"That faculty which perceives and recognizes the noble proportions in what is given to the senses, and in other things situated outside itself, must be ascribed to the soul. It lies very close to the faculty which supplies formal schemata to the senses, or deeper still, and thus adjacent to the purely vital power of the soul, which does not think discursively […] Now it might be asked how this faculty of the soul, which does not engage in conceptual thinking, and can therefore have no proper knowledge of harmonic relations, should be capable of recognizing what is given in the outside world. For to recognize is to compare the sense perception outside with the original pictures inside, and to judge that it conforms to them." (Johannes Kepler, "Harmonices Mundi" ["Harmony of the World"] , 1619)
"This formal and pure condition of sensibility to which the employment of the concept of understanding is restricted, we shall entitle the schema of the concept. The procedure of understanding in these schemata we shall entitle the schematism of pure understanding.
The schema is in itself always a product of imagination. Since, however, the synthesis of imagination aims at no special intuition, but only at unity in the determination of sensibility, the schema has to be distinguished from the image." (Immanuel Kant," Critique of Pure Reason", 1781)
“This schematism of our understanding, in its application to appearances and their mere form, is an art concealed in the depths of the human soul, whose real modes of activity nature is hardly likely ever to allow us to discover, and to have open to our gaze.” (Immanuel Kant, “Critique of Pure Reason”, 1781)
"Thus then does the Doctrine of Knowledge, which in its substance is the realisation of the absolute Power of intelligising which has now been defined, end with the recognition of itself as a mere Schema in a Doctrine of Wisdom, although indeed a necessary and indispensable means to such a Doctrine: - a Schema, the sole aim of which is, with the knowledge thus acquired, - by which knowledge alone a Will, clear and intelligible to itself and reposing upon itself without wavering or perplexity, is possible, - to return wholly into Actual Life; - not into the Life of blind and irrational Instinct which we have laid bare in all its nothingness, but into the Divine Life which shall become visible to us." (Johann G Fichte, "Outline of the Doctrine of Knowledge", 1810)
"Everything which distinguishes man from the animals depends upon this ability to volatilize perceptual metaphors in a schema, and thus to dissolve an image into a concept. For something is possible in the realm of these schemata which could never be achieved with the vivid first impressions: the construction of a pyramidal order according to castes and degrees, the creation of a new world of laws, privileges, subordinations, and clearly marked boundaries - a new world, one which now confronts that other vivid world of first impressions as more solid, more universal, better known, and more human than the immediately perceived world, and thus as the regulative and imperative world." (Friedrich Nietzsche, "On Truth and Lie in an Extra-Moral Sense", 1873)
"That immense framework and planking of concepts to which the needy man clings his whole life long in order to preserve himself is nothing but a scaffolding and toy for the most audacious feats of the liberated intellect. And when it smashes this framework to pieces, throws it into confusion, and puts it back together in an ironic fashion, pairing the most alien things and separating the closest, it is demonstrating that it has no need of these makeshifts of indigence and that it will now be guided by intuitions rather than by concepts. There is no regular path which leads from these intuitions into the land of ghostly schemata, the land of abstractions. There exists no word for these intuitions; when man sees them he grows dumb, or else he speaks only in forbidden metaphors and in unheard - of combinations of concepts. He does this so that by shattering and mocking the old conceptual barriers he may at least correspond creatively to the impression of the powerful present intuition." (Friedrich Nietzsche, "On Truth and Lie in an Extra-Moral Sense", 1873)
"Every definite image in the mind is steeped and dyed in the free water that flows around it. With it goes the sense of its relations, near and remote, the dying echo of whence it came to us, the dawning sense of whither it is to lead. The significance, the value, of the image is all in this halo or penumbra that surrounds and escorts it, - or rather that is fused into one with it and has become bone of its bone and flesh of its flesh; leaving it, it is true, an image of the same thing it was before, but making it an image of that thing newly taken and freshly understood. […] Great thinkers have vast premonitory glimpses of schemes of relations between terms, which hardly even as verbal images enter the mind, so rapid is the whole process. We all of us have this permanent consciousness of whither our thought is going." (William James, "The Principles of Psychology”, 1890)
"This is the greatest degree of impoverishment; the image, deprived little by little of its own characteristics, is nothing more than a shadow. It has become that transitional form between image and pure concept that we now term ‘generic image’, or one that at least resembles the latter. The image, then, is subject to an unending process of change, of suppression and addition, of dissociation and corrosion.
This means that it is not a dead thing; it is not at all like a photographic plate with which one may reproduce copies indefinitely. Being dependent on the state of the brain, the image undergoes change like all living substance, - it is subject to gains and losses, especially losses. But each of the foregoing three classes has its use for the inventor. They serve as material for different kinds of imagination - in their concrete form, for the mechanic and the artist; in their schematic form, for the scientist and for others." (Théodule-Armand Ribot, "Essay on the Creative Imagination", 1900)
"But surely it is self-evident that every theory is merely a framework or scheme of concepts together with their necessary relations to one another, and that the basic elements can be constructed as one pleases." (Gottlob Frege, [in "On the Foundations of Geometry and Formal Theories of Arithmetic" 1971] cca. 1903-1909)
"If the fresh facts which come to our knowledge all fit themselves into the scheme, then our hypothesis may gradually become a solution." (Arthur C Doyle, "The Adventure of Wisteria Lodge", 1908)
“A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts. But these concepts serve the purpose of bringing a multiplicity of real or imaginary sensory experiences into connection in the mind. To ‘visualise’ a theory, or bring it home to one's mind, therefore means to give a representation to that abundance of experiences for which the theory supplies the schematic arrangement” (Albert Einstein, “Geometry and Experience”, 1921)
"This is the reason why mechanical explanations are better understood than stories, even though they are more difficult to reproduce. The exposition, even if it is faulty, excites analogous schemas already existing in the listener’s mind; so that what takes place is not genuine understanding, but a convergence of acquired schemas of thought. In the case of stories, this convergence is not possible, and the schemas brought into play are usually divergent." (Jean Piaget, "The Language and Thought of the Child", 1926)
"At first sight the assimilative tendency shown by thought seems sufficient to secure stability in judgments. To assimilate, in psychology as in biology, is to reproduce oneself by means of the external world; it is to transform perceptions until they are identical with one’s own thought, i.e. with previous schemas. Assimilation is therefore preservation and, in a certain sense, identification." (Jean Piaget, "Judgement and Reasoning in the Child", 1928)
"In the presence of certain objects of thought or of certain affirmations the child, in virtue of previous experiences, adopts a certain way of reacting and thinking which is always the same, and which might be called a schema of reasoning. Such schemas are the functional equivalents of general propositions, but since the child is not conscious of these schemas before discussion and a desire for proof have laid them bare and at the same time changed their character, they cannot be said to constitute implicit general propositions. They simply constitute certain unconscious tendencies which live their own life but are submitted to no general systematization and consequently lead to no logical exactitude. To put it in another way, they form a logic of action but not yet a logic of thought." (Jean Piaget, "Judgement and Reasoning in the Child", 1928)
"The methods of progress in theoretical physics have undergone a vast change during the present century. The classical tradition has been to consider the world to be an association of observable objects (particles, fluids, fields, etc.) moving about according to definite laws of force, so that one could form a mental picture in space and time of the whole scheme. This led to a physics whose aim was to make assumptions about the mechanism and forces connecting these observable objects, to account for their behaviour in the simplest possible way. It has become increasingly evident in recent times, however, that nature works on a different plan. Her fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies. (Paul A M Dirac, "The Principles of Quantum Mechanics", 1930)
"[T]he sudden inventions characteristic of the sixth stage [of infant development] are in reality the product of a long evolution of schemata and not only of an internal maturation of perceptive structures. [..] This is revealed by the existence of a fifth stage, characterized by experimental groping. […] What does this mean if not that the practice of actual experience is necessary in order to acquire the practice of mental experience and that invention does not arise entirely preformed despite appearances? (Jean Piaget, "The origin of intelligence in children" 1936)
"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." (Jean Piaget, "The Construction Of Reality In The Child", 1950)
"Accommodation of mental structures to reality implies the existence of assimilatory schemata apart from which any structure would be impossible." (Jean Piaget, "The Construction Of Reality In The Child", 1950)
"What in fact is the schema of the object? In one essential respect it is a schema belonging to intelligence. To have the concept of an object is to attribute the perceived figure to a substantial basis, so that the figure and the substance that it thus indicates continue to exist outside the perceptual field. The permanence of the object seen from this viewpoint is not only a product of intelligence, but constitutes the very first of those fundamental ideas of conservation which we shall see developing within the thought process." (Jean Piaget, "The Psychology of Intelligence", 1950)
"A conceptual scheme is never discarded merely because of a few stubborn facts with which it cannot be reconciled; a conceptual scheme is either modified or replaced by a better one, never abandoned with nothing left to take its place."(James B Conant, "Science and Common Sense", 1951)
"Common sense […] may be thought of as a series of concepts and conceptual schemes which have proved highly satisfactory for the practical uses of mankind. Some of those concepts and conceptual schemes were carried over into science with only a little pruning and whittling and for a long time proved useful. As the recent revolutions in physics indicate, however, many errors can be made by failure to examine carefully just how common sense ideas should be defined in terms of what the experimenter plans to do." (James B Conant, "Science and Common Sense", 1951)
"As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries - not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer." (Willard v O Quine, "From a Logical Point of View", 1953)
"As perceivers we select from all the stimuli falling on our senses only those which interest us, and our interests are governed by a pattern-making tendency, sometimes called a schema. In a chaos of shifting impressions each of us constructs a stable world in which objects have recognisable shapes, are located in depth and have permanence." (Mary Douglas, "Purity and Danger", 1966)
"We realize, however, that all scientific laws merely represent abstractions and idealizations expressing certain aspects of reality. Every science means a schematized picture of reality, in the sense that a certain conceptual construct is unequivocally related to certain features of order in reality […]" (Ludwig von Bertalanffy, "General System Theory", 1968)
"Imagining is not perceiving, but images are indeed derivatives of perceptual activity. In particular, they are the anticipatory phases of that activity, schemata that the perceiver has detached from the perceptual cycle for other purposes. […] The experience of having an image is just the inner aspect of a readiness to perceive the imagined object. (Ulrich Neisser, "Cognition and reality" 1976)
"A schema is a configuration within the brain, either inborn or learned, against which the input of the nerve cells is compared. [...] the conscious mind [...] can fill in details that are missing from the actual sensory input and create a pattern in the mind which is not necessarily present in reality. In this way, the gestalt of objects - the impression [...] - is aided by the taxonomic powers of the schemata." (Edward O Wilson, "On Human Nature", 1978)
"A schema, then is a data structure for representing the generic concepts stored in memory. There are schemata representing our knowledge about all concepts; those underlying objects, situations, events, sequences of events, actions and sequences of actions. A schema contains, as part of its specification, the network of interrelations that is believed to normally hold among the constituents of the concept in question. A schema theory embodies a prototype theory of meaning. That is, inasmuch as a schema underlying a concept stored in memory corresponds to the meaning of that concept, meanings are encoded in terms of the typical or normal situations or events that instantiate that concept." (David E Rumelhart, "Schemata: The building blocks of cognition", 1980)
"Once we have accepted a configuration of schemata, the schemata themselves provide a richness that goes far beyond our observations. […] In fact, once we have determined that a particular schema accounts for some event, we may not be able to determine which aspects of our beliefs are based on direct sensory information and which are merely consequences of our interpretation." (David E Rumelhart, "Schemata: The building blocks of cognition", 1980)
"Mental schemas are not rigid. By lasting and laborious processes the mental schemas accommodate themselves, in the long run, to the features of real situations and become progressively more fit to manage them and to solve the problems with which we are faced. Each period of mental development is characterized by a system. of basic mental schemas which determine the capacity of the child to learn, to interpret, and to use the information he gets." (Efraim Fischbein, "Intuition and Proof", For The Leaning of Mathematics 3 (2), 1982)
"The basic idea is that schemata are data structures for representing the generic concepts stored in memory. There are schemata for generalized concepts underlying objects, situations, events, sequences of events, actions, and sequences of actions. Roughly, schemata are like models of the outside world. To process information with the use of a schema is to determine which model best fits the incoming information. Ultimately, consistent configurations of schemata are discovered which, in concert, offer the best account for the input. This configuration of schemata together constitutes the interpretation of the input. (David E Rumelhart, Paul Smolensky, James L McClelland & Geoffrey E Hinton, "Schemata and sequential thought processes in PDP models", 1986)
"If we are to have meaningful, connected experiences; ones that we can comprehend and reason about; we must be able to discern patterns to our actions, perceptions, and conceptions. Underlying our vast network of interrelated literal meanings (all of those words about objects and actions) are those imaginative structures of understanding such as schema and metaphor, such as the mental imagery that allows us to extrapolate a path, or zoom in on one part of the whole, or zoom out until the trees merge into a forest." (William H Calvin, "The Cerebral Code", 1996)
[Schemata are] knowledge structures that represent objects or events and provide default assumptions about their characteristics, relationships, and entailments under conditions of incomplete information. (Paul J. DiMaggio, "Culture and Cognition", Annual Review of Sociology 23, 1997)
No comments:
Post a Comment