PHI 1301 Lecture 3

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Principle of Non-Contradiction

No such statement will disturb us, then, or make us believe the same thing can be, do, or undergo opposites, at the same time, in the same respect, and in relation to the same thing.Republic 436e

The following cannot stand for statement or belief ($S$ is subject, $P$ is predicate or attribute):

• $A\implies \neg A$ cannot stand, or,
• in alternate format, $\left\{S\ {\text{is}}\ P\right\}\wedge \left\{S\ {\text{is}}\ \neg P\right\}$ cannot both hold

Thrasymachus	Socrates
Justice is advantage of the stronger
	Advantage of stronger is plenty of good food?
Advantage of stronger is strong rulership, serving interests of ruler
	Rulers can mistakenly tell subjects to do what is disadvantageous to ruler Therefore, justice is not advantage of stronger
CONTRADICTION!