Logical Connections Quotes

A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.

Science, in its ultimate ideal, consists of a set of propositions arranged in a hierarchy, the lowest level of the hierarchy being concerned with particular facts, and the highest with some general law, governing everything in the universe. The various levels in the hierarchy have a two-fold logical connection, travelling one up, one down; the upward connection proceeds by induction, the downward by deduction.

Nothing fortuitous happens in a child's world. There are no accidents. Everything is connected with everything else and everything can be explained by everything else. . . . For a young child everything that happens is a necessity.

It is the consistency of the information that matters for a good story, not its completeness. Indeed, you will often find that knowing little makes it easier to fit everything you know into a coherent pattern.

In complex trains of thought signs are indispensable.

All abstract sciences are nothing but the study of relations between signs.

The really smart conspiracies are the ones that explain, 'This is why this is plausible,' not, 'This is what happened.' If it makes sense and if it's possible, I'd investigate it.

I once knew an otherwise excellent teacher who compelled his students to perform all their demonstrations with incorrect figures, on the theory that it was the logical connection of the concepts, not the figure, that was essential.