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The Applicability of Mathematics as a Philosophical Problem
 
 
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The Applicability of Mathematics as a Philosophical Problem (Paperback)

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Editorial Reviews

Review

The book is clear despite its often technical subject matter, and the main theses are well argued for. It's packed with interesting examples from physics—particularly quantum mechanics…[and] is a valuable addition to the philosophy of science and philosophy of mathematics literature. It presents a rigorous and detailed presentation of a puzzle that I believe is crying out for attention.
--Mark Colyvan (Mind )

If mathematics is about finding solutions to well-defined problems, then philosophy is about finding problems in what previously we thought were well-established solutions. Mark Steiner's The Applicability of Mathematics as a Philosophical Problem mirrors both sides of this statement, admitting that mathematics is the key to solving problems in the physical sciences, but also asserting that this very applicability of mathematics to physics constitutes a problem...Steiner's challenge to naturalism is accessible, powerful, and well worth pondering.
--William A. Dembski (Books & Culture )


Product Description

This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics appears to assign the human mind a special place in the cosmos.

Mark Steiner distinguishes among the semantic problems that arise from the use of mathematics in logical deduction; the metaphysical problems that arise from the alleged gap between mathematical objects and the physical world; the descriptive problems that arise from the use of mathematics to describe nature; and the epistemological problems that arise from the use of mathematics to discover those very descriptions.

The epistemological problems lead to the thesis about the mind. It is frequently claimed that the universe is indifferent to human goals and values, and therefore, Locke and Peirce, for example, doubted science's ability to discover the laws governing the humanly unobservable. Steiner argues that, on the contrary, these laws were discovered, using manmade mathematical analogies, resulting in an anthropocentric picture of the universe as "user friendly" to human cognition--a challenge to the entrenched dogma of naturalism.

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Product Details

  • Paperback: 224 pages
  • Publisher: Harvard University Press (September 30, 2002)
  • Language: English
  • ISBN-10: 0674009703
  • ISBN-13: 978-0674009707
  • Product Dimensions: 8 x 5 x 0.6 inches
  • Shipping Weight: 8.6 ounces (View shipping rates and policies)
  • Average Customer Review: 1.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon.com Sales Rank: #1,921,586 in Books (See Bestsellers in Books)

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Mark Steiner
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9 of 25 people found the following review helpful:
1.0 out of 5 stars A disappointing book on a subject deserving better..., April 13, 2004
By Joao Leao "free-lance cosmologist" (Cambridge, Mass., United States) - See all my reviews
(REAL NAME)   
The "unreasonable effectiveness of mathematics in the physical world" as E.P. Wigner once called it is an very interesting and forgotten problem which is now a hot topic of philosophical speculation (Max Tegmark's recent article in Scientific American called "Parallel Universes" is a good introduction to the way physicists are trying to unravel it). But Mark Steiner's misleadingly titled book is not about this subject at all! Though he mentions Wigner's query --- and idiotically faults him for only counting the successes of math in physics, as if any or all of the "failures", none of which he identifies, would make the successes less surprising! --- the book turns out to be little more than a diatribe aiming to show that physicists, since Maxwell, have been (sin of sins!) resorting to "anthropocentric" reasoning! He identifies two "strains" of this dangerous trend
which he calls "Pythagorianism" and "Formalism" and he gives some anedoctical historically unfounded episodes which he diagnoses as examples of either of these nasty habits suggesting this shows some sort of reasoning in bad faith (ah ha!). It is clear from the text that Steiner has no background in contemporary physics and his examples rely on what he heard from other people and was quite unable to digest. But his real failings are, however, as a philosopher who seems as completely unaware of the recent debates
which animate the Philosophy of Physics as, for that matter, of any Philosophy of Math this side of Frege! Perhaps the most glaring misaprehension in this book is his unquestioned assimilation of Pythagorianism --- the belief that the ultimate components of the world are mathematical entities, as he puts it)
with anthropocentrism (the notion that human interests, values,
concerns must take center stage in any explanation). The fact is that 99% of all working physicists (and mathematecians) subscribe, consciously of unconsciously, to some variety of platonist realism which places mathematical essences in a realm transcendent of human concerns or mental categories of any sort!
Rather than facing this obvious fly in his ointment Steiner merely states: "but this is not a book about Platonism." which
apparently is good enough reason for him to ignore its existence!
(If you are wondering, his indictment of "nominalism" is not more
convincing...). In all a real waste of time and paper.
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