# Traditional Logic, Modern Logic and Natural Language

@article{Hodges2009TraditionalLM, title={Traditional Logic, Modern Logic and Natural Language}, author={Wilfrid Hodges}, journal={Journal of Philosophical Logic}, year={2009}, volume={38}, pages={589-606} }

In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e…

## 17 Citations

Mill on logic

- Philosophy
- 2017

: Working within the broad lines of general consensus that mark out the core features of John Stuart Mill’s (1806–1873) logic, as set forth in his A System of Logic (1843–1872), this chapter provides…

THE FORMAL AND THE FORMALIZED: THE CASES OF SYLLOGISTIC AND SUPPOSITION THEORY

- Philosophy
- 2015

As a discipline, logic is arguably constituted of two main sub-projects: formal theories of argument validity on the basis of a small number of patterns, and theories of how to reduce the…

Sı̄nā ’ s view of the practice of logic

- Philosophy
- 2010

In the last half century Ibrahim Madkour revolutionised the study of Arabic logic by making available a modern edition of the text of the Logic section of Ibn Sı̄nā’s Šifā’. Ibn Sı̄nā’s account of…

on analysis. Proof search. Abstract machines as a tool for history of logic.

- Computer Science
- 2022

The 11th century Arabic-Persian logician Ibn Sīnā (Avicenna) in Section 9.6 of his book Qiyās gives what appears to be a proof search algorithm for syllogisms, which is confirmed by extracting all the essential ingredients of an abstract state machine from Ibn Sínā’s text.

HISTORY OF LOGICAL CONSEQUENCE

- Philosophy
- 2012

Consequence is a, if not the, core subject matter of logic. Aristotle’s study of the syllogism instigated the task of categorising arguments into the logically good and the logically bad; the task…

Ibn Sina on Analysis: 1. Proof Search. Or: Abstract State Machines as a Tool for History of Logic

- Computer Science, PhilosophyFields of Logic and Computation
- 2010

The 11th century Arabic-Persian logician Ibn Sīnā (Avicenna) in Sect. 9.6 of his book Qiyās gives what appears to be a proof search algorithm for syllogisms. We confirm that it is indeed a proof…

The Move from One to Two Quantifiers

- Philosophy
- 2015

Ibn Sīnā (Persian, 980–1037) made a dramatic extension to Aristotle’s syllogistic by adding quantifiers over times or situations, thus introducing multiple and mixed quantification. The extension is…

David Makinson and the extension of classical logic

- Philosophy
- 2014

David Makinson has a leading role as proponent of the inferential-preferential method in which classical logic is combined with representations of preference or choice, which has turned out to be a highly efficient and versatile method.

Proofs as Cognitive or Computational: Ibn Sı̄nā’s Innovations

- Philosophy
- 2018

We record the advances made by the eleventh century Persian logician Ibn Sina—known in the West as Avicenna—away from a purely cognitive view of proofs and towards a more computational view, and the…

Formal Languages in Logic: A Philosophical and Cognitive Analysis

- Philosophy
- 2012

This book discusses the history, purposes and limitations of formal languages, and how to do reason, and the need for counterbalance in science.

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