more from 'Elements of Mathematical Logic' by Jan Lukasiewicz

Single Idea 8942

[catalogued under 4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic]

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'.

Clarification

See Idea 1703 for the sea-battle

Gist of Idea

Lukasiewicz's L3 logic has three truth-values, T, F and I (for 'indeterminate')

Source

report of Jan Lukasiewicz (Elements of Mathematical Logic [1928], 7.I) by Jennifer Fisher - On the Philosophy of Logic

Book Reference

Fisher,Jennifer: 'On the Philosophy of Logic' [Thomson Wadsworth 2008], p.94


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.

Related Idea

Idea 1703 It is necessary that either a sea-fight occurs tomorrow or it doesn't, though neither option is in itself necessary [Aristotle]