
George Boole and the Calculus of Thought (2018) - headalgorithm
https://www.3quarksdaily.com/3quarksdaily/2018/02/george-boole-and-the-calculus-of-thought-5.html
======
just_steve_h
Fantastic article that sheds beautiful light on the core of modern digital
computers.

------
midgetjones
What a lovely article! I happened to walk past his house in Cork last year,
not having known he'd lived there. My partner couldn't work out why I was so
excited, but then there's only 10 types of people in this world etc

------
Tor3
From the article: " _It is impossible that the same quality should both belong
and not belong to the same thing … This is the most certain of all principles
… For it is by nature the source of all the other axioms._ " Aristotle

And yet.. quantum mechanics managed to break the most certain of all
principles. Or actually.. the man who says "I always lie", does he belong to
the group of people who always lie, or does he not belong to it?

The universe we live in turns out to be an interesting place, at least.

~~~
pulisse
> And yet.. quantum mechanics managed to break the most certain of all
> principles.

That's false. Quantum logic satisfies the principle of non-contradiction (the
logical property described in the quotation from Aristotle).

The mistake you're making is misinterpreting the superposition of _p_ and _~p_
, which is a combination of being _p_ with some probability and _~p_ with some
probability, with the simultaneous possession of _p_ and _~p_ with certainty
in both cases. Quantum mechanics doesn't say the latter is possible.

~~~
theaeolist
You are confusing "excluded middle" (¬p⋁p) with "non-contradiction" (¬(p∧¬p)).
The former is not valid in e.g. constructive logic, whereas the latter is a
basic statement of consistency.

~~~
pulisse
My edit to correct that raced with your comment, but thanks. In any case, my
point about quantum logic stands.

~~~
theaeolist
Or as Lewis Caroll puts it, through Tweedledee: "if it was so, it might be;
and if it were so, it would be; but as it isn't, it ain't. That's logic."

