I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.
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Grundlagen einer allgemeinen Mannigfaltigkeitslehre [Foundations of a General Theory of Aggregates] (1883)Georg Cantor
That from the outset they expect or even impose all the properties of finite numbers upon the numbers in question, while on the other hand the infinite numbers, if they are to be considered in any form at all, must (in their contrast to the finite numbers) constitute an entirely new kind of number, whose nature is entirely dependent upon the nature of things and is an object of research, but not of our arbitrariness or prejudices.
Georg Cantor
I can also tell you on the Internet in China, you can have access to a lot of postings that are quite critical about the government. It is exactly through reading these critical opinions on the Internet that we try to locate problems and further improve our work. I don't think a system or a government should fear critical opinions or views. Only by heeding those critical views would it be possible for us to further improve our work and make further progress. I frequently browse the Internet to learn about a situation.
Wen Jiabao
Here is such a definition of truth: An objective uncertainty, held fast through appropriation with the most passionate inwardness, is the truth, the highest truth there is for an existing person. At the point where the road swings off (and where that is cannot be stated objectively, since it is precisely subjectivity), objective knowledge is suspended. Objectively he then has only uncertainty, but this is precisely what intensifies the infinite passion of inwardness, and truth is precisely the daring venture of choosing the objective uncertainty with the passion of the infinite. I observe nature in order to find God, and I do indeed see omnipotence and wisdom, but I also see much that troubles and disturbs. The sum total of this is an objective uncertainty, but the inwardness is so very great, precisely because it grasps this objective uncertainty with all the passion of the infinite. In a mathematical proposition, for example, the objectivity is given, but therefore its truth is also an indifferent truth.
Soren Aabye Kierkegaard
The essence of the Liberal outlook lies not in what opinions are held, but in how they are held: instead of being held dogmatically, they are held tentatively, and with a consciousness that new evidence may at any moment lead to their abandonment.
Bertrand Russell
Pythagoras, as everyone knows, said that "all things are numbers." This statement, interpreted in a modern way, is logical nonsense, but what he meant was not exactly nonsense. He discovered the importance of numbers in music and the connection which he established between music and arithmetic survives in the mathematical terms "harmonic mean" and "harmonic progression." He thought of numbers as shapes, as they appear on dice or playing cards. We still speak of squares or cubes of numbers, which are terms that we owe to him. He also spoke of oblong numbers, triangular numbers, pyramidal numbers, and so on. These were the numbers of pebbles (or as we would more naturally say, shot) required to make the shapes in question.
Pythagoras
Cantor, Georg
Capa, Robert
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