What a Mathematics Course Can Teach You About Transcendental Arguments

Some time ago, I was taking a Mathematics course and we were dealing with Set Theory - particularly the set of Real Numbers.

I won't bore you with the details, but we were talking about the axioms of addition, multiplication, binary operations, etc. And basically, all it was was the abstract foundation of the ordinary basic arithmetic that we do.

In the middle of the lecture, what crossed my mind was how abstract all of it was. When people do ordinary addition or multiplication, they do not have all this abstract set theory in mind. And this thought drew my mind towards the distinction between the a priori and the a posteriori, timeless logic and temporal facts.

Just because we can posit some axioms, prove abstract theorems, and deduce certain general truths, it does not mean that it would be useful in our ordinary contingent experience.

It was a clear illustration of Van Til's argument that there needs to be a way to bridge the gap between logic and fact. The unbeliever doesn't have a suitable bridge. Only the Christian worldview does.

It was an interesting experience that I thought I'd share with you. And I think it shows that, even though on the surface the transcendental argument may seem highly abstract, if we pay attention, we can find various illustrations of it in our everyday experience.

Have a wonderful day!

P. S.: I explain this argument - the relationship between logic and reality, how it's a problem for unbelieving philosophies, and how Christianity solves it - in my book, If Logic then God. You can grab a copy here.

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