I ON THE PRIMITIVE TERM OF LOGISTICf IN this article I propose to establish a theorem belonging to logistic concerning some connexions, not widely known, ...

2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive (...) reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can be given, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but no proved until much later. In the same way, solutions to problems can be guessed, and a god guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser."-From the Dust Jacket. (shrink)

Hans Krebs' discovery, in 1932, of the urea cycle was a major event in biochemistry. This article describes a program, KEKADA, which models the heuristics Hans Krebs used in this discovery. KEKADA reacts to surprises, formulates explanations, and carries out experiments in the same manner as the evidence in the form of laboratory notebooks and interviews indicates Hans Krebs did. Furthermore, we answer a number of questions about the nature of the heuristics used by Krebs, in particular: How domain‐specific are (...) the heuristics? To what extent are they idiosyncratic to Krebs? To what extent do they represent general strategies of problem‐solving search?The relative generality of KEKADA allows us to view the control structure of KEKADA and its domain‐independent heuristics as a model of scientific experimentation that should apply over a broad domain. (shrink)

Fourteen subjects were tape‐recorded while they undertook to find a law to summarize numerical data they were given. The source of the data was not identified, nor were the variables labeled semantically. Unknown to the subjects, the data were measurements of the distances of the planets from the sun and the periods of their revolutions about it—equivalent to the data used by Johannes Kepler to discover his third law of planetary motion.Four of the 14 subjects discovered the same law as (...) Kepler did (the period varies as the 3/2 power of the distance), and a fifth came very close to the answer. The subiects' protocols provide a detailed picture of the problem‐solving searches they engaged in, which were mainly, but not exclusively, in the space of possible functions for fitting the data, and provide explanations as to why some succeeded and the others failed.The search heuristics used by the subjects are similar to those embodied in the BACON program, computer simulation of certain scientific discovery processes. The experiment demonstrates the feasibility of examining some of the processes of scientific discovery by recreating, in the laboratory, discovery situations of substantial historical relevance. It demonstrates also, that under conditions rather similar to those of the original discoverer, a law can be rediscovered by persons of ordinary intelligence (i.e., the intelligence needed for academic success in a good university). The data for the successful subjects reveal no “creative” processes in this kind of a discovery situation different from those that are regularly observed in all kinds of problem‐solving settings. (shrink)

The task of axiomatizing physical theories has attracted, in recent years, some interest among both empirical scientists and logicians. However, the axiomatizations produced by either one of these two groups seldom appear satisfactory to the members of the other. It is the purpose of this paper to develop an approach that will satisfy the criteria of both, hence permit us to construct axiomatizations that will meet simultaneously the standards and needs of logicians and of empirical scientists.