“The man who blames the supreme certainty of mathematics feeds on confusion, and can never silence the contradictions of sophistical sciences which lead to an eternal quackery.”

Source: Science and Hypothesis (1901), Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Context: The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A!... Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive?... If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.<!--pp.5-6

Reported in Josiah Hotchkiss Gilbert, Dictionary of Burning Words of Brilliant Writers (1895), p. 36.

Part 3: "The Sense of Human Dignity", §6 (p. 63–64)
Science and Human Values (1956, 1965)
Context: Tolerance among scientists cannot be based on indifference, it must be based on respect. Respect as a personal value implies, in any society, the public acknowledgements of justice and of due honor. These are values which to the layman seem most remote from any abstract study. Justice, honor, the respect of man for man: What, he asks, have these human values to do with science? [... ]
Those who think that science is ethically neutral confuse the findings of science, which are, with the activity of science, which is not.

Source: The Sign of Four

Alistair Cameron Crombie, Medieval and Early Modern Science (1952) as quoted by John Freely in Before Galileo: The Birth of Early Modern Science in Medieval Europe http://books.google.com/books?id=MfhjAAAAQBAJ (2012).

Bk. 1, ch. 4. Translated by Robert B. Burke, in: Edward Grant (1974) Source Book in Medieval Science. Harvard University Press. p. 93
Opus Majus, c. 1267

As quoted in Carl Friedrich Gauss: Titan of Science (1955) by Guy Waldo Dunnington. p. 306

Human Nature and Social Theory (1969)
Context: One will be conducive to cooperation and solidarity another social structure to competition, suspiciousness, avarice; another to child-like receptiveness, another to destructive aggressiveness. All empirical forms or human needs and drives have to be understood as results of the social practice (in the last analysis based on the productive forces, class structure, etc., etc.) but they all have to fulfill the functions which are inherent in man’s nature in general, and that is to permit him to relate himself to others and share a common frame of reference, etc. The existential contradiction within man (to which I would now add also the contradiction between limitations which reality imposes on his life, and the virtually limitless imagination which his brain permits him to follow) is what I believe to be one of the motives of psychological and social dynamics. Man can never stand still. He must find solutions to this contradiction, and ever better solutions to the extent to which reality enables him.
The question then arises whether there is an optimal solution which can be inferred from man’s nature, and which constitutes a potential tendency in man. I believe that such optimal solutions can be inferred from the nature of man, and I have recently found it quite useful to think in terms of what in sociology and economy is now often called »system analysis«. One might start with the idea, in the first place, that human personality — just like society — is a system, that is to say, that each part depends on every other, and no part can be changed unless all or most other parts are also changed. A system is better than chaos. If a society system disintegrates or is destroyed by blows from the outside the society ends in chaos, and a completely new society is built upon its ruins, often using the elements of the destroyed system to build the new. That has happened many times in history. But, what also happens is that the society is not simply destroyed but that the system is changed, and a new system emerges which can be considered to be a transformation of the old one.