Representation and Invariance of Scientific Structures

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences.

Advance Praise for Patrick Suppes

This work is a summa of Professor Suppes' contributions extending over fifty years to the theory of set-theoretical theories and representations, with emphasis on theories in the empirical sciences. This is surely a work that belongs in the library of every serious student and scholar in the philosophy of science, as well as researchers in mathematical psychology and the foundations of statistics.
–Ernest W. Adams
University of California, Berkeley

The chapter on probability is an admirable, entirely new synthesis on a subject that has been a continuing concern for Suppes. The thorough discussion of no less than six representations—among them propensity as a fully-fledged approach—definitely cracks the sterile “objective versus subjective” forced choice, and will bring a major liberation for all who are concerned by probability, especially statisticians.
–Henry Rouanet
Université René Descartes

Suppes makes the case that scientific theories are, above all, hierarchies of models that represent phenomena at various levels of abstraction. They range from models of empirical structures to models of theoretical structures, bridging experimentation and abstract theoretical formulations by means of invariant properties. From his extensive examination of both structures there emerges a constructivist approach to the philosophy of science, characterized by a distinctive pluralistic and pragmatic flavor.
–Maria Carla Galavotti
Università di Bologna

Translated into Chinese.

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10/1/2002