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I am wondering if the rejection of the positivism movement in philosophy lead to any major discoveries in mathematics and natural sciences? I am thinking it might have been able to contribute to those fields, but knowing almost nothing about the history of philosophy, I am not sure where to find the answer.

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    Workers in mathematics and natural sciences paid little attention to developments in philosophy, be it logical positivism or its rejection. If anything, logical positivism stimulated work in logic and set theory, which produced results leading to its rejection (Godel's incompleteness, for example), and the Copenhagen interpretation was in the positivist spirit. Behaviorism in psychology was also inspired by positivism, and its rejection after Chomsky led to modern cognitive science. But Quine was also a behaviorist, so it is unclear if positivism's rejection was crucial even there. – Conifold Apr 20 at 0:06
  • We still have a long way to go before we get over the effects of positivism, we may never recover. – Gordon Apr 30 at 5:21
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The most important development in the rejection of positivism, from the metaphysical perspective, is that it allowed for a revisit and reexamination of the philosophical systems thinkers, like Aristotle, Spinoza, Kant and Hegel. This resulted in a renewed appreciation for the fact that any study of knowledge or science or reality could not be reduced to any arbitrarily selected set of 'primary' and 'secondary' qualities and that the reduction of the field of what is knowable is not even remotely acceptable. This not only opened new possibilities in earth sciences but eventually allowed for concepts in cosmology and astrophysics, like black holes, dark matter and alternative universes to be put forward and accepted as reasonable. For a solid overview of what this rejection meant in Biology, Evolutionary studies and theories of Consciousness see "The Foundations of Metaphysics", by Errol E. Harris,(Humanities Paperback Library, June 1992). Charles M Saunders

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Positivism took its general shape during the 19th when "Naturphilosophie" went out of fashion and science and philosophy became separate realms. In Comte's account humanity evolved from religious views to metaphysics and ultimately to positivism. As positivism mimics science it could not really obstruct discoveries. Actually nothing in (history of) mathematics is positivistic.

The most famous case against positivism is the denial of atomism by German thinkers such as E. Mach or W. Ostwald but it mostly slowed down the reception of some results and ideas without preventing them to develop.

So the "rejection of positivism" had no tangible effect in maths and natural science. An analogy with the rejection of Aristotelianism could be conjectured behind the question but it is an altogether different story: "Äristotelianism" stands for "The Church"; people however avoided confronting openly its monopoly on ideas.

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    The rejection of atomism by Mach and others was probably the main cause of Boltzmann's suicide, though, insensitively, one might say that he'd done his best work by then. – Philip Wood Apr 19 at 22:15
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Logical positivism basically evolved into analytic philosophy in the 1950's to point where I think few if any contemporary philosophers regard themselves as "logical positivists" at least in the classic sense. Logical positivism turned Anglo-American philosophical orthodoxy in the direction of analytic philosophy, which took off from there, especially with the publication of J.L. Austin's "How To Do Things With Words" and W.O Quine. Analytics is very semantic-analysis oriented where logical positivism was a bit more just strictly empiricist. So to answer your question, no. As far as I can tell, logical positivism has had pretty much zero effect on scientific and mathematical progress. I suppose Kurt Godel's Incompleteness Theorem (and proof) also pretty well destroyed positivism so that would an example of the opposite effect, I think.

  • Logical positivism started with the Vienna circle's appropriation of Wittgenstein's Tractatus in 1920-s. Analytic philosophy originated with Frege, Moore and Russell decades earlier, none of whom were positivists. Neither was the Oxford school, to which Austin belonged, along with Ryle and Strawson. So positivism did not evolve into analytic philosophy, it was a subcurrent in the middle of it, nor was it responsible for the linguistic turn in 1950-s, that was more due to late Wittgenstein, Quine, and ordinary language philosophers from Oxford and Cambridge. – Conifold Apr 20 at 4:10
  • More or less what I said in different words. But in my understanding there is a sense in which logical positivism is prior to analytic philosophy and, as you point out, they are closely related. It would require a book to elaborate on their interconnections. I believe the phrase is "tangled web".... – William Pennat Apr 22 at 1:24

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