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" Logic and mathematics are nothing but specialised linguistic structures. "
Jean Piaget
Logic
Mathematics
Structures
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" Our problem, from the point of view of psychology and from the point of view of genetic epistemology, is to explain how the transition is made from a lower level of knowledge to a level that is judged to be higher. "
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" It is with children that we have the best chance of studying the development of logical knowledge, mathematical knowledge, physical knowledge, and so forth. "
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" The practice of narrative and argument does not lead to invention, but it compels a certain coherence of thought. "
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" On the one hand, there are individual actions such as throwing, pushing, touching, rubbing. It is these individual actions that give rise most of the time to abstraction from objects. "
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" Logical activity is not the whole of intelligence. One can be intelligent without being particularly logical. "
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" With regard to moral rules, the child submits more or less completely in intention to the rules laid down for him, but these, remaining, as it were, external to the subject's conscience, do not really transform his conduct. "
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" To reason logically is so to link one's propositions that each should contain the reason for the one succeeding it, and should itself be demonstrated by the one preceding it. Or at any rate, whatever the order adopted in the construction of one's own exposition, it is to demonstrate judgments by each other. "
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" This means that no single logic is strong enough to support the total construction of human knowledge. "
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" Logical reasoning is an argument which we have with ourselves and which reproduces internally the features of a real argument. "
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" Every acquisition of accommodation becomes material for assimilation, but assimilation always resists new accommodations. "
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Acquisition
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" Scientific knowledge is in perpetual evolution; it finds itself changed from one day to the next. "
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" In other words, knowledge of the external world begins with an immediate utilisation of things, whereas knowledge of self is stopped by this purely practical and utilitarian contact. "
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" I have always detested any departure from reality, an attitude which I relate to my mother's poor mental health. "
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" During the earliest stages the child perceives things like a solipsist who is unaware of himself as subject and is familiar only with his own actions. "
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" I always like to think on a problem before reading about it. "
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Problem
" The current state of knowledge is a moment in history, changing just as rapidly as the state of knowledge in the past has ever changed and, in many instances, more rapidly. "
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Moment
History
Knowledge
" To express the same idea in still another way, I think that human knowledge is essentially active. "
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" Play is the answer to the question, 'How does anything new come about?' "
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" To accustom the infant to get out of its own difficulties or to calm it by rocking it may be to lay the foundations of a good or of a bad disposition. "
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" Egocentrism appears to us as a form of behavior intermediate between purely individual and socialized behavior. "
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Individual
Behavior
" During the first few months of an infant's life, its manner of taking the breast, of laying its head on the pillow, etc., becomes crystallized into imperative habits. This is why education must begin in the cradle. "
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Head
Habits
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" Knowing reality means constructing systems of transformations that correspond, more or less adequately, to reality. "
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" Scientific thought, then, is not momentary; it is not a static instance; it is a process. "
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Then
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" In genetic epistemology, as in developmental psychology, too, there is never an absolute beginning. "
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Genetic
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" Before playing with his equals, the child is influenced by his parents. He is subjected from his cradle to a multiplicity of regulations, and even before language he becomes conscious of certain obligations. "
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" The principle goal of education in the schools should be creating men and women who are capable of doing new things, not simply repeating what other generations have done. "
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" The child of three or four is saturated with adult rules. His universe is dominated by the idea that things are as they ought to be, that everyone's actions conform to laws that are both physical and moral - in a word, that there is a Universal Order. "
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" Logical positivists have never taken psychology into account in their epistemology, but they affirm that logical beings and mathematical beings are nothing but linguistic structures. "
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" Reflective abstraction, however, is based not on individual actions but on coordinated actions. "
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" The goal of education is not to increase the amount of knowledge but to create the possibilities for a child to invent and discover, to create men who are capable of doing new things. "
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