Weaving Self-Evidence: A Sociology of Logic

February 26, 2009

Author: Claude Rosental

Edition: First

Publisher: Princeton University Press

Pages: 296

Price: £61.00 and £17.95

ISBN 9780691137414 and 9401

For philosophers, logic provides the normative foundations for all thought. Thus, they readily appeal to "proof", "demonstration" and "self-evidence" when discussing logic. But this language is based largely on mathematics, which rests on the manipulation of artificial symbols by a finite set of well-defined rules. "2 + 2 = 4" is true even in a world that consists of only three things. Logic is not meant to be quite so artificial. It must also connect with the things we normally think about to be truly foundational.

We have a sociological problem here: how does one show to others that logical formalism captures aspects of our reasoning that are sufficiently interesting to serve as a standard for our normal reasoning? This text has the distinct pedagogical virtue of showing how the question is handled in novice and expert settings. In the first case, Rosental is a participant-observer in an elementary logic class. In the second, he monitors an electronic newsgroup focused on assessing the validity of a purported proof concerning the limits of fuzzy logic.

When Rosental observes how elementary logic instructors try to persuade sceptical students about the logically correct translation of ordinary language statements, he finds that they dismiss any metaphysical notions that logic sifts the "intrinsic" meaning of a statement from "extrinsic" associations. Instead, they ask students to imagine how the statement would be made in the language of mathematics. If that fails, the instructors invoke the sheer mechanical application of the rules. The lesson seems to be that when threatened with philosophical doubt, one should revert to authoritarian sociology.

In the case of the fuzzy logic theorem, the doubters are as competent as the person who proposes to teach them a lesson with his new proof. Rosental documents a much more Hobbesian environment that intersperses personal and technical comments, until a journal that everyone recognises as authoritative formalises a resolution to the dispute. This sanitised published version then becomes the dispute's canonical presentation, which logicians may subsequently build on or contest.

Philosophers are often sceptical of the sociology of knowledge, because sociologists can't seem to tell the difference between detail and depth. In response, sociologists ask exactly what it is that they themselves have missed, since philosophical practice - as opposed to talk about practice - never makes it clear. Those gripped by this dialectic will find Weaving Self-Evidence an engaging text.

Who is it for? Advanced students in sociology, philosophy and maths.

Presentation: Laboured, but may help the less mathematical reader.

Would you recommend it? Decent secondary text.

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