8942
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Lukasiewicz's L3 logic has three truth-values, T, F and I (for 'indeterminate') [Lukasiewicz, by Fisher]
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Full Idea:
In response to Aristotle's sea-battle problem, Lukasiewicz proposed a three-valued logic that has come to be known as L3. In addition to the values true and false (T and F), there is a third truth-value, I, meaning 'indeterminate' or 'possible'.
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From:
report of Jan Lukasiewicz (Elements of Mathematical Logic [1928], 7.I) by Jennifer Fisher - On the Philosophy of Logic
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A reaction:
[He originated the idea in 1917] In what sense is the third value a 'truth' value? Is 'I don't care' a truth-value? Or 'none of the above'? His idea means that formalization doesn't collapse when things get obscure. You park a few propositions under I.
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9463
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Classical logic is bivalent, has excluded middle, and only quantifies over existent objects [Jacquette]
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Full Idea:
Classical logic (of Whitehead, Russell, Gödel, Church) is a two-valued system of propositional and predicate logic, in which all propositions are exclusively true or false, and quantification and predication are over existent objects only.
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From:
Dale Jacquette (Intro to I: Classical Logic [2002], p.9)
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A reaction:
All of these get challenged at some point, though the existence requirement is the one I find dubious.
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