Mathematics: Is God Silent?

The central philosphical argument is that the similarity of structure of the physical world and that of many branches of mathematics shows that God made them both, and therefore that mathematics is Platonically pre-existing and hence discovered, not invented, by man.

The fallacy, I think, is that most of mathematics, and especially most of the mathematics Nickel cites, was occasioned and designed for the explicit purpose of providing models for nature. In short, I cannot be surprised that the models resemble the things modeled, any more than that a map should resemble the terrain it describes. .

As an evangelical Christian mathematician and computer scientist, I was hoping for a book that set forth the "discovered, not invented" argument with logical clarity, for I have been puzzled by that view. Disappointingly, this book isn't it. Fundamentally it presses the argument first by assertion, and then by testimonials of agreement by various mathematicians. Nickels also extensively uses quotations from the many works of theologian and philosopher of science Stanley Jaki. He does not, so far as I see, address the "mathematics as modeling tool" argument.

Nickels does a fair and clear job of expressing what he calls "the majority view", that mathematics is invented, and he cites various scientists holding that view.


Poorly argued and rather intellectually disreputable   September 1, 2009
Ethan M. (Holt, MI USA)
2 out of 4 found this review helpful

Fred Brook's review here on Amazon does much to address how poorly argued Nickel's book is. For some reason, there is a tendency amongst theological circles to accept an assertion for an argument. I am reminded of the joke about the Scientist, the Engineer, and the Mathematician, all of whom are bedded up in different rooms of a hotel struck suddenly by fire. Each one responds differently, with the engineer finding practical ways to escape, the scientist analyzing the fire and its cause and choosing the appropriate extinguisher to stifle the flames, and finally the mathematician holed up in his room as the flames lick the door, asserting "a solution exists!" and going back to bed. Perhaps the theistic tendency to accept assertion (the "Let there be light" argument) for argument is compounded in mathematical circles.

Whatever the reason Nickel's fails to make any real arguments doesn't really matter, of course, what matters is the fact itself, and there is really nothing but assertion in this book. Assertion, and, as Fred Brooks put it, "testimonials of agreement by various mathematicians." Unfortunately, while Mathematicians have a certain sort of clever in them for solving certain types of problems, they need not necessarily be good philosophers in the sense requisite here.

Unfortunately, instead of presenting or explaining the "discovered" view of Mathematics, by resorting to argumentum ad populum (or perhaps better put argumentum ad minorityum) and argumentum ad bare assertium, Nickels makes it seem like there really is no logical argument for the minority position he espouses. The real purpose of any argument is to make those with opposing views feel that your view is at least first of all rational, and secondarily, if possible, perhaps convince them it's correct. Nickels fails terribly at even the first goal of argument.

Richard Routh's review agrees with Fred Brook's in as far as the tracing of historical mathematical development goes, but I have to disagree with them both. The historical tracing is shallow at best, and often misleading and inaccurate.

The earliest review here by "A Customer" is worth responding to, making the common claim (or at least common in 1998) that only a theistic view allows for a world that is ordered and rational. Of course, this argument is incredibly weak, because the God presented in the Bible is affected by emotion, by whim, has regrets, and intervenes constantly with miraculous events that defy the laws of nature. Indeed, that theists make "the Universe follows laws, therefore God exists" argument is a testament to how much theism and religion has had to fumble to survive in a post-enlightenment age. It is enlightening to track the progress of religion from those who imagined God intervening in everything (from first-hand belief in the supernatural) to essentially various trends of deism.

A final note to those reading who are not Christians or theists: you won't like this book at all. It reads like a poor evangelical tract, and you will feel like it is insulting your intelligence. Those with skeptical minds need not apply, only the most ardent and credulous believers will appreciate the tone or content of this book.