Quotes about methodology
page 2
L.K. Frank (1948) "Foreword". In L. K. Frank, G. E. Hutchinson, W. K. Livingston, W. S. McCulloch, & N. Wiener, Teleological mechanisms. Ann. N. Y. Acad. Sc., 1948, 50, 189-96; As cited in: Ludwig von Bertalanffy (1968) "General System Theory: Foundations, Development, Applications". p. 16-17

“Methodological rules are for science what rules of law and custom are for conduct.”
Source: The Division of Labor in Society (1893), p. 364

"Who Was Milton Friedman?", The New York Review of Books (February 15, 2007)
The New York Review of Books articles
1978 Turing Award Citation https://web.archive.org/web/20070708004814/http://awards.acm.org/citation.cfm?id=4173633&srt=all&aw=140&ao=AMTURING.
About
Source: Essays on object-oriented software engineering (1993), p. 5

Ackoff (1999). "Disciplines, the two cultures and the scianities". Systems Research and Behavioral Science. 16 (6), p. 537. Cited in: Sherryl Stalinski (2005) A Systems View of Social Systems, Culture and Communities. Saybrook Graduate School. p. 5.
1990s

Source: What is Philosophy? (1964), pp. 19-20
Source: Systems Thinking, Systems Practice, 1981, p. 162 cited in: Rob Pooley, Pauline Wilcox (2003) Applying UML: Advanced Applications. p. 50

Source: 1970's, Interview with Louwrien Wijers, 1979, p. 249; Also cited in: Louwrien Wijers (1996). Writing as Sculpture: 1978 - 1987. p. 40
Sudden Origins: Fossils, Genes, and the Emergence of Species (1999)

Kenneth Arrow, "Some Developments in Economic Theory Since 1940: An Eyewitness Account" Annu. Rev. Econ. 2009
New millennium
William Barnett, Adrien Presley, Mary Johnson, and Donald H. Liles (1994) "An architecture for the virtual enterprise." Systems, Man, and Cybernetics, 1994.' Humans, Information and Technology'., 1994 IEEE International Conference on. Vol. 1. IEEE, 1994

quoted in Classic Essays on Twentieth-Century Music, ISBN 0028645812
Hartshorne (1958) "The concept of geography as a science of space, from Kant and Humboldt to Hettner" in: Annals of the Association of American Geographers Vol 48 (2). p. 97
Source: Metasystems Methodology, (1989), p. 3 Cited in: Derek Hitchins (2007) " Systems Methodology http://www.hitchins.net/The%20Systems%20Approach.pdf"
On Hinduism (2000)
Source: Just a Theory: Exploring the Nature of Science (2005), Chapter 4, “Falsificationism: If It Might Be Wrong, It’s Science” (p. 75)

New Mindset on Consciousness (1987)
Context: I think time will show that the new approach, emphasizing emergent "macro" control, is equally valid in all the physical sciences, and that the behavioral and cognitive disciplines are leading the way to a more valid framework for all science. Although the theoretic changes make little difference in physics, chemistry, molecular biology, and so on, they are crucial for the behavioral, social, and human sciences. They don't change the analytic, reductive methodology, just the interpretations and conclusions. There seems little to lose, and much to gain.

1990s, Why "Free Software" is better than "Open Source" (1998)
Context: While free software by any other name would give you the same freedom, it makes a big difference which name we use: different words convey different ideas.
In 1998, some of the people in the free software community began using the term "open source software" instead of "free software" to describe what they do. The term "open source" quickly became associated with a different approach, a different philosophy, different values, and even a different criterion for which licenses are acceptable. The Free Software movement and the Open Source movement are today separate movements with different views and goals, although we can and do work together on some practical projects.
The fundamental difference between the two movements is in their values, their ways of looking at the world. For the Open Source movement, the issue of whether software should be open source is a practical question, not an ethical one. As one person put it, "Open source is a development methodology; free software is a social movement." For the Open Source movement, non-free software is a suboptimal solution. For the Free Software movement, non-free software is a social problem and free software is the solution.

pg. 32, Italics are Feyerabend's.
Against Method (1975)
Context: My intention is not to replace one set of general rules by another such set: my intention is, rather, to convince the reader that all methodologies, even the most obvious ones, have their limits. The best way to show this is to demonstrate the limits and even the irrationality of some rules which she, or he, is likely to regard as basic. In the case that induction (including induction by falsification) this means demonstrating how well the counterinductive procedure can be supported by argument.

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.

Quoted in Antonio de Nicolas, Krishnan Ramaswamy, and Aditi Banerjee (eds.) (2007), Invading the Sacred: An Analysis Of Hinduism Studies In America (Publisher: Rupa & Co., p. 39)
About Wendy Doniger
Peter Bernus and Laszlo Nemes (1996) "A framework to define a generic enterprise reference architecture and methodology." Computer Integrated Manufacturing Systems Vol 9 (3) p. 179
Donald Reisler http://space.mit.edu/home/tegmark/everett/everett.html
2010s, League Confederation Goes Outer-Track (September 2018)

Can scientific methods prove the existence of God? https://www.americamagazine.org/content/all-things/god-and-science-qa-robert-spitzer-sj (December 29, 2015)

"Logic of Discovery or Psychology of Research?", Criticism and the growth of knowledge edited by Imre Lakatos and Alan Musgrave (1970)
Ockhamist Comments on Strawson, in Anthony Freeman (ed.), Consciousness and its Place in Nature: Does Physicalism Entail Panpsychism?, Exteter, 2006, pp. 158-159
Other quotes
Source: Vatican Observatory examines theological implications of finding alien life https://www.catholicnewsagency.com/news/17651/vatican-observatory-examines-theological-implications-of-finding-alien-life (10 November 2009)