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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&

What Is “The Impossibility of the Contrary”?

If one has studied Presuppositional Apologetics even a little, one would no doubt have come across the phrase “the impossibility of the contrary”. But what does it mean? Well, obviously it means that the contrary is impossible. But what is the contrary and in what sense is it impossible? And if it is impossible, what significance does that have to our apologetic approach? Logically speaking, two propositions are said to be contraries if they cannot both be true. For example, the propositions ‘I am currently in Athens’ and ‘I am currently in Barcelona’ are contraries because they cannot both be true at the same time and in the same sense. Contraries, though, can both be false. Contradictories, on the other hand, are propositions which always have opposite truth values. In other words, A and B are contradictories if whenever A is true, B is false, and vice versa. The phrase “impossibility of the contrary” should rather be called “impossibility of the contradictory” if we are being techni

The Battle of Presuppositions

OBJECTION : "Logic, uniformity of nature, causation, a mind-independent reality, reliability of sense perception, etc are merely presuppositions of my worldview. They are properly basic and do not need to be justified. We both presuppose them so why do you need to add an extra entity (i.e. God)?" This kind of objection is encountered rather frequently and is used by unbelievers who have been faced with the insurmountable difficulty of answering the presuppositionalist's questions about these things. But there are three problems I'd like to point out with such a response.  First, it is incredibly naive to think that one can just posit these things without a broader worldview in which they can be made intelligible. Sure, they may be presuppositions in a sense and as such more basic than other beliefs. But without a metaphysical background to give them meaning they are, to use Van Til's terms, just rocks in a bottomless ocean. There needs to be a hard place where the