Something that has fascinated me ever since I understood logic was, why are computers based on traditional logic, or even logic at all? I thought to myself, hmmm, I am able to walk around, eat, avoid objects, sleep, drink, dance, listen to music etc, and yet, nowhere in my body and soul AFAIK is there a
NAND gate.
It is many years later when I learned about the
Principle of Computational Equivalence that I understood that it need not be so! Digging deeper, it turns out that computer scientists have been influenced immensely by one of the greatest undertaking in western culture,
Principia Mathematica.
But is truth necessarily tied to logic, or at least, to
propositional logic? Principia Mathematica uses a system of discovery using the rules of
predicate logic and set theory - a far richer system than propositional logic. Today we know that even this is not rich enough, and we seek
Topos and Category Theory.
As computers reach the molecular level, will they ultimately have to change from this antiquated logic to quantum logic? Does this magically give you consciousness as a side effect?
