Sense, Causality and Paradoxes: A logico-philosophical essay on the modelling of natural reasoning and its application to the study of paradoxes (in English)
Synopsis "Sense, Causality and Paradoxes: A logico-philosophical essay on the modelling of natural reasoning and its application to the study of paradoxes (in English)"
What mechanisms are involved in the emergence of paradoxical situations? This is one of the main questions that the present work endeavours to tackle and explore by an ab initio approach essentially resting on observation and intuition, though rigorously carried out and deliberately free from any dogmatic basis. The first part, devoted to the identification of the conditions of emergence and preservation of sense, shows how the law of causality, which rules the physical world such as we perceive it, implicitly extends its authority to the abstract universe of language. The second part first explores the concept of truth, experimentally ascertains the impossibility of adequately accounting for the physical world by means of only two truth values, i.e. true and false, then summarily and informally expounds the methods of construction of a logical, natural system, called "CNL", and finally provides an intuitive, immediately understandable interpretation of the results of this system. The third part of this work, the longest one, describes in detail how the results of the CNL system, as introduced and explained in the second part, apply to the most widely known paradoxes and paradoxical arguments, including Gödel's Incompleteness Theorem and Cantor's Diagonal Argument. Lastly, the fourth part, which fulfils the function of a technical appendix whose reading is optional for the comprehension of the preceding developments, expounds in a more formal way the various stages of the construction of the CNL system, explores its principal properties, and shows that this system, which is at the same time 3-valued, modal, extensional, and respectful of both the law of excluded middle and the law of non-contradiction, encompasses classical, binary logic.
