This past semester was a whirlwind of reading and writing for me. I spontaneously decided that I wanted to extract a liberal education from my university experience, and took three philosophy classes, each one extremely different. I took Introduction to Political Philosophy, in which we studied Plato, Machiavelli, Hobbes, Rousseau, Marx, Mill, and Weber. I took Wisdom of the Moderns, in which we studied Shakespeare, Adam Smith, Mill, Nietzsche, Conrad, Dostoyevsky, Rand, and a few others. And I took Theories of Gender and Sexuality, in which we studied numerous feminist (and related) thinkers, including Beauvoir, Bem, Wittig, Fanon, Foucault, Butler, and Fausto-Sterling. Needless to say, it was rather overwhelming, and I imagine I am going to process it for years.
Alarm. The dream wasn’t too interesting anyway. It was about… zebras? I already can’t remember. It must have really not been interesting.
Below we will consider a few lines of logical thought. They will all take the form of proof by contradiction. This type of proof assumes the opposite of what it wants to prove, and then shows that this assumption leads to a contradiction. A contradiction occurs when a proposition is said to be both true and false at the same time and in the same sense. It is fundamental and obvious that contradictions cannot be true. For example, the material world cannot be the only world that exists and also not the only world that exists. If some proposition necessarily leads to a contradiction, then that proposition must be false. Thus, its opposite is true. So there’s some introductory logic for you.