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Series:   Elements in Philosophy and Logic

Free Logic

A Generalization

Published online by Cambridge University Press:  09 January 2025

Greg Frost-Arnold
Greg Frost-Arnold
Affiliation:
Hobart and William Smith Colleges

Summary

Classical logic assumes that names are univocal: every name refers to exactly one existing individual. This Principle of Univocality has two parts: an existence assumption and a uniqueness assumption. The existence assumption holds that every name refers to at least oneindividual, and the uniqueness assumption states that every name refers to at most one individual. The various systems of free logic which have been developed and studied since the 1960s relax the existence assumption, but retain the uniqueness assumption. The present work investigates violations of both halves of the Principle of Univocality. That is, whereas the free logics developed from the 1960s are called 'free' because they are free of existential assumptions, the current Element generalizes this idea, to study logics that are free of uniqueness assumptions. We explore several versions of free logic, comparing their advantages and disadvantages. Applications of free logic to other areas of philosophy are explored.
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Keywords

free logicconfusionambiguityexistenceMeinongianism
Type
Element
Information
Series: Elements in Philosophy and Logic
Online ISBN: 9781009122764
Publisher: Cambridge University Press
Print publication: 30 January 2025

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