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...
| Publicado en: | Synthese Vol. 206; no. 1; pp. 1 - 60 |
|---|---|
| Autor principal: | |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Jul2025
|
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=186350945&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 186350945 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Jul2025 vid: 206 iid: 1 pid: 237 pub: Springer Nature artinfo: ui: 186350945 10.1007/s11229-025-04981-0 ppf: 1 ppct: 59 formats: fmt: – @attributes: type: T – @attributes: type: P size: 8.8MB tig: atl: Formalizing the conditionals of Diodorus Cronus and Chrysippus: logic and potential applications in human thinking. aug: au: Łukowski, Piotr affil: https://ror.org/03bqmcz70 Department of Logic, Institute of Philosophy, Jagiellonian University in Kraków, Kraków, Poland sug: 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2025. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2025 holdings: @attributes: islocal: N |
|---|