Category confusion persists

In My first post on this blog, I touched on the notion that formal systems are not derived from empirical facts, but are the result of the constructions we make to simplify the way we interact with reality. This would seem to be a very simple and elementary observation, but one that routinely escapes the notice of the believers in the supernatural, even those with philosophical backgrounds. One of the latest examples comes from the Maverick Philosopher, in his discussion of kinds of ontological arguments.

In particular, I find that the examples he chooses for his proof and disproof on the existence of non-divine items are counter-productive, assuming he wishes to treat God as actually existing, because notions such as circle, square, and logical truth are assigned notions, as opposed to items with an independent existence of their own. The entire system of logic that we use is a constuct, highly useful in many ways, but ultimately the result of arbitrary decisions that were built into its construction. For example, the Law of the Excluded Middle and the Law of Non-Contradiction are results of the initial decision that there will be exactly two truth values, and that every proposition will receive exactly one of these values. If you choose to create your model differently (such as the addition of additional truth-states), one or both of these laws becomes untrue in the new system.

The other example actually makes for a bit of fun. If you use the definition for "circle" as the set of point in a plane that are the same distance from a given point, and the definition of square is "regular four-sided polygon", then all you need is to choose the appropriate difinition of distance, and in fact every circle will be a square, though not every square will be a circle. The taxi-cab metirc will do nicely.

I don't know if there are sound ontological proofs of the sort Dr. Vallicella mentions. I am sure that, by making his non-divine arguments strictly in the area of formal systems, he is basically saying that the primary proofs for God amount to making inital assumpitons about God and setting up rules that insure God's existence. Certainly, this has always seemed the case to me but I would nothave thought Dr. Vallicella would agree.
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The 113 Skeptics Circle

Skeptics circle #133 is up and running at The Uncredible Hallq. Low quantity, but high quality (whether that is despite my not having a post, or in part because of it, is left as an exercise to the reader).
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Easier means harder, at least this time

I teach math at a local community college, as an adjunct. This past school year that mean 13 credit hours each fall and spring, and now 7 this summer. One of the courses is the Liberal Arts math class. I have taught this quite a few times, and really enjoy it. The other course is the one I am struggling with.

I received a Review of Arithmetic course (the high-school equivalent of pre-algebra). Honestly, I had been avoiding this course, but it was all they had left. I feel completely inadequate to teach it. 15-20 years ago, I really struggled to relate to students at this level, and usually came across as condescending and smug (although I never felt that way). This go-round, I've actually been working my way "down" the ladder (College Algebra, than Intermediate Algebra, then Geometry, and Introductory Algebra last summer).

I have never felt so intimidated about teaching a class, though. This summer will tell me a lot about myself, one way or another. Here's to learning, teaching,and learning by teaching!
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