### Single Idea 9520

#### [catalogued under 5. Theory of Logic / B. Logical Consequence / 8. Material Implication]

Full Idea

The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q. That is, since Napoleon was French, then if the moon is blue then Napoleon was French; and since Napoleon was not Chinese, then if Napoleon was Chinese, the moon is blue.

Gist of Idea

The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q

Source

E.J. Lemmon (Beginning Logic [1965], 2.2)

Book Reference

Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.60

A Reaction

This is why the symbol → does not really mean the 'if...then' of ordinary English. Russell named it 'material implication' to show that it was a distinctively logical operator.