I recently read a blog post by a Christian apologist written to show that philosophical arguments are superior to scientific and mathematical arguments especially as used by presuppositional apologetics. The article seemed to base this thesis on three arguments: that science is always changing, that most mathematicians do not think numbers are real, and that the atheist could always say that the laws of logic and science can be explained by their necessity to the nature of reality; that is, because reality is as it is, then the laws of logic and science are as they are and need no cause or further explanation. To be fair, the article clearly pointed out that scientific arguments do have great value, but not as presented by presuppositional apologetics. My impression of the article was that it had a limited view of reality and did not fully understand how presuppositional apologists use these arguments.
I do agree with the first of these arguments. Science deals with what works and is much better at showing something is false than in establishing truth. The conclusions accepted by the majority of scientists are constantly changing. Furthermore, most scientist hold to a naturalistic-materialistic paradigm that drives their conclusions. We, therefore, must be very careful how we frame our arguments based on science. For instance, while the author of this article, along with many other apologists, accepts the Standard Model of cosmogony (which I do not), he yet points out a number of problems with giving it too much weight in argumentation. I think this article did properly warn apologists concerning their use of science.
I understand that most mathematicians think of numbers as mere devices and not real things and mathematical reasoning as a set of agreed upon rules that works which make mathematical conclusions to be inventions used to describe reality as we see it and not real discoveries of reality. If this were the case, then mathematical arguments are, at the best, very limited and could usually be explained away as being overly subjective. Those of us who do use mathematical arguments need to realize that the predominance of this philosophy limits the effectiveness of these arguments. We need to realize that when we use them, we need to be prepared to engage the larger debate concerning the philosophy of mathematics. Certainly, there are in math many formalisms that do not correspond with reality, but that does not mean that all of mathematics in merely devised methodology independent from, though useful to describe, actual reality. Furthermore, I believe the article is wrong in claiming that numbers could only be considered real in a neo-platonic paradigm. I think the article confuses reality with physicality. No one argues that there are physical numbers and algorithms that exist as physical entities in our universe or that there is a special world of ideas which are represented in physical correspondence. Numbers are real and the relationship between numbers and physical descriptions are real in the same way love, justice, and freedom are real though not physical entities. We can talk about the various aspects of mathematics in the same way we can discuss the various characteristics of love and hatred, justice and injustice. In this view, mathematicians can make discoveries that are real. This view has been held by some very important mathematicians such as Gödel and is used by Dr. Robert Herrmann, former professor of mathematics at the Naval Academy, Dr. John Lennox, a professor of mathematics and philosophy of science at Oxford and astrophysicist Dr. Jason Lisle among others. In fact, the physical sciences, especially theoretical physics, contend that mathematical models do indeed model reality. Much of quantum physics (string theory, super-symmetry) and cosmology (inflation, descriptions of the early universe moments after the supposed Big Bang) are based almost entirely on theoretical mathematics and are commonly presented in documentaries as representing reality, the way things are. If mathematics does not discover truths about reality, then all such theories should not be taken seriously at all, at least not until there is more observational support (cf. Lost in Math by Sabine Hossenfelder which I recently reviewed). If we can take seriously these quantum and cosmological models as proving how the universe really began, as is almost always stated in popular scientific literature, then we can also take the mathematical arguments supporting the existence of God seriously. The author of this article accepts the standard model and so, I would suppose, accepts what cosmologist say happened one millionth of a second after the start of the big bang and the existence of an inflationary period both of which are based almost completely on mathematical modeling and yet reject the idea that mathematics can provide evidence for the existence of God. If we can take seriously these quantum and cosmological models as proving how the universe really began, then we can also take the mathematical arguments supporting the existence of God seriously.
Finally, I think this article completely misses presuppositional methodology. The article seems to think those using scientific, mathematical, or presuppositional arguments are seeking to absolutely prove God’s existence by those arguments. First, a good apologist does not use the cosmological and teleological arguments based on science as absolutely proving the existence of the God of the Bible. We should all be aware of the weaknesses of these arguments and only use them as introductory to the discussion of the reality and nature of God. Furthermore, as I have previously discussed, there is no “knockout” proof of God’s existence anyway. God has so designed reality that faith is necessary (Habakkuk 2:4; II Corinthians 5:7; Hebrews 11:6). Our arguments only point to the God Who then reveals Himself showing that faith in Him is more rational than any other faith. Secondly, the article misses the nature of the presuppositional argument from the existence of logic and the laws of nature. Of course, reality as it is, necessarily includes the laws of logic and nature we observe. However, that does not mean that they do not need an explanation or cause. Both the philosopher’s “every possible world” and the cosmologists “multiverse” points to the fact that our reality does not necessarily have to be the way it is. The point presuppositionalists make is that we can, and should, ask why reality is the way it is. Why are the laws of logic and nature the way they are? Why is the universe fine-tuned for life on earth? Why does mathematics so-well describe reality (see my post on mathematical arguments)? Presuppositionalists argue that the very nature of reality makes sense only in a theistic world-view. It is true that atheists will often argue that reality is as it is without needing explanation or cause, but they cannot do so consistently. No atheist, for instance, would say that thunderstorms occur because that is the way reality is and so we do not need to search for a further explanation. An atheist may say, though, that there is a difference because thunderstorm formation is a scientific matter where as the existence of the laws of logic and nature are philosophical question. Many such atheists, following Stephen Hawking, even deny the validity of philosophy as a means of discovering truth; but, if that idea were accepted, then the whole point of the article, that philosophical arguments are best, would be invalid. If philosophical arguments are indeed best, then such philosophical questions as what caused the laws of logic and nature or why is reality the way it is and not some other way are also valid. Hence the approach of presuppositionalists is also valid.
I argue that, because people are all different, different approaches to apologetics will be more effective with some individuals and less effective with others. There is, then, value in all the major approaches to apologetics such as the philosophical arguments, and all these approaches have weaknesses including presuppositionalism. Certainly, philosophical arguments will be much more effective than other arguments for many individuals. While this article does indeed point out some pitfalls into which apologists may fall and some limitations in the use of some arguments, yet it does not successfully invalidate the use of mathematical and presuppositional arguments. If philosophy itself is valid, then the presuppositional approach criticized in this article is also valid and can be used very effectively.