Formalizing the conditionals of Diodorus Cronus and Chrysippus: logic and potential applications in human thinking.

Although formal logics are supposed to express some aspects of human thinking, none of them achieve the desired success. These failures sometimes cause - at conferences - voices of resignation claiming that logic is not a science whose object is human thinking. And yet Aristotle considered logic to...

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Publicado en:Synthese Vol. 206; no. 1; pp. 1 - 60
Autor principal: Łukowski, Piotr
Formato: Artículo
Publicado: Springer Nature Jul2025
Acceso en línea:Ver este registro en EBSCOhost
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        au: Łukowski, Piotr
        affil: https://ror.org/03bqmcz70 Department of Logic, Institute of Philosophy, Jagiellonian University in Kraków, Kraków, Poland
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      keyword:
        Angell’s system
        Aristotle’s theses
        Boethius theses
        Conditional
        Connexive logic
        Content implication
        Frege’s axiom
        Hyperintensional implication
        Hyperintensionality
        Intensional implication
        Material implication
        Non-Fregean logic
        Non-monotonicity
        Paraconsistency
        Parry’s system
        Principle of explosion
        Principle of implosion
        Proscriptive principle
        Rule of addition
        Sentence content
        Sentential identity
        Synonymy
      ab: Although formal logics are supposed to express some aspects of human thinking, none of them achieve the desired success. These failures sometimes cause - at conferences - voices of resignation claiming that logic is not a science whose object is human thinking. And yet Aristotle considered logic to be an organon, or tool for practicing other sciences. Accepting this point of view, the present paper starts from the assumption that the main incompatibilities of formal logics with our thinking are due to the fact that the implications defined in these logics are very distant in nature from the conditional we use in everyday thinking. Our paper presents two proposals to formalize conditional in such a way that both they and the inferences defined by them do not have properties alien to our thinking. To achieve this goal, we make the assumption that the content of sentences must play a fundamental role in the formal reconstruction of both implication and inference. An essential idea of our approach is that the truth of a conditional is grounded in the inference relation between antecedent and consequent, and more precisely, it should depend on the possibility or impossibility of deriving a contradiction from acceptance and/or rejection of the antecedent and consequent content – an approach characteristic for inferentialism. Since the essence of the paper is a conditional, propositional logic is a sufficient field of consideration.
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