Leibniz's laws of consistency and the philosophical foundations of connexive logic
DOI:
https://doi.org/10.12775/LLP.2019.004Keywords
connexive logic, Leibniz’s logic, term logic vs. propositional logicAbstract
As an extension of the traditional theory of the syllogism, Leibniz’s algebra of concepts is built up from the term-logical operators of conjunction, negation, and the relation of containment.
Leibniz’s laws of consistency state that no concept contains its own negation, and that if concept A contains concept B, then A cannot also contain Not-B. Leibniz believed that these principles would be universally valid, but he eventually discovered that they have to be restricted to self-consistent concepts.
This result is of utmost importance for the philosophical foundations of connexive logic, i.e. for the question how far either “Aristotle’s Thesis”, ¬(α → ¬α), or “Boethius’s Thesis”, (α → β) → ¬(α → ¬β), should be accepted as reasonable principles of a logic of conditionals.
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