It's questionable whether any particular type of thinking could be said to be peculiar to philosophy, or Philosophy with a big P. Even as far back as Leibniz there was an urge to end the demarcation between philosophy and science. Frege's task consisted of trimming up the language to make it more suitable for physical sciences, mathematics, and scholarly work, retro-fitting the outdated syllogistic forms with quantifiers and predicates. Aristotelian cat. syllogisms updated with quantifiers and predicates more or less defines modern formal logic.
Frege/Russell are also in an important sense semanticists, as much as philosophers or logicians. Given the advances of the physical sciences, the positivists desired to sort of reduce language and statements to pure symbolism; and with both Frege and Russell there was an impulse to view all language as comprised of propositions, functions, quantifiers, variables, predicates, and the needed mathematics. Witt. of the Tractatus, and then later Quine continue this reductionism, for better or worse. Verification of course was another key analytical issue, as is probability; in strictly logical terms, the Tractatus demonstrates deductive logic reduces to tautologies and contradictions, tho there are a few paradoxes (which however are generally not an issue except for a very limited set of self-referential expressions. Your OS works fine: Goedel be damned).
So that propositional aspect is not really so philosophical as much as about eliminating ambiguity of ordinary language and creating semantic efficiency: the symbolic language then may be used for different purposes, whether philosophy of science, or programming or inductive endeavors.
The Big P philosophy, Der Weltanschauung-- conceptualization, system building, philosophy of science, phil. of history/time/process, ethics, even theology or whatever it is Heideggerians do-- is affected by the move to the symbolic language; once the positivists decide on permitting only synthetic/analytic truths, a lot of metaphysical baggage was eliminated as well. Ethics becomes in some sense closer to psychology and sociology. Political philosophy ala Hobbes or Rousseau, Marx, more akin to Econ. or poli sci. But these disciplines hardly deny the positivist advances; indeed behaviorism depended on positivism and pragmatism for a lot of its core doctrine.
You seem like you are suggesting a sort of thoroughly inductive political and educational philosophy, which would encompass other disciplines. I do not think that is likely to occur; indeed it could be argued that ethics and political philosophy have mostly been absorbed into various social sciences: doesn't Dewey sort of suggest that as well? Cognitive studies and lingustics (tho I'm not so sure what linguistics is anymore, except a sort of ultra-grammar) absorb philosophy of mind and epistemology, really. Philosophy of science remains, but scientists are generally more suited to those investigations than traditional philosophers: tho a critique of the economics, methods, and ethics of Big Science, especially academic science, remains important, and a Feyerbend should be taught along with Popper and Kuhn. Of course with the rise of PostMod Inc. a lot of metaphysics, or quasi-metaphysics is back, with plenty of aesthetics and the perennial marxism, but I would hold Russellianism to be more authentically progressive than most postmod. The Big P philosophy is dead (if it wasn't in 1885 when the Cambridge people began to trash on Hegel and Kant), and that is not necessarily a bad thing.
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