{"title":"Modal Homotopy Type Theory. The Prospect of a New Logic for Philosophy","authors":"A. Klev, C. Zwanziger","doi":"10.1080/01445340.2022.2107383","DOIUrl":"https://doi.org/10.1080/01445340.2022.2107383","url":null,"abstract":"Published in History and Philosophy of Logic (Vol. 44, No. 3, 2023)","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Bounds of Transcendental Logic","authors":"S. Kovač","doi":"10.1080/01445340.2022.2078596","DOIUrl":"https://doi.org/10.1080/01445340.2022.2078596","url":null,"abstract":"","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42197917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Knowledge and the Philosophy of Number","authors":"Richard Lawrence","doi":"10.1080/01445340.2022.2080373","DOIUrl":"https://doi.org/10.1080/01445340.2022.2080373","url":null,"abstract":"project to provide a new for the philosophy of number inspired by the idea that numbers are magnitudes . Hossack advocates understanding magnitudes as properties of , a which pluralities, continua, and series a natural is a property of a plurality, a real is a property of a continuum, and an ordinal is a property of a series. The out a modern theory of quantity and magnitude, based on the ancient theory of quantity in and in order to argue that we can have a priori knowledge of the natural numbers, the real numbers, and the ordinals. It is a refreshing and innovative attempt at that longstanding goal.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41881465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Essays on Argumentation in Antiquity","authors":"M. Scanlan","doi":"10.1080/01445340.2022.2063669","DOIUrl":"https://doi.org/10.1080/01445340.2022.2063669","url":null,"abstract":"","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48412475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Husserl and Mathematics","authors":"M. Roubach","doi":"10.1080/01445340.2022.2065615","DOIUrl":"https://doi.org/10.1080/01445340.2022.2065615","url":null,"abstract":"Ariew, R. 2014. Descartes and the First Cartesians, Oxford: Oxford University Press. Ariew, R. 2015. ‘La Logique de Port-Royal, les premiers Cartésiens et la scolastique tardive’, Archives de Philosophie, 78 (1), 29–48. Ariew, R. 2021. ‘The Nature of Cartesian Logic’, Perspectives on Science, 29 (3), 275–91. Biard, J. 2015. ‘La Sémiologie de Port-Royal’, Archives de Philosophie, 78 (1), 9–28. Chomsky, N. 1966. Cartesian Linguistics. A Chapter in the History of Rationalist Thought, New York: Harper & Row. Pécharman,M. 2007. ‘Port-Royal et l’analyse augustinienne du langage’, in L. Devillairs (ed.),Augustin au XVIIe siècle, Florence: Olschki, pp. 101–34.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49594916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stipulations Missing Axioms in Frege's Grundgesetze der Arithmetik","authors":"Gregory Landini","doi":"10.1080/01445340.2022.2062664","DOIUrl":"https://doi.org/10.1080/01445340.2022.2062664","url":null,"abstract":"Frege's Grundgesetze der Arithmetik offers a conception of cpLogic as the study of functions. Among functions are included those that are concepts, i.e. characteristic functions whose values are the logical objects that are the True/the False. What, in Frege's view, are the objects the True/the False? Frege's stroke functions are themselves concepts. His stipulation introducing his negation stroke mentions that it yields But curiously no accommodating axiom is given, and there is no such theorem. Why is it that some of Frege's informal stipulations never made appearances as axioms? I offer an explanation that sheds new light on the Grundgesetze. No axioms should over-determination the True as a logical object. Perhaps the True = 0, as would be common in the mathematics of characteristic functions. But the logical objects that are cardinal numbers are value ranges correlated with second-level numerical concepts by a non-homogeneous second-level value-range function . The existence of concepts would be ontologically circular if the True is itself a number. We find this circularity perfectly agreeable to Frege, and suggest that he had accepted that the existence of functions that are concepts in his cpLogic may well be ontologically inseparable from the existence of his value-range function. His cpLogic itself stands or falls with the viability of some value-range function.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44366954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Logic of Gilles Deleuze","authors":"H. Somers-Hall","doi":"10.1080/01445340.2022.2063668","DOIUrl":"https://doi.org/10.1080/01445340.2022.2063668","url":null,"abstract":"logical movement of ‘mediation’. They want to put metaphysics in motion, in action. They want to make it act, and make it carry out immediate acts. It is not enough, therefore, for them to propose a new representation of movement; representation is already mediation’ (Deleuze 1994, 8). Here, I think, Deleuze would say that Priest attempts to put the discrete multiplicity of classical logic in motion, rather than recognise the need for a non-propositional account of problems, such as Deleuze develops. As such, my suspicion is that Shores in the end collapses the difference in kind between the two multiplicities that is at the heart of Deleuze’s logic of multiplicities. Shores notes in the conclusion of the work that this is the opening of a broader project on Deleuze and logic, so perhaps these issues will be resolved as the project develops. I suspect Shores would see much of his work here as a provocation to further thought, and he notes that while Priest’s logic offers the best mapping of Deleuze’s logic, this mapping does not cover the whole range of Deleuze’s thought. In providing such a provocation, the book is a success, and despite the reservations above, I would recommend it to those interested in this intersection of Deleuze and logic. Ultimately the engagement with formal logic here is well worked out, with the clearest analyses of Deleuze’s engagements with the philosophy of logic so far available to us.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41465723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Arthur N. Prior and the Lvov-Warsaw School","authors":"Zuzana Rybaříková","doi":"10.1080/01445340.2022.2062696","DOIUrl":"https://doi.org/10.1080/01445340.2022.2062696","url":null,"abstract":"This paper presents the link between Arthur N. Prior and logicians that belonged to the Lvov-Warsaw School. Although certain members of the Lvov-Warsaw School influenced Prior’s views, the amount and the form of the impact are still under discussion. Prior also cooperated with some of them in the development of his systems of logic. This paper focuses on four main areas in which Prior admitted adopting ideas from the Lvov-Warsaw School: systems of propositional logic, the history of logic, modal and temporal logic and ontology. Prior’s published works as well as his correspondence, which is stored in Prior’s Nachlass, are used to describe the influence.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45619754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Cartesian Semantics of the Port Royal Logic","authors":"E. Cassan","doi":"10.1080/01445340.2022.2045129","DOIUrl":"https://doi.org/10.1080/01445340.2022.2045129","url":null,"abstract":"types of argumentation. The results are unsatisfactory both because of unclarity in Aristotle’s classification and because of the fact that argumentation, at least as conceived by Walton, is a much broader category of verbal persuasive interaction than dialectic is for Aristotle and other ancient Greek authors. Reading the entire collection has given me the unfortunate impression that I am even more confused about what ‘dialectic’ and ‘argumentation’ are than when I began. This is not the fault of the authors but seems to be a problem with the concepts. For dialectic we are faced with trying to find some connection between the episteme producing dialectic of Republic VII and the competitive training exercises that Aristotle discusses in TopicsVIII. For argumentation we seem to be faced with an open-ended process of evaluation, counterargument, questioning, responding, etc., as indicated by Walton at the beginning of his article. One of the articles refers to a possible 40-year argumentation between a couple on some recurring problem in their relationship. To have a unified theory about this daunting range of material seems problematic. It seems as achievable as a unified theory of the novel or of football. This is not to say there aren’t interesting or even important things to be said about dialectic and argumentation, but certainly a novice should beware of a false impression of unity where there is rather diversity.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47841640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Expressive Power of the N-Operator and the Decidability of Logic in Wittgenstein’s Tractatus","authors":"Rodrigo Ferreira","doi":"10.1080/01445340.2022.2056687","DOIUrl":"https://doi.org/10.1080/01445340.2022.2056687","url":null,"abstract":"The present text discusses whether there is a tension between aphorisms 6.1-6.13 of the Tractatus and the Church-Turing theorem about the decidability of predicate logic. We attempt to establish the following points: (i) Aphorisms 6.1-6.13 are not consistent with the Church-Turing theorem. (ii) The logical symbolism of the Tractatus, built from the N-operator, can (and should) be interpreted as expressively complete with respect to first-order formulas. (iii) Wittgenstein’s reasons for believing that Logic is decidable were purely philosophical and the undecidability result shows that there are aspects of his criticisms of Frege and Russell that become unjustified in light of these results.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44563869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}