Great, you’ve just read a genuine contradiction. In classical logic, once your assumptions contain something of the form “P and not P”, the system explodes: from that point on you can prove \*\*anything\*\* you like. (yes, we assume "is" is a symmetric equality)
Want to “prove” that God does not exist? Or that He/She/They (Upper case!) does? Or that I’m a potato and P=NP? No problem. With a contradiction in your axioms, every statement and its negation are now theorems.
That’s the principle called \*ex contradictione quodlibet\* (“from a contradiction, whatever you like”): if your foundations are inconsistent, your logic turns into a wish-fulfilment machine.
I'm just creating my phd defense slides atm and thought i can share some funny thoughts :) I can highly recommend everyone slightly familiar with cryptographic terminilogy and concepts reading the articles from Matthew Green on random oracle or the current fiat-shamir RO-inconsistency-based attacks. ([https://blog.cryptographyengineering.com/2025/02/04/how-to-prove-false-statements-part-1/](https://blog.cryptographyengineering.com/2025/02/04/how-to-prove-false-statements-part-1/))
I wish i could find the time for writing such posts. But maybe after the defense. But even then, i fear that my creativity is rather limited =P For now consider this fun example:
Rough setup:
1. Crypto proof says: \*“If H is a random oracle, then scheme Π with H is secure.”\*
2. Theory says: \*“There are schemes that are secure in the random-oracle world, but for every concrete hash function h they are actually insecure.”\*
3. "Folklore" says: \*“Our favorite hash H₀ (e.g. SHA-3) is "basically" a random oracle.”\* (where we assume that is "basically" is basically a symmetric equality)
Now glue this together:
\- From (1) + “H₀ is a random oracle” → Π with H₀ is \*\*secure\*\*.
\- From (2) + “H₀ is a concrete hash” → Π with H₀ is \*\*insecure\*\*.
Voila: same scheme, same hash, \*both\* secure and insecure at once.
That’s not deep metaphysics, that’s just what happens when you treat a heuristic (“SHA-3 is like a random oracle”) as if it were a theorem.
a nice little contradiction. Not that anyone in the academia would claim (3), but i heard it in the industry frequently enough. And i guess, without the claim of working with formally sound theorems, then even such contradictions that can make everything formally sound true are not needed...These people just miss an opportunity on proving that God exists. \^\^
EDIT: Oh that slightly exploded. :) Please dont take these considerations too seriously. Some people seem to peer-review a reddit post lol. I will try to find the time to discuss in the evening.
