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Mathematics: Is God Silent?

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This is a pretty good book on the history and philosophy of mathematics for interested laymen and high-school and college students. There is a wealth of interesting material, an extensive bibliography, and a careful and complete index.

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.

James Nickel's work is a masterpiece! It does an excellent job of tracing the historical development of mathematics and reviewing its impact on history and philosophy. It is relatively easy reading, but not for lower than the high school level. Nickel clearly communicates the loud voice mathematics has had in showing God's hand in creation. He shows, from philosophical history, the societal implications when men fail to explicitily recognize God's role in mathematics.

This book is delightful reading and a great aid to the Christian mathematics teacher. Nickels put mathematics into its historical context and in so doing shows how its development requires a fundamental assumption that the world we live in is rational and harmoniously ordered. Only the biblical God provides such a context.

This book is delightful reading and a great aid to the Christian mathematics teacher. Nickels put mathematics into its historical context and in so doing shows how its development requires a fundamental assumption that the world we live in is rational and harmoniously ordered. Only the biblical God provides such a context.

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.

The great mathematician Paul Erdos remarked, "Mathematics is the only infinite human activity." He admitted, "It will be millions of years before we'll have any understanding and even then it won't be a complete understanding, because we're up against the infinite." Mathematics cannot be explained by the physical world alone. Erdos goes on to profess, "If you believe in God, the answer is obvious. Mathematical truths are there ... and you just rediscover them." Number theorist Andre Weil quipped, "God exists since mathematics is consistent, and the Devil exists since we cannot prove it."

Truth and oddities found in Mathematics can bring great glee, yet there is also awesome power within. And in James Nickel's, "Mathematics: Is God Silent?" one finds how the apologetic of Van Til relates to mathematics. Nickel shows why mathematics can only be accounted for by Christian theism; He reveals how the ontic attributes of God are evidenced in mathematical truths as he demonstrates that the application and understanding of math is never neutral.

Infinite numbers exist in theory and only presupposing an infinite triune God can epistemically justify infinite numbers. One can count from one to two to three... and go on infinitely. Yet our vast universe is finite. God is the a priori truth condition for infinite numbers. Without an infinite God, one cannot account for infinite numbers whereas the cosmos is finite and lacks the capacity to account for mathematics; something not limited to the material finite universe but something transcendent is the only ground possible.

Mathematics: God's Diversity in Unity

Great is our Lord, and mighty in power; His understanding is infinite (Psalms 147:5).

Newsweek magazine reluctantly conceded its ignorance with the question: "Why are the laws of nature mathematical? It's something that's been gnawing at scientists for about 2500 years." God sustains and holds all things together. This is the reason that mathematical truth applies to the physical sciences and physics. God lays the foundation, so that rational mankind can trust and utilize mathematics and physics. The diverse parts (diversity of particular numbered things - the many) and specific applications of mathematics agree (agreement is an expression of unity - the one) with one another because of the tri-unity of God. Without God, one could not study mathematics because it is a theological study of the unity and the diversity in our world. The eternal and infinite God is the absolute precondition that makes mathematics possible.

Mathematics Requires Morality

The use of mathematics demands morality. Disclaim God and His moral law and there is no obligation to affirm that two plus two equal four, and that "A" cannot be "A" and "non-A" at the same time, in the same way. "Must" I affirm mathematical or logical truth? If so, I must provide objective unchanging moral grounds for the obligation, and that requires an unchanging God. For two plus three not to be four, anywhere at any time, requires a universal truth: which presupposes an all-knowing God (who supplies the moral law). God's law commands all men to tell the truth and forbids lying. This is the reason we "ought" to affirm two plus three equal five.

Presupposing God as the solution to all questions and the standard for truth does not mean that we must construct a theological postulate just to perform mundane tasks. Yet every simple task and every piece of routine communication presupposes the triune God because we use logic and morality in all those endeavors. God is the precondition for all logic and morality. If we presuppose anything other than God as our starting point, we end up with absurd and contradictory affirmations. The tri-unity of God--the Father, the Son, and the Holy Spirit--is inescapable if we want to make sense out of our world. To reject the triune God is to end up asserting your own philosophical demise. Deny God and you commit logical suicide.

James Nickel offers many sundry quotes concerning the history of mathematics and delivers numerous assertions pertaining to the necessity for the theistic grounding of math (yes many are touching on Ad Verecundiam, but all treatises must at times tread this ground for communication purposes). This is a great book for apologists, philosophers, ministers, and is written in an accessible style for students.

Your throne is established from of old; You are from everlasting (Psalms 93:2).
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