This paper is a discussion of Gabriel, Hülser and Schlotter’s 2009 article on a possible causal relation between Stoic logic and Frege. The paper provides detailed argument for why Rudolf Hirzel should not be taken as the qualified middleman in philosophical discussion with whom Frege learned what he ‘borrowed’ without acknowledgement from Stoic logic. Additionally, this paper offers some modest findings about some aspects of Frege's and Hirzel's lives and work habits, which may help us understand a little better Frege's (...) connection to Hirzel and to Stoic logic as well as Frege’s failure to acknowledge the Stoics. This paper is a purely historical offshoot of my essay ‘Frege plagiarized the Stoics’. Zero direct insights into either Frege’s or Stoic philosophy are offered. OPEN ACCESS. Choose 'without proxy' below. (shrink)

This very brief paperli provides plausible answers to the two residual questions that Jamie Tappenden states, but leaves unanswered, in his 2024 paper ‘Following Bobzien: Some notes on Frege’s development and engagement with his environment’, namely, why Frege read Sigwart’s Logik and what caused Frege to read Prantl. (This paperli is merely historical and offers no special philosophical insights of any sort.) ---------- OPEN ACCESS. Choose 'without proxy' below.

This very brief paper provides plausible answers to the two residual questions that Jamie Tappenden states, but leaves unanswered, in his 2024 paper ‘Following Bobzien: Some notes on Frege’s development and engagement with his environment’, namely, why Frege read Sigwart’s Logik and what caused Frege to read Prantl.

In this paper we give a detailed comparison of the key elements of Frege’s formal language of thought and apparently similar views in Stoic formal logic. That is, we compare their views on the following topics: connectives, negation, simple sentences, propositional content, predicates and their incompleteness, and quantifications. We show that in most of these cases the similarities between Frege’s views and the Stoic views are only superficial. Frege’s views are far more systematic, better developed and can in no case (...) directly or fully be traced back to Stoic ideas. Furthermore, we show that Prantl, pace Bobzien 2021, is in most of these cases not a reliable source with respect to Stoic logic and that it is very unlikely that Frege’s views on logic were influenced by Prantl’s interpretation of Stoic formal logic. (shrink)

In many accounts of the history of logic, especially from the second half of the twentieth century and partly still today, Frege’s first book, Begriffsschrift (1879), is singled out as the beginnin...

Loosely connected reflections on some issues raised by Susanne Bobzien concerning the extent to which Frege interacted with scholars in his environment, and what he may have learned from them. I first note a pattern in Frege's pre-Grundlagen writings: his references to other logicians tend to be in response to criticism. I then discuss the period 1885–1891, suggesting that Frege may have been more engaged with his teaching and his colleagues than is sometimes believed, in response to the ‘unsatisfied need (...) for communication’ that he describes in an 1882 letter. Finally, I explore one of the ways that the influence of Frege's environment may be reflected in the language and philosophical framing he uses to communicated with a philosophical audience, noting the ways that the philosophical language and metaphors of Grundlagen, §88 may have been shaped by Frege's relationship with Rudolf Eucken. (shrink)

The paper gives, in the first place, a performative reading of Frege's account of non-alethic modalities. Second, it asks the question whether there is an influence of Kant's writings on Frege's notion of assertive force. It is generally acknowledged that the Neo-Kantian tradition has been essential to Frege's development. The paper shows that it can also be fruitful to look at more direct influences of Kant himself, especially on the early Frege. The paper shows that Kant's notion of assertoric modality (...) must have been an inspiration for Frege to make the distinction between judgement, including the assertoric force, and judgeable content. Kant's logical I may also have played a role in Frege's account of judgement in terms of the judging agent, the first person. The conclusion of the paper, though, is that Frege is not a Kantian philosopher, as his idea of logic as providing a positive standard of objectivity is completely new. (shrink)

The paper gives, in the first place, a performative reading of Frege's account of non-alethic modalities. Second, it asks the question whether there is an influence of Kant's writings on Frege's notion of assertive force. It is generally acknowledged that the Neo-Kantian tradition has been essential to Frege's development. The paper shows that it can also be fruitful to look at more direct influences of Kant himself, especially on the early Frege. The paper shows that Kant's notion of assertoric modality (...) must have been an inspiration for Frege to make the distinction between judgement, including the assertoric force, and judgeable content. Kant's logical I may also have played a role in Frege's account of judgement in terms of the judging agent, the first person. The conclusion of the paper, though, is that Frege is not a Kantian philosopher, as his idea of logic as providing a positive standard of objectivity is completely new. (shrink)

One of Gottlob Frege’s most original contributions to logic and philosophy was his logical notation, his ‘Begriffsschrift’. While long criticized, dismissed, or simply ignored, the recent secondary literature contains some helpful re-evaluations and partial defenses of it. These rely largely on technical, pragmatic, or cognitive-psychological considerations. In this paper, we reconsider Frege’s own reasons for valuing his notation highly. We argue that there is a further semiotic dimension, one that matters epistemologically. This dimension becomes evident once one takes seriously, partly (...) also literally, some striking visual metaphors Frege uses. The result is an interpretation highlighting a side of Frege’s position that is not widely known. It involves his views about the indispensable role that language, or sign systems more generally, play for human thought, and especially, for logic and mathematics. More particularly and as we read Frege, a good logical notation allows for expressing conceptual/inferential relations in a ‘visually inscribed’, thus ‘perspicuous’ way, and this leads to a special kind of ‘insight’ in mathematics. Or as we elaborate this point further, it involves a kind of articulation and understanding hardly possible without it. Frege designed his Begriffsschrift with that specific goal in mind. (shrink)

Conventionalism about logic claims that logical truth has its source in linguistic convention. Conventionalism about mathematics claims the same for mathematical truth. Conventionalism was popular...

The problem of precise characterisation of traditional forms of reasoning applied in mathematics was independently investigated and successfully resolved by Jaśkowski and Gentzen in 1934. However, there are traces of earlier interests in this field exhibited by the members of the Lvov-Warsaw School. We focus on the results obtained by Jaśkowski and Leśniewski. Jaśkowski provided the first formal system of natural deduction in 1926. Leśniewski also demonstrated in some of his papers how to construct proofs in accordance with intuitively correct (...) principles. (shrink)

We classify two of Bertrand Russell's theories of events within the point-free ontology. The first of such approaches was presented informally by Russell in ‘The World of Physics and the World of Sense’ (Lecture IV in Our Knowledge of the External World of 1914). Based on this theory, Russell sketched ways to construct instants as collections of events. This paper formalizes Russell's approach from 1914. We will also show that in such a reconstructed theory, we obtain all axioms of Russell's (...) second theory from 1936 and all axioms of Thomason's theory of events from 1989. Russell's work certainly influenced the works of Stanisław Leśniewski, his student Alfred Tarski, and Czesław Lejewski – prominent members of the Lvov-Warsaw School (LWS). We see our work in the tradition of the research of Leśniewski and Tarski. Building on the technical tools developed in this environment and in the spirit of the traditional research of the LWS, we engage here, in particular, with two classic works by Russell on fundamental ontology. (shrink)

AbstractŁukasiewicz introduced a new methodological approach to the history of logic. It consists of the use of modern formal logic in the research of the history of logic. Although he was not the first to use formal logic in his historical research, Łukasiewicz was the first who used it consistently and formulated it as a requirement for a historian of logic. The aim of this paper is to present Łukasiewicz's contribution and the history of its formulation. In addition, the paper (...) will present its reception. There are two main themes in Łukasiewicz’s work on the history of logic. He discussed Stoic logic and Aristotle’s syllogistic. The second part of the paper focuses on current reception of Łukasiewicz’s contribution and on the question of whether there is a difference between knowledge about his contribution to Stoic logic and to Aristotle’s syllogistic, given that it has been hypothesised that Łukasiewicz’s contribution is currently more known among Aristotelian scholars than among those who focus on Stoic logic. Based on the papers that have appeared in the last five years at Web of Science and Scopus this hypothesis has not been confirmed. (shrink)

We take into account two areas of the logical research of the Lvov-Warsaw School. First, we consider a new approach to research in the history of logic introduced and practiced by Łukasiewicz and some of his followers. In this style of doing history of logic, the knowledge of original philosophical and logical texts was combined with competence in modern logic. This method resulted in many important discoveries both in history and in logic and philosophy. At the same time, we pay (...) attention to contemporary historical research devoted to the logic created by the School itself. In this context, we present an overview of the six papers included in the special issue ‘Logic and its History in the Lvov-Warsaw School’. These papers were presented at an international symposium, ‘History in/of the Lvov-Warsaw School’, held in October 2022 in Warsaw, and they cover various aspects of historical-logical and logical achievements of the School. They concern topics from history of ancient logic, history of modern proof theory, and the issues of applying logic to philosophy and theology in the same way as the one implemented at the Lvov-Warsaw School. (shrink)

The twentieth-century logical mainstream, derived from works by Łukasiewicz and Scholz, pictures the history of logic for the most part as the prehistory of Boolean–Fregean mathematical logic. Particularly, with respect to classical propositional calculus, the Stoic logic has been pictured as an early stage of it and Aristotle's or the Peripatetics' logic as a theory that assumes it. Although it was not emphasised, it follows that the ancient logics contain the principle of explosion. In the endmost quarter of the twentieth (...) century, a competitive view began to spread to the effect that the ancient systems of logic were paraconsistent or relevantistic. In the twenty-first century, the latter view prevails and has every chance of becoming a new orthodoxy. It is claimed that although in Łukasiewicz's argument for the classicality of ancient logics, there are gaps, it may be demonstrated that the ancient logics contain the principle of explosion. (shrink)

We present how the theory of reasoning developed by Tadeusz Czeżowski, a Polish logician and a member of the Lvov-Warsaw School (LWS) can be applied to the mediaeval texts which interpret the Bible, which we collectively call as Biblical exegesis (BE). In the first part of the paper, we characterise Czeżowski's theory of reasoning with some modifications based on remarks of Kazimierz Ajdukiewicz. On these grounds, we discuss the nature of reasoning and its different types, as well as the problem (...) of textual representation of reasoning. In the second part, we describe the analytical nature of some BE at the end of twelfth century and in the thirteenth century by referring to the examples of Stephen Langton, Robert Grosseteste, Bonaventure, Albert the Great and Thomas Aquinas. We argue that they represented an analytical approach in BE, characterised by advanced use of logic and specific methods, including reasoning reconstruction and logical analysis. In the third part, we present selected examples to show how Czeżowski's framework helps in identifying various types of reasoning. We indicate some universal problems with the textual representation of reasoning found in the BE of the authors in question. Lastly, we point out how Czeżowski's framework enables the understanding of phenomena such as ‘Special Biblical Inference’. Thanks to this experiment, we can see how a framework as advanced as that offered by LWS representatives can be put to the test using mediaeval Biblical commentaries, yielding interesting results. (shrink)

Justification of theorems plays a vital role in any rational human activity. It is indispensable in science. The deductive method of justifying theorems is used in all sciences and it is the only method of justifying theorems in deductive disciplines. It is based on the notion of proof, thus it is a method of proving theorems. In the Warsaw School of Logic (WSL) – the famous branch of the Lvov-Warsaw School (LWS) – two types of the method: axiomatic deduction method (...) and natural deduction method were developed and practiced. In this paper, both of these methods are briefly discussed with an emphasis on their historical, groundbreaking significance for logic. The axiomatic method by means of rejection (proposed by Jan Łukasiewicz – a co-creator of the WSL), which is the method of the so-called rejection proof (rejection/refutation method) in logical systems and the proving method of generalized natural deduction, which is a hybrid deduction–refutation method of proving theorems, are also outlined in the paper. The author discusses their historical significance. This paper also contains a brief mention of the most significant results which the application of the discussed methods introduced into contemporary scientific research, not only logical one. (shrink)

This paper advances a version of the theory whereby logic had deep origins in democracy, by re-reading Gorgias’ Encomium of Helen. Democracy, ‘the government by debate’, called political (and scientific) attention to the inferential abilities of citizens and to politicians’ ability of taking advantage of them. Sophists, in particular, discovered that people’s inferences follow constant repeatable forms, that these forms have impact on choices and decisions concerning public good, and then by dominating them you dominate politics in democracy. With the (...) Encomium Gorgias launched these ideas, so laying the ground for Aristotle’s science of deduction. (shrink)

The article illustrates the different meanings of the term “logic” in Weber's work and then proceeds to discuss his approach to the explanation of historical events and in particular to counterfactual analysis. Weber's epistemology is first situated within the neo-Kantian debates of his time as well as legal positivism and historical jurisprudence. The article then focuses on this author's conception of science as a value sphere, on the aims and methods of explanation in the social and historical sciences and on (...) the key concepts of possibility judgements and adequate causation. The central role played by counterfactuals and modal logic is illustrated through the example of the battle of Marathon, which Weber himself saw as the starting point of a causal chain leading to the rise of Western rationalism. The article concludes by highlighting the pioneering role of Weber's counterfactualism for the subsequent development of possible worlds theory and its use in the causal analysis of singular historical events. (shrink)

The paper is about the connection between logic and discrimination, with special focus on Plumwood’s ideas in her groundbreaking article ‘The Politics of Reason. Towards a Feminist Logic’ (1993). Although Plumwood’s paper is not focused on the notion of discrimination, what she writes is useful for illuminating some basic mechanisms of thought that are at the basis of discriminatory practices. After an introductory section about the concepts of logic and discrimination and their possible interconnections, I present Plumwood’s ideas in 1993 (...) with a special focus on their relevance for understanding the nature of discrimination. More specifically, I use examples of discriminatory practices that make the connection between logical operations and oppression envisaged by Plumwood clear. I focus especially on two questions: Can logic produce discrimination? Can logic contribute to the fight against discrimination? If so, how? (shrink)

The focus of the article is the notion of normativity in logic and politics and their possible intersections. The twentieth-century divide between the analytical and the continental idea of logic is explored, by noting that they both – with significant differences – can be seen as proposing a ‘bottom-up normativity’, which may have immediate political effects. Logical normativity postulates universality, and a connection between reality and reason able to orient actions universalistically. For a bottom-up conception (as specifically advanced by Deleuze’s (...) logic of sense), the universalistic approach does not descend from above on an elusive reality but is a self-organization of multiple processes occurring in a horizon which is typically affected by political facts and choices. (shrink)

‘Feminist logic’ may sound like an impossible, incoherent, or irrelevant project, but it is none of these. We begin by delineating three categories into which projects in feminist logic might fall: philosophical logic, philosophy of logic, and pedagogy. We then defuse two distinct objections to the very idea of feminist logic: the irrelevance argument and the independence argument. Having done so, we turn to a particular kind of project in feminist philosophy of logic: Valerie Plumwood's feminist argument for a relevance (...) logic. Plumwood's work serves as our primary case study as we turn to the project of considering three different ways we might understand her argument and revisionist arguments like it: as a priori theorizing, as ameliorative conceptual engineering, or as instances of anti-exceptionalist approaches to logic. After arguing that the anti-exceptionalist approach seems to provide the most promising means of understanding the kind of project undertaken in a feminist challenge to classical logic, we briefly address the consequences that this might have for logic instruction. Here, we argue for the perhaps unexpected conclusion that feminist programs ought to offer more, not less, instruction in logic for those who take interest. (shrink)

The paper examines the interplays between logic and politics in the Polish School of Logic starting from 1914. The Polish School of Logic flourished between 1920 and 1939. Philosophically, it was influenced by Kazimierz Twardowski (1866–1938). For Twardowski logic is fundamental for every kind of human activity, professional and private and this means that every argument should be formulated and proceed by correct inferential rules. These rules involve semiotics, formal logic and methodology of science. The paper shows how this position (...) was shared by Twardowski’s students, including Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz and Tadeusz Kotrabiński, as well as by the next generation of logicians and philosophers and especially by Alfred Tarski. These authors considered logic, philosophy and science as completely neutral with respect to politics and ideology but they also considered logical skills as indispensable in political activities. (shrink)

Reasoning with diagrams is considered to be a peculiar form of reasoning. Diagrams are often associated with imagistic representations conveyed by spatial arrangements of lines, points, figures, or letters that can be manipulated to obtain knowledge on a subject matter. Reasoning with diagrams is not just ‘peculiar’ because reasoners use spatially arranged characters to obtain knowledge – diagrams apparently have cognitive surplus: they enable a quasi-intuitive form of knowledge. The present paper analyses the issue of diagrams’ cognitive value by enquiring (...) into the tradition of symbolic cognition developed by Leibniz, Lambert, and Kant. The proposal resulting from this enquiry is to question the idea that the cognitive value of diagrams lies solely in allowing evidence for inferences. The imaginative dimension of diagrams connects reasoning to doxastic attitudes of meditation and enquiry. (shrink)