Picture: Billy Vaughn Koen: In the footsteps of René Descartes

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3 PROFESSIONAL ENGLISH TRANSLATION Tinkerer with a Method Everyone is an engineer, says engineer Billy Vaughn Koen. And because engineers do not think theoretically but heuristically, everything is a heuristic. Picture: Billy Vaughn Koen: In the footsteps of René Descartes One of the most daring books of the 17 th century was written by René Descartes: Discours de la méthode. In it, Descartes was so bold as to doubt that truth could be found only through Aristotle or divine inspiration. He preferred to rely on his own intellect. His Discours, published anonymously in light of Galileo s experience with the inquisition, is considered to be the seminal document of modern theory of science. Billy Vaughn Koen, Professor of Mechanical Engineering at the University of Texas at Austin, is no less daring. What Descartes has done for science, Koen wants to do for engineering and more than that, still: To be human is to be an engineer, he writes. Koen has been working on his intellectual construct for almost four decades. He is sufficiently experienced to introduce his impositions gently. Unlike scientists, engineers are not interested in exploring the world, but in changing it, he says. In place of theories, they employ heuristics. What is a heuristic? Anything that provides a plausible aid or direction in the solution of a problem. It needn t be true, or right, or without contradiction, only helpful. For example: One gram of plutonium gives one mega-watt day of energy might be the heuristic of the nuclear engineer, or, more generally: Allocate your resources to the weakest link. Which heuristic is used depends on the engineer s state of the art, which can change from time to time and from person to person. Up to this point, Koen s approach is suitable as a starting point for a future theory of engineering. From page 111 on, however, his path diverges from the Cartesian model, and slowly and progressively, he declares everything to be a heuristic. Literally, everything. Truth? Logic? Progress? Koen judges these terms to be unworthy of being set as absolutes. But they are suitable as heuristics. Even absoluteness is a heuristic. The term heuristic itself is a heuristic. Koen becomes assailable at the point where he ventures into unknown territory. The depiction of Gödel s theorem as a Texan comic, for example, is original but incorrect because these theorems do not apply to general arithmetic but to certain formal systems of arithmetic only. Those, however, who would precipitously launch an attack on Koen s central idea, soon find themselves in a trap. Koen can always deflect a pretty heuristic. As most radically skeptical positions, Koen s is almost entirely unfalsifiable. Fortunately, Koen does not have a compelling argument to support it. Tobias Hürter Billy Vaughn Koen: Discussion of the Method. Conducting the Engineer s Approach to Problem Solving. Oxford University Press,

4 The author responds: I am honored to have my book, Discussion of the Method: conducting the engineer s approach to problem solving, reviewed in the German edition of Technology Review, all the more so since MIT was my alma mater. I do take genteel exception to three points. First, inadvertently plutonium was substituted for uranium in the heuristic quoted in the review, One gram of uranium gives one mega-watt day of energy, that appears correctly on pages 66 and 254 of the original text. Second, it is not entirely clear what the purported error is in the concern over Gödel's Proof. If the issue is the passage from the comic characters to Gödel's Proof, the only purpose of the example was to capture the feel for the incompleteness aspect of Gödel for those who are unfamiliar with the concept. The mapping between Gödel and the Texans is, admittedly, extremely difficult and subtle, but correct. If the concern is with the scope of Gödel s Proof, we must simply disagree. I have checked with my sources, colleagues, and professionals in theoretical mathematics and we feel it is fair to claim that Gödel applies to all formal axiomatic systems that are sufficiently rich to include the expressive power of arithmetic. It is not clear what the reviewer could mean by general arithmetic that would not meet the criteria for susceptibility to Gödel s work. Unfortunately I must read the review in translation and may have misconstrued some salient points. And finally, the characterization of the author s position as unfalsifiable is answerable and the grave chide that fortunately, Koen does not have a compelling argument to support it. is very old. The unfairness in allowing one participant in a game (in the present case, a rationalist in a discussion between a rationalist and a skeptic) to make up the rules of the game (that is, to force the skeptic to produce a rational argument in support of his position) goes back at least to Sextus Empiricus 1 in the 2 nd or 3 rd Century C.E.. It is seen often in skeptical literature, perhaps most notably in Montaigne, who indicated that the Pyrrhonians needed a nonassertive language to state their case. Readers of my book will realize that the requirement to produce an argument in support of the Radical Skeptical position in a world in which everything is to be taken as heuristic is but one more interesting heuristic. In a similar fashion, the notions of unfalsifiablity (presumably a reference to Karl Popper s view that a statement must be falsifiable to be taken as scientific) and the concept of Radical Skepticism must also be taken as heuristics. So, too dare I say it must science itself. This is the trap the reviewer very astutely foresaw. These are but three, small quibbles, however, and I appreciate the reviewer s thoroughness, scholarship, and interest in my work. 1 Outline of Pyrrhonism I, 90, Loeb Classical Library, Harvard University Press

5 The reviewer responds: Dear Professor Koen, thank you for your letter concerning the review of your book in the German edition of Technology Review! I wrote the review -- and I wished there wre more books to review as original and inspiring as yours. I apologize for confusing uranium and plutonium, any resulting errors in German nuclear power plants are on my behalf. Concerning Gödel's theorem, my remark has the following background: Let us take set theory as our ambient theory for the moment, Zermelo-Fraenkel axioms or a bit weaker. Now consider the set T of all sentences true in the structure consisting of the natural numbers and the operations and relations of number theory. This is a complete and consistent theory, and a strengthening of Peano arithmetic. But it is NOT haunted by Gödel incompleteness. Of course, T is not recursively axiomatizable. The point is that Gödel's theorems only apply to theories that have semirecursive sets of axioms (you can strengthen this a bit). Anyway, your reasoning goes completely unaffected by this. I loved your book! With best regards --Tobias Huerter -- Tobias Hürter Technology Review Helstorfer Straße Hannover Germany phone +49 (511) (secr. -764) fax +49 (511)