Two propositions are said to be contraries if they cannot both be true, though they might both be false. Consider these two propositions provided by http://www.dictionary.com/ as an example:
1. All judges are male.
2. No judges are male.
If Proposition 1 (an A proposition) is true and all judges are male, then Proposition 2 (an E proposition), cannot be true. If Proposition 2 is true and no judges are male, then Proposition 1 cannot be true. It cannot be true that all judges are male while at the same time and in the same respect no judges are male. However, Proposition1 and Proposition 2 may both be false at the same time and in the same respect. It is actually false that all judges are male. At the same time and in the same respect it is actually false that no judges are male. Proposition 1 and Proposition 2 are what are known as contraries in logic. Contraries differ from contradictories.
Recently I came across a user on Youtube named RedBeetle who asks, “Did Cornelius Van Til and Greg Bahnsen understand basic logic? Does [sic] the followers of these two Neo-orthodox theologians understand basic logic?” He goes on to answer his own question, “Apparently not, for they still maintain that they can prove God exists from the impossibility of the contrary”. RedBeetle maintains that the claim that the existence of God can be proven from the impossibility of the contrary is not a claim that would be made by someone who understands basic logic; however he fails to support his position and it is easily shown to be incorrect.
RedBeetle claims that in his video he is attempting to explain to “…these Van Tillians that contraries can both be false…” and hopes to do this, “despite the paradoxical madness permeating the minds of Van Tilians [sic]”. Frankly this comes across as nothing more than an empty and condescending remark on his part given the philosophical understanding of many Van Tillians. I, for one, do not need RedBeetle to explain to me what a contrary in logic is, as I already know and have shown as much above. Nevertheless I still use the Transcendental Argument for the Existence of God. Thus RedBeetle’s underlying assumption that those who understand basic logic will not use TAG has been falsified. No doubt RedBeetle might attribute my understanding of logical contraries with my simultaneous use of TAG to paradoxical madness permeating my mind, but I think it has much more to do with my actually trying to understand Van Til and Bahnsen in their contexts rather than hastily attempting to dismiss them as “neo-orthodox” and “foolish”. There are other problems with RedBeetle’s assertions as well. For example, given the background and learning of both Van Til and Bahnsen, it is not plausible to attribute a lack of understanding regarding basic logic to the two men. There is a much better explanation for what is going on here than what RedBeetle provides.
The meaning of “contrary” in logic is often counterintuitive to beginners in that field of study. The reason is a familiarity with the popular use of the term. The term “contrary” is used in much broader circles than just philosophers in logic. The first definition for contrary at http://www.dictionary.com/ is “opposite in nature or character; diametrically or mutually opposed”. The contrary of Christianity in this sense of the word is non-Christianity with its many manifestations.
Notice that Christianity and non-Christianity are not propositions. The use of the term contrary within the context of logic applies only to A and E propositions, not to whole worldviews summed up in one word labels. RedBeetle thus shows himself to be rather confused when he writes, “So, for example, by claiming Christianity and Hinduism are contraries, the possibility remains that both may actually be false! “. This statement may be true if it is used in a strictly logical sense, but since “Christianity” and “Hinduism” are not propositions this possibility is precluded. RedBeetle is guilty of a misapplication of contrary as he has defined it in his video per Copi. There is a sense in which Christianity and Hinduism are contrary since Hinduism is non-Christian and hence opposed in nature and character to Christianity. It is rather hard to miss this understanding of the topic before us upon a fair reading of Van Til and Bahnsen given the abundant use of “antithesis” to describe the relationship between Christianity and non-Christianity among other things. RedBeetle’s entire presentation appears to be based on an equivocation.
We see the potential for this type of mistake elsewhere as well. For example, I have heard many an intelligent person use the phrase “which begs the question” followed by a question someone might ask after having discovered some piece of information. Obviously the person who uses this phrase in such a context is not referring to the fallacy of ”begging the question”. The reason we know this is because we listen to and interpret the person making the statement in the best possible light within his or her context as we should do if we are to be honest and fair in our endeavors.
When I write and speak of the impossibility of the contrary of Christianity I write and speak of the impossibility of anything which is opposed to Christ in terms of epistemology. Given that Christianity and non-Christianity are worldviews rather than propositions, that presuppositionalists who share my position would never assert that the Bible may be false but in actuality assert the opposite, that Van Til and Bahnsen were fallible but certainly not uneducated, given that we should interpret even the works of our strongest enemies in the best possible light, and given that there is a popular definition for “contrary” which makes good sense in the context of TAG; there is no reason to conclude that presuppositionalists of the school represented on this site mean anything other than what is meant by the popular usage of the term “contrary”. Christianity is not false, and we do not believe that it possibly can be.