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On Three Levels of Abstractness in Peirce’s Beta Graphs 论Peirce β图的三个抽象性层次
IF 0.5 3区 哲学
History and Philosophy of Logic Pub Date : 2023-01-02 DOI: 10.1080/01445340.2022.2056781
R. Atkins
{"title":"On Three Levels of Abstractness in Peirce’s Beta Graphs","authors":"R. Atkins","doi":"10.1080/01445340.2022.2056781","DOIUrl":"https://doi.org/10.1080/01445340.2022.2056781","url":null,"abstract":"Peirce’s beta graphs are roughly equivalent to our first-order predicate logic. However, Bellucci and Pietarinen have recently argued that the beta graphs are not well-equipped to handle asymmetric relative terms. I survey four proposed solutions to the problem and find them all wanting. I offer a fifth solution according to which Peirce’s beta graphs function at three different levels of abstractness from natural language. I diagnose the problem of asymmetric relative terms as arising when we transition from the first to the second level of abstractness. Making grammatical information encoded in natural language explicit at the first level of abstractness and interpreting graphs at the second level of abstractness as shorn of grammatical information resolves the problem. The solution is both well-motivated by Peirce’s own commitments and increases the expressiveness of the beta graphs.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44452478","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}
引用次数: 0
Bolzano on Bolzano: A Hitherto Unknown Announcement of Bolzano’s Beyträge 博尔扎诺对博尔扎诺：迄今为止未知的博尔扎诺的Beyträge公告
IF 0.5 3区 哲学
History and Philosophy of Logic Pub Date : 2022-12-28 DOI: 10.1080/01445340.2022.2147750
Elías Fuentes Guillén
{"title":"Bolzano on Bolzano: A Hitherto Unknown Announcement of Bolzano’s Beyträge","authors":"Elías Fuentes Guillén","doi":"10.1080/01445340.2022.2147750","DOIUrl":"https://doi.org/10.1080/01445340.2022.2147750","url":null,"abstract":"ABSTRACT In 1817, in the preface to his Rein analytischer Beweis, Bernard Bolzano revealed that he had decided to postpone the publication of any subsequent instalment of his Beyträge zu einer begründeteren Darstellung der Mathematik because of the few and ‘superficial’ reviews of its first instalment, published in 1810. Bolzano’s transcriptions of the only two known reviews of this book are conserved at the Literární archiv Památníku národního písemnictví / Muzea literatury, in Prague, together with another manuscript on his Beyträge, the provenance of which was unknown to Bolzano’s scholars until recently. In this paper it is shown that this latter manuscript is a draft of an announcement that was published at the time and that was indeed written at least to some extent by Bolzano himself. This hitherto unknown announcement of Bolzano’s Beyträge not only solves the mystery surrounding that manuscript, but also helps to date the publication of this book more precisely and provides an unusual insight into what we must take Bolzano himself to have considered most noteworthy about his work, namely his study on logic. The paper includes a transcription of the manuscript and an English translation of the announcement.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43951876","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}
引用次数: 0
Note on the Negative Approach of al-Shahīd al-Thānī Towards Logic in al-Iqtiṣād wa al-Irshād 关于al- shah<e:1> al-Thānī在al-Iqtiṣād wa al-Irshād中对逻辑的否定态度的注解
IF 0.5 3区 哲学
History and Philosophy of Logic Pub Date : 2022-12-21 DOI: 10.1080/01445340.2022.2143219
Mahmood Zeraatpisheh
{"title":"Note on the Negative Approach of al-Shahīd al-Thānī Towards Logic in al-Iqtiṣād wa al-Irshād","authors":"Mahmood Zeraatpisheh","doi":"10.1080/01445340.2022.2143219","DOIUrl":"https://doi.org/10.1080/01445340.2022.2143219","url":null,"abstract":"Aversion towards logic is a characteristic feature of the Islamic traditionalists. There is in fact a history of opposition to logic in Islam. As any other areas of history, here also the correct picture will not be achieved unless all of the pieces are put together. In what follows, I am going to shed light on a chapter written by Zayn al-Dīn al-ʿĀmilī (d. 966/1558), the Twelver Shīʿī Scholar better known as al-Shahīd al-Thānī. The chapter not only shows al-Shahīd al-Thānī’s negative stance towards logic, but also is important because it is a part of less studied Shīʿite traditionalists’ tendencies towards logic; those who are considered as the most influential figures in Iranian seminaries from the Safavid period up until today.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45821781","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}
引用次数: 0
Prior’s big Y and the Idea of Branching Time Prior的大Y与时间分支思想
IF 0.5 3区 哲学
History and Philosophy of Logic Pub Date : 2022-12-19 DOI: 10.1080/01445340.2022.2147809
P. Øhrstrøm, M. González
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引用次数: 1
Russell Contra Sense/Reference, the ‘Mont Blanc’ Correspondence Russell Contra Sense/Reference，“勃朗峰”通信
IF 0.5 3区 哲学
History and Philosophy of Logic Pub Date : 2022-12-12 DOI: 10.1080/01445340.2022.2153214
Clarence L. Hay
{"title":"Russell Contra Sense/Reference, the ‘Mont Blanc’ Correspondence","authors":"Clarence L. Hay","doi":"10.1080/01445340.2022.2153214","DOIUrl":"https://doi.org/10.1080/01445340.2022.2153214","url":null,"abstract":"ABSTRACT It is argued that Russell before 1905 saw no value in Frege's sense/reference distinction. This is clearest in the Mont Blanc correspondence. It is argued that Russell and Frege failed to engage because Frege lacked a grasp on the internal/external relations distinction. For Russell sense is either an external relation, objectionably separating out thought and reference, or an internal relation, so what is thought is altered such that we do not know what we are talking about. The novelty of the present paper lies in the arrangement of the parts and the claim that Russellian propositions are not made up of the things themselves but of transparent representatives thereof.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47933309","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}
引用次数: 0
How to Distinguish Simple Objectless Ideas 如何区分简单的无对象思想
IF 0.5 3区 哲学
History and Philosophy of Logic Pub Date : 2022-12-09 DOI: 10.1080/01445340.2022.2142462
J. Claas
{"title":"How to Distinguish Simple Objectless Ideas","authors":"J. Claas","doi":"10.1080/01445340.2022.2142462","DOIUrl":"https://doi.org/10.1080/01445340.2022.2142462","url":null,"abstract":"Bernard Bolzano offers a criterion of individuation for ideas, according to which ideas are distinct if and only if they represent different objects or are composed differently. It fails to individuate ideas that are both simple and fail to represent, in particular syncategorematic ideas and logical constants. However, Bolzano also provides the means to close this gap. He suggests that we can distinguish ideas if they are not substitutable for each other in propositions, which we can, in turn, distinguish in terms of their truth-values. This paper explicates this suggestion and develops it into an improved individuation criterion for ideas: ideas also are distinct if we cannot replace them for one another in propositions salva veritate.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43147566","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}
引用次数: 0
John von Neumann’s Discovery of the 2nd Incompleteness Theorem 约翰·冯·诺依曼对第二不完全性定理的发现
IF 0.5 3区 哲学
History and Philosophy of Logic Pub Date : 2022-11-28 DOI: 10.1080/01445340.2022.2137324
G. Formica
{"title":"John von Neumann’s Discovery of the 2nd Incompleteness Theorem","authors":"G. Formica","doi":"10.1080/01445340.2022.2137324","DOIUrl":"https://doi.org/10.1080/01445340.2022.2137324","url":null,"abstract":"ABSTRACT Shortly after Kurt Gödel had announced an early version of the 1st incompleteness theorem, John von Neumann wrote a letter to inform him of a remarkable discovery, i.e. that the consistency of a formal system containing arithmetic is unprovable, now known as the 2nd incompleteness theorem. Although today von Neumann’s proof of the theorem is considered lost, recent literature has explored many of the issues surrounding his discovery. Yet, one question still awaits a satisfactory answer: how did von Neumann achieve his result, knowing as little as he seemingly did about the 1st incompleteness theorem? In this article, I shall advance a conjectural argument to answer this question, after having rejected the argument widely shared in the literature and having analyzed the relevant documents surrounding his discovery. The argument I shall advance strictly links two of the three letters written by von Neumann to Gödel in the late 1930 and early 1931 (i.e. respectively that of November 20, 1930 and that of January 12, 1931) and finds the key for von Neumann’s discovery in his prompt understanding of the Gödel sentence A – as the documents refer to it – as expressing consistency for a formal system that contains arithmetic.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44755081","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}
引用次数: 0
Kant’s Die falsche Spitzfindigkeit and Proof-theoretic Semantics Kant(37岁)有错吗
IF 0.5 3区 哲学
History and Philosophy of Logic Pub Date : 2022-11-17 DOI: 10.1080/01445340.2022.2142461
Tiago Rezende de Castro Alves
{"title":"Kant’s Die falsche Spitzfindigkeit and Proof-theoretic Semantics","authors":"Tiago Rezende de Castro Alves","doi":"10.1080/01445340.2022.2142461","DOIUrl":"https://doi.org/10.1080/01445340.2022.2142461","url":null,"abstract":"According to Schroeder-Heister 2018, proof-theoretic semantics is ‘an alternative to truth-condition semantics. It is based on the fundamental assumption that the central notion in terms of which meanings are assigned to certain expressions of our language, in particular to logical constants, is that of proof rather than truth. In this sense proof-theoretic semantics is semantics in terms of proof. Proof-theoretic semantics also means the semantics of proofs, i.e. the semantics of entities which describe how we arrive at certain assertions given certain assumptions.' This text advocates that proof-theoretic semantics, as described above, was an approach to semantical issues in logic that appeared in mainstream philosophical literature at least a couple of centuries before the tradition of general proof theory (cf. Prawitz 1971) came into being. This is done by means of an interpretive analysis of Kant’s 1762 essay Die falsche Spitzfindigkeit der vier syllogistischen Figuren, in which two theses are argued: first, that the issue of justifying the logical validity of inferences is approached by Kant in this text, in a strong sense, in terms of proofs; and second, that the purpose of his effort is to establish a point concerning the semantical equivalence between certain distinct valid inferences.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59177883","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}
引用次数: 1
Ramsey's Lost Counterfactual 拉姆齐的《迷失的反事实
IF 0.5 3区 哲学
History and Philosophy of Logic Pub Date : 2022-09-19 DOI: 10.1080/01445340.2022.2110011
Caterina Sisti
{"title":"Ramsey's Lost Counterfactual","authors":"Caterina Sisti","doi":"10.1080/01445340.2022.2110011","DOIUrl":"https://doi.org/10.1080/01445340.2022.2110011","url":null,"abstract":"In contemporary works on conditionals, the Ramsey test is a procedure for the evaluation of conditional sentences. There are several versions of the test, all inspired by a footnote by the British philosopher and mathematician Frank Ramsey, in his General Propositions and Causality. However, no study on Ramsey's own account of conditionals has been put forth so far. Furthermore, the footnote seems to cover indicative conditionals only, and this has led to the belief that no account of counterfactuals can be found in Ramsey's work. In this paper, I recover Ramsey's account of counterfactuals and show that it is sketched in the footnote too. The result is a well-developed account of counterfactuals that resembles many contemporary ones. But Ramsey uses the same approach also for other types of conditionals, and this casts doubts on the current criteria for the classification of this type of sentences.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46702236","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}
引用次数: 0
Lvov-Warsaw School. Past and Present Logic 利沃夫华沙学校。过去和现在的逻辑
IF 0.5 3区 哲学
History and Philosophy of Logic Pub Date : 2022-09-19 DOI: 10.1080/01445340.2022.2114059
K. Gan-Krzywoszyńska, P. Leśniewski
{"title":"Lvov-Warsaw School. Past and Present Logic","authors":"K. Gan-Krzywoszyńska, P. Leśniewski","doi":"10.1080/01445340.2022.2114059","DOIUrl":"https://doi.org/10.1080/01445340.2022.2114059","url":null,"abstract":"Lvov-Warsaw School. Past and Present Logic, by Á. Garrido and U. Wybraniec-Skardowska, Studies in Universal Logic, Springer Birkhäuser, 2018, xviii+ 815 pp., EUR 58.84 (Hardcover Book), ISBN: 978-3-319-65429-4, EUR 53.49 (Softcover Book), ISBN: 978-3-030-09740-0, EUR 42.79 (eBook), ISBN: 978-3-319-65430-0. Reviewed by K. GAN-KRZYWOSZYŃSKA and P. LEŚNIEWSKI, Faculty of Philosophy, Adam Mickiewicz University, ul. Szamarzewskiego 89C, 60-568 Poznań, Poland, katarzyna.gan-krzywoszynska@amu.edu.pl, grus@amu.edu.pl","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49074692","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}
引用次数: 0
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