1. Clarifying what are "paradigms" (or whatever they are) and how they evolve requires extensive historical research.
2. Historical, sociological, psychological, perceptual, linguistic, etc. studies on the extent to which "seeing" really is determined by belief, conceptual scheme, etc. are needed.
3. What, if any, is the "rationality" which governs the evolution of the historical change of the conceptual schemes of science?
4. The problem of theory choice as described by Kuhn suggests the need for a sociological analysis of the structure of communities of practicing scientists. Those who are generally known as "strong program" sociologists of science (the Edinburgh school) want to argue that all epistemic decisions -what scientists "accept" and what they "reject" in the way of belief- is fully determined by what may be called "sociological" factors describing the community in which these scientists find themselves, both the "scientific community" and the world at large. Some versions of this thesis have strong veins of Marxist theses running through them. Much of the interest in sociology of science also derives from Continental philosophers writing in the hermeneutic tradition.
5. How much of Kuhn's "historicist" approach to philosophy of science, or something like his view, can one accept and yet get "reality" back into the philosophical account of science? The defense of realism now seems to many philosophers to suggest that the Kuhnian lesson speaks in favor of abandoning a representational correspondence theory of truth in favor of some alternative conception of truth. However, many relativists and anti-realists would claim that realism requires that there be a single true account which "represents" an objective, observer-independent world, thus if one abandons the correspondence notion of truth, one ipso facto abandons realism. Can one defend realism without a commitment to the correspondence theory, and/or can that theory be reconstructed so as to retain realism and yet capture much of what Kuhn's historical perspective has taught us?
6. To what extent does Kuhn's account justify a normative stance concerning science? For example Kuhn tells us in effect that "normal science" is good, that we ought to engage in it most of the time, and that we ought not to countenance revolutionary rivals unless our current paradigm is in very dire straits in the face of proliferating anomalies. Thus Kuhn's analysis seems to suggest a good use for "dogmatism" in order to allow normalcy to develop: there are times when science ought to adhere to a relatively dogmatic acceptance of the paradigm beliefs. Popperians counter with the claim that science ought always proliferate rival theories and that every conjecture, no matter how central to our belief system, must be constantly subjected to potential refutation. Kuhn wants to "articulate" paradigm theories, Popper wants to "put them on the rack" and subject them to the severest testing we can devise.
7. Can the philosophy of science assume a normative platform from which to specify what one ought or ought not to believe in order to do "good" science? If one abandons normativity and reduces the philosophy of science to the descriptive task of merely accounting for the way in which epistemic decisions are in fact made by scientists or by human beings generally, does philosophy of science -and epistemology- reduce to "cognitive science"? The attempt to reduce epistemology -and with it the philosophy of science- to a science, is known as "epistemic naturalism." Does naturalism eliminate a normative dimension for philosophy of science and/or epistemology in general?
8. Although Kuhn strongly emphasizes a relativist view at the level of theory choice in science, he tends to be rather anti-relativist (or "essentialist") in his characterization of the aims and values of "science," for he tends to elevate them to a timeless status, forming a kind of "essence of science." The rules of the game may change, but not its ultimate goals; to disregard them is to opt out of the game of science. But Kuhn's historicist attack could well be extended to this level as well; perhaps there is change even at the "axiological" level of the goal(s) and purpose(s) of science. If so, what "reasoning process" or "rationality" -if any- drives this change?
9. Can the philosophy of science become "naturalized," i.e. can we transform philosophy of science into a scientific discipline which studies empirically the nature of scientific methodology -as actually practiced- as itself a natural phenomenon calling for scientific explanation? A naturalized epistemology of science would explain how scientific methodology -the procedures actually used to determine theory choice- itself has changed and continues to change as our beliefs about the world change. Those who advocate this view strongly disagree among themselves as to how to naturalize philosophy of science and what that entails. Some argue that philosophy of science must be purely descriptive and not prescribe any norms for good scientific research. Others defend the view that a naturalized epistemology can retain the traditional "normativity" of philosophy of science and stipulate what constitutes "good" method and what scientists "ought" to do in concrete cases of theory choice. Furthermore, those advocating naturalizing epistemology of science disagree radically over whether this move defends or weakens the appeal to realism.