Aristotle’s definition of the Principle, which he extolled as: ‘The Surest Principle..Itself not an assumption…but a beginning for all other axioms‘, the one Principle: ‘Which one must have to understand anything whatsoever’, is as follows:
‘It is impossible for the same thing at the same time to belong and not to belong to the same thing and in the same respect.’
Here is Immanuel Kant [whose own work was an extension of Aristotle’s models] 2000 years later:
‘The proposition: ‘No subject can have a predicate that contradicts it’ is called the Principle of Contradiction..and we must hold [this Principle] to be the universal and fully sufficient principle of all analytic cognition..and the fact that no cognition can be at variance with this Principle without nullifying itself, constitutes the Principle Sine Qua Non..‘
Here is Aristotle in Metaphysics:
‘The possibility of a middle between contraries is excluded: for it is necessary to assert or deny one thing or another. This is clear from the definition of Truth and Falsity: either what is, is affirmed or denied, or else what is not, is affirmed or denied, there can be no middle ground..
Similarly, every thought and concept is expressed as an affirmation or a negation, this is clear from the definition of Truth and Falsity.
Hence also, the frequent saying befalls all such arguments, that they destroy themselves. For he who says that all things are true presents even the statement contrary to his own as true, and therefore his own as not true: whereas he who says that all things are false presents also himself as false.’
Aristotle called such an appeal a ‘Self-Destroying Argument’. A perfect and precise phrase, vintage Aristotle.
Does it ring a loud bell?