Magic: The Logical Operator

Story time!

In Logic I at uOttawa last year, I was short on time on an exam and wrote “Magic!” as a justification for a step in natural deduction. I was going for part-marks. Fast-forward to Logic II the following semester, and my professor mentioned in class that you “can’t just write ‘magic’ as a rule of inference” if you’re stuck, as “one student did”. Ha! I promised him that day that I would either prove magic, which, I’m happy to say, I did not, or provide him with an explanation of the rules I used, which I did. My Logic II final exam ended with a page introducing a new operator, magically P, into logic.

This year, that page is taped to my professor’s door. I must  now proudly share my wisdom.


Suppose P, Q and R are propositions.

If you have P, then you have Magically Q. If you have Magically P, then you have P. Semantically, if you know that magically φ is true, where φ is some formula, then φ is true. If you find yourself with a false instance of a magical operator, you know that your interpretation is contradictory.

Important corollaries are “P if and only if Magically P” and, more importantly, for any proposition P, P is magically true.

Hey, there are people out there who accept modal realism. They may as well accept this. Thanks to Professor Paul Rusnock for promoting my madness.

I never update this blog anymore. I considered closing it, but instead I’m going to start bashing metaphysics and continental philosophy instead of writing ridiculous things. Starting…. now?

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