Algebra, number theory, and mathematical logic

Logical analysis applied to mental phenomenon shows that there is but one law of mind, namely that ideas tend to spread continuously and to affect certain others which stand to them in a peculiar relation of affectibility. In this spreading they lose intensity, and especially the power of affecting others, but gain generality and become welded with other ideas.

This fallacy [appeal to authority] is not in itself an error; it is impossible to learn much in today’s world without letting somebody else crunch the numbers and offer us explanations. And teachers are sources of necessary information. But how we choose our "authorities" and place a value on such information, is just another skill rarely taught in our education systems. It’s little wonder that to most folk, sound bites and talking heads are enough to count as experts. […] Teaching is reinforcing the appeal to authority, where anybody who seems more intelligent than you must ultimately be right. […] We educators must simply role-model critical thinking. […] Educators themselves have to be prepared to show that “evidence” and “answers” are two separate things by firmly believing that, themselves.

Practical life is not necessarily directed toward other people, as some think; and it is not the case that practical thoughts are only those which result from action for the sake of what ensues. On the contrary, much more practical are those mental activities and reflections which have their goal in themselves and take place for their own sake.