Yanofsky, Noson S.: The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us.

Weigel, Peter

YANOFSKY, Noson S. The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us. Cambridge, Mass.: The MIT Press, 2013. xiv + 403 pp. Cloth, $29.95--The author explores "what science, mathematics, and reason tell us cannot be revealed" by examining the limits of language, logic and identity, mathematics and infinity, computing technology, and science and cosmology. The author, a computer scientist, wants to focus on how scientists and mathematicians approach problems of knowledge, rather than how philosophers and epistemologists do. The book's philosophical outlook leans positivistic. Its length and range of topics suggest just giving summary highlights here.

Chapter one anticipates the main themes. The first sentence claims "a civilization can be measured" by the progress of "its science and technology" because, as the author assumes, areas like art, literature, politics, and morality "do not build on themselves." Chapter two explores the limits of language in self-referential paradoxes such as the liar's and Russell's. Chapter three on "Philosophical Conundrums" treats Zeno's paradoxes, emphasizing the limits of logic. The author sees ongoing philosophical disagreement over the Ship of Theseus problem as reason for his "extreme nominalism," where objects' identities and classifications are all in our mind as collections of sensations associated with names. He considers thinking that concrete objects possess identities and categories an ideology of extreme Platonism, an odd choice of label given the historical range of positions and issues here. (The author, to his credit, mentions he did not consult a robust range of sources here.) Elsewhere, and without obvious reasons, he finds that our "sense of beauty, wonder, ethics, and values" are "beyond reason and defy rational explanation."

Chapter four explains counterintuitive ideas about mathematical infinity "central to modern science," covering Cantor's work and whether mathematics and geometry are "discovered" or invented. Chapters five and six consider the tasks computers "can and cannot perform." He explains Turing's Halting Problem and interestingly how limits in computing strikingly affect other types of inquiry.

Chapters seven and eight explore limits and philosophical perplexities in the physical sciences. Yanofsky covers chaos theory, which studies systems where small differences in input yield widely divergent results (butterfly effect). Experimental paradoxes in quantum mechanics suggest to some physicists that the observer's own consciousness actively determines certain quantum outcomes. Some see these paradoxes as further implying a universe of significantly mind- or observer-dependent features, which collapses the very idea of scientific laws. Critics note that experimental choice affecting which quantum properties systems display need not warrant that consciousness itself determines it. If ideas made things, observes one philosopher, everyone would be an Einstein. Current well-known interpretations of quantum mechanics the author critically surveys and assesses as proving unsatisfactory. But quantum oddities and spatiotemporal paradoxes in relativity challenge the limits of science and ordinary intuition.

In chapter eight, Yanofsky sees Hume's problem of induction striking "at the core of science." He then examines why mathematics and geometry map the world so well. Since a deity explaining the world's intelligibility is "unsatisfactory" for nonbelievers, scientists prefer "less metaphysical ... testable" explanations. Discussion segues to the anthropic principle. Originally only a selection principle for cosmologies, one basic version states that the fundamental conditions of the universe must be such as to "permit the existence of intelligent human observers," since there are such observers. Some read it (more strongly) as implying finality or a Creator. Others in rejoinder posit the multiverse (ours as one of many) in order to argue that conscious life is still due to blind chance. The author ably surveys several positions on "our fine-tuned universe," concluding that we "simply do not know" the explanation.

Chapter nine returns to mathematics and logic as "the language of reason." Galois theory treats why certain math problems cannot be solved. Discussion winds down (appropriately) with Godel's incompleteness theorem; indeed, its applications are still debated. The concluding chapter observes that systems often impose limits on themselves. Language paradoxes stem from its self-referential capacities. The author sees reason's basic character as revolving around the principle of noncontradiction and striving for truth. Reason, he concludes, remains an inferentially limited tool.

Yanofsky allows that some prefer a more multifaceted conception of reason, with philosophers emphasizing wisdom and understanding in contrast with the book's stated formal and empirical emphases. Though not a trained philosopher, he offers some balanced and informed assessments; others could use more nuance or speculative caution, perhaps aided by looking into broader sources. A strength of the book is its considerable information on limits, perplexities, and current progress in logic, math, physics, and computing. One normally has to go to multiple books for this kind of information. Stanley Jaki covers similar themes as a philosopher of science, notably in The Limits of a Limitless Science and Other Essays.--Peter Weigel, Washington College