Concept

"A systematic revolution of basic concepts begins with Einsteinian science. In the very detail of its concepts a relativism of the rational and the empirical is established. Science then undergoes what Nietzche called "an upheaval of concepts," as if the earth, the universe, things, possessed a different structure from the fact that their explanation rests upon new foundations. All rational organization is "shaken" when the fundamental concepts undergo dialectical transformation."

"There are three aspects of thinking as more or less complete stages of it. These are, conception, judgment, and reasoning. They are not to be considered three distinct acts; not even three successive stages. No one of them could occur without each of the others."

"Conception is taking together into one idea the element of meaning common to a number of objects and things. ...Conception is... the simplest act of thinking; it is the apprehension of the universal, as perception is the apperception of the particular. We perceive this man; we conceive man. ...it is universal through its ideal element, or what it points to, not from its existence."

"Concepts that have proven useful in ordering things easily achieve such an authority over us that we forget their earthly origins and accept them as unalterable givens. Thus they come to be stamped as “necessities of thought,” “a priori givens,” etc. The path of scientific advance is often made impassable for a long time through such errors. For that reason, it is by no means an idle game if we become practiced in analyzing the long commonplace concepts and exhibiting those circumstances upon which their justification and usefulness depend, how they have grown up, individually, out of the givens of experience. By this means, their all-too-great authority will be broken. They will be removed if they cannot be properly legitimated, corrected if their correlation with given things be far too superfluous, replaced by others if a new system can be established that we prefer for whatever reason."

"Concepts have meaning only if we can point to objects to which they refer and to rules by which they are assigned to these objects."

"The belief in an external world independent of the percipient subject is the foundation of all science. But since our sense-perceptions inform us only indirectly of this external world, or Physical Reality, it is only by speculation that it can become comprehensible to us. From this it follows that our conceptions of Physical Reality can never be definitive; we must always be ready to alter them, that is, [to alter] the axiomatic basis of physics, in order to take account of the facts of perception with the greatest possible logical completeness."

"Concepts can only acquire content when they are connected, however indirectly, with sensible experience. But no logical investigation can reveal this connection; it can only be experienced. ...this connection ...determines the cognitive value of systems of concepts."

"I believe that the first step in the setting of a "real external world" is the formation of the concept of bodily objects... Out of the multitude of our sense experiences we take, mentally and arbitrarily, certain repeatedly occurring complexes of sense impressions... and we correlate to them a concept—the concept of a bodily object. Considered logically, this concept is not identical with the totality of sense impressions referred to; but it is a free creation of the human (or animal) mind. ...by means of such concepts and mental relations between them, we are able to orient ourselves in the labyrinth of sense impressions. These notions and relations, although free mental creations, appear to us stronger and more unalterable than the individual sense experience itself, the character of which... is never completely guaranteed."

"The aim of science is... a comprehension, as complete as possible, of the connection between the sense experiences in their totality, and... the accomplishment of this aim by the use of the minimum of primary concepts and relations."

"All concepts, even those which are closest to experience, are from the point of view of logic freely chosen conventions."

"Often it is only after immense intellectual effort, which may have continued over centuries, that humanity at last succeeds in achieving knowledge of a concept in its pure form, by stripping off the irrelevant accretions which veil it from the eye of the mind."

"We may come back to the more general question, what one should consider as the characteristic features of such a closed system of axioms and definitions. Perhaps the most important feature is the possibility of finding a consistent mathematical representation for it. This representation must guarantee that the system does not contain contradictions. Then the system must be suited to describe a wide field of experience. The great variety of phenomena in the field should correspond to the great number of solutions to the equations in the mathematical representation. The limitations of the field can generally not be derived from the concepts. The concepts are not sharply defined in their relation to nature, in spite of the sharp definition of their possible connections. The limitation will therefore be found from experience, from the fact that the concepts do not allow a complete description of the observed phenomena."

"[H]ow free are we in choosing the concepts for formulating our questions? Any scientific work can only be defined by formulating the questions... But in order to formulate the questions we need concepts by which we hope to get hold of the phenomena. These concepts are usually taken from the past history of science; they suggest already a possible picture of the phenomena. But if we are going to enter into a new realm of phenomena, these concepts may act as a collection of prejudices, which hamper progress... Even then we have to use concepts, and we can't help falling back on those given to us by tradition."

"The logical acts of the understanding by which concepts are generated as to their form are: 1. comparison, i.e., the likening of mental images to one another in relation to the unity of consciousness; 2. reflection, i.e., the going back over different mental images, how they can be comprehended in one consciousness; and finally 3. abstraction or the segregation of everything else by which the mental images differ... In order to make our mental images into concepts, one must thus be able to compare, reflect, and abstract, for these three logical operations of the understanding are essential and general conditions of generating any concept whatever. For example, I see a fir, a willow, and a linden. In firstly comparing these objects, I notice that they are different from one another in respect of trunk, branches, leaves, and the like; further, however, I reflect only on what they have in common, the trunk, the branches, the leaves themselves, and abstract from their size, shape, and so forth; thus I gain a concept of a tree."

"Concepts, like individuals, have their histories, and are just as incapable of withstanding the ravages of time as are individuals."

"Kant says that concept without percepts are empty, percepts without concepts are blind; it would perhaps be truer to say that concepts and percepts are inseparable; and if torn asunder, they are nothing."

"[W]hen we set out to apply... an idealized term, the operative question is not whether actual instances exist in reality to be designated by the new term. Rather, the question is, on what conditions the new idealized concept has any empirical relevance, and how it succeeds in throwing light, both on those situations to which it directly applies, and on those to which it does not. No actual object exemplifies with unlimited precision the mathematician's specification for a 'geometrical point' or 'Euclidean straight line', no real-life material system fully answers to the physical definition of a 'rigid body' or ; no human being conforms unfailingly to the judicial ideal of a 'reasonable man'; nor are there any absolutely perfect instances of the economist's 'free market'. Yet this leaves the explanatory significance of such idealized concepts unaffected and undiminished. Theoretically speaking, indeed, they can be just as revealing in negative as in positive cases. When we consider, for instance, why departs from the physicist's ideal of a 'perfect gas' more strikingly than oxygen, or when we discuss the conditions on which the workings of an can approximate to those of a 'free' market, it is the explanatory fruits of the concepts that matter, not their exemplifications."

"... mathematics is the science of skillful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts. Mathematics would soon run out of interesting theorems if these had to be formulated in terms of the concepts which already appear in the axioms. Furthermore, whereas it is unquestionably true that the concepts of elementary mathematics and particularly elementary geometry were formulated to describe entities which are directly suggested by the actual world, the same does not seem to be true of the more advanced concepts, in particular the concepts which play such an important role in physics."

"Abstraction"

"Conceptual model"