BOOK REVIEWS

“An Epitome of Scientific and Rigorous Research on the Human Mind”, December 3, 2014

This review is for Mathematical Principles of Human Conceptual Behavior: The Structural Nature of Conceptual Representation and Processing (Scientific Psychology Series) Format: Hardcover Verified Purchase “First and foremost I should state that I have previous exposure to the work of Vigo. I have read his articles thoroughly and have applied his theories to various research projects. Even so, I was pleasantly surprised with the breadth of new material that can be found throughout the book. Indeed, I have noticed myself understanding certain aspects of the theory better (e.g., the construct of “categorical invariance”) after reading some of the novel descriptions and explanations, which cannot be found in his published articles. I was impressed with the apparent amount of thought and effort invested by Vigo in constructing each sentence throughout the book. One could say that Vigo succeeds in making each sentence clear, concise, and maximally informative. Although certain material is indeed technical, Vigo does interpret constructs in multiple ways, which in my opinion makes the vast majority of the text understandable by a scientific layman. Overall, the book provides a novel framework for systematically studying cognition in organisms and succeeds in presenting experimental paradigms that, in my opinion, are leading examples of how scientific psychology research should be conducted. Notwithstanding, the principle contribution, in my opinion, is the rigorous formulation of a new mathematical construct of invariance that transcends domain specific boundaries and incorporates constructs from three areas of mathematics. Indeed, the notion of categorical invariance put forth by Vigo is general enough to be applied to a plethora of scientific domains, not just in studying the nature of the human conceptual system.”
“A brilliant intellectual tour de force, a great contribution to cognitive science” By twf_neurosci_PhD on December 13, 2014 Format: Hardcover Verified Purchase “Why has greater progress in psychology, especially cognitive psychology, not been achieved compared to the regular and applied advances we have come to expect from physics, chemistry and biology? Over one hundred years after the first attempts at experimental research in psychology we have seen many theories come and go with a few peaks and many dark and barren valleys. For the most part, we have been left with many landmark studies, a collection of facts useful in particular contexts and domains, but with no key unifying conceptions that are empirically supported and little sense of direction. This is why psychology so desperately needs works like this. This book is a great achievement of original, universal and systematic thinking about the human mind. I recommend it enthusiastically to anyone who wants to become familiar with an alternative and powerful new way of understanding the mind as a non-probabilistic information processing system. In a clear style, the author integrates mathematical, philosophical, cognitive, psychological, logical, physical and computational insights in a manner that is, for the most part, within the grasp of well-educated and scientific laymen. The one exception might be the more technical mathematical portions, but they are so well set-up and explained that I was able to decipher them or translate around them to profitably mine their meaning. Vigo claims that “there is one particular property that ‘cracks’ the human code of concept formation” which he calls “categorical invariance.” This structural property enables us to extract essential information and patterns about the environment. This structured information is required to form concept representations, such as prototypes and rules, which form the basis of most of human thought and its consequent behavior. Vigo develops new formal notions of invariance—such as categorization, perception, information and choice—in order to decipher the mysteries of the mental universe and human behavior. His non-probabilistic unifying framework made me better appreciate how the “hard” sciences (physics and chemistry) and “soft” psychology need not be very far apart from a methodological standpoint. One of Vigo’s aims is to put scientific psychology on a much firmer experimental footing by providing a framework for developing deterministic models, methods and experimental designs analogous to those of classical physics. In addition, Vigo claims the elegant deterministic methods introduced in the book may be applied to several scholarly fields, such as the social sciences, computer science, informatics and even the physical sciences. Through his novel framework (called “categorical invariance theory” and “generalized invariance structure theory”), Vigo unifies under a single mathematical construct new measures of fundamental scientific ideas (e.g., information , similarity, and complexity) in terms immediately applicable in experimental designs. Experts who seek the mathematical details will find them in meticulous appendices. The work appears to be written to communicate to a wide audience with a critical interest in thinking and concept formation, which should be almost any cognitive psychologist. By the very nature of the subject matter, it is must reading for mathematical psychologists. Because of the broad applicability of Vigo's two main theories and their methodological framework to information research, this work will be useful to computer scientists, artificial intelligence researchers, systems neuroscientists, linguistic theorists, solid state electrical engineers, physicists, and probably many other scientists. Because of its clarification of constructs central to any empirical epistemology, it should be of strong interest to philosophers of psychology, of language, and of mind. Because Vigo's framework lays the foundation for a theory of universal science, it should be of strong interest to philosophers of science. The author first sets the tone of the book by claiming from the start that his theory should be viewed as taking “baby steps” toward a set of ultimate goals. Yet, I found the book to be a gigantic leap forward in terms of the number of unique, universal, and powerful new paradigms and formal ideas that it explores without relying on probability theory. Many precise ideas are introduced, such as categorical invariance, toward the creation of a completely original and elegant mathematical framework that has a realistic potential of unifying cognitive science. I could be wrong, but I believe that not since Newton in his Principia, has a scientist invented a whole new applied mathematical theory in order to overcome the limits of existing ones in predicting the phenomena of a particular scientific domain. Even better, the models actually fit the data with great precision and with few to no parameters. Perhaps it is my long search—through numerous great works of the twentieth century in psychology and philosophy—for the coherence of solutions that Vigo proposes that has brought me with a parched brain to this work that seems like an intellectual oasis. The sheer magnitude of mathematical and conceptual creativity is impressive and inspiring enough, but that thrill would wane if it were not for the fact that Vigo's discoveries are incredibly useful to researchers not only in the brain and behavioral sciences but, I am convinced, in many other sciences as well. I don't know how else to put it, this work is that ground- breaking. In my humble opinion, in time, I believe this book will join the ranks of the great scientific and philosophical works. Another review in this page compares Vigo’s systematic treatment of cognitive phenomena to the two seminal books by Chomsky and Marr. Yet, as great as are those theoretical works, neither of them achieves what Vigo achieves here, including support for his hypotheses by carefully controlled experiments. Their proposed theoretical frameworks were borrowed from well-known mathematical instruments and their proposed models did not fit human empirical data with the same degree of accuracy. Although I do not know for certain whether Vigo’s proposed “laws” are really laws in the strictest sense (only more experimentation will tell), after reading the book, I believe that they are very strong candidates. Besides, the rest of the contributions in the book are so diverse, useful, imaginative, unifying, and far reaching that they transcend the contribution of any one model in the book, law or not. One initial detraction was a few typos which anyone familiar with the field would recognize but others would not. After some Google digging, I found that Vigo has established a web site with an errata page at www.mathematicalprinciples.net, so potential buyers need not worry. Scientific psychology is finally coming out of its infancy. Rigorous methodology of the sort Vigo expounds will be its nursemaid, grounded in general and generative mathematical formulations free of the vagaries of probabilistic conceptions of behavior. Comprehensive, synthetic and unifying theories like Vigo's will be the parents of psychology's previously wayward progeny.”
***** 5/5
***** 5/5
***** 5/5
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II. Comment by Amazon.com user
“Praise for "Mathematical Principles of Human Conceptual Behavior"” December 4, 2014 Format: Kindle Edition Verified Purchase “This book is groundbreaking in a way attained by very few cognitive/perceptual works and I find myself comparing its significance to classics like Marr’s Vision and Chomsky’s Syntactic Structures. Few researchers have achieved the level of precision that is on display in this book. In my opinion, the framework described by Vigo has many potential applications. The core framework is specific enough to make very accurate predictions in a given cognitive domain (namely, classification learning) and general enough to make predictions across many domains (informativeness judgments, eye movements, choice, etc.). I predict that many researchers will (and indeed should) adopt the general framework described in order to account for results in many additional areas of cognitive research. I look forward to seeing what happens when these approaches are widely adopted by cognitive scientists and, indeed, by scientists in general.”
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The Structural Nature of Conceptual Representation and Processing

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MATHEMATICAL PRINCIPLES OF HUMAN CONCEPTUAL BEHAVIOR