Sublime

Aristotelian logic cannot think in threes. From Aristotle’s law of contradiction, also called the law of the excluded middle, to the binary logic—0 or 1—in our computer programs, our mind sets up its systems in pros and cons, in either-or’s. Descartes did concede a tiny space for a third, right in the middle of the brain. He placed the soul in the

but from the study of logic and mathematics. It’s a very weird framework that doesn’t come out of empiricism, but of a certain kind of armchair philosophizing that turned out to be very useful. So the minimality expectations can be dropped. You could have a very, very cumbersome computational system that produces the correct output. So that’s

Attributed to William of Ockham (or Occam), the fourteenth-century logician and philosopher, this thinking tool is actually a much older rule of thumb. A Latin name for it is lex parsimoniae, the law of parsimony. It is usually put into English as the maxim “Do not multiply entities beyond necessity.” The idea is straightforward: don’t concoct a

Laplace continued his research throughout France’s political upheavals. In 1810 he announced the central limit theorem, one of the great scientific and statistical discoveries of all time. It asserts that, with some exceptions, any average of a large number of similar terms will have a normal, bell-shaped distribution.

Observations and assumptions can exist only within an already largely structured system of thinking, one that is a priori riddled with errors.