Logic in Early Modern Thought (original) (raw)

Frege’s relation to Aristotle and the emergence of modern logic

Bloomsbury Academic eBooks, 2023

Gottlob Frege's works are o en taken to mark the beginning of modern logic. More speci cally, the year 1879, when Frege's Begri sschri was published, is seen as witnessing its birth. 'Modern logic' is here contrasted with traditional Aristotelian logic, especially the theory of syllogism that is central for it. In this chapter, I will reconsider the transition from Aristotelian logic to modern logic in Frege's and related writings. I will con rm that Frege's works do, indeed, contain innovations that contributed to a radical transformation of logic. At the same time, I will argue that the story of that transformation is complex, including the fact that Frege's works contain remnants of Aristotelian ideas that make it not fully modern. e chapter will proceed as follows: In Section 1, I will start with several claims that the publication of Begri sschri constituted a 'revolution' in logic, while noting some immediate challenges to that claim as well. In Section 2, I will turn to Frege's central logical innovations and to logicism as the driving force behind them. Next, I will consider Frege's relationship to Aristotle, both in terms of Aristotelian views Frege rejected explicitly, in Section 3, and features that still tie him to Aristotle's model of science implicitly, in Section 4. In Section 5, nally, I will reconsider the ways in which Frege's contributions were crucial for a 'second birth' of logic, including by being articulated further in the works of later logicians. 1 A Fregean revolution in logic? Since the 1950-1960s, the publication of Frege's Begri sschri has o en been seen as the start of modern, post-Aristotelian logic. Crucial roles in assigning a central part to Frege were played by Alonzo Church, W. V. O. Quine and J. v. Heijenoort. As Quine wrote in 1952, '[l]ogic is only now emerging from a renaissance such as was undergone by physics centuries ago. […] e logical renaissance might be identi ed with the publication of Frege's Begri sschri in 1879'. 1 Or more pointedly in Quine's Methods of Logic (1950): 'Logic is an old subject, but since 1879 it has been a great one. ' 2 e same perspective shapes Jean van Heijenoort's in uential collection, From Frege to Gödel: A

Logic in Seventeenth-Century Scottish Academic Philosophy

Scottish Philosophy in the Seventeenth Century, Edited by Alexander Broadie (OUP), 2020

For a seventeenth-century Scottish regent, logic was preliminary to all other disciplines and secondary only to Latin. Logic was the trait-d’union between natural language (Latin, grammar, classical literature, the Bible) and the technical philosophical jargon. Logic was also important for theology and apologetics. Until the 1650s, logic is scholastic, centred on the trivium of logic, rhetoric, and grammar. The influence of Humanism, especially Ramism, is visible in the importance of induction, the treatment of method as a branch of logic, the orientation of logic towards practical tasks. Later in the century, alongside Aristotle, the key figures are René Descartes and Francis Bacon. The ‘old’ Aristotelian logic is made compatible with the ‘new’ method for the acquisition of new truths developed from Cartesian and Baconian insights. The reception of Descartes and Bacon has a common root in scholastic empiricism.

THE HISTORICAL SYNTAX OF PHILOSOPHICAL LOGIC

European philosophical and historical discourse, 2022

This article analyzes the historical development of the philosophical logic syntax from the standpoint of the unity of historical and logical methods. According to this perspective, there are three types of logical syntax: the elementary subject-predicate, the modified definitivespecificative, and the standard propositional-functional. These types are generalized in the grammatical and mathematical styles of logical syntax. The main attention is paid to two scientific revolutions in elementary subject-predicate syntax, which led to the emergence of modified definitive-specific and standard propositional-functional syntaxes and created the syntactic conditions for the development of contemporary philosophical logic. The specifics of contemporary philosophical logic and the methodological possibilities of its application to philosophical discourse are studied. The article aims to reevaluate the undeservedly forgotten systems of philosophical logic of the continental tradition, created by such prominent representatives as Aristotle, G.W.F. Hegel, and E. Husserl, and to actualize these logics in the context of contemporary philosophical culture. The potential of the above-mentioned logics is not fully involved in the philosophical discourse of modernity, primarily because they primarily used an imperfect elementary subject-predicate syntax and modified definitive-specificative syntax as its slightly improved version. Both syntaxes have one thing in common: the grammatical style of sentence structure. Nevertheless, they also have one common flaw-a high dependence on grammar formalism. As a result, the interaction between these syntaxes and Frege's standard propositional-functional syntax is impossible, because the latter is based on mathematical formalism, which operates on the philosophical logic of the analytic tradition. The article substantiates the way to solve this problem by constructing a modified subject-predicate syntax of contemporary philosophical logic. This syntax provides information interaction between Aristotle's elementary subject-predicate syntax, and Frege's standard propositional-functional syntax based on Hegel's modified definitive-specificative syntax. The proposed solution to this problem can create new opportunities for complementarity and mutual enrichment between the philosophical logic of continental and analytical traditions. The theoretical basis for the construction and study of contemporary philosophical logic is a functional analysis of contemporary symbolic logic, which improves the grammatical analysis of traditional formal logic. Functional-grammatical analysis is a way to rehabilitate the philosophical logic of the continental tradition. The novelty of this paper lies in the substantiation of the modified subjectpredicate syntax of contemporary philosophical logic. It makes it possible to establish a dialogue between continental and analytical traditions, which is designed to promote the further development of philosophy.