19th Century Logic

volumes of his work, in his discussions of what underlay a Wissenschaftslehre or theory of science in the sense of his conception; he did so with such purity and scientific strictness, and with such a rich store of original, scientifically confirmed and fruitful thoughts, that we must count him as one of the greatest logicians of all time. He must be placed historically in fairly close proximity to Leibniz, with whom he shares important thoughts and fundamental conceptions, and to whom (...) he is also philosophically akin in other respects.". (shrink)

Celebrated today for his groundbreaking work in logic and the foundations of mathematics, Bernard Bolzano was best known in his own time as a leader of the reform movement in his homeland . As professor of religious science at the Charles University in Prague from 1805 to 1819, Bolzano was a highly visible public intellectual, a courageous and determined critic of abuses in Church and State. Based in large part on a carefully argued utilitarian practical philosophy, he developed a non-violent (...) program for the reform of the authoritarian institutions of the Empire, which he himself set in motion through his teaching and other activities. Rarely has a philosopher had such a great impact on the political culture of his homeland. This volume contains a substantial collection of Bolzano's writings on ethics and politics, translated into English for the first time. It includes a complete translation of the treatise On the Best State, his principal writings on ethics, an essay on the contemporary situation in Ireland, and a selection of his Exhortations, dealing with such topics as enlightenment, civil disobedience, the status of women, anti-Semitism and Czech-German relations in Bohemia. It will be of particular interest to students of central European philosophy and history, and more generally to philosophers and historians of ideas. (shrink)

It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively sufficient as far as the first-order completeness is concerned. (...) In this short note we confirm that the missing axiom is derivable from his stated axioms and inference rules, and hence the logic system in the Begriffsschrift is indeed first-order complete. (shrink)

This volume collects nine essays that investigate the work of Gottlob Frege. The contributors address Frege’s work in relation to literature and fiction (Dichtung), the humanities (Geisteswissenschaften), and science (Wissenschaft). Overall, the essays consider internal connections between different aspects of Frege’s work while acknowledging the importance of its philosophical context. -/- There are also further common strands between the papers, such as the relation between Frege’s and Wittgenstein’s approaches to philosophical investigations, the relation between Frege and Kant, and the place (...) of Frege’s work in the philosophical landscape more generally. The volume is therefore of direct relevance to several current debates in philosophy in general, in addition to Frege and Wittgenstein research in particular. -/- Even though Frege’s great significance for contemporary philosophy is not disputed, the question of how we are to understand the character and aims of his project is debated. The debate has a starting point in Frege’s specific conception of logic. The volume elucidates this conception as well as the relation between natural language and the Begriffsschrift. It will help philosophers, researchers, and students better understand the nuances of this great thinker. By extension, it will also help readers seeking to understand Wittgenstein’s approach to philosophical difficulties and his struggle to find an apt form of presentation for his philosophical investigations. (shrink)

There are a lot of studies on Ahmed Cevdet Paşa who has been considered as statesman, politician, jurist, historian, sociologist and educationalist. At the same time Ahmet Cevdet Paşa’s studies on logic are critically important when we deal with the last period of the Ottoman Empire. His book which is called Miyar-ı Sedad had both influenced the development of instruction of logic education in madrasahs and created a turning point in the studies on modern logic. For this reason we have (...) discussed his opinions about logic and science in this study and we have also tried to show that how his opinions on these issues affecected the instruction and the other fields. (shrink)

Contemporary orthodoxy affirms that singular terms cannot be predicates and that, therefore, ‘is’ is ambiguous as between predication and identity. Recent attempts to treat names as predicates do not challenge this orthodoxy. The orthodoxy was built into the structure of modern formal logic by Frege. It is defended by arguments which I show to be unsound. I provide a semantical account of atomic sentences which draws upon Mill's account of predication, connotation and denotation. I show that singular terms may be (...) predicates, that it is highly implausible that there is an ‘is’ of identity in natural languages, and that modern formal logic is deficient in that it cannot recognize sentences, including singular existentials, in which singular terms are predicates, or inferences which depend upon the logical role rather than the logical category of expressions. (shrink)

Os grafos existenciais (GE) são uma notação lógica de caráter topológico e estão entre as mais originais invenções de C.S. Peirce (1839-1914). Trata-se de um sistema gráfico de diagramas lógicos por meio do qual, segundo Peirce, “qualquer desenvolvimento do pensamento pode ser representado com precisão” (CP 4.530). Eles se dividem em três subsistemas – alfa, beta e gama –, aproximadamente equivalentes ao cálculo proposicional clássico, ao cálculo de predicados clássico de primeira ordem, e a um tipo de lógica modal. Nosso (...) propósito é apresentar o sistema beta. O que apresentaremos se restringe ao cálculo de predicados monádicos, com ênfase na silogística categórica de Aristóteles. (shrink)

The “sign of consequence” is a notation for propositional logic that Peirce invented in 1886 and used at least until 1894. It substituted the “copula of inclusion” which he had been using since 1870.

I review Stefan Roski's "Bolzano's Conception of Grounding".

We discuss the many aspects and qualities of the number one: the different ways it can be represented, the different things it may represent. We discuss the ordinal and cardinal natures of the one, its algebraic behaviour as a neutral element and finally its role as a truth-value in logic.

This is a collection of new investigations and discoveries on the theory of opposition (square, hexagon, octagon, polyhedra of opposition) by the best specialists from all over the world. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic.

In this pa­per we aim to pin­po­int so­me of the key mar­kers of the de­velop­ment of lo­gic in Ser­bia, star­ting from the fo­un­ding of the Lyce­um in 1836 un­til the end of the 19th cen­tury. Our main goal is to un­der­li­ne the ro­le that Lju­bo­mir Ne­dić, a phi­lo­sop­her and li­te­rary cri­tic, had in this con­text. Alt­ho­ugh he did not le­a­ve any ori­gi­nal con­tri­bu­ti­ons in lo­gic, Ne­dić played a sig­ni­fi­cant part by ex­po­sing con­tem­po­rary re­sults in symbo­lic lo­gic, which we­re to lead, (...) thro­ugh Fre­ge’s la­ter work, to the cre­a­tion of mo­dern lo­gic. (shrink)

Panorama of the concept of logic century-by-century since Aristotle.

The development of symbolic logic is often presented in terms of a cumulative story of consecutive innovations that led to what is known as modern logic. This narrative hides the difficulties that this new logic faced at first, which shaped its history. Indeed, negative reactions to the emergence of the new logic in the second half of the nineteenth century were numerous and we study here one case, namely logic at Oxford, where one finds Lewis Carroll, a mathematical teacher who (...) promoted symbolic logic, and John Cook Wilson, the Wykeham Professor of Logic who notoriously opposed it. An analysis of their disputes on the topic of logical symbolism shows that their opposition was not as sharp as it might look at first, as Cook Wilson was not so much opposed to the « symbolic » character of logic, but the intrusion of mathematics and what he perceived to be the futility of some of its problems, for logicians and philosophers alike. (shrink)

Symbolic logic faced great difficulties in its early stage of development in order to acquire recognition of its utility for the needs of science and society. The aim of this paper is to discuss an early attempt by the British logician Lewis Carroll (1832–1898) to promote symbolic logic as a social good. This examination is achieved in three phases: first, Carroll’s belief in the social utility of logic, broadly understood, is demonstrated by his numerous interventions to fight fallacious reasoning in (...) public debates. Then, Carroll’s attempts to promote symbolic logic, specifically, are revealed through his work on a treatise that would make the subject accessible to a wide and young audience. Finally, it is argued that Carroll’s ideal of logic as a common good influenced the logical methods he invented and allowed him to tackle more efficiently some problems that resisted to early symbolic logicians. (shrink)

This paper is mainly a response to Charles Morgan's criticisms (this journal, pp. 511-25) of the author's model of the (formal aspects of) explanation. It is claimed in the paper that with two modifications and some additional specifications the model withstands Morgan's criticisms.