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Full Idea
In Weak Kleene Logic, with truth-value gaps, a sentence is neither true nor false if one of its components lacks a truth value. A line of the truth table shows a gap if there is a gap anywhere in the line, and the other lines are classical.
Gist of Idea
In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 18)
Book Ref
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.263
A Reaction
This will presumably apply even if the connective is 'or', so a disjunction won't be true, even if one disjunct is true, when the other disjunct is unknown. 'Either 2+2=4 or Lot's wife was left-handed' sounds true to me. Odd.
| 8942 | Lukasiewicz's L3 logic has three truth-values, T, F and I (for 'indeterminate') [Lukasiewicz, by Fisher] |
| 14263 | Strong Kleene disjunction just needs one true disjunct; Weak needs the other to have some value [Fine,K] |
| 21602 | Many-valued logics don't solve vagueness; its presence at the meta-level is ignored [Williamson] |
| 18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
| 8943 | Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher] |
| 16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
| 16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |