Indicative and Material Conditional

The Material Conditional

• Aims to capture indicative conditional, 'if - then -' sentences
• False only when the antecedent is true, and the consequent is false
• Logically equivalent to ¬A v C, and ¬(A ^ ¬C).

Justifying the Truth Table

Edgington: Shape example ('If any shape is grey, it is also circular.')

Smith:  ¬AvC, and ¬(A^¬C) are both implied by and imply 'If A then C'

• If A then C rules out having A true, while C is false, so it implies ¬(A ^ ¬C); if I think that A cannot be true while C is false, this implies that if A is true, C must be too.
• Or -- A then C combined with law of excluded middle: we'll either have ¬A or A so C…