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In order to clarify what I mean by this question, I suppose that I should give at least one example! Let's consider certain arcane astronomical studies, such as the study of active galactic nuclei (AGNs). There are many other examples that can be given, and studies often have some type of spinoff that might be put to practical use, but let's assume there are no such practical spinoffs. EDIT: Let me rephrase this question so that I can get a straightforward answer from an Objectivist. (I'm not looking to debate anything here. Thank you.) Is knowledge of value only because it has practical application?
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There scads of examples in the history of knowledge where "pure science" or theoretical developments in math or whatever with absolutely no conceivable application, nonetheless found their way into wholly practical uses. I marvel at the more remote cases I've learned of, but I also anticipate this sort of thing because reality is a causally-connected whole -- which is why we strive to make our knowledge of the world a single integrated whole. How would someone justify treating one bit of knowledge about one fact as fundamentally unrelated to the rest of one's knowledge of the rest of reality?
Greg's comment is, essentially, the answer to this question.
All knowledge has some value, because all knowledge is about the whole which is the universe. Any new information about how objects behave in distant space has some impact on our understanding of how objects behave in our immediate presence. All behavior is related.
There is no pure science, including in the field of mathematics. The idea of "pure" science is ill-founded.
Theory informs practice, and practice refines theory. The two are inextricably linked.
Any new information about how objects behave in distant space has some impact on our understanding of how objects behave in our immediate presence. That statement is true only if it uncovers new physical principles, methods, or ideas -- which is sometimes true, but not always. (So my original question still stands.)