Leibniz's laws of consistency and the philosophical foundations of connexive logic
DOI:
https://doi.org/10.12775/LLP.2019.004Słowa kluczowe
connexive logic, Leibniz’s logic, term logic vs. propositional logicAbstrakt
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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