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- The Problem of Learning
- Problemistics Courseware
- Corso su Problemistica
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Problemistics - Problémistique - Problemistica
The Art & Craft of Problem Dealing
Theory
Definition (Siegfried Frederick Nadel)
Definition (Karl Popper)
Definition (Deobold B. Van Dalen)
Formation (Abraham Kaplan)
The scientific outlook (Peter Caws)
Abstraction and reality (Manfred Eigen and Ruthild Winkler)
Classification (Albert Einstein)
Function (Albert Einstein and Leopold Infeld)
Function (George A. Kelly)
Function (John Ziman)
Function (Deobold B. Van Dalen)
Function (Abraham Kaplan)
New patterns (Abraham Kaplan)
Theory and empirical foundations (John Madge)
Theory and practice (Leonardo da Vinci)
Theory and practice (John Dewey)
Theory and practice (Abraham Kaplan)
Theory and understanding (Albert Einstein and Leopold Infeld)
Theory and knowledge (Abraham Kaplan)
Theory and prediction (Robert K. Merton)
Theory Evaluation (Neil McKinnon Agnew and Sandra W. Pyke)
Theory Validation (Abraham Kaplan)
Norms of Validation (Abraham Kaplan)
Theory Falsification (Thomas S. Kuhn)
Parsimony (John Ziman)
Fallibility (Ernest H. Hutten)
Plurality of theories (Albert Einstein and Leopold Infeld)
Plurality of theories (Thomas S. Kuhn)
Development and decline of theories (Albert Einstein and Leopold Infeld)
Old and new theories (Albert Einstein and Leopold Infeld)
[1962, First Edition 1957] Siegfried Frederick Nadel, The Theory of Social Structure
“Broadly speaking, we mean by a theory a body of interconnected propositions (hypotheses, generalizations) concerned with a particular problem area and meant to account for the empirical facts in it.” (p. 1)
“But ‘theory’ can also be understood in another, less ambitious, sense, namely as a body of propositions (still interconnected) which serve to map out the problem area and thus prepare the ground for its empirical investigation by appropriate methods.” “‘Theory’ here equals conceptual scheme or logical framework.” (p. 1)
[1959] Karl Popper, The Logic of Scientific Discovery
“Theories are nets cast to catch what we call ‘the world’: to rationalize, to explain, and to master it. We endeavour to make the mesh ever finer and finer.” (Chapter III, p. 59)
[1979, First edition 1962] Deobold B. Van Dalen, Understanding Educational Research. An Introduction, McGraw-Hill Book Company, New York
“A scientific theory consists of statements which connect concepts in a logically unified way to provide an interpretation of a particular segment of phenomena.”
“A scientific theory consists of concepts and their relations to one another.” (Chapter 3. p. 53)
[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania.
“... the formation of a theory is not just the discovery of a hidden fact; the theory is a way of looking at the facts, of organizing and representing them.” (Chapter VIII, p. 309)
[1965] Peter Caws, The Philosophy of Science
“Scientific theory ... constitutes a particular outlook on the world. The term comes, after all, from the Greek ‘theorein’, ‘to look at’; and a fair translation of ‘scientific theory’ would be ‘knowledgeable outlook’.”
“This is not to say that science ought to be adopted as the world outlook, to the exclusion of everything else; there are other ways of looking at the world, and we may not always want to look at it in the scientific way.”
(Part I, Chapter 12, p. 88)
[1983, First German Edition 1975] Manfred Eigen and Ruthild Winkler, Laws of the Game
“Theories are based on abstraction. They abstract what is regular and readily reproducible from reality and present it in an idealized form, valid only under certain assumptions and boundary conditions.” (p. 16)
“... no theory stands beyond experience. Indeed, observation of facts always precedes understanding.” (p. 117)
[1964] Albert Einstein in Abraham Kaplan, The Conduct of Inquiry
“We can distinguish various kinds of theories in physics. Most of them are constructive. They attempt to build up a picture of the more complex phenomena out of the materials of a relatively simple formal scheme from which they start out ... Along with this most important class of theories there exists a second, which I will call ‘principle-theories’. These employ the analytic, not the synthetic method. The elements which form their basis and starting point are not hypothetically constructed but empirically discovered ones, general characteristics of natural processes, principles that give rise to mathematically formulated criteria which the separate processes or the theoretical representations of them have to satisfy ... The advantages of the constructive theory are completeness, adaptability and clearness, those of the principal theory are logical perfection and security of the foundations.” (Chapter VIII, p. 299)
[1938] Albert Einstein and Leopold Infeld, The Evolution of Physics
“The aim of every theory is to guide us to new facts, suggest new experiments, and lead to the discovery of new phenomena and new laws.” (Chapter II, p. 76)
[1955] George A. Kelly, The Psychology of Personal Constructs
“A theory may be considered as a way of binding together a multitude of facts so that one may comprehend them all at once. When the theory enables us to make reasonably precise predictions, one may call it scientific.” (p. 18)
[1968] John Ziman, Public Knowledge. The social dimension of science, Cambridge University Press
"The strongest argument, surely, is that a theory provides a logical ordering, a pattern, for observations." (p. 38)
[1979, First edition 1962] Deobold B. Van Dalen, Understanding Educational Research. An Introduction, McGraw-Hill Book Company, New York
"Theories serve as tools and goals, as means and ends. As goals, they provide explanations for specific phenomena with maximal probability and exactitude. As tools, they provide a guiding framework for observation and discovery."
Some functions of a theory:
- Identification of relevant facts
- Formulation of logical constructs
- Classification of phenomena
- Summarization of facts
- Prediction of facts
- Revelation of needed research
(from Chapter 3, pp. 56-58)
[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania.
“It is true that the systematization effected by a theory does have the consequence of simplifying laws and introducing order into congeries of facts. But this is a by-product of a more basic function: to make sense of what would otherwise be inscrutable or unmeaning empirical findings.”
“Theory ... functions throughout inquiry and does not come into its own only when inquiry is successfully concluded.” “It guides the search for data, and for laws encompassing them.”
(Chapter VIII, p. 302)
[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania.
“The scientific achievement - especially in the formation of theories - often consists in discovering new significance in the old data, giving them significance by ordering them differently, making manifest a new pattern. It is in this way that descriptions often play an explanatory role: they allow us to see relations which had previously escaped notice.” (Chapter IX, p. 336)
“The theory explains, not just by virtue of the fact that it permits certain deductions, but because it institutes a more comprehensive pattern, of which the patterns constituted by the laws to be explained are recognizable components.”
“It is by allowing such diverse phenomena to be fitted into a pattern that the theory provides understanding.” (Chapter IX, p. 343)
[1965, First published 1953] John Madge, The Tools of Social Science, Longmans, London
“All theory requires some empirical foundation, however distant, and virtually all empirical inquiry is based on some theoretical grounds, however naive these may be.” (Introduction, p. 9)
Leonardo da Vinci in [1992, German Edition 1991] Bernhard E. Bürdek, Design
“Coloro che si innamorano della pratica senza scienza sono come quel timoniere che senza timone e compasso sale sulla nave e non è mai sicuro di dove va. La pratica deve essere fondata sempre su una teoria valida.” (p. 126) (original quotation from "Frammenti Letterari e Filosofici")
[1916] John Dewey, Essays in Experimental Logic
“The paradox of theory and practice is that theory is with respect to all other modes of practice the most practical of all things, and the more impartial and impersonal it is, the more truly practical it is.” (Chapter XIV, p. 441)
[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania.
“Theory is of practice, and must stand or fall with its practicality, provided only that the mode and contexts of its application are suitably specified.” (Chapter VIII, p. 296)
[1938] Albert Einstein and Leopold Infeld, The Evolution of Physics
“Science forces us to create new ideas, new theories. Their aim is to break down the wall of contradictions which frequently blocs the way of scientific progress. All the essential ideas in science were born in a dramatic conflict between reality and our attempt at understanding.” (Chapter IV, p. 280)
[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania.
“The truism that theory organizes knowledge should not be allowed to conceal the equally important truth that it changes the content of knowledge as well as the form.” (Chapter VIII, p. 306)
[1968] Robert K. Merton, Social Theory and Social Structure, Enlarged Edition
“The more precise the inferences (predictions) which can be drawn from a theory, the less the likelihood of alternative hypotheses which will be adequate to these predictions.”
“It is well known that verified predictions derived from a theory do not prove or demonstrate that theory; they merely supply a measure of confirmation, for it is always possible that alternative hypotheses drawn from different theoretic systems can also account for the predicted phenomena.”
(Part 1 - Chapter 4, p. 152)
[1969] Neil McKinnon Agnew and Sandra W. Pyke, The Science Game
“If we are comparing one theory with another, we can use the following guidelines:
(1) Which theory is the simplest to learn and use?
(2) Which theory is more readily open to test?
(3) Which theory provides us with sufficiently relevant and precise information at each step in our decision making in dealing with the question at hand?
(4) Which theory provides us with the most unique and original information, or allow us to predict the most new facts or solutions?
(5) Which theory best fits with other accepted facts or theories?
(6) Which theory is internally consistent, that is, doesn’t contradict itself?”
(Chapter 14, p. 163)
[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania.
“... a theory is not validated merely because it is accepted; rather it is accepted - by scientists at any rate - because it is believed to be validated.”
“The validation of a theory is not the act of granting an imprimatur but the act of deciding that the theory is worth being published, taught, and above all, applied - worth being acted on in contexts of inquiry or of other action. The acceptability of a theory will in any case be a matter of degree.”
(Chapter VIII, p. 312)
[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania.
“Norms of validation can be grouped according to the three major philosophical conceptions of truth: correspondence or semantical norms, coherence or syntactical norms, and pragmatic or functional norms.” (p. 312)
(a) Norms of correspondence. “We say that a theory is true if it ‘fits the facts’, that is, if the predictions made on the basis of the theory are in fact fulfilled. Yet it cannot be forgotten that how we conceptualize facts in turn depends on the theories which play a part in the cognition. The circle is not ... a vicious one, necessarily; it become vicious only if the facts are wholly constituted by the theory they are adduced to support, if they lack an observational core, and if the theory makes them out of whole cloth.” (p. 313)
“What counts in the validation of a theory, so far as fitting the facts is concerned, is the convergence of the data brought to bear upon it, the concatenation of the evidence.” (p. 314)
(b) Norms of coherence. “Coherence is a conservative principle, which ruthlessly suppresses as rebellion any movement of thought which might make for a scientific revolution." “Nevertheless, the point remains that theories can not be validated as though they were wholly self-contained.” “We could say, indeed, that the whole of our knowledge is brought to bear, for there are no fixed boundaries of possible relevance to the acceptability of the theory.” (p. 315)
(c) Pragmatic norms. "... success in what is usually called ‘practical’ applications is neither a necessary nor a sufficient condition for validation.” (p. 319)
“... the value of a theory lies not only in the answers it gives but also in the new questions it raises.” “The value of a theory is heuristic.” “... a good theory serves to explain old laws and to predict new ones.” (p. 321)
“A theory is validated, not by showing it to be invulnerable to criticism, but by putting it to good use, in one’s own problems or in those of coworkers.” (p. 322)
[1970] Thomas S. Kuhn, The Structure of Scientific Revolutions, Second Edition Enlarged
“... no theory ever solves all the puzzles with which it is confronted at a given time; nor are the solutions already achieved often perfect. On the contrary, it is just the incompleteness and imperfection of the existing data-theory fit that, at any time, define many of the puzzles that characterize normal science. If any and every failure to fit were ground for theory rejection, all theories ought to be rejected at all times.”
(Chapter XII, pp. 146-147)
[1968] John Ziman, Public Knowledge
“The oldest principle of the Philosophy of Science is Occam’s Razor (*) - the hypothesis of maximum simplicity. If knowledge is to be useful, it must be simple; it must subserve the greatest variety of phenomena to the most economical set of laws.” (Chapter 6, p. 125)
(*) “Entia non (sunt) multiplicanda praeter necessitatem." (William of Ockham)
[1962] Ernest H. Hutten, The Origins of Science
“... any established theory must be revisable in the light of new discovery, just as any new theory must be always open to any attempt at refuting it. Only infallible theories are fallacious.” (Chapter XVI, p. 226)
[1938] Albert Einstein and Leopold Infeld, The Evolution of Physics
“... there are phenomena, such as the rectilinear propagation of light, which can be equally well explained by the quantum and the wave theory of light.”
“There seems no likelihood of forming a consistent description of the phenomena of light by a choice of only one of the two possible languages. It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do!”
(Chapter IV, pp. 277-278)
[1970] Thomas S. Kuhn, The Structure of Scientific Revolutions, Second Ed. Enlarged
“Philosophers of science have repeatedly demonstrated that more than one theoretical construction can always be placed upon a given collection of data.” (Chapter VII, p. 76)
[1938] Albert Einstein and Leopold Infeld, The Evolution of Physics
“There are no eternal theories in science. It always happens that some of the facts predicted by a theory are disproved by experiment. Every theory has its period of gradual development and triumph, after which it may experience a rapid decline.”
“Nearly every great advance in science arises from a crisis in the old theory, through an endeavour to find a way out of the difficulties created. We must examine old ideas, old theories, although they belong to the past, for this is the only way to understand the importance of the new ones and the extent of their validity.”
(Chapter II, pp. 77-78)
[1938] Albert Einstein and Leopold Infeld, The Evolution of Physics
“The new theory shows the merits as well as the limitations of the old theory and allows us to regain our old concepts from a higher level.”
“To use a comparison, we could say that creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.” (Chapter III, pp. 158-159)