Intuitionist Reasoning in the Tri-Unitarian Theology of Nicholas of Cues (1401-1464)

Journal of Applied Logic 6 (6):1143-1186 (2019)
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The main subject of Cusanus’ investigations was the name of God. He claimed to have achieved the best possible one, Not-Other. Since Cusanus stressed that these two words do not mean the corresponding affirmative word, i.e. the same, they represent the failure of the double negation law and there￾fore belong to non-classical, and above all, intuitionist logic. Some of his books implicitly applied intuitionist reasoning and the corresponding organization of a theory which is governed by intuitionist logic. A comparison of two of Cusanus’ short writings shows that throughout his life he substantially improved his use of this kind of logic and ultimately was able to reason consistently within such a logic and recognize some of its basic laws. One important idea developed by him was that of a proposition composed of a triple repetition of “not-other” expressing “the Tri-unity of concordance” i.e. the “best name for the Trinity”. I complete his application of intuitionist logic to theological subjects by charac￾terizing the inner relationships within the Trinity in such a way that there are no longer contradictions in the notion. Generally speaking, the notion of the Trin￾ity implies a translation from intuitionist to classical logic, to which Cusanus closely approximated. Moreover, I show that the main aspects of Christian rev￾elation, including Christ’s teachings, are represented both by this translation and by some doubly negated propositions of intuitionist logic. Hence, intuition￾ist logic was introduced into the history of Western theological thinking with Christian revelation, as only Cusanus partly recognized. Appendix 1 summa￾rizes a detailed analysis of Cusanus’ second short writing. Appendix 2 shows that the Athanasian creed regarding the Christian Trinity is a consistent se￾quence of intuitionist propositions provided that some verbal emendations are added, showing that ancient trinitarian thinking was also close to intuitionist reasoning.

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