§ 1.
Linear Associative Algebra (1882)
Context: The sphere of mathematics is here extended, in accordance with the derivation of its name, to all demonstrative research, so as to include all knowledge strictly capable of dogmatic teaching. Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims; and neither law can rule nor theory explain without the sanction of mathematics. It deduces from a law all its consequences, and develops them into the suitable form for comparison with observation, and thereby measures the strength of the argument from observation in favor of a proposed law or of a proposed form of application of a law.
Mathematics, under this definition, belongs to every enquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement, but they must be curiously transposed before they can be applied to the living speech and verified by, observation.
§ 2.
Linear Associative Algebra (1882)
Context: The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.
[Shewhart, Walter A., Deming, William E., Statistical Method from the Viewpoint of Quality Control, The Graduate School, The Department of Agriculture, 1939, 18]
Economic Control of Quality of Manufactured Product,1931
"The Departments of Mathematics, and their Mutual Relations," Journal of Speculative Philosophy, Vol. 5, p. 164. Reported in Moritz (1914)
Journals
Das Naturgesetz und die Struktur der Materie (1967), as translated in Natural Law and the Structure of Matter (1981), p. 34
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
The Evolution of Physics (1938) (co-written with Leopold Infeld)
1930s
Science and the Unseen World (1929)
Context: It remains a real world if there is a background to the symbols—an unknown quantity which the mathematical symbol x stands for. We think we are not wholly cut off from this background. It is to this background that our own personality and consciousness belong, and those spiritual aspects of our nature not to be described by any symbolism... to which mathematical physics has hitherto restricted itself.<!--III, p.37-38
"Anarchism and homicidal outrage" in What Is Anarchism?: An Introduction by Donald Rooum, ed. (London: Freedom Press, 1992, 1995) p. 43.
Context: The genuine Anarchist looks with sheer horror upon every destruction, every mutilation of a human being, physical or moral. He loathes wars, executions and imprisonments, the grinding down of the worker's whole nature in a dreary round of toil, the sexual and economic slavery of women, the oppression of children, the crippling and poisoning of human nature by the preventable cruelty and injustice of man to man in every shape and form.
