Book contents
- The Cambridge Companion to Ancient Logic
- Other Volumes in the Series of Cambridge Companions
- The Cambridge Companion to Ancient Logic
- Copyright page
- Contents
- Contributors
- Introduction
- I The Development of Logic in Antiquity
- II Key Themes
- 5 Truth as a Logical Property and the Laws of Being True
- 6 Definition
- 7 Terms and Propositions
- 8 Validity and Syllogism
- 9 Demonstration
- 10 Modalities and Modal Logic
- 11 Fallacies and Paradoxes
- 12 Logic in Ancient Rhetoric
- 13 Ancient Logic and Ancient Mathematics
- III The Legacy of Ancient Logic
- Bibliography
- Abbreviations
- Index of Passages
- General Index
- Other Volumes in the Series of Cambridge Companions
10 - Modalities and Modal Logic
from II - Key Themes
Published online by Cambridge University Press: 29 April 2023
- The Cambridge Companion to Ancient Logic
- Other Volumes in the Series of Cambridge Companions
- The Cambridge Companion to Ancient Logic
- Copyright page
- Contents
- Contributors
- Introduction
- I The Development of Logic in Antiquity
- II Key Themes
- 5 Truth as a Logical Property and the Laws of Being True
- 6 Definition
- 7 Terms and Propositions
- 8 Validity and Syllogism
- 9 Demonstration
- 10 Modalities and Modal Logic
- 11 Fallacies and Paradoxes
- 12 Logic in Ancient Rhetoric
- 13 Ancient Logic and Ancient Mathematics
- III The Legacy of Ancient Logic
- Bibliography
- Abbreviations
- Index of Passages
- General Index
- Other Volumes in the Series of Cambridge Companions
Summary
Ever since the beginnings of philosophical thought in Greek antiquity, philosophers have made use of modalities. In particular, the concepts of necessity and ‘what must be’ played an important role in Pre-Socratic thought.1 For example, Anaximander maintained that things perish into that from which they came to be ‘in accordance with what must be’ (kata to chreōn).2 Heraclitus held that ‘everything comes about in accordance with strife and what must be (kat’ erin kai chreōn)’.3 In his poem, Parmenides asserts that what is (to eon) is entirely still and changeless because ‘powerful Necessity (Anankē) holds it in the bonds of a limit, which encloses it all around’.4 Among the atomists, Democritus identified necessity with a whirl of atoms, holding that ‘everything comes about in accordance with necessity, inasmuch as the whirl – which he calls necessity – is the cause of the coming about of all things’.5 Finally, Plato in the Timaeus describes the creation of the cosmos as the result of the interplay between divine demiurgic Intelligence and natural Necessity.6
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- The Cambridge Companion to Ancient Logic , pp. 216 - 235Publisher: Cambridge University PressPrint publication year: 2023
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