PHLA10H3 Lecture Notes - Lecture 3: Necessity And Sufficiency, Possible World, Alf Landon
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Deductive arguments conditionals: basic argument structure: Note we defined validity using a conditional: valid vs invalid conditionals. X > y; therefore y : valid. X > y; therefore x : invalid affirming the consequent. If all squares are rectangles, then all rectangles are squares. X> y, not-x; therefore not-y : invalid denying the antecedent. X>y, not-y; therefore not-x : valid: necessary vs sufficient conditions. Given if x then y , x is a sufficient condition for y. Given if x then y , y is a necessary condition for x. A necessary condition must be present to produce/sustain an outcome. A necessary condition: oxygen in the room. However, oxygen is not sufficient to match the light. It doesn"t guarantee that the match will spontaneously light. Sufficient condition for death: brain shutting down; not a necessary condition. Sufficient condition: the political party you lead must gain the most votes. Problem: more than one system of sentences can be coherent (ex.
