Logic and mathematics are nothing but specialised linguistic structures.
Reflective abstraction, however, is based not on individual actions but on coordinated actions.
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.
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.
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.
During the earliest stages of thought, accommodation remains on the surface of physical as well as social experience.
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.
The self thus becomes aware of itself, at least in its practical action, and discovers itself as a cause among other causes and as an object subject to the same laws as other objects.
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.
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.
Every acquisition of accommodation becomes material for assimilation, but assimilation always resists new accommodations.
The more the schemata are differentiated, the smaller the gap between the new and the familiar becomes, so that novelty, instead of constituting an annoyance avoided by the subject, becomes a problem and invites searching.
I have always detested any departure from reality, an attitude which I relate to my mother's poor mental health.
In genetic epistemology, as in developmental psychology, too, there is never an absolute beginning.
This means that no single logic is strong enough to support the total construction of human knowledge.
The principle goal of education is to create men who are capable of doing new things, not simply of repeating what other generations have done - men who are creative, inventive and discoverers
Knowing reality means constructing systems of transformations that correspond, more or less adequately, to reality.
From this time on, the universe is built up into an aggregate of permanent objects connected by causal relations that are independent of the subject and are placed in objective space and time.
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.
To express the same idea in still another way, I think that human knowledge is essentially active.
It is with children that we have the best chance of studying the development of logical knowledge, mathematical knowledge, physical knowledge, and so forth.
We recall how, starting with purely practical and quasi-physiological groups, the child begins by elaborating subjective groups, then arrives at objective groups, and only then becomes capable of representative groups.
Scientific thought, then, is not momentary; it is not a static instance; it is a process.
Knowledge, then, is a system of transformations that become progressively adequate.
The first type of abstraction from objects I shall refer to as simple abstraction, but the second type I shall call reflective abstraction, using this term in a double sense.
Scientific knowledge is in perpetual evolution; it finds itself changed from one day to the next.
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