The statement is so frequently made that the differential calculus deals with continuous magnitude, and yet an explanation of this continuity is nowhere given; even the most rigorous expositions of the differential calculus do not base their proofs upon continuity but, with more or less consciousness of the fact, they either appeal to geometric notions or those suggested by geometry, or depend upon theorems which are never established in a purely arithmetic manner. Among these, for example, belongs the above mentioned theorem, and a more careful investigation convinced me that this theorem, or any one equivalent to it, can be regarded in some way as a sufficient basis for infinitesimal analysis. It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity. I succeeded Nov. 24, 1858.
Richard DedekindRelated topics
above arithmetic base calculus continuity definition differential example geometry given infinitesimal less magnitude nowhere real theorem thus way yetRelated quotes
[We are now] in a position to judge of the validity of the objection which has been made, that the principle of Natural Selection depends on a succession of favourable chances. The objection is more in the nature of an innuendo than of a criticism, for it depends for its force upon the ambiguity of the word chance, in its popular uses. The income derived from a Casino by its proprietor may, in one sense, be said to depend upon a succession of favourable chances, although the phrase contains a suggestion of improbability more appropriate to the hopes of the patrons of his establishment. It is easy without any very profound logical analysis to perceive the difference between a succession of favourable deviations from the laws of chance, and on the other hand, the continuous and cumulative action of these laws. It is on the latter that the principle of Natural Selection relies.
Ronald Fisher
The concept of the « struggle for existence » has been applied to microbial interrelationships in nature in a manner comparable to the effects assigned by Darwin to higher forms of life. It has also been suggested that the ability of a microbe to produce an antibiotic substance enables it to survive Giom. in competition for space and for nutrients with other microbes. Such assumptions ppear to be totally unjustified on the basis of existing knowledge. Before we proceed with a discussion of the formation and activities of antibiotics under natural conditions, we must consider certain fundamental aspects of the problem of antibiotic production under controlled laboratory or factory conditions... All the discussion of a "struggle for existence" in which antibiotics are supposed to play a part, is merely a figment of the imagination, and an appeal to the melodramatic rather than the factual.
Selman Waksman
Approximately, three billion people of the world live on less than 2.5 dollars a day, and over a billion people live without having even one sufficient meal on a daily basis. Forty-percent of the poorest world populations only share five percent of the global income, while twenty percent of the richest people share seventy-five percent of the total global income. More than twenty thousand innocent and destitute children die every day in the world because of poverty.
What is the justification for the presence of hundreds of US military and intelligence bases in different parts of the world...? An assembly of people in contradiction with the inner human instincts and disposition who also have no faith in God and in the path of the divine prophets, replace their lust for power and materialistic ends with heavenly values. To them, only power and wealth prevail, and every attempt must bring into focus these sinister goals...
Mahmoud Ahmadinejad
Man experiences a multitude of needs, on whose satisfaction his happiness depends, and whose non-satisfaction entails suffering. Alone and isolated, he could only provide in an incomplete, insufficient manner for these incessant needs. The instinct of sociability brings him together with similar persons, and drives him into communication with them. Therefore, impelled by the self-interest of the individuals thus brought together, a certain division of labor is established, necessarily followed by exchanges. In brief, we see an organization emerge, by means of which man can more completely satisfy his needs than he could living in isolation.This natural organization is called society.The object of society is therefore the most complete satisfaction of man's needs. The division of labor and exchange are the means by which this is accomplished.
Gustave de Molinari
Taking again as an example the need to appear perfect, I would be interested primarily in understanding what this trend accomplishes for the individual (eliminating conflicts with others and making him feel superior to others), and also what consequences the trend has on his character and his life. The latter investigation would make it possible to understand, for example, how such a person anxiously conforms with expectations and standards to the extent of becoming a mere automaton, and yet subversively defies them; how this double play results in listlessness and inertia; how he is proud of his apparent independence, yet actually is entirely dependent on the expectations and opinions of others; how he is terrified lest anyone should discover the flimsiness of his moral strivings and the duplicity which has pervaded his life; how this in turn has made him seclusive and hypersensitive to criticism.
Karen Horney