In my November 29, 2007, posting, “Theology and Science? What about Philosophy?”, I asked why it was that just the two disciplines of science and theology were being singled out for treatment in John Polkinghorne’s Science and Theology, because I saw two other theories or disciplines that were at least as pertinent to theology as Polkinghorne’s science: philosophy and mathematics. In that posting I argued for the pertinence of philosophy, noting that the title for the work that I would have then written would have been Theology, Philosophy, and Science. I also said that, in the near future, I would turn to the role of mathematics and noted that the title for the work that would at that time come to my mind would be Theology, Philosophy, Mathematics, and Science. I will at least begin to consider the relationship or relationships that may obtain between mathematics and theology in today’s posting.
As I have noticed at least once or twice in earlier postings, Polkinghorne’s Science and Theology recognizes (p. 18) an important difference between science and theology:
Just as the object of scientific enquiry is the physical world, so the object of theological enquiry is God.
But he also views them as having an equally important similarity (p.20), in that they both “originate in interpreted experience.”
As with science, so even more with theology, the search for verisimilitudinous knowledge is subtle and manifold. Its character is cannot be reduced to a simple, flat description. For both disciplines, critical realism provides a concept that both acknowledges that there is a truth to be found and also recognizes that the finding of that truth is not achievable through the application of some straightforward and specifiable technique. Both disciplines are concerned with the search for motivated belief and their understandings originate in interpreted experience.
I am quite sceptical about the analogy, in particular about the implied thesis, that theologians “encounter” divine reality or somehow experience the divine. For while, as I said in my December 12, 2007, posting, “The Parallelism of Science and Theology,” it is evident in sensory experience that the physical reality of science exists, it is just not evident in sensory experience that a divine reality exists.I do not think, then, that we have a religious or theological experience, from which theology originates, that is analogous to the scientific experience from which science originates. That is the reason why religions like Judaism, Christianity, and Islam adopt versions of fideism, the thesis that we can have, but only can have, a genuine knowledge of the divine through faith, faith dispensing with evidence.
My reflections on Polkinghorne’s understanding that there is such a religious experience brought to mind a book I read a couple of decades ago, Philip J. Davis and Reuben Hersh’s The Mathematical Experience (Boston: Houghton Mifflin Company, 1981).
The title is significant and I will take up the notion of mathematical experience in a subsequent posting or two, for one might well think that the understanding that Davis and Hersh have of mathematical experience might suggest a way of supporting Polkinghorne’s thesis. In this posting, however, I want to lay some groundwork for that discussion.
Let’s start by taking note that, just as Polkinghorne sees there to be a parallelism between science and theology, so Davis and Hersh (p. 111-112) see there to be one between mathematics and theology or religion, of which theology is the theoretical component. First, they see a similarity between the subject realms of the two disciplines, in that both subject realms are nonmaterial.
Belief in a nonmaterial reality removes the paradox from the problem of mathematical existence, whether in the mind of God or in some more abstract and less personalized mode. If there is a realm of nonmaterial reality, then there is no difficulty in accepting the reality of mathematical objects which are simply one particular kind of nonmaterial object.
For now at least I’ll pass by the “simply” in “simply one particular kind of nonmaterial object” because I wish to enjoy the question that Davis and Hersh go on to ask and the breath-taking answer that they give to it.
So far, we have discussed the intereaction between the discipline of mathematics established religions. We might also ask to what extent does mathematics itself function as a religion. Insofar as the “laws of mathematics” are properties possessed by certain shared concepts, they resemble doctrines of an established church. An intelligent observer, seeing mathematicians at work and listening to them talk, if he himself does not study or learn mathematics, might conclude that they are devotees of exotic sects, pursuers of esoteric keys to the universe.
Then, just as Polkinghorne sees there to be a dissimilarity between science and theology, Davis and Hersh note one between mathematics and theology.
Nonetheless, there is remarkable agreement among mathematicians. While theologians notoriously differ in their assumptions about God, still more in the inferences they draw from these assumptions, mathematics seems to be a totally coherent unity with complete agreement on all important questions; especially with the notion of proof, a procedure by which a proposition about the unseen reality can be established with finality and accepted by all adherents. It can be observed that if a mathematical question has a definite answer, then different mathematicians, using different methods, working in different centuries, will find the same answers.
Seeing mathematics thus enjoying that mode of superiority, Davis and Hersh go on to ask:
Can we conclude that mathematics is a form of religion, and in fact the true religion?
I am not sure how far this was asked with tongue in cheek. But it doesn’t matter, because, whether intentionally or not, they have raised a serious point. That is, if we have made the determination that two disciplines both exist as genuine disciplines, then the question of what relationship or relationships there may be between them arises. And one at least logically possible relationship is that of identity; if the two are not distinct, they are identical. Here, Davis and Hersh have directed our attention to the at least logical possibility that mathematics and the true religion, or true theology, are identical.
If we hold that mathematics is the science of nondivine sets and numbers, while theology is the science of God, we’ll not be inclined to identify the two disciplines. If, however, we hold that sets and numbers are the divine realities, we’ll be inclined to join the ranks of the Pythagoreans and identify mathematics and theology.
To return to science and theology: if we have made the determination that the two disciplines exist both exist as genuine disciplines, then the question of what relationship or relationships there may be between them arises. And one at least logically possible relationship is that of identity; if the two are not distinct, they are identical. Here again, Davis and Hersh have, albeit indirectly, directed our attention to the at least logical possibility that science and theology are identical.
If we hold that science is the theory of nondivine physical reality, while theology is the science of God, we’ll not be inclined to identify the two disciplines. If, however, we hold that physical reality is the divine reality, we’ll be inclined to join the ranks of the disciples of some Spinoza and identify science and theology.
One last thought, one that I enjoy thinking about even though I am not in the least tempted to go in its direction: if mathematics were to be identical to theology and science too were to be identical to theology and, then, of course, all three would be identical.
January 2, 2008 at 3:15 pm
In addition to the points you make in comparing theology to mathematics, I offer the following:
Theology starts with the existence of “God” (or some supernatural concept) and attempts to understand the world (or parts of it) in terms of this “axiom”. Mathematics (often) starts from axioms and works out the implications to see if anything interesting arises, often with little regard to whether they have any bearing on the “real” world. So theology and mathematics are similar in that they use axioms. However, mathematics is both more modest and more accountable than theology. More modest, because mathematicians (most of them, anyway) do not claim that math axioms (regardless of how fascinating the resulting implications may be) are necessarily embodied in the real world (other than the world of ideas … let’s set aside questions of the “reality” of ideas for now, which I think boil down largely to word games). More accountable, because, as you pointed out, there is a rigorous standard of mathematical “proof”.
The whole enterprise of theology is built upon the assumption that there is indeed a God (which has a different flavor depending on the particular theology). But this “axiom” is open to question, as evidenced by the fact that there are numerous theologies with competing “1st axioms” that demand often radically different interpretations of what we see in the world (including rejection of well-established scientific theories and the facts that underlie them).
It can be an interesting exercise to take a particular “God axiom” and consider what other assumptions must be made in order to reconcile it with the world as we know it. It can even be a valuable exercise: If the other assumptions are too ridiculous, it calls into question either the God axiom or our confidence in our “observations” of the world. Generally theologians make the minimal changes to the God concept necessary to minimally reconcile it with the world (and then go through the process again and again over the centuries as the reach of reliable “observations” has grown) and keep themselves in business. A theologian that rejects the God-axiom is no longer a theologian in anything other than the “mathematical” sense (in which working out the consequences of or consistency of axioms is an interesting exercise in its own right but not necessarily relevant to anything out there in the real world).
January 2, 2008 at 4:13 pm
Dear Rational Reader and Readers of Rational Reader:
An probing and thought-provoking blog…
In my view, an issue arises when Polkinghorne makes reference to a “nonmaterial reality”. It makes it seem as though the object of a discipline has to be a kind of “thing”. Physics and chemistry and biology deal with tangible physical or organic “things” — look: We can see them; mathematics also deals with things, but non-material things.
I don’t believe that it is helpful to say that mathematics deals with things. If we want to see sets as “things”or “objects”, at best they are “objects” of consciousness, in the intentional sense — as objects of an act. Mathematics, I would suggest, is constructed through action and symbolic action; I don’t believe it is helpful to say, for example, that mathemmaticians “discover” sets and groups and all of that as if these words refer to extant realities or non-material forms that exist in the world (or in heaven).
A small thought experiment might help me make my point. (This comes from Piaget). A child is counting pebbles. She counts the pebbles and finds that there are 8. Then, starting with a different pebble, she counts again, and comes up with 8. And then again! She performs three different acts of counting. In yet another constructive act, she then abstracts what is common to all of these acts to construct the idea of conservation of number — the number remains the same despite how one counts them.
Is the notion of conservation a property of the world? Of a rational mind? Is it an “object” that exists in Platonic Heaven? I would suggest that the notion of conservation of number is a product of action-on-the-world; it is produced through what Piaget called “reflective abstraction”. Note: I’m not abstracting over objects; I’m abstracting over my actions-on-objects — a crucial difference!
And so, mathematics is very much grounded, I would say. It is grounded in the regularities that we find in our actions and symbolic actions. (This, actually is also the case for sciences, but that’s a somewhat different story.)
Mathematics is different from theology!
M.
January 4, 2008 at 2:32 am
Let me think this over, Craig. But one thought that comes to mind right away is that, if we distinguish axioms from theorems, as we should, a God-axiom would either be self-evident, as a tautology would be, or a postulate. It would hardly seem to be self-evident, which leaves it as a postulate and leaves the one affirming it in the same position of your modest mathematician.
January 6, 2008 at 3:03 pm
[...] have had two very substantial comments bearing on my January 2, 2008, posting, Religious Experience and Mathematical Experience I, the first from Craig Looney and the second from Michael Mascolo. They both deserve fuller [...]
January 13, 2008 at 5:32 pm
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