## Bulletin of Symbolic Logic

- Bull. Symbolic Logic
- Volume 5, Number 4 (1999), 433-450.

### 19th Century Logic between Philosophy and Mathematics

#### Abstract

The history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole's The Mathematical Analysis of Logic of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical development of logic, although logic is evidently one of the basic disciplines of philosophy. One needs only to recall some of the standard 19th century definitions of logic as, e.g., the art and science of reasoning (Whateley) or as giving the normative rules of correct reasoning (Herbart). In the paper the relationship between the philosophical and the mathematical development of logic will be discussed. Answers to the following questions will be provided: 1. What were the reasons for the philosophers' lack of interest in formal logic? 2. What were the reasons for the mathematicians' interest in logic? 3. What did "logic reform" mean in the 19th century? Were the systems of mathematical logic initially regarded as contributions to a reform of logic? 4. Was mathematical logic regarded as art, as science or as both?

#### Article information

**Source**

Bull. Symbolic Logic, Volume 5, Number 4 (1999), 433-450.

**Dates**

First available in Project Euclid: 20 June 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.bsl/1182353650

**Mathematical Reviews number (MathSciNet)**

MR1792357

**Zentralblatt MATH identifier**

0941.03002

**JSTOR**

links.jstor.org

**Keywords**

History of Logic Algebra of Logic Mathematical and Philosophical Context of the Emergence of Symbolic Logic Quantification of the Predicate Logic and Metaphysics The Logical Question Psychologism Symbolical Algebra, Calculus of Operations Combinatorial Algebra Inductive Logic Reception of Symbolic Logic

#### Citation

Peckhaus, Volker. 19th Century Logic between Philosophy and Mathematics. Bull. Symbolic Logic 5 (1999), no. 4, 433--450. https://projecteuclid.org/euclid.bsl/1182353650