The Christian Vanguard

The following is an essay I had to turn in for my analytic philosophy class.  Analytic philosophy begins with Immanuel Kant and his distinction between analytic and synthetic propositions. Analytic propositions are those which express nothing in the predicate which is not already in the concept, whereas synthetic propositions are those which do predicate something to the subject, and thus amplifies our knowledge (“Prolegomena” p.10).1Because the predicate is already thought up in the concept, all analytic propositions have the property of being a priori in nature, whereas synthetic propositions can be either a priori or a posteriori (Ibid. p.10).2There is some contention about whether there really is synthetic a priori knowledge, however, since synthetic judgments are often thought to come from experience, which doesn’t seem to be part of what it means to be a priori.3Kant argues that mathematical judgements are synthetic a priori, since they do not directly rely on the principle o...

I had to give a 5 min presentation on Gottlob Frege for my Analytic Philosophy class. I had a powerpoint, but I wrote out the entirety of what I said. Here it is. Frege had several important ideas, and one of the more important ones was his championing of this view called “Logicism”. So what is Logicism? So Logicism is the view that math can be reduced to logical statements, thus making math a branch of logic. Just as there are branches in philosophy, like Ethics, Logic, Metaphysics, and those branches have sub branches, like in Ethics you can branch off into ethical theory, and applied ethics, so Frege wants to say that math is a branch of Logic. Which was a real trip at the time because it was something of a common opinion that math was a generalization of our experiences. And this view was held by philosophers like John Stuart Mill. So for example, when I have two dollars, and then I have another two dollars, I then learn that I have four dollars, and so I draw from my own personal ...