Boole’s Untruth Tables
The Formal Conditions of Meaning Before the Emergence of Propositional Logic
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Date
2022
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Book Chapter
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yes
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Abstract
This paper looks into what can reasonably be regarded as truth-table devices in one of Boole’s late manuscripts, as a way of ad- dressing Boole’s relation to modern propositional logic. A careful in- vestigation of the divergences between those table devices and our cur- rent conception of truth tables offers an opportunity to reassess the singularity of Boole’s logical system, especially concerning the relation between its linguistic and mathematical aspects. The paper explores Boole’s conception of the compositional structure of symbolic expres- sions, the genesis of table devices from his method of development into normal forms, and the non-logical origin of the constants 0 and 1 as dual terms. Boole’s system of logic is in this way shown to be chiefly concerned with the problem of the formal interpretability conditions of symbolic expressions, rather than with the truth conditions of logical propositions.
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published
Book title
Logic in Question: Talks from the Annual Sorbonne Logic Workshop (2011–2019)
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Pages / Article No.
119 - 149
Publisher
Birkhäuser
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Software
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Subject
George Boole; Truth tables; Propositional Logic; Interpretability; Dual algebra; Boolean algebra; Compositionality; Series expansions; Method of development
Organisational unit
09591 - Wagner, Roy / Wagner, Roy