---
title: "History of logic"
chunk: 7/13
source: "https://en.wikipedia.org/wiki/History_of_logic"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:59:53.898187+00:00"
instance: "kb-cron"
---

=== Logic and psychology ===
Between the work of Mill and Frege stretched half a century during which logic was widely treated as a descriptive science, an empirical study of the structure of reasoning, and thus essentially as a branch of psychology. The German psychologist Wilhelm Wundt, for example, discussed deriving "the logical from the psychological laws of thought", emphasizing that "psychological thinking is always the more comprehensive form of thinking." This view was widespread among German philosophers of the period:

Theodor Lipps described logic as "a specific discipline of psychology".
Christoph von Sigwart understood logical necessity as grounded in the individual's compulsion to think in a certain way.
Benno Erdmann argued that "logical laws only hold within the limits of our thinking".
Such was the dominant view of logic in the years following Mill's work. This psychological approach to logic was rejected by Gottlob Frege. It was also subjected to an extended and destructive critique by Edmund Husserl in the first volume of his Logical Investigations (1900), an assault which has been described as "overwhelming". Husserl argued forcefully that grounding logic in psychological observations implied that all logical truths remained unproven, and that skepticism and relativism were unavoidable consequences.
Such criticisms did not immediately extirpate what is called "psychologism". For example, the American philosopher Josiah Royce, while acknowledging the force of Husserl's critique, remained "unable to doubt" that progress in psychology would be accompanied by progress in logic, and vice versa.

== Rise of modern logic ==
The period between the fourteenth century and the beginning of the nineteenth century had been largely one of decline and neglect, and is generally regarded as barren by historians of logic. The revival of logic occurred in the mid-nineteenth century, at the beginning of a revolutionary period where the subject developed into a rigorous and formalistic discipline whose exemplar was the exact method of proof used in mathematics. The development of the modern "symbolic" or "mathematical" logic during this period is the most significant in the 2000-year history of logic, and is arguably one of the most important and remarkable events in human intellectual history.
A number of features distinguish modern logic from the old Aristotelian or traditional logic, the most important of which are as follows: Modern logic is fundamentally a calculus whose rules of operation are determined only by the shape and not by the meaning of the symbols it employs, as in mathematics. Many logicians were impressed by the "success" of mathematics, in that there had been no prolonged dispute about any truly mathematical result. C. S. Peirce noted that even though a mistake in the evaluation of a definite integral by Laplace led to an error concerning the moon's orbit that persisted for nearly 50 years, the mistake, once spotted, was corrected without any serious dispute. Peirce contrasted this with the disputation and uncertainty surrounding traditional logic, and especially reasoning in metaphysics. He argued that a truly "exact" logic would depend upon mathematical, i.e., "diagrammatic" or "iconic" thought. "Those who follow such methods will ... escape all error except such as will be speedily corrected after it is once suspected". Modern logic is also "constructive" rather than "abstractive"; i.e., rather than abstracting and formalising theorems derived from ordinary language (or from psychological intuitions about validity), it constructs theorems by formal methods, then looks for an interpretation in ordinary language. It is entirely symbolic, meaning that even the logical constants (which the medieval logicians called "syncategoremata") and the categoric terms are expressed in symbols.

== Modern logic ==

The development of modern logic falls into roughly five periods:

The embryonic period from Leibniz to 1847, when the notion of a logical calculus was discussed and developed, particularly by Leibniz, but no schools were formed, and isolated periodic attempts were abandoned or went unnoticed.
The algebraic period from Boole's Analysis to Schröder's Vorlesungen. In this period, there were more practitioners, and a greater continuity of development.
The logicist period from the Begriffsschrift of Frege to the Principia Mathematica of Russell and Whitehead. The aim of the "logicist school" was to incorporate the logic of all mathematical and scientific discourse in a single unified system which, taking as a fundamental principle that all mathematical truths are logical, did not accept any non-logical terminology. The major logicists were Frege, Russell, and the early Wittgenstein. It culminates with the Principia, an important work which includes a thorough examination and attempted solution of the antinomies which had been an obstacle to earlier progress.
The metamathematical period from 1910 to the 1930s, which saw the development of metalogic, in the finitist system of Hilbert, and the non-finitist system of Löwenheim and Skolem, the combination of logic and metalogic in the work of Gödel and Tarski. Gödel's incompleteness theorem of 1931 was one of the greatest achievements in the history of logic. Later in the 1930s, Gödel developed the notion of set-theoretic constructibility.
The period after World War II, when mathematical logic branched into four inter-related but separate areas of research: model theory, proof theory, computability theory, and set theory, and its ideas and methods began to influence philosophy.

=== Embryonic period ===