# Logic as calculus and logic as language

@article{Heijenoort2004LogicAC, title={Logic as calculus and logic as language}, author={Jean van Heijenoort}, journal={Synthese}, year={2004}, volume={17}, pages={324-330} }

Answering SchrSder's criticisms of Begriffsschrift, Frege states that, unlike Boole's, his logic is not a calculus ratiocinator, or not merely a calculus ratiocinator, but a lingua charactericaJ If we come to understand what Frege means by this opposition, we shall gain a useful insight into the history of logic. Before settling down to this task, I would like to review, or rather simply enumerate, Frege's contributions to logic, in order to provide the proper background for our discussion… Expand

#### 52 Citations

Calculus as method or calculus as rules? Boole and Frege on the aims of a logical calculus

- Synthese
- 2021

By way of a close reading of Boole and Frege’s solutions to the same logical problem, we highlight an underappreciated aspect of Boole’s work—and of its difference with Frege’s better-known… Expand

LINGUA CHARACTERICA AND CALCULUS RATIOCINATOR: THE LEIBNIZIAN BACKGROUND OF THE FREGE-SCHRÖDER POLEMIC

- Computer Science, Philosophy
- The Review of Symbolic Logic
- 2020

It is argued that Frege’s project of constructing a lingua characterica was not tied to his later logicist programme, more being seen by Frege as a tool that could be applied to scientific disciplines. Expand

STUDIES IN LOGIC, GRAMMAR AND RHETORIC 4 (17) 2001

- 2011

Logic as a formal mathematical theory is interesting in itself. It poses problems, like any other body of knowledge. Some of them, especially questions concerning axiomatization, consistency,… Expand

Preface of an Anthology of Universal Logic

- 2012

This book is a retrospective on universal logic in the 20th century. It gathers papers and book extracts in the spirit of universal logic from 1922 to 1996. Each of the 15 items is presented by a… Expand

The Versatility of Universality in Principia Mathematica

- Philosophy
- 2011

In this article, I examine the ramified-type theory set out in the first edition of Russell and Whitehead's Principia Mathematica. My starting point is the ‘no loss of generality’ problem: Russell,… Expand

A New–old Characterisation of Logical Knowledge

- Mathematics
- 2012

We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in… Expand

Calculus ratiocinator versus characteristica universalis? The two traditions in logic, revisited

- Mathematics
- 2004

It is a commonplace that in the development of modern logic towards its actual shape at least two directions or traditions have to be distinguished. These traditions may be called, following the… Expand

A completeness theorem for unrestricted first- order languages

- Mathematics
- 2003

Here is an account of logical consequence inspired by Bolzano and Tarski. Logical validity is a property of arguments. An argument is a pair of a set of interpreted sentences (the premises) and an… Expand

LOGICAL CONTEXTUALITY IN FREGE

- Computer Science, Mathematics
- The Review of Symbolic Logic
- 2018

A formal framework, based on the modern tool of fibrations, is set out to explain and justify Frege's universalism and to compare Frege and Tarski, by formalizing Frege’s suggestion and by presenting Tarskis’ semantics in a generalized setting. Expand

The Liar Paradox: A Consistent and Semantically Closed Solution

- Mathematics
- 2011

1 This thesis develops a new approach to the formal denition of a truth predicate that allows a consistent, semantically closed denition within classical logic. The approach is built on an analysis… Expand