Representation and invariance of scientific structures (Q2736604)

``I began this book as a young man [\dots]. I finish it [\dots] at the age of 80'', Suppes writes in the preface. Here are some key words related to his interests and to this book: logic, model, learning, axiomatics, probability, statistics, randomness, automata, grammars, language, visual space, measurement, perception, robots, utility, brain-wave representation, hidden variables; we add the key words brought to attention by the title of this book: representation, invariance and scientific structures. In all fields related to these concepts, Suppes has provided essential contributions. His results are concerned with fields such as pure mathematics (especially probability theory, geometry and mathematical logic), mathematical psychology, artificial intelligence, philosophical logic, philosophy of science, foundations of mathematics and of physics, mathematical and computational linguistics, mathematical sociology.NEWLINENEWLINENEWLINEThe present book goes across all these topics. It is organized in a preface, eight parts, a summary table of representation and invariance theorems by chapter, a list of references, an author index and an index of terms.NEWLINENEWLINENEWLINEPart 1, Introduction, gives a general view, explains what is a scientific theory and how to read this book. Part 2, Axiomatic definition of theories, discusses models in science, theories with standard formalization, theories defined by set-theoretical predicates and historical perspectives on the axiomatic method. Part 3, Theory of isomorphic representation, is concerned with various kinds of representation, isomorphism of models, representation theorems, representation of elementary measurement structures, machine representation of partial recursive functions, philosophical views of mental representations. Part 4, Invariance, discusses invariance, symmetry and meaning, invariance of qualitative visual perceptions, invariance in theories of measurement, the lack of invariance of fundamental equations of physical theories and entropy as a complete invariant in ergodic theory. Part 5, Representations of probability, discusses the formal approach, the classical approach, the logical approach and the subjective probability, randomness for finite and for infinite sequences, the propensity representations of probability and pragmatism about probability. Part 6, Representations of space and time, discusses the classical and the relativistic space-time as well as various aspects of the visual space. Part 7, Representations in mechanics, analyses the classical particle mechanics, the representation theorems for hidden variables in quantum mechanics and the weak and strong reversibility of causal processes. Part 8, Representations of language, is concerned with the Chomskian hierarchy of formal languages, the representation theorems for grammars, the stimulus-response representation of finite automata, the representation of linear models of learning by stimulus-sampling models, the robotic machine learning of comprehension grammars for ten languages and the language-brain relation.