadsworth/Thomson Learning.
Farrelly, D. M. J. (1964). Predestination, Grace, and Free Will. Westminster, Maryland: The Newman Press.
Fitzgerald, A. D. (Ed.) (1999). Augustine through the ages. Grand Rapids, M. I.: Erdmans Publ. Co.
Hume, D. (1977). A treatise of human nature. London: Dent; New York: Dutton.
Husserl, E. (1988). Vorlesungen über Ethik und Wertlehre, 1908-1914 [Lectures on Ethics and Value Theory, 1908-1914]. Husserliana, 28. Dordrecht: Kluwer.
Kleene, S. C. (1967). Mathematical logic. New York: Wiley.
Kristeller, P. O. (1964). Eight philosophers of the Italian Renaissance. Stanford, C. A.: Stanford Iniversity Press.
Lancel, S. (2002). Saint Augustine. L.: SCM Press.
Leibniz, G. W. (1971). Elementa Juris Naturalis. In G.W. Leibniz. Philosophishe Schriften. Erster Band (1663-1672). Berlin: Akademie-Verlag.
Lobovikov, V. (1984). Modal Logic of Evaluations and of Norms from the Viewpoint of Contents of Ethics and Law. Krasnoyarsk: University of Krasnoyarsk Press.
Lobovikov, V. (1988). Artificial Intelligence, Formal Ethics, and Moral-Legal Choice. Sverdlovsk: Ural State University Press.
Lobovikov, V. (1990). Formalization of Activity (Values and Norms). The Hab. Doctor Dissertation. Sverdlovsk: Ural State University.
Lobovikov, V. (1998). Mathematical Jurisprudence. Part 1: The Natural Law. Yekaterinburg: The Ural State Law Academy Press; Liberal Arts University Press.
Lobovikov, V. (1999). Mathematical Jurisprudence and Mathematical Ethics (A mathematical simulation of the evaluative and the normative attitudes to the rigoristic sub-systems of the Positive Law and of the Natural-Law-and-Morals). Yekaterinburg: The Ural State Law Academy Press; Liberal Arts University Press.
Lobovikov, V. (2007). Mathematical Ethics, Metaphysics and the Natural Law (Algebra of Metaphysics as Algebra of Formal Axiology). Yekaterinburg: Institute of Philosophy and Law of Ural Branch of Russian Academy of Sciences.
Lobovikov, V. (2009a). Mathematical Logic as a Particular Case of Mathematical Ethics (Algebra of Formal Ethics as a Generalization of Algebra of Formal Logic). In Costas Drossos; Pavlos Peppas; Constantine Tsinakis (Eds.) Proceedings of the 7th Panhellenic Logic Symposium (PLS7) at Patras University, Greece, July 15-19, 2009 (pp. 109-111). Patras, Greece: Patras University Press.
Lobovikov, V. (2009b). Mathematical simulating formal axiological semantics of natural languages (A fundamental generalization of mathematical philosophy: from truth-values to axiological ones). In Philosophy, mathematics, linguistics: aspects of interconnection: Proceedings of the International scientific conference, November 20-22, 2009, Sankt-Petersburg, L. Euler International mathematical institute (pp. 128-132). St.-Petersburg: VVМ.
Lobovikov, V. (2014a). Algebra of Morality and Formal Ethics. In Katarzyna Bronk (Ed.) Looking Back to See the Future: Reflections on Sins and Virtues (pp. 17-41). Oxford, United Kingdom: Inter-Disciplinary Press.
Lobovikov, V. (2014b). Augustine-the-Blessed’s doctrine of God’s reward from the viewpoint of two-valued algebra of formal ethics. Yearbook of the Institute of Philosophy and Law of the Ural Branch of the Academy of Sciences, 2, 52-66.
Lobovikov, V. (2015a). Discrete Mathematical Representations of the Heresies of Pelagius and Leo Tolstoy, and of their Interrelations with St. Augustine’s Doctrine of Grace and Free Choice. In Abstracts of the International Conference “Formal Methods and Science in Philosophy”, March 26-28, 2015, Croatia (pp. 16-17). Dubrovnik: Inter-University Centre.
Lobovikov, V. (2015b). The Trinity Triangle and the Homonymy of the Word “Is” in Natural Language: Eliminating the Illusion of Logical Inconsistency by Precise Formulating the Principle of Separation of Facts and Values in Algebra of Formal Ethics. In Ricardo Sousa Silvestre and Jean-Yves Beziau (Eds.), Handbook of the 1st World Congress on Logic and Religion, João Pessoa, April 1-5, 2015, Brazil (pp. 176-177). João Pessoa: Federal University of Campina Grande; Federal University of Paraiba; Federal University of Rio de Janeiro; Brazilian Academy of Philosophy.
Lobovikov, V. (2015c). The Trinity Triangle and the Homonymy of the Word “Is” in Natural Language (A Logically Consistent Discrete Mathematical Representation of the Trinity by Means of Algebra of Morality and Formal Ethics). Philosophy Study, 5(7), 327-341 (2015), doi: 10.17265/2159-5313/2015.07.001.
Lobovikov, V. (2015d). Two Worlds, Two Languages, Two Semantics, Two Linguistic Principles of Compositionality, and Two Kinds of Nonsenses (Criticizing Wittgenstein’s philosophy of morals and of metaphysics by means of discrete mathematical modeling a formal-ethical aspect of his worldview). Journal of Siberian Federal University. Series: Humanities & Social Sciences, 8(5), 901-911.
Lobovikov, V. (2015e). The Principle of Compositionality in Formal-Axiological Semantics of Natural Language. Journal of Ural Federal University. Series 3: Social Sciences, 140(2), 84-97.
Lobovikov, V. (2016). An Equivalence of Moore’s Paradox and Gödel’s Incompleteness Sentence in Two-Valued Algebra of Formal Ethics. Philosophy Study, 6(1), 34-55, doi: 10. 17265/2159-5313/2016.01.004.
Lobovikov, V. (2017). Proving God’s Omnipresence by Calculating Compositions of Evaluation-Functions in Two-Valued Algebra of Metaphysics as Formal Axiology. In Book of Abstracts of the 2nd World Congress on Logic and Religion, Warsaw, June 18-22, 2017 (p. 56). Warsaw: Institute of Philosophy of the University of Warsaw.
Lobovikov, V. (2019). Analytical Theology: God’s Omnipotence as a Formal-Axiological Law of the Two-Valued Algebra of Formal Ethics (Demonstrating the Law by “Computing” Relevant Evaluation-Functions). Tomsk State University Journal of Philosophy, Sociology, and Political Science, 47(1), 87-93, doi: 10.17223/1998863Х/47/9.
Mates, B. (1961). Stoic Logic. The University of California Press.
Mares, E. D. (2004). Relevant logic: A philosophical interpretation. Cambridge: The University Press.
Mendelson, E. (1997). Introduction to mathematical logic. London; New York: Chapman & Hall.
Moore, G. E. (2004). Principia Ethica. Mineola, N. Y.: Dover Publications.
Pohle, J. (1911). Pelagius and Pelagianism. In Catholic Encyclopedia. Vol. 11. N. Y.: Robert Appleton Company.
Priest, G., Routly, R., & Norman, J. (Eds.). (1989). Paraconsistent logic: Essays on the inconsistent. München: Philosophia Verlag.
Pseudo-Dionysius. (1980). The Divine Names and Mystical Theology. Milwaukee, W. I.: Marquette University Press.
Rist, J. M. (1994). Augustine: Ancient thought baptized. N. Y.: Cambridge University Press.
Schwiebert, E. G. (1950). Luther and his times. St. Louis: Concordia Publishing House.
Tillich, P. (1968). A history of Christian Thought. N. Y.: Harper & Row.
Tolstoy, L. (1942). What then must we Do? London: Oxford University Press.
Tolstoy, L. (1970). The law of love and the law of violence. London: Anthony Blond.
Tolstoy, L. (1990). Government is violence: Essays on anarchism and pacifism. London: Phoenix Press.
Tolstoy, L. (2005). The Kingdom of God is within you: Christianity not as a mystical religion but as a new theory of life. N. Y.: Barnes & Noble Books.
Tolstoy, L. (2009). My Religion-What I Believe. Guildford: White Crow Books.
Watson, P. S. (1959). The concept of Grace. Philadelphia: Muhlenburg Press.
Wetzel, J. (1992). Augustine and the Limits of Virtue. N. Y.: Cambridge University Press.
Woleński, J. (2019). Lvov-Warsaw School. In Edward N. Zalta (Ed.), Stanford Encyclopedia of Philosophy (Spring 2019 Edition). Retrevied from http://plato.stanford.edu/archives/spr2019/entries/lvov-warsaw/.
Yates, J. P. (2006). Selected remarks on some of Augustine’s unique exegesis of the catholic epistles in the pelagian controversies. In F. Young (Ed.), Studia Patristica Vol. XXX. Papers presented at the Fourteenth International Conference on Patristic Studies held in Oxford 2003 (pp. 303-321). Leuven: Peeters.