# „Is it always permissible to speak of the extension of a concept, of a class? And if not, how do we recognize the exceptional cases? Can we always infer from the extension of one concept's coinciding with that of a second, that every object which falls under the first concept also falls under the second?“

Grundgesetze der Arithmetik, 1893 and 1903

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##### Gottlob Frege5
deutscher Mathematiker, Logiker und Philosoph 1848 - 1925

## Ähnliche Zitate

### „First is the conception of being or existing independent of anything else. Second is the conception of being relative to, the conception of reaction with, something else. Third is the conception of mediation, whereby a first and second are brought into relation.“

—  Charles Sanders Peirce American philosopher, logician, mathematician, and scientist 1839 - 1914

The Architecture of Theories (1891)
Kontext: Three conceptions are perpetually turning up at every point in every theory of logic, and in the most rounded systems they occur in connection with one another. They are conceptions so very broad and consequently indefinite that they are hard to seize and may be easily overlooked. I call them the conceptions of First, Second, Third. First is the conception of being or existing independent of anything else. Second is the conception of being relative to, the conception of reaction with, something else. Third is the conception of mediation, whereby a first and second are brought into relation.

### „Carnap calls such concepts as point, straight line, etc., which are given by implicit definitions, improper concepts. Their peculiarity rests on the fact that they do not characterize a thing by its properties, but by its relation to other things. Consider for example the concept of the last car of a train. Whether or not a particular car falls under this description does not depend on its properties but on its position relative to other cars. We could therefore speak of relative concepts, but would have to extend the meaning of this term to apply not only to relations but also to the elements of the relations.“

—  Hans Reichenbach American philosopher 1891 - 1953

The Philosophy of Space and Time (1928, tr. 1957)

### „Mathematics is that form of intelligence in which we bring the objects of the phenomenal world under the control of the conception of quantity. [Provisional definition. ]“

—  George Holmes Howison American philosopher 1834 - 1916

"The Departments of Mathematics, and their Mutual Relations," Journal of Speculative Philosophy, Vol. 5, p. 164. Reported in Moritz (1914)
Journals

### „A philosophy which emphasises the idea of the One, is generally a dualistic philosophy in which the conception of Second receives exaggerated attention: for this One (though of course involving the idea of First) is always the other of a manifold which is not one.“

—  Charles Sanders Peirce American philosopher, logician, mathematician, and scientist 1839 - 1914

The Architecture of Theories (1891)
Kontext: The origin of things, considered not as leading to anything, but in itself, contains the idea of First, the end of things that of Second, the process mediating between them that of Third. A philosophy which emphasises the idea of the One, is generally a dualistic philosophy in which the conception of Second receives exaggerated attention: for this One (though of course involving the idea of First) is always the other of a manifold which is not one. The idea of the Many, because variety is arbitrariness and arbitrariness is repudiation of any Secondness, has for its principal component the conception of First. In psychology Feeling is First, Sense of reaction Second, General conception Third, or mediation. In biology, the idea of arbitrary sporting is First, heredity is Second, the process whereby the accidental characters become fixed is Third. Chance is First, Law is Second, the tendency to take habits is Third. Mind is First, Matter is Second, Evolution is Third.

### „The spurious axioms of the third kind from conditions proper to the subject whence they are transferred rashly to the object are plentiful, not, as in those of the Second Class, because the only way to the intellectual concept lies through the sensuous data, but because only by aid of the latter can the concept be applied to that which is given by experience, that is, can we know whether something is contained under a certain intellectual concept or not. To this class belongs the threadbare one of the schools: whatever exists contingently does at some time not exist. This spurious principle springs from the poverty of the intellect, having insight frequently into the nominal, rarely into the real, marks of contingency or necessity.“

—  Immanuel Kant German philosopher 1724 - 1804

Section V On The Method Respecting The Sensuous And The Intellectual In Metaphysics

### „My conception of freedom is no narrow conception. It is co-extensive with the freedom of man in all his majesty.“

—  Mahatma Gandhi pre-eminent leader of Indian nationalism during British-ruled India 1869 - 1948

Harijan (June 1942)
1940s

### „Just as the witticism brings two very different real objects under one concept, the pun brings two different concepts, by the assistance of accident, under one word.“

—  Arthur Schopenhauer, buch Die Welt als Wille und Vorstellung

The World as Will and Representation (1819; 1844; 1859)

### „Frege's pair of concepts (nominatum and sense) is compared with our pair (extension and intension). The two pairs coincide in ordinary (extensional) contexts, but not in oblique (nonextensional) contexts.“

—  Rudolf Carnap German philosopher 1891 - 1970

Quelle: Meaning And Necessity (1947), p. 124 as cited in: E. Cornell Way (1991) Knowledge Representation and Metaphor. p. 183

### „Objects do not depend on the concepts we have of them.“

—  Carlos Gershenson Mexican researcher 1978

Quelle: Artificial Societies of Intelligent Agents (2001), p. 5

### „OOA - Object-Oriented Analysis - is based upon concepts that we first learned in kindergarten: objects and attributes, wholes and parts, classes and members.“

—  Ed Yourdon American software engineer and pioneer in the software engineering methodology 1944 - 2016

Quelle: Object-oriented design (1991), p. 1; cited in: Sten Carlsson and Benneth Christiansson. (1999) " The Concept of Object and its Relation to Human Thinking: Some Misunderstandings Concerning the Connection between Object-Orientation and Human Thinking http://www.vits.org/publikationer/dokument/289.pdf." Informatica, Lith. Acad. Sci. 10.2. p. 147-160.

### „OOA - Object-Oriented Analysis - is based upon concepts that we first learned in kindergarten: objects and attributes, wholes and parts, classes and members.“

—  Peter Coad American software entrepreneur 1953

Peter Coad & Ed Yourdon (1991, p. 1); cited in: Sten Carlsson and Benneth Christiansson. (1999) " The Concept of Object and its Relation to Human Thinking: Some Misunderstandings Concerning the Connection between Object-Orientation and Human Thinking http://www.vits.org/publikationer/dokument/289.pdf." Informatica, Lith. Acad. Sci. 10.2. p. 147-160.

### „Reality is reality. It transcends every concept. There is no concept which can adequately describe it, not even the concept of interdependence.“

—  Thich Nhat Hanh Religious leader and peace activist 1926

The Miracle of Mindfulness (1999)

### „Neutrality has increasingly become obsolete and, except under very exceptional circumstances, it is an immoral and shortsighted conception.“

—  John Foster Dulles United States Secretary of State 1888 - 1959

[Ian Shapiro, Containment: Rebuilding a Strategy against Global Terror, https://books.google.com/books?id=i7L6if3mwzsC&pg=PA145, 2009, Princeton University Press, 145–]

### „From a very early age, we form concepts. Each concept is a particular idea or understanding we have about our world. These concepts allow us to make sense of and reason about the things in our world. These things to which our concepts apply are called objects.“

—  James Martin (author) British information technology consultant and writer 1933 - 2013

James Martin (1993, p. 17) as cited in: " CIS330 Object Oriented Approach Ch2 http://webcadnet.blogspot.nl/2011/04/cis330-object-oriented-approach-text_3598.html" webcadnet.blogspot.nl. 2011/04/16

### „If a is any definite number, then all numbers of the system R fall into two classes, A1 and A2, each of which contains infinitely many individuals; the first class A1 comprises all numbers a1 that are < a, the second class A2 comprises all numbers a2 that are > a; the number a itself may be assigned at pleasure to the first or second class, being respectively the greatest number of the first class or the least of the second. In every case the separation of the system R into the two classes A1, A2 is such that every number of the first class A1 is less than every number of the second class A2.“

—  Richard Dedekind German mathematician 1831 - 1916

p, 125
Stetigkeit und irrationale Zahlen (1872)

### „We can also see the class basis of the emerging concept of child hood in the system of child education that came in along with it. If childhood was only an abstract concept, then the modern school was the institution that built it into reality.“

—  Shulamith Firestone, buch The Dialectic of Sex

Quelle: The Dialectic of Sex (1970), Chapter Four

### „The intellect is prompted by nature to comprehend the whole breadth of being. … Under the concept of truth it knows all, and under the concept of the good it desires all.“

—  Marsilio Ficino Italian philosopher 1433 - 1499

Quelle: Five Questions Concerning the Mind (1495), p. 199

### „I think that my first poetic impulse is for music; second a definite conception with the ring of the universe…“

—  Vachel Lindsay American poet 1879 - 1931

A Poet in America (1935)

### „Every object that we perceive appears in innumerable aspects. The concept of the object is the invariant of all these aspects.“

—  Max Born physicist 1882 - 1970

The close of his Nobel lecture: "The Statistical Interpretations of Quantum Mechanics" (11 December 1954) http://nobelprize.org/nobel_prizes/physics/laureates/1954/born-lecture.html
Kontext: Can we call something with which the concepts of position and motion cannot be associated in the usual way, a thing, or a particle? And if not, what is the reality which our theory has been invented to describe?
The answer to this is no longer physics, but philosophy. … Here I will only say that I am emphatically in favour of the retention of the particle idea. Naturally, it is necessary to redefine what is meant. For this, well-developed concepts are available which appear in mathematics under the name of invariants in transformations. Every object that we perceive appears in innumerable aspects. The concept of the object is the invariant of all these aspects. From this point of view, the present universally used system of concepts in which particles and waves appear simultaneously, can be completely justified. The latest research on nuclei and elementary particles has led us, however, to limits beyond which this system of concepts itself does not appear to suffice. The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road.

### „Until now, Central America has always understood that governments that we recognize and support stay in power, while those we do not recognize and support, fall“

—  Noam Chomsky american linguist, philosopher and activist 1928

Quotes 1960s-1980s, 1980s, Talk at University of California, Berkeley, 1984
Kontext: There have been times, however, when US officials have described what's going on in relatively frank terms; sometimes quite clearly. One put the matter in these words: "The Central American area down to and including the Isthmus of Panama constitutes a legitimate sphere of influence for the United States [... ] We do control the destinies of Central America and we do so for the simple reason that the national interest absolutely dictates such a course [... ] We must decide whether we shall tolerate the interference of any other power in Central American affairs, or insist upon our own dominant position [... ] Until now, Central America has always understood that governments that we recognize and support stay in power, while those we do not recognize and support, fall [... ] Nicaragua has become a test case, it is difficult to see how we can afford to be defeated." That's fairly familiar. These remarks were made by Under Secretary of State Robert Olds in 1927, and the outside power that he was concerned about was Mexico. [audience laughter] Mexico at that time was a Russian proxy. We were no longer fighting Huns in the Dominican Republic, now we were fighting Russians in Nicaragua, and in particular the Russian proxy Mexico. Mexico was then a proxy of the Bolsheviks, so the Marines had to be sent in, once again, and they established Somoza, and established the National Guard which was the basis for American power throughout the region, and in fact one of the most effective murder-incorporated forces down there for many years. They killed Sandino, he was killed off by stealth couple of years later, the guerilla leader. As President Coolidge sent the Marines in, he made the following declaration: "Mexico is on trial before the world." Mexico is on trial before the world as a proxy of the Soviet Union when we send the Marines into Nicaragua. Now things have changed a little bit, now it's Nicaragua that's threatening Mexico as a Russian proxy... But again there's the same conclusion, you know, kill the spics and the niggers and so on. That follows no matter who's the proxy for who. And all of this is repeated at every moment of history with great seriousness and awe and so on as if it had some meaning, as if it wasn't just some black comedy.