Historians of logic often distinguish between two traditions in symbolic logic at the turn of the twentieth century: the 'algebra of logic' or 'algebraic logic', on the one hand, and 'mathematical logic' or 'logistic', on the other hand. Moreover, many scholars have claimed that logistic instigated a 'Fregean revolution' in logic that has rendered the algebra of logic obsolete. In this paper, I problematize this common conception of a Fregean revolution by focusing on the work of Louis Couturat (1868-1914). First, I draw on the work of Couturat to illustrate that the question of what logical system one regards as most fruitful, crucially depends on one's underlying conception of the aims of logical symbolism as such. Second, I use Couturat as a counterexample to the common conception of a Fregean revolution. I argue that Couturat's logistic synthesized Russell's logic and algebraic logic. The motivation behind this synthesis was the realization that both Russell's logic and algebraic logic were fundamentally flawed as they only partially fulfilled the aims of logic as understood by Couturat. I conclude by raising further questions on the proclaimed independency of logistic from the algebra of logic.
Suppose we're at a horserace, and you turn to me and say, 'Eclipse is at the finish line!' But by the time you've finished saying this - by the time your utterance is complete - Eclipse is already well past the finish line, and what you've said is no longer true. But you did say something true. More generally, we can - and often do - say true things about events that take up less time than our utterances themselves. We can also contradict each other about such events - something that takes even more time. How is all this possible? In the twentieth century, this problem was discussed by Arthur Prior. In the 14th, John Buridan treated an older - probably twelfth-century - version of it. Buridan's treatment is more successful than Prior's, which runs into Zeno's paradox of the arrow. Buridan avoids the paradox, but faces further puzzles for his account of contradiction. In untangling these, we'll uncover important latent features of his pragmatics and temporal logic - features that are supported by more recent research in linguistics. Ultimately, our considerations here will turn up new insight into the Gricean Cooperative Principle. In a slogan: to contradict is to cooperate.
The paper examines and critically discusses the transition from Peirce's earlier Entitative Graphs (EntGs) to the later Existential Graphs (EGs). We explore the dual notions of denial and disjunction and examine their implications for the philosophy of logical notation. We investigate the sheet of assertion's role in both systems, the duality between conjunction and disjunction, and the implications of assertion's distribution over conjunction versus disjunction. Our study reveals Peirce's preference for EGs due to their naturalness and iconicity, despite the expressive equivalence of both systems. The paper concludes with philosophical reflections on the normativity of logic as illuminated by Peirce's early yet impactful contribution to the theory of graphical methods of logic and analysis.
Kazimierz Twardowski is the founder of the Lvov-Warsaw School, from which many outstanding logicians emerged, such as Jan & Lstrok;ukasiewicz, Stanis & lstrok;aw Le & sacute;niewski, and Alfred Tarski. Twardowski taught logic at this school from 1895 to 1926. Two volumes of various notes by Twardowski related to his lectures on logic delivered in Lvov have been published in Polish, and earlier his Viennese lectures on logic were also released. These documents constitute important material for studying the Lvov-Warsaw School and its founder. Historians and educators of logic, as well as proponents of a minimally formalized approach to logic, will also find them of interest. In this article, we will provide a general characterization of the edition and contents of the published notes for Twardowski's Lvov lectures related to broadly understood logic, and we will outline the following issues: Twardowski's understanding of logic, the state of research on it, and the question of the influence his approach to logic had on the scientific development of his students. We do not intend to discuss the full richness of the published documents.
The concept of 'ideology' is reconstructed as a disease affecting the use of logic in politics. The first section presents the paradox of the dead knower (the man who believed he was dead) as a paradigmatic case of ideological thought. In the second section, the focus is on Hannah Arendt's analysis of totalitarian ideologies (in Origins of Totalitarianism), which confirms what is suggested in the first section and gives a philosophical explanation of how 'ideological logic' works. The last section briefly considers the role of ideologies (in Arendt's sense) in infocratic-digitalized democracies.
