Selected Topics in the Philosophy of Science, Part I: Gödel's Theorem

A few weeks ago I listened to Dr. Binswanger's lecture "Selected Topics in the Philosophy of Science", and I noted three topics that seemed wrong to me in some way. I've been listening to it again, and will share my thoughts as the issues come up.

The first topic I want to cover is Gödel's Theorem. Dr. Binswanger doesn't talk about it in this lecture, but he does say that he had talked about it in a previous lecture. Since I don't know the content of the previous lecture, I'm not going to criticize Dr. Binswanger's discussion of the issue, but rather the common view I've seen amongst Objectivists who know anything about the theorem.

Many Objectivists say that since the theorem says that there is knowledge that cannot be gained through reason and yet can be known to be true, it must be wrong. But what does the theorem actually say? Like many issues in math and science (see, for example, the second half of this comic), there are two interpretations: the interpretation that actually reflects the math or science involved, and the interpretation that takes the wording of the first interpretation and proceeds to apply it in completely inappropriate contexts. The popular expression of the theorem, that there are statements we can know to be true but can never verify by logic, is not supported by the math and was in fact vehemently fought by Gödel himself. In essence, what the theorem actually says is this (it's slightly more nuanced, but that's not relevant to my point): If you have a finite set of propositions taken as given and are only allowed to use deductive reasoning from those propositions, there exist certain statements which you cannot prove. So, rather than proving that reason is not our only means of knowledge, the theorem proves that deduction is not our only means of knowledge.

Now I should point out that the theorem technically only applies to formal mathematical systems complex enough to express algebra, and not to knowledge in general, but the points I want to make remain true: first, that the theorem is correct (and as ironcladly proven as the Pythagorean theorem), and, more importantly, that the popular formulation of science is almost always different from the actual meaning. Before you jump to criticize something from math or science as philosophically invalid, you have to make sure you know what the actual science says, instead of what the popular interpretation of that science is.

Part I Part II Part III