Could philosophy reasonably be said to search the unknown and consider the structure of the known, with detachment from the structure to the end of revising or adding to structure if useful?
The known is structured, as one might prefer, as in math, and firm processes make up the structure. Alternatively, ossification of philosophical method could be dangerous to philosophical health. The known is inducted from or explained from the unknown, yet the known may also become a composite to which elements of the unknown are added. I won’t write anything here about induction of the unknown onto anything besides the known composite.
The idea of the relation I had between the unknown and structures might be better said to be that of Hilbert space to various modal universes within Hilbert Space (like Venn diagram bubbles) with x to the nth elements that could be added or synthesized at the intersections.
The relation between the unknown and structures of various kinds should be fairly abstract initially, with concrete structures and forms differing so much from others as they can. Structures (there is a philosophical branch called structuralism) of various material and social or immaterial field-objects can be very different in actualization whereas the unknown is at some meta-place purely abstract and without form.
Errors and false leads can assuredly happen. Ossification of method might exemplify some of those ineffective methods. Applying a method inappropriately or exclusively because it is the preferred, ossified method (such as using deductive logic for a problem requiring inductive logic, has happened before.
Edmund Husserl’s Logical Investigations sought after a way to make philosophy a rigorous science yet phenomenology didn’t actually accomplish that, I seem to recall.
Descartes’ Meditations and the cogito passage seems a try at not selecting a pre-existing method to ‘compute’ in with thought. The epistemological work is to know the self from first principles, or the BIOS of self-awareness as it were. He tried to think before BIOS as a sentient CPU of mind.
One might consider the challenges about reality from within and without presented at the 1927 Solvay Conference whereat Einstein had a different point of view than Bohr and Heisenberg on the quantum world and nature of reality. The dispute continues unto the present. A good book about it was published in 2018 (here is a nature article about the book)
Philosophy perhaps hasn’t a more rigorous scientific methodical approach to solving the unknown that would be better than those used by scientists. Because philosophy covers potentially very diverse fields and recombines them in thought to form novel concepts, where alternatively scientists tend to pursue particular threads of investigation proximally to induct or deduce solutions to particular problems, the methods may not always be similar. Philosophical approaches discover or find things even more than solving particular problems (perhaps).
If the Einstein-Bohm opinion about the quantum world not being the same as the Copenhagen interpretation were correct, the implication is that one solution is the infinite Multiverse could be a hypothetical description consistent with the implications, and that would bring philosophical interest concerning epistemology, theology and so forth of a Multiverse. While science can consider testing and verification of quantum experiments to prove or trace the accuracy of the Allegory of the Cave from the spot on the floor of the Cave, philosophers may pursue any other approach that is possible as well as consider the epistemological and/or theological ramifications of being prisoners chained to the floor of a cave, and if their perception of the cave determines that the cave exists, and who if anyone made it so.