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The Principle of Non-Contradiction

I have had an interesting conversation with Aristotle on twitter about the principle of non-contradiction, and I would continue it except I am locked from twitter. Actually I deliberately locked myself out of twitter by changing my password and forgetting it, because I suspected it of being an akratic activity on my part to go on twitter. It sucked up my focus and did so because it was deliberately designed to do so — nicotine for the brain. As it happened I figured out a work around for my no password policy — twitter let me go on line with my email address — but just now twitter figured out this workaround and detected unusual activity — it asked me to remember or reset my password. Which I didn’t want to do — seemed annoying — so my original attempt to block myself worked, as I was unable to come up for a work around to my work around.

I can however still talk to Aristotle as this wordpress account automatically posts to twitter. And to the handful of people who follow this wordpress account.

To catch you up, I was reading Pippin on Hegel who invoked the idea that if we can’t understand it it doesn’t exist. That the ability to understand shows us what exists. And this strikes me as wrong — there could be things that nobody can ever understand. After all, why not? Ten thousand years ago there were things nobody could understand — we know about some of them now. Maybe there are things that are like that, but we will never understand them. There are conative goals no one will ever reach perhaps — or at least the idea that “what we can get shows us what good things there are” seems false. Why should it be different with our cognitive goals.

Pippin invoked Aristotle to support this claim, and I know Aristotle is on twitter and have spoken to him before. He invoked the Principle of Non Contradiction. For some reason the “Principle of Cognizability” is justified by the “Principle of Non Contradiction”. Possibly because Aristotle believes to know something requires not accepting contradictions? Not sure! I never found out the connection between the POC and the PNC because Aristotle wanted me to accept the PNC and I don’t. It seems to me perfectly possible that there are things that are a and not a.

This ended up in a discussion about what the force of “the same respect” is in the PNC which says nothing can be a and not a (or maybe p and not p — not sure!) “at the same time and in the same respect”.

I cannot figure out what this means. And if it is vague then the PNC seems neither true nor false, because empty.

One formulation Aristotle offered was that nothing can be p and not p without qualification.

But this seems to be a consequence of a principle that I think is true — the POQ or Principle of Qualification. Nothing can be p without qualification.

IOW if you say “a is a circle” or “b is good” it is always with some qualification. How? In what context? In what respect? are always questions somebody could ask.

So if we substitute “p and not p” for p it is true that nothing can be “p and not p” without qualification.

But that does not give us a PNC. Because the POQ also applies to contradictions.

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3 thoughts on “The Principle of Non-Contradiction

  1. If we let p = “X is long” and q = “X is short,” then the long and the short of it is that Aristotle’s Twitter account is fake. It’s actually run by Kurt Gödel, who doesn’t want anyone to know he’s still alive. He’s in the Witness Protection Program because he saw Marvin Farber commit a non sequitur.

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