Thinking for decisions : deductive quantitative methods

C. West Auerbach, Leonard, ; Sadan, Simcha, Churchman

The pedagogy of this text is based on two theories, one related to learning and the other to the nature of mathematics. The theory of learning says that the student of decision making who is exposed to fairly rigid and precise materials needs constantly to be reaching out toward reality. Our purpose has been to create a text which proceeds as a pendulum; when the technical materials swing toward rigor, we introduce an example in which the student can sense the limits of rigor as well as its uses. The real world is basically ambiguous; rigor is one method of coping with ambiguity. The theory of the nature of mathematics is extremely reactionary. We do not subscribe to the fairly recent notion that mathematics is an abstract language based, say, on set theory. In many ways it is unfortunate that philosophers and mathematicians like Russell and flilbert were able to tell such a convincing story about the meaning-free formalism of mathematics. In Greek, mathematics simply meant learning, and we have adapted this original meaning to define the term as "learning to decide." Mathematics is a way of preparing for decisions through thinking. Sets and classes provide one way to subdivide a problem for decision preparation; a set derives its meaning from decision making, and not vice versa.

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