“From the methodological standpoint, however, we see that 'mechanism' and 'vitalism' by no means form the mutually exclusive disjunction they have been supposed to do. If a 'non-mechanist' wishes to deny the assumption of methodological mechanism that biological explanations must also be physico-chemical ones, it is obviously by no means intended that the required explanation must be 'vitalistic', i. e. involving the assumption that in living organisms factors analogous to psychical ones are 'at work'. A 'non-mechanistic' theory which is not all 'vitalistic' thus appears to be logically possible, and if we make a critical study of mechanism and vitalism this possibility will be seen to be of special importance.”

Pg 295-296.
Against Method (1975)
Context: Naive falsificationism takes it for granted that the laws of nature are manifest an not hidden beneath disturbances of considerable magnitude. Empiricism takes it for granted that sense experience is a better mirror of the world than pure thought. Praise of argument takes it for granted that the artifices of Reason give better results than the unchecked play of our emotions. Such assumptions may be perfectly plausible and even true. Still, one should occasionally put them to a test. Putting them to a test means that we stop using the methodology associated with them, start doing science in a different way and see what happens.

Source: Confession (1882), Ch. 9

Source: 1930s, Modern Theory of Development, 1933, 1962, p. 46

Source: The Brain As A Computer (1962), p.1 as cited in: T. Zetenyi (1988) Fuzzy Sets in Psychology. p.346

Pg. 304.
Against Method (1975)
Context: Is it not a fact that a learned physician is better equipped to diagnose and to cure an illness than a layman or the medicine-man of a primitive society? Is it not a fact that epidemics and dangerous individual diseases have disappeared only with the beginning of modern medicine? Must we not admit that technology has made tremendous advances since the rise of modern science? And are not the moon-shots a most and undeniable proof of its excellence? These are some of the questions which are thrown at the impudent wretch who dares to criticize the special positions of the sciences. The questions reach their polemical aim only if one assumes that the results of science which no one will deny have arisen without any help from non-scientific elements, and that they cannot be improved by an admixture of such elements either. "Unscientific" procedures such as the herbal lore of witches and cunning men, the astronomy of mystics, the treatment of the ill in primitive societies are totally without merit. Science alone gives us a useful astronomy, an effective medicine, a trustworthy technology. One must also assume that science owes its success to the correct method and not merely to a lucky accident. It was not a fortunate cosmological guess that led to progress, but the correct and cosmologically neutral handling of data. These are the assumptions we must make to give the questions the polemical force they are supposed to have. Not a single one of them stands up to closer examination.

Source: Economics Of The Welfare State (Fourth Edition), Chapter 4, State Intervention, p. 73

Footnote: In the future by 'mathematics' will always be meant 'pure mathematics'.
The Foundations of Mathematics (1925)

Source: Time is the Simplest Thing (1961), Chapter 10 (p. 75)