How do Science and Religion Relate?

             For centuries, the highest figure in human culture and society was the resident religious head.  The Jewish high priests of antiquity, the Catholic Popes and the oracles of ancient Greece were all held in the highest esteem.  Even the Pharaohs of ancient Egypt were considered to be high priests of the gods.  If a great problem arose in society, everyone would look to their religious leaders for a solution.   As such, theology went unquestioned as the highest possible avenue of study. 

                This all changed with the advent of modern science.  Men and women in lab coats are now the popular experts on any number of academic and intellectual issues.  Yet, religion continues on in a very prominent way.  Very few of the six or so billion people on earth would consider themselves atheists.  So how do we, who revere science, understand our religion in light of the secular academy?  And how do we practice our secular sciences in light of our religious beliefs?  It seems that a model is needed to help us relate the disciplines of science and religion.  In this paper, four such models will be offered.  One of these models will be supported, defended and illustrated using two separate test cases.

Barbour’s Four Models

                Historically, there have been a variety of ways by which people have attempted to relate science and theology. Ian Barbour categorizes these attempts into four broad models: Conflict, Independence, Dialogue and Integration.[1] 

                The conflict model holds that science and theology are consistently at odds with one another.  Either science is being impeded by religious belief, or religion is being besieged by atheistic science.  Some hold this position because they believe religion holds back honest scientific inquiry.  Evolutionary biologist Richard Dawkins has been quoted as saying, “I am against religion because it teaches us to be satisfied with not understanding the world.”[2]  Others point to the lack of a moral compass in science to show that it is in conflict with moral religion.  Atrocities committed in the name of scientific progress are often cited.  Religious peoples favoring the conflict model often cite the Nazi regime of the 1940s.  Historian Richard Evans reports the gruesome experiments carried out on Jews in the Nazi concentration camps but writes that the Nazis saw these as necessary for the advancement of science. “German medical science had uncovered the causes of several major diseases and contributed massively to improving the health of the population over the previous decades. Surely, therefore, it was justified in eliminating negative influences as well?”[3]  The conflict model is also the most popular model today.  For example, the trial of Galileo under the Catholic Church for proposing a heliocentric universe is taught to students of all ages.  It seems natural, then, to assume science and religion are in constant conflict with one another.

                Others have held that science and religion merely address mutually exclusive truth claims.  This is known as the independence model.  Stephen Jay Gould’s principle of non-overlapping magisterial, or NOMA, is a popular example of this model.  While Gould believes both science and religion are equally important and necessary in human life, “they remain logically distinct and fully separate in style of inquiry, however much and however tightly we must integrate the insights of both magisteria to build the rich and full view of life traditionally designated as wisdom.”[4]  Within such a model, if either science or religion appears to be in conflict, it is because one or the other has overstepped its boundary.  While both address objective truth claims, they cannot both address the same aspect of reality at the same time and in the same meaning. 

                Barbour’s third model is the dialogue model.  As the name suggests, this model encourages the idea that science and religion can engage in discussions and learn from each other.  They may ask where one discipline begins and the other ends, or they may share methodological schemes as in when one tries to apply empirical tests in the world of theology. 

The fourth of Barbour’s models is integration.  Examples of this model can include when one tries to infer the existence of God from natural sources, when scientific theories are integrated into one’s theological understanding, or when one arrives at a comprehensive understanding of reality that includes both scientific and theological truths.  Garry DeWeese uses the term “Convergence” for this model, as he believes that science and theology should retain their disciplinary integrity.[5]  This is the model that I favor and the model that the remainder of this paper will endeavor to support. 

Against Scientism

                Those that ascribe to the conflict model or the independence model often hold to a strong or weak view of scientism, views that the integration model rejects.  Strong scientism is the view that science defines rationality and is the only method by which one can discern truth.  If something cannot be known by scientific investigation, then it is not true or rational.  Weak scientism, which is more popular, holds that truths of a non-scientific nature may exist and that they may have some status of rationality.  However, scientific rationality and truths have authority and have more value than any other form of inquiry.  While someone may have their own thoughts about the mind, the authoritative view is that the mind is best explained via neurophysiology and psychology.  If either strong or weak scientism is true, then a convergence model of science and religion cannot be correct.  However, if we can show that strong scientism and weak scientism are deficient views, then we can show that aspects of the conflict, independence and versions of the dialogue models are left wanting.   For if science is not the only method, or even the strongest method for arriving at truth, then it must be supplemented by other avenues of inquiry and rationality.  I propose that theology, within a convergence model, should be and is one of those avenues.

                Strong scientism, as the more severe of the scientism positions, is relatively easy to dismiss.  First, it is self-refuting.  The statement that “science is the only legitimate foundation to find truth” is not itself a scientifically verifiable statement.  It is a philosophical statement about science.  Moreover, there are several other non-scientific presuppositions that allow science to be practiced.  The laws of logic and mathematics, for example, cannot be proven scientifically.  Yet they are foundational to the scientific enterprise. Since these problems are easily seen and difficult to ignore, most who favor scientism have adopted weak scientism.

                Yet weak scientism is not without faults.  First, along with strong scientism, weak scientism has a difficult time allowing for the philosophical presuppositions that are foundational for the practice of science.  J.P. Moreland and William Lane Craig provide a list of several scientific presuppositions that are merely assumed aside from the aforementioned laws of logic and mathematics.  They include the existence of a theory-independent world, the orderly nature of the external world, the knowablility of the external world, the existence of truth, the uniformity of nature and the ability to trust induction as a method to find truth.[6]  Since these presuppositions are not scientific, weak scientism would have us believe that they are somehow less authoritative than scientific statements.  Yet these scientific statements would not exist if not for the non-scientific foundational truths that were previously assumed.  It seems to follow then that the presuppositional truths must be assumed to be just as authoritative if not more so than the generated scientific truths.

                Second, neither form of scientism adequately allows for the existence of true and rationally held beliefs outside of science.  Moral truths and self-evidential truths serve as examples.  Moreover, many of these truths seem to have better justification than many truth claims believed within science.  One cannot prove scientifically that rape is wrong, but most people hold this to be true.  Moreover, they hold this to be true and have more justification than the theory of Darwinian evolution.   A further problem for scientism that parallels its inability to allow for these truths is that scientific truths have changed repeatedly throughout history while many truths outside of science have remained consistent.  The objective truth that murder is wrong has persisted over many different cultures and centuries.  The scientific truths regarding the placement of the earth in the universe has changed dramatically and repeatedly over the same time span.  Moreland and Craig write, “It is not hard to believe that many of our currently held scientific beliefs will and should be revised or abandoned in one hundred years, but it would be hard to see how the same could be said of the extrascientific propositions.”[7]

                Thus we can confidently conclude that science cannot be the only source, nor even the most important source, of truth.  Many truths about philosophy, morality and theology seem to be more foundational and more objective than many scientific truths we accept today.  Moreover, some of these truths provide the very foundation on which science functions, thus rendering the conflict and independence models insufficient.  What is often overlooked is that the philosophical idea of naturalism functions as a sort of religion for many scientists.  Regarding science’s implicit religious doctrines, Van Till writes, “What often confuses the issue… is the fact that this particular ‘religion’ of naturalism is so commonly embedded in works that are presented to readers as being no more than popularizations of modern science.”[8]  Furthermore, the dialogue model, which supposes a distinction between scientific knowledge and non-scientific knowledge, fails to recognize the role that non-scientific truth claims play in all scientific inquiry.  We are thus left with the integration model of relating science and religion.   However, we are not left with integration merely as a process of elimination.  Integration has its own strengths which strengthen its claim as the appropriate means to relate science and religion.  We will now turn to how one may approach the integration of theological claims with scientific claims.

Application of Integration

                While I favor DeWeese’s use of the term “Convergence,” I will continue to utilize Barbour’s term of integration for continuity’s sake.  However, the idea of convergence does seem to more appropriately capture the idea that there is one collective and objective truth that both science and religion are attempting to describe.  Indeed, the existence of such an objective truth is something that both science and religion recognize regardless of which model one ascribes to.  Furthermore, science and religion are both tools that purportedly exist to find and describe objective truth.  As such, they have a common goal.  If one has the goal of constructing a skyscraper, it makes little sense to utilize different tools in a conflicting or independent way.  Instead, one would utilize cranes, bulldozers, dump trucks and excavators in an integrative way.  As we have seen, religious truths and scientific truths are integrated in a complex and complete unity of objective truth.  Therefore, we must investigate this truth with tools that are equally integrated.

                It is one thing to recognize the need for integration.  It is another to describe how one might apply such a model.  In some cases, integration causes no controversy as it is not necessarily applied.  The scientific fact that every macroscopic physical action causes an equal and opposite reaction does not seem to carry much theological weight.  Likewise, the theological claim that Abraham’s trust in God was credited to him as righteousness appears to have no bearing in the scientific realm.  In such cases, there appears to be no overlap between religious truth and scientific truth.  While they both point to the same objective reality, there is no chance for conflict or active integration.

                In cases of overlap, there may either be mutual strengthening or conflict.  In the case of strengthening, scientific evidence may directly support religious claims or vice versa.  The current scientific model of the Big Bang supports the Biblical claim that the universe had a beginning when God created it.  Likewise, many theological teachings encourage the study of the natural world in order to gain a deeper understanding of reality.  Such overlap offers explicit support for the integration model.

                However, conflict often arises when theological and scientific claims overlap.  While the aforementioned Big Bang theory does offer support to the Christian theological doctrine of creation, it also seems to contradict a young earth interpretation of the Genesis narrative.  The scientific theory of Darwinian Evolution is at odds with varying version of theological creationism.  Human stem cell research clashes with deeply held theological convictions regarding the human soul and personhood.  In order for the integration model to be successful, it must first show that it can successfully handle such conflicts.

                According to the integration model being proposed, both science and religion are attempting to explain the same external reality.  It follows then that if science and religion are claiming two mutually incompatible things about this external reality that one or both are incorrect in their claims.  This does not mean that science or religion is illegitimate as a method of arriving at objective truth.  Rather, it means that both enterprises are carried out by people who make mistakes.  Thus, when conflict arises within the integration model, one should look at one’s science or theology for flaws.  This must be done on a case by case basis.  While in one case one’s theological reasoning may be flawed and thus in conflict with science, in another case it might be one’s scientific reasoning that may be flawed.  But it if is to be done on a case by case basis, on what criteria is it to be judged?  DeWeese and others have offered several questions to ask in order to direct our adjudication,[9] and I offer several of them here.

                First, assuming that an actual contradiction is at hand, one should first look to see if either the scientific or the theological claims are axiomatic within their discipline.  For example, if one’s scientific claims contradict one’s Christian claim to the deity of Christ, then one must first look for errors within one’s scientific claims.  Otherwise, one’s Christian theology would be utterly destroyed.  Similarly, science necessitates the human ability to observe the external world as it is.  If one’s theology teaches that demons actively and continually distort our perception of reality, then this would strike at the core of scientific inquiry and one’s theological beliefs ought to be suspect.

                Second, one must consider the amount of independent support for conflicting theological and scientific claims.  One scientific experiment does not warrant the repudiation of a hundred clear theological teachings.  Nor do one or two obscure Scriptural texts render a well-established scientific theory null and void.  For example, a cursory reading of Genesis might lead one to believe that there was no pain or suffering among the animals before the creation of Adam.  However, an in depth fossil record shows ample evidence that carnivorous animals existed long before mankind.  Since the Bible is largely silent on the issue of pre-fall animal suffering, and since the scriptures that apparently speak to this are few and less than explicit, one should not discredit the fossil record evidence based on theological reasons.

                Third, one should take care to make sure that neither the scientific claims nor the theological claims suffer from significant internal problems.  Internal logical contradictions, such as those mentioned in strong scientism above, render any claims to be fallacious.  But there are other lesser types of internal problems.  New archaeological finds may render one’s interpretation of historical theology questionable.  A new scientific discovery may call into question long standing scientific theories.  Such internal problems need not discredit a claim made by science or theology, but they may weaken them.  Thus, if these weakened claims come into conflict with an opposing scientific or theological claim, their weakened status should be further considered.

                Fourth, one may wish to suspend judgement altogether if a decision is not forced and if neither the theological evidence nor the scientific evidence is strong enough to persuade a reconsideration of the other.  This is typically the case when the two claims are not central to the truth claims made by either side.  For example, one might believe the Pharaoh described in the book of Exodus to be Ramses I instead of Amenhotep II or Thutmose II.  However, all have historical evidences in their favor and none is conclusive.  Therefore, it is advisable to suspend judgement in the absence of further historical evidence.        

Objections to Integration

                Before we move on to case studies involving our proposed integration model, we should first briefly discuss a couple objections that have been raised against it.  First, it has been argued that by integrating religion into science, we have introduced a “god-of-the-gaps” mentality in which god is merely inserted into areas which science has not yet spoken to.  This is then used as an apologetic by theists much like the natural theologians of years past.  Furthermore, it is argued that since science is increasingly filling these gaps, this is really just a slow weening off of religion altogether. 

                This is clearly just a reassertion of weak scientism that assumes that scientific knowledge is superior to any and all religious knowledge.  There are several replies that may be offered in turn.  First, there is nothing in the integration model which limit’s the activity of a deity.  If one were to adopt a Christian perspective, it is clear that God is sovereign of all of nature and continually upholds it.  As such, he upholds science as well.  Moreover, there need not be any apologetic aim within the integration model at all.  Moreland and Craig write, “A Christian theist may simply believe that he or she should consult all we know or have reason to believe is true – including theological beliefs – in forming, evaluation and testing scientific theories and in explaining scientific phenomena.”[10]

                Second, the integration model does not seek to insert theology only when science is lacking.  Certain theological truths are more central and should be expected to play a more pivotal role in nature.  The falleness of man and nature should be expected to manifest itself in natural pain and suffering.  One should have theologically expected the universe to have had a beginning even before the Big Bang became a popular theory. 

                Third, while it may be true that scientific theories are covering more ground and the gaps are getting smaller, it does not follow that there will eventually be no gaps at all.  Indeed, biogenesis and cosmogenesis are two examples of phenomena that are doubtful to ever be explained by science.  If God acts in a primary way via miracles, gaps should be expected.  Moreover, rarity is an attribute of miraculous events.  This means that most of God’s actions are through secondary causes, which are able to be investigated via science.  God’s actions through primary causes are thus all the more obvious because they are so rare.

                Finally, one needs to differentiate between historical science and empirical science when discussing a “god-of-the-gaps” theology.  Empirical science is carried out within a laboratory setting and is based on repeatable, regularly occurring events.  As such, it is immune from talk of the miraculous.  However, historical science focuses on past events which are not repeatable.  It is thus legitimate to discuss God’s primary causal activity in the historical sciences while it is not in the empirical sciences.  If something is not yet explainable by science in the empirical sense, it ought to remain an open question instead of a hasty assertion of the miraculous.

                The second objection to the integration model is similar to the sentiment posed by Richard Dawkins earlier in this paper, namely that religion stifles scientific inquiry.  It is argued that God’s primary causal activity is not fruitful in guiding new research or yielding testable results.  Therefore, an appeal to God’s direct causation cannot be an acceptable scientific practice.  Regarding this idea, Richard Dickerson writes, “The most insidious evil of supernatural creationism is that it stifles curiosity and therefore blunts the intellect.”[11]

                In response, one might first point out that something can be true without being fruitful in guiding new inquiry.  If God truly did create the universe out of nothing via a Big Bang like process, this would be a onetime occurrence that would never be repeatable.   Thus, further research in the specific area of “creation ex nihilo” would be impossible.  Yet, while further research in this area would be halted, it would not necessarily entail the fallaciousness of the creation claim, especially if the claim were made for good theological and scientific reasons.  Secondly, even if one were to grant that theological concepts have not yet generated new lines of inquiry, it does not follow that such lines of inquiry would not be developed in the future.  Lastly, it may be that in a theological framework a certain phenomenon may be considered basic while in a naturalistic framework it is not and vice versa.  This will clearly have implications on further inquiry into the phenomenon for the different frameworks. 

Case Studies for Integration

                Now that we have briefly defended the integration model against objections, it is time we look at case studies.  I will look at two separate case studies that exemplify different capabilities of the integration model.  The first example will showcase how the model may offer mutual enrichment for both science and religion in areas that are not necessarily fiercely debated, but could be problematic.  The second example will show how the integration model can deal with a historically contentious issue where science and religion appear to be in outright conflict.

                Our first example will be the so-called problem of the applicability of mathematics.  Most, if not all of science is based on the language of mathematics.  Quantum physics is almost entirely explained using mathematical equations.  Yet, we have very little philosophical reason (and no scientific reason) to expect the abstract world of mathematics to interact this way with the physical world.  Einstein once asked, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?”^[12]

                Historically, there have been two views on this problem, neither of which necessitates a Christian or theistic worldview, and both of which have flaws as solutions.  The first is the platonic or realist view of mathematics.  This view holds that mathematics exists as an objective reality outside of the natural world.  Oxford mathematical physicist Roger Penrose says, “Mathematical truth is not determined arbitrarily by the rules of some ‘man-made’ formal system, but has an absolute nature, and lies beyond any such system of specifiable rules.”^[13] As such, mathematics is unchanging and outside of the human mind.  It can thus be harvested to explain things that do occur in the natural realm.  The shortcoming of this view is that it does not offer an explanation as to why or how the external mathematical realm has any active or passive influence whatsoever on the physical world.

                Of course, an objective non-physical mathematical world does not fit into the philosophical naturalism that many practitioners of modern science adopt.  As such, many have come to adopt an anti-realist view of mathematics.  The Einstein quote above hints at how anti-realists view mathematics.  They believe that it is a purely human construct.  Since man is the direct result of natural selection acting upon random variation, mathematics is likewise a product of evolution.  It is easy to see how an individual who “puts two and two together” in an appropriate way has a survival edge over one who does not.  As a survival tool, math became genetically ingrained into the human brain.  According to such a naturalist perspective, math has no existence outside of the human brain.  Furthermore, since humanity has supposedly evolved from one or very few common ancestors, this genetically imbedded mathematics is common to all humanity.  Thus, mathematics merely appears universal. 

                The naturalistic problem is that the anti-realist position sheds no light on the applicability problem.  The math required for most scientific application is superbly complex.  It is in no way clear that such abstract and complex mathematics was at any point beneficial for the survival of the human species.  Furthermore, if our mathematics is subjective to the human race, then the science based on that math is also subjective.  In other words, if we were to contact another intelligent race in the universe, they might have an entirely different system of logic, math and physical sciences.  This runs contrary to the very claim of naturalism that science is “true” in some objective sense. 

                However, if one were to view the applicability problem within an integration model, the problem may be solved almost immediately.  We may first look at the internal problems within the anti-realist position and favor the platonic position.  Next, we see that the problem with the platonic position (that it is not obvious how the mathematical realm interacts with the physical) is easily solvable once an intelligent deity is allowed to be the conduit for which mathematics is consistently applied to the physical world.  Christian mathematician John Byl writes, “Within the context of Christianity it makes sense to talk about the objective existence of numbers and mathematical truths.  Once God is removed, there is nowhere to place abstract mathematical concepts and nobody to guarantee their truthfulness.”^[14]  By integrating one’s religious ideas with the realm of scientific application, one is left with a mutually enriched perspective which allows for the applicability of mathematics in and objective and fruitful way.

            A second test case in which conflict can be resolved using the integration model is that of the evolution-creation debate. It can be safely assumed that the reader is well aware of the conflict between naturalistic Darwinian evolution and the Judeo-Christian view of creation.  The Darwinian side claims that it is based on science and reason.  The Judeo-Christian side claims to have divine revelation in its favor.  How does the integration model here presented handle this situation?

            First, we should look to see if the conflict impinges upon foundational or axiomatic claims on either side. It seems that it does in both cases.   On the Darwinian side, the claim that God miraculously created life impinges upon the foundational scientific assumption of uniformitarianism.  Moreover, it contradicts the naturalistic assumptions of many Darwinists.  Conversely, this naturalism is directly contradictory to the claim that God is actively involved in creation and contradicts the doctrine of God as creator and sustainer of all things.

            Thus, we must look at independent support for each side.  It seems that there is ample evidence for God as creator from other fields such as philosophy, cosmology, ethics and logic.  Meanwhile, there is little support for naturalism as a position other than a mere axiomatic assertion.  However, there is ample evidence within the fossil record that shows a slow progression of ever more complicated biological lifeforms over the past billion years. This lends support to the general idea of evolution, but not necessarily to a naturalistic form of the theory.

            Third, we shall consider if either side has significant internal problems.  Here we see some headway in our integration model, for the naturalistic assumptions behind Darwinian evolution are seen to be fatally flawed.  Within naturalism, there is a deeply ingrained belief in scientism.  As we have seen, scientism is deeply flawed.  Moreover, Darwinian evolution has no answer as to how life began to exist.  Conversely, if one were to adopt a young earth creationism, there appears to be ample physical evidence that supports an old earth fostering millions of years of biological change.  If, however, one adopts an old-earth reading of Genesis, these internal conflicts decrease dramatically.

            Lastly, we may entertain the idea of suspending judgement.  While this is certainly possible in this case, I do not think it is necessary.  I believe once naturalism has been removed from the theory of Darwinian evolution and the idea of God as creator and sustainer of the process has been included, the previous conflict has been greatly reduced if not eliminated. 

Conclusion

            We can therefore conclude that the integration model is preferable over the conflict, independence and dialogue models.  After one rejects a strong or weak form of scientism, the integration model rises to the top as the model of choice.  The application of the application model can be approached methodically and thoughtfully so as to not explicitly favor either science or religion uniformly in all cases.  Objections against integration are generally offshoots of scientism and naturalism and can sufficiently answered.  Finally, we saw that the integration model can be used to mutually enrich both science and religion as well as resolving apparent conflicts between the fields.

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[1] Ian G. Barbour, Religion and Science: Historical and Contemporary Issues (San Francisco: HarperSanFrancisco, 1997), pp. 77-105.

[2]Michael Ruse, Science and Spirituality: Making Room for Faith in the Age of Science (Cambridge: Cambridge University Press, 2010), p. 3.  Ruse attributes this quote to RichardDawkins.net, quote 49.

[3] Richard Evans, “How Hitler Perverted the Course of Science,” The Telegraph. December 1^st, 2008. Web. Accessed December 12^th, 2016.

[4] Stephen Jay Gould, Rocks of Ages: Science and Religion in the Fullness of Life, (New York, NY: Ballantine Books, 1999),  p. 59.

[5] Garry DeWeese, “Understanding Nature,” Doing Philosophy, March 22^nd, 2011. p. 291.

[6] J.P. Moreland & William Lane Craig, Philosophical Foundations for a Christian Worldview, (Downers Grove, IL: IVP Academic, 2003). p.248.

[7] Moreland & Craig, p. 350.

[8] Howard Van Till, “Partnership: Science and Christian Theology as Partners in Theorizing,” Science and Christianity: Four Views, (Downers Grove, IL: InterVarsity Press, 2000). p. 201.

[9] DeWeese, pp. 292-293.

[10] Moreland & Craig, p. 363.

[11] Richard Dickerson, “The Game of Science: Reflections After Arguing with Some Rather Overwrought People,” Perspectives on Science and Christian Faith. 44 (June 1992). P. 137.

[12] Max Jammer, Einstein and Religion, Princeton University Press, 1921.

[13] Roger Penrose, Shadows of the Mind, Searching for the Missing Science of Consciousness (Oxford, England: Oxford University Press, 1994). P. 418.

^[14]John Byl, The Divine Challenge: On Matter, Mind, Math & Meaning. (Carlisle, PA: Banner of Truth,2004). p. 255.

Why Mathematics Points to Something Greater than Ourselves

        I teach math for a living.  I find it relaxing and challenging.  Math is predictable, concrete and as simple or abstract as one cares to make it.  However, my students rarely share these thoughts.  The slightest deviance from the "norm" elicits moans and complaining that one would expect to hear in an emergency room waiting area.  One of the topics that almost always brings out the worst in math students in the introduction of the so-called "imaginary" numbers.  These are the numbers that include the square roots of negative numbers.  These are set up in opposition to the "real numbers" that we are used to in day to day life.  My students will always whine, "Why do we have to learn about numbers that aren't even real?"  To this I respond, "Point to the number 2.  Show me where it is. Once you can show my that real numbers are somehow more real than imaginary numbers, then we can stick to the real ones."         

                The problem is that mathematical ideas are just that – ideas.  They are not contrived as tools to better understand the world around us.  Instead, they exist external to ourselves and are developed within a human mind simply for the sake of further thought.  However, more often than one might otherwise suppose, these abstract mathematical ideas show their face in the fabric of the physical world in ways that were never imagined in the mind where the mathematical idea first took root.  Here, we will look at a few of these mathematical “surprises” and see just how far their influences can reach.

                First, let us consider a perfect circle.  Mathematically defined, a perfect circle is the set of all points in a plane that are at a given distance from a given point, the center.  While we can all imagine such a perfect circle, it is actually quite difficult to find one in reality.  Even a circle drawn with a computer or a compass, pen and paper will have slight variations in it.  Indeed, at the atomic or quantum level, there can be no continuous curve that would constitute a circle existing!  Yet, the idea is simple and clear in our minds. 

                From this concept of a perfect circle, many of the ancients attempted to find the ratio of its circumference to its diameter.  The Egyptians, around 1650 BC, thought this to be a fraction slightly above 3.[1] The ancient Israelites also had a figure around three.  Their understanding of this ratio is recorded in their sacred texts: “Then he made the sea of cast metal. It was round, ten cubits from brim to brim, and five cubits high, and a line of thirty cubits measured its circumference.”[2] Ultimately, after centuries of increased precision, we came to know this ratio as the irrational number named after the Greek letter pi. Thus, pi was the outworking of a completely mental exercise to determine the ratio of one dimension to another of an abstract object that does not exist in the physical world.  Yet, this is not the end of the story regarding pi.  Not even close.  Pi unexpectedly and repeatedly shows up in a plethora of physical applications.  Mario Livio relates the example of Buffon’s Needle.[3]  In this example, a sheet of paper with a series of parallel lines each one inch apart is laid on a table.  A needle that is also one inch long is then randomly dropped on the sheet of paper.  What is the probability that the needle will land in such a way so as to intersect one of the lines?  Surprisingly, it is exactly pi divided by two.

                Another ratio, about which Mario Livio wrote an entire book because of its surprising applications, is known as phi, or the Golden Ratio.  This ratio is found when one takes a line segment and cuts it into two sections such that the ratio of the original to the longer section is the same as the ratio of the longer section to the shorter section.  This ratio (calculated at approximately 1.61803) was originally found by Euclid of Alexandria around 300 B.C. for purely geometric purposes.  Centuries later, and totally apart from Euclid’s endeavors, a man named Leonardo Fibonacci generated an infinite series of numbers (0,1,1,2,3,5,8,13,… ) in which the sum of the previous two numbers equals the value of the next number in the series.  The Fibonacci numbers and Euclid’s phi have nothing to do with one another.  However, if one takes the ratio of a certain Fibonacci number with its direct predecessor, the series of these numbers approaches the value of phi exactly!  This is indeed a surprising result.  Moreover, the Fibonacci numbers and phi are found consistently in nature.  Flower petals, seed heads, pinecones, sea shells, spiral galaxies, hurricanes, human fingers, and even DNA molecules all exhibit the golden ratio and the Fibonacci numbers.[4]  This is indeed surprising.  Two separate ideas generated solely in the minds of men have unexpectedly shown themselves in hundreds of ways in nature.

                A more complex and abstract mathematical idea is that of symmetries.  Although it is too technical for the purpose of this paper, we can recognize that a square has a set of 4 rotations that will reproduce the same square.  An equilateral triangle has three.  A circle has infinitely many.  Thus we can say a circle is somehow more symmetric than a square than a triangle.  We can start with a circular table, but if we generate a mathematical group of its symmetries, we have something different.  When considering this, mathematician Edward Frenkel writes, “We cannot touch or hold the set of symmetries of a table, but we can imagine it, draw its elements, study it, talk about it.”[5]  Yet objects seemingly do not generate such symmetries.  In other words, symmetric objects merely have the objective and unchanging mathematical property of being symmetrical.  If there were no symmetrical objects in existence, humans could still imagine such objects and study them.   However, we know that symmetry runs rampant in nature.  Almost all life exhibits some form of symmetry.  This is another mathematical surprise that mankind takes for granted, but there is no reason to expect this to be the case.

               

The Platonic Answer

                Einstein once asked, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?”[6]  This is the question we will attempt to answer in the remainder of this paper.  Indeed, many have attempted to answer this question.  From these attempts, two main answers have arisen.  I will show that both of these answers are lacking in lesser or greater degrees, and I will show that intelligent design seems to hold the key.

                The first proposed answer is given by those that have been called the mathematical Platonists, or mathematical realists.  Regarding mathematical knowledge, Edward Frankel remarks, “The fact that such objective and enduring knowledge exists is nothing short of a miracle.  It suggests that mathematical concepts exist in a world separate from physical and mental worlds – which is sometimes referred to as the Platonic world of mathematics.”^[7] According to such a view, if humanity went extinct overnight, two rocks plus another two rocks would continue to be four rocks.  The ideal of a perfect circle, the Fibonacci numbers and ratios such as pi and phi would persevere in our absence.  Furthermore, man has no role in the creation of mathematics.  Oxford mathematical physicist Roger Penrose says, “Mathematical truth is not determined arbitrarily by the rules of some ‘man-made’ formal system, but has an absolute nature, and lies beyond any such system of specifiable rules.”[8] Man does not generate mathematics but merely discovers it as he goes along.  This is the position of the Platonist.

                Such a position requires that there be some “other” world apart from the physical world where we reside where mathematical entities “exist” in some very real sense.  However, the Platonic view by itself does nothing to explain why these two words should overlap.  Even if one were to adopt the view that the Platonic mathematical world somehow underpins the physical world, there still is not an explanation as to why that would be the case.  We might see evidence for it, but it is just as “surprising” as it was before.  I propose there to be a simple and intuitive solution to this Platonic problem, but let us first consider the naturalists’ answer to the surprising effectiveness of mathematics.

The Naturalist Answer

                It should be clear by this point that the Naturalist simply cannot accept the Platonic answer to the effectiveness question.  Naturalism asserts that the physical world is all there is.  Mathematician and naturalist Yehuda Rav has written that “there are no preordained, predetermined mathematical ‘truths’ that just lie out or up there.  Evolutionary thinking teaches us otherwise.”[9] Thus, to assert that there is a completely different world that contains objective and eternal mathematical truths would akin to denying Naturalism.  So what option is left to the Naturalist?

                Clearly, the first thing a naturalist is inclined to do is reject platonic mathematical realism.  John Byl notes that while mathematicians are practical realists, this isn’t the case with other academics. “Nowadays,” write Byl, “most philosophers of mathematics reject mathematical realism, primarily because of its perceived ill fit with naturalism.”[10]  It should not be overlooked that it is inherently not the case that mathematics leads to naturalism.  Rather, the presumption of naturalism’s truth has led some to reject the platonic ideals foundational to objective mathematics.  But if that is the case, what is left of mathematics?  How does one explain the apparent objectiveness and universalness of mathematical truths? 

                The naturalist answers by saying that mathematics is a manmade invention.  Furthermore, since man is the direct result of natural selection acting upon random variation, mathematics is likewise a product of evolution.  It is easy to see how an individual who “puts two and two together” in an appropriate way has a survival edge over one who does not.  As a survival tool, math became genetically ingrained into the human brain.  According to such a naturalist perspective, math has no existence outside of the human brain.  Furthermore, since humanity has supposedly evolved from one or very few common ancestors, this genetically imbedded mathematics is common to all humanity.  Thus, mathematics merely appears universal.  Citing different psychological experiments, Mario Livio relates, “Experiments show that babies have innate mechanisms for recognizing numbers in small sets and that children acquire simple arithmetical capabilities spontaneously, even without much formal instruction.”[11]  Also, legions on the inferior parietal cortex in the brain adversely affect one’s mathematical ability.  According to the naturalist, these physical evidences lend support to their conclusion that math is a product of the brain and nothing more.

Problems with the Naturalist Answer

                While the Platonic view of mathematics has problems of its own, the naturalist has problems that seem insurmountable.  How, for example, does Darwinian evolution account for abstract algebra and complex analysis?  Paul Davies notes that “While a modicum of intelligence does have a good survival value, it is far from clear how such qualities as the ability to do advanced mathematics… ever evolved by natural selection.” Indeed, evolution does not even guarantee that our mathematics is correct.  It merely asserts that the mathematics we developed were the best as helping us survive. Moreover, Davies adds, “Most biologists believe… human brain has changed little over tens of thousands of years, which suggests that higher mental functions have lain largely dormant until recently.”[12]  If the human brain has remained unchanged for millennia, then mathematics (including the most abstract varieties) must have been genetically imbedded long before the time of the Greeks.  This seems at best to be wishful thinking spawned by cognitive dissonance.  At worst, it’s simply absurd.

                A second problem with the naturalistic perspective is its implicit denial that mathematics in objective.  When one investigates a crime, they do so with the understanding that there is an objectively true series of events that happened. Without an objective truth “out there,” there is substantially less motivation to do mathematical research and investigating.  Even if a mathematician were to adopt the anti-realist philosophy of the naturalist, they would have to pretend that math was objective in order to carry out their research with any real purpose.  Furthermore, if math is not objective, then how can we have any confidence that intelligence elsewhere in the universe would have formulated anything remotely similar to the mathematics humanity has developed?  Indeed, SETI has been sending out signals for years based on mathematical communications.  If our concepts of prime number, for example, are merely evolutionary, then we can have absolutely no confidence that a “prime number” is even a concept some extraterrestrial civilization would have developed.  The final, and perhaps most fatal, problem with naturalism’s lack of mathematical objectivity is that almost all of our science is founded upon mathematics.  Physics has been so successful primarily because it is basically mathematical.  Quantum mechanics is almost entirely explained using equations.  If, however, mathematics is the result of random variation and natural selection, then so is science.  This makes science less than objective.  But science is the bedrock on which naturalism is founded.  In a sense, then, the rejection of the objectivity of mathematics by the naturalist is self-refuting.

                This rejection of objective mathematics becomes even more problematic when we see that mathematics is intimately tied with logic, which is itself critical to reasonable human thought.  When we say that some a statement “A” and the statement “not A” cannot be both true at the same time and in the same meaning (this is the logical law of non-contradiction), this seems to be an objective truth rooted in an external platonic world of logic.  If, however, there exists no such platonic world and if evolution explains the existence of mathematics and the logical rules it plays by, then the law of non-contradiction is the product of random variation and natural selection.  In other words, we can have no confidence that the law of non-contradiction is a law at all outside of the biological human brain.  This is clearly an enormous problem for the naturalist who wishes to do away with platonic ideals.

                A third problem for the naturalist is that is simply does nothing to address the problem at the outset of this paper.  Namely, why is mathematics so powerful in explaining the universe?  Why do abstract mathematical ideas formed centuries ago show up in completely separate physical studies and the sciences of today?  Outside of evolutionary hand-waving, which is less than objective as we have seen, there does not seem to be a satisfactory answer. 

                With all of these shortcomings in mind, I believe it is time we consider the solution that Intelligent Design offers.

Intelligent Design as the Solution to the Applicability Problem of Mathematics

                Thus far I have not spoken much of intelligent design and its role in abstract mathematics.  I have reserved its role for the present simply because intelligent design, once entertained, is a simple and obvious solution to the problem of the applicability of mathematics.  Indeed, there was once a time when an intelligent designer was simply assumed, and during that time there were not mathematical “surprises.”  Johannes Kepler believed that geometry “supplied God with patterns for the creation of the world, and passed over to Man along with the image of God; and was not in fact taken through the eyes.”[13]  The great physicist and mathematician Pierre-Simon de Laplace wrote in 1812:

               

Given for one instant and intelligence which comprehends all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom.[14]

                The thinkers from centuries past may not have been evangelical Christians, but then again many of the members of the current intelligent design movement are not Christian either.  What they all have in common is the belief that behind the physical universe, there exists some sort of intelligent and purposeful designer.  In such a scheme, the fact that platonic mathematics influences and describes physical phenomena is hardly surprising.

                However, with the rise of philosophical naturalism, there ceased to be any valid account for a platonic view of mathematics and why it should be applicable to the universe.  Indeed, even a realist perspective without such a designer still lacks the necessary step to go from the platonic world to the physical world.  Thus we have arrived at the critical point of this analysis:  The problem is not that mathematics is inexplicably effective for describing the universe.  The real problem is that philosophical naturalism forces us to believe that the applicability of mathematics is a problem.  John Byl writes, “within the context of Christianity it makes sense to talk about the objective existence of numbers and mathematical truths.  Once God is removed, there is nowhere to place abstract mathematical concepts and nobody to guarantee their truthfulness.”[15]

                By incorporating the possibility for an intelligent designer into our understanding of the world, the objectivity of mathematics gains a firm foundation.  Furthermore, we gain confidence that our laws of logic are grounded and are able to lead us to objective truth.  The importance of this cannot be overstated.  This entire paper, and many others like it, has the purpose of arguing for the truth of one position over another.  If our laws of logic are not universal, then this argumentation is pointless and its fruit will be random. 

                An intelligent designer also allows us to think objectively about an actual infinity instead of just a possible infinity. Why is this the case?  Modern quantum mechanics has shown that there exists the smallest of discrete sizes in the universe.  Big Bang cosmology asserts that the universe is finite in age and is finite in size.  Taken together, we see that physically the universe does not contain the infinite or the infinitesimal.  Why is this such a big deal for mathematics?  The entirety of the calculus is based on there being a conceptually real idea of the infinitesimal.  Taking an integral or a derivative of a mathematical function demands that the function not be discrete.  Such calculus is used in almost all of our engineering today.  Even though an actual infinity does not exist, we can still conceptualize it and apply it in everyday life.  This seems illogical if there is not some external world where an actual infinity exists.  It also seems logical that if an intelligent designer exists, it would be infinite in nature (though such arguments lie outside the scope of this paper).

                But what should we make of the physical evidences offered in favor of the naturalistic view of mathematics?  How is it that brain legions affect mathematical ability?  Why are children seemingly born with an innate ability to do mathematics?  Doesn’t this all seem to point to the truth of naturalistic evolution and physicalism?  I assert that it does not.  In these cases, the evidences favor intelligent design just as much as naturalism if not more so.  Intelligent design allows for the anti-naturalist position of mental dualism, the idea that the mind and the body are distinct.  In such a framework, the brain and the mind are related.  If the brain is physically injured, this could create difficulties for the mind.  More profoundly, an intelligent designer could uphold not only objective mathematics, but also the “pre-programming” of the human mind.  Thus the innate ability of children to mathematics is far from a “proof” that mathematics is the result of human evolution. 

Conclusion

                Mathematics is pervasive and dense in the world around us.  It is everywhere in the universe and even seems to lie behind everything.  Ancient mathematical ideas continue to show themselves in the physical world in areas that were never even thought of before.  The overwhelmingly successful application of mathematics to the physical world generates an important question.  Why is this the case?  Platonism gets close to answering this question, but cannot quite explain why an external mathematical world should have anything to do with the physical world.  Naturalism fairs much worse that Platonism as it casts doubt on the objectivity and universality of mathematics and logic.  In the end, the best possible answer is that there is an external world of objective mathematical truth, and there exists and intelligent designer that actively incorporates these mathematical truths into the very fabric of the universe. 

               

Bibliography

Allen, Donald G. “Pi, A Brief History.” (Texas A&M University: College Station, TX). Web. http://www.math.tamu.edu/~dallen/masters/alg_numtheory/pi.pdf

The Bible. English Standard Version Study Bible.  Crossway Books, 2012.

Byl, John. The Divine Challenge: On Matter, Mind, Math & Meaning. (Carlisle, PA: Banner of Truth,2004)

Davies, Paul. Are We Alone. (New York, NY: Basic Books, 1995).

Frankel, Edward.  Love and Math. (New York, NY:Basic Books, 2012).

Jammer, Max. Einstein and Religion, Princeton University Press, 1921.

Johnson, Philip. “Evolution as Dogma: The Establishment of Naturalism,” First Things (October 1990). Web. http://www.arn.org/docs/johnson/pjdogma1.htm.  Accessed Nov. 28, 2016.

Kepler, Johannes,  E. J. Aiton, Alistair Matheson Duncan, Judith Veronica Field. The Harmony of the World, Vol. 209. (Philadelphia, PA: American Philosophical Society, 1997).

Leplace, Pierre-Simon. Philosophical Essay on Probabilities (1814), 5th edition (1825), trans. Andrew I. Dale (1995).

Livio, Mario. The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. (New York, NY: Broadway Books, 2002).

Meyer, Stephen. Darwin’s Doubt: The Explosive Origin of Animal Life and the Case for Intelligent Design. (New York, NY: Harper One, 2014).

Penrose, Roger. Shadows of the Mind, Searching for the Missing Science of Consciousness. (Oxford, England: Oxford University Press, 1994).

Rav, Yahuda. Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education. (Albany, NY: SUNY Press, 1993).

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[1] G. Donald Allen, “Pi, A Brief History.” (Texas A&M University: College Station, TX). Web. http://www.math.tamu.edu/~dallen/masters/alg_numtheory/pi.pdf Accessed, Nov. 28, 2016.

[2] 1 Kings 7:23, ESV.

[3] Mario Livio. The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. (New York, NY: Broadway Books, 2002). P. 2.

[4] Mario Livio discusses these and many other natural occurrences in his book.

[5] Edward Frankel.  Love and Math. (New York, NY:Basic Books, 2012). P. 21.

[6] Max Jammer, Einstein and Religion, Princeton University Press, 1921.

[7] Frankel, 23.

[8] Roger Penrose. Shadows of the Mind, Searching for the Missing Science of Consciousness. (Oxford, England: Oxford University Press, 1994). P. 418.

[9] Yahuda Rav. Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education. (Albany, NY: SUNY Press, 1993). P 100.

[10]John Byl, The Divine Challenge: On Matter, Mind, Math & Meaning. (Carlisle, PA: Banner of Truth,2004). 137.

[11] Livio, 244.

[12] Paul Davies. Are We Alone. (New York, NY: Basic Books, 1995). Pp. 85-86.

[13] Johannes Kepler, E. J. Aiton, Alistair Matheson Duncan, Judith Veronica Field. The Harmony of the World, Vol. 209. (Philadelphia, PA: American Philosophical Society, 1997). P. 304.

[14] Pierre-Simon de Leplace. Philosophical Essay on Probabilities (1814), 5th edition (1825), trans. Andrew I. Dale (1995), 2. 

[15] Byl, 255.