“must we not say that it is part of the deep sickness of our culture that ever since Descartes, we have been seduced by the idea of a kind of knowledge which could not be doubted, in which we would be absolutely secure from personal risk? And has not this seduction taken two forms which, even if they disclaim all relationship with each other, are really twin brothers? One is biblical fundamentalism which supposes that adherence to the text of the Bible frees me from the risk of error and therefore gives me a security which does not depend on my own discernment of the truth. The other is a type of scientism which supposes that science is simply a transcript of reality, of the "facts" which simply have to be accepted and call for no personal decision on my part, a kind of knowledge which is "objective" and free from all the bias of subjectivity.”

Opera Omnia, ser. 1, vol. 2, p. 459 Spcimen de usu observationum in mathesi pura, as quoted by George Pólya, Induction and Analogy in Mathematics Vol. 1, Mathematics and Plausible Reasoning (1954)
Context: It will seem a little paradoxical to ascribe a great importance to observations even in that part of the mathematical sciences which is usually called Pure Mathematics, since the current opinion is that observations are restricted to physical objects that make impression on the senses. As we must refer the numbers to the pure intellect alone, we can hardly understand how observations and quasi-experiments can be of use in investigating the nature of numbers. Yet, in fact, as I shall show here with very good reasons, the properties of the numbers known today have been mostly discovered by observation, and discovered long before their truth has been confirmed by rigid demonstrations. There are many properties of the numbers with which we are well acquainted, but which we are not yet able to prove; only observations have led us to their knowledge. Hence we see that in the theory of numbers, which is still very imperfect, we can place our highest hopes in observations; they will lead us continually to new properties which we shall endeavor to prove afterwards. The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful.

Remarks at the presentation of NASA's Distinguished Service Medal to Astronaut Alan B. Shepard (8 May 1961) http://www.presidency.ucsb.edu/ws/index.php?pid=8119 — Video of presentation at YouTube http://www.youtube.com/watch?v=M0OurosNBFo
1961
Context: Commander Shepard has pointed out from the time that this flight began and from the time this flight was a success, that this was a common effort in which a good many men were involved. I think it does credit to him that he is associated with such a distinguished group of Americans whom we are all glad to honor today, his companions in the flight into outer space, so I think we want to give them all a hand. … I also want to take cognizance of the fact that this flight was made out in the open with all the possibilities of failure, which would have been damaging to our country's prestige. Because great risks were taken in that regard, it seems to me that we have some right to claim that this open society of ours which risked much, gained much. … This is a civilian award for a great civilian accomplishment, and therefore I want to again express my congratulations to Alan Shepard. We are very proud of him, and I speak on behalf of the Vice President, who is Chairman of our Space Council and who bears great responsibilities in this field, and the Members of the House and Senate Space Committee who are with us today. [accidentally drops the medallion, and picks it up] This decoration which has gone from the ground up — here.

Speech in the White House (29 July 1966), quoted in The Times (30 July 1966), p. 1.
Prime Minister

Source: Tristes Tropiques (1955), Chapter 38 : A Little Glass of Rum, pp.385-386

The Crosswicks Journal, The Irrational Season (1977)

The Magnificent Defeat (1966)

Source: 1960s, Economics As A Moral Science, 1969, p. 12

Radio broadcast, 1 June 1967, as quoted in Michael Scott-Bauman (1998) Conflict in the Middle East: Israel and the Arabs.