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 ReichenbachRelated topics
car concept description example extend fact given last line meaning particular peculiarity point position relation relative speak straight term thing train under etc relations elements things fallsRelated quotes
Preservation, renewal, and reform of the Union was my main political and, if you will, moral task in my position as president of the USSR. I consider it my greatest sorrow and misfortune that I did not succeed in preserving the country as a single whole. All my efforts were focused on trying to preserve that unity. Incidentally, more and more statements are heard today, including some by participants in the Belovezh accord, that the "soft form of Union Gorbachev proposed" might have protected our nations and nationalities from painful experiences. But, as the saying goes, the train has already left the station.
Mikhail Gorbachev
Saussure took the sign as the organizing concept for linguistic structure, using it to express the conventional nature of language in the phrase "l'arbitraire du signe". This has the effect of highlighting what is, in fact, the one point of arbitrariness in the system, namely the phonological shape of words, and hence allows the non-arbitrariness of the rest to emerge with greater clarity. An example of something that is distinctly non-arbitrary is the way different kinds of meaning in language are expressed by different kinds of grammatical structure, as appears when linguistic structure is interpreted in functional terms.
Michael Halliday
I do not think that the time is right to talk about democracy in its absolute concept. Arab societies marginalized their modern thinkers and scholars for the elders who stopped their time before fourteen centuries, which is the difference between us and them .. Therefore, it was necessary to work on spreading a more realistic culture in which modern science has a more open place. Take, for example, if we asked the Tunisian people (he meant former President Bourguiba then and not now) to hold a referendum on his position on women's education, then I can assure that 99.99% will refuse her education.
Habib Bourguiba
Our mathematical concepts, structures, ideas have been invented as tools to organise the phenomena of the physical, social and mental world. Phenomenology of a mathematical concept, structure, or idea means describing it in its relation to the phenomena for which it was created, and to which it has extended in the learning process of mankind, and, as far as this description is concerned with the learning process of the young generation, it is didactical phenomenology, a way to show the teacher the places where the learner might step into the learning process of mankind.
Hans Freudenthal
The method of successive approximations is often applied to proving existence of solutions to various classes of functional equations; moreover, the proof of convergence of these approximations leans on the fact that the equation under study may be majorised by another equation of a simple kind. Similar proofs may be encountered in the theory of infinitely many simultaneous linear equations and in the theory of integral and differential equations. Consideration of semiordered spaces and operations between them enables us to easily develop a complete theory of such functional equations in abstract form.
Leonid Kantorovich
