Sarukkai, Sundar. “Philosophy and Method,” in Mapping Scientific Method: Disciplinary Narrations, edited by Gita Chadha and Renny Thomas (London; New York: Routledge, 2023), pp. 85-103.
This is an interesting essay which I nonetheless consider to be an elementary introduction to the question. Sarukkai broadens the usual terms of debate in the anglophone world (characterized as a restrictive focus on Western philosophy) to include Indian philosophy in the mix, which resonates with the phenomenological tradition in the West. Sarukkai suggests the complementary nature of focusing on the subject-object relation by addressing the approaches of phenomenology and science respectively. Of interest in particular is the Nyāya 16-step process as a model for philosophical method.
The narrowness Sarukkai confronts is most characteristic of analytical philosophy. Sarukkai’s broadening of the base of discussion is welcome, but his pluralism has limitations. He accepts the now-conventional categories of analytical and continental philosophy as givens. He mentions Marxism and Critical Theory in passing, but his entire discussion bypasses Hegel, Marx, and the Frankfurt School, which would lend themselves to an overview of disparate methods and schools of thought from a decidedly different perspective.
And there is the question of the nature of method and the manner of its applicability, an issue that applies also to critical thinking in general. Interpretation is not algorithmic or formalistic; it requires non-mechanical judgment of specific content even with the cognizance of general principles.
See also my bibliographies:
Indian Logic & Argumentation: Selected Bibliography
Argumentation & Controversies: Selected Bibliography
Thinking Critically About Critical Thinking: A Guide
Philosophical Style: Selected Bibliography
Philosophy of History of Philosophy & Historiography of Philosophy: Selected Bibliography