Science, in its ultimate ideal, consists of a set of propositions arranged in a hierarchy, the lowest level of the hierarchy being concerned with particular facts, and the highest with some general law, governing everything in the universe. The various levels in the hierarchy have a two-fold logical connection, travelling one up, one down; the upward connection proceeds by induction, the downward by deduction.
Bertrand RussellPhilosophers, for the most part, are constitutionally timid, and dislike the unexpected. Few of them would be genuinely happy as pirates or burglars. Accordingly they invent systems which make the future calculable, at least in its main outlines.
Bertrand RussellThe Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes.
Bertrand RussellThe scientific attitude of mind involves a sweeping away of all other desires in the interests of the desire to know-it involves suppression of hopes and fears, loves and hates, and the whole subjective emotional life, until we become subdued to the material, able to see it frankly, without preconceptions, without bias, without any wish except to see it as it is, and without any belief that what it is must be determined by some relation, positive or negative, to what we should like it to be, or to what we can easily imagine it to be.
Bertrand Russell