“A physical theory, like an abstract science, consists of definitions and axioms as first principles, and of propositions, their consequences; but with these differences:—first, That in an abstract science, a definition assigns a name to a class of notions derived originally from observation, but not necessarily corresponding to any existing objects of real phenomena, and an axiom states a mutual relation amongst such notions, or the names denoting them; while in a physical science, a definition states properties common to a class of existing objects, or real phenomena, and a physical axiom states a general law as to the relations of phenomena; and, secondly,—That in an abstract science, the propositions first discovered are the most simple; whilst in a physical theory, the propositions first discovered are in general numerous and complex, being formal laws, the immediate results of observation and experiment, from which the definitions and axioms are subsequently arrived at by a process of reasoning differing from that whereby one proposition is deduced from another in an abstract science, partly in being more complex and difficult, and partly in being to a certain extent tentative, that is to say, involving the trial of conjectural principles, and their acceptance or rejection according as their consequences are found to agree or disagree with the formal laws deduced immediately from observation and experiment.”

Part II. Ch. 2 : Mathematical Definitions and Education, p. 131
Science and Method (1908)
Context: Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have proved that it involves no contradiction either in its terms or with the truths previously admitted.

Source: General System Theory (1968), 4. Advances in General Systems Theory, p. 90-91

The Logic of Condillac (trans. Joseph Neef, 1809), "Of the Method of Thinking", p. 3.

"The Laws of Science and the Laws of Ethics" (1950)
1950s, Out of My Later Years (1950)

Kant's Inaugural Dissertation (1770), Section V On The Method Respecting The Sensuous And The Intellectual In Metaphysics

testimony in Kitzmiller v. Dover Area School District, trial transcript: day 11 http://www.talkorigins.org/faqs/dover/day11pm.html#day11pm132 (18 October 2005).

100 Years of Mathematics: a Personal Viewpoint (1981)

The Philosophy of Space and Time (1928, tr. 1957)

"The Magic of Science" in Imperial Oil Review (Spring, 1994) http://sites.utoronto.ca/jpolanyi/public_affairs/public_affairs4f.html.
Context: It is not the laws of physics that make science possible but the unprovable proposition that there exists a grand design underlying the physical world. And not just any old "grand design" but one that is accessible to the limited senses and modest reasoning powers of the species to which we belong. Scientists subscribe with such conviction to this article of faith that they are willing to commit a lifetime to the pursuit of scientific discovery. It is hardly surprising that an activity so magical is also undefinable. Science is what scientists do. And what they do is look around themselves for messages written in the sky, the earth, the oceans and all living things – messages that tell of the unity of creation. These messages have been there – unseen, though at times written in letters miles high – since the dawn of history. But we have just passed through an epoch in which, quite suddenly, scientists seem to have learnt speed reading. Discoveries have been coming at an unprecedented pace. In the wake of such a period it is common to consider that we may be approaching the point where all that is readable in nature will have been read. We should be skeptical of such claims. Success in reading some messages brings with it a temporary blindness to others. We forget that between the words written in black in nature's book there are likely to be messages of equal importance written in white. It is a truism that success in science comes to the individuals who ask the right questions.