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?
The Contradiction Principle demands that all derivations meet its condition of internal-consistency. But what then is the defending criterion for this celebrated Principle itself?
In Aristotle’s words: ‘The beginning of demonstration cannot [itself] be demonstrated..those who insist on being refuted by argument seek the impossible; for in insisting that they be proven to be self-contradictory, they already contradict themselves..’.
The Principle of Contradiction, the criterion for Logico-Mathematical ‘Proof’, itself has no proof, cannot be proven in a rational framework.
If ‘All things are False’-so is the claim: ‘All things are False!’ If ‘Nothing is True’- so is the declaration: ‘Nothing is True!
But hold on just a second. To say; ‘Nothing is True!’ is not a lie. In fact, I have no idea what it is. For I am firmly in the grip of the Self-Loop.
The principal defense of the Principal Principle, Aristotle’s ‘Self-Destroying Argument’ is contained in a Self-Eating Expression.
Why should you not violate the Principle of Contradiction?
You should not violate the Principle of Contradiction because if you violate the Principle of Contradiction you thereby contradict yourself and thereby violate the Principle of Contradiction.
Check out the Post on ‘The Mathematical Truth of the Century’ and see if you can spot any similarities 2,000 years apart.
So what are we saying? The Principle of Contradiction is wrong? No. As with the notion of’Self’, of ‘Substance’, we need to extract ourselves in imagining some unnecessary and unverifiable universe of stable ‘Inner Entities’ that are at war when in violation of the Principle.
Red is not blue; nor is an orange an apple. They are not so, not because the apple has an ‘Inner Apple Center’ different from an ‘Inner Orange Center’. They are not so because we have defined them that way in a complex interwoven structure of Sign and Symbol, Alphabet and Numeral, Logic and Language. And that is all that we need to accept.
[You know, Logician’s are at heart Mystics, vociferously in denial of the deep mystical roots at the base of their Profession.]