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Are there any 20/21th century philosophers that talk about a different approach to the study of nature other than science? Are there any that criticize science?

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    Science is not the problem, rather it is science plus man's will that is the problem. There is a deep insecurity which "requires" man who look at nature in an instrumental fashion. There was a time when we could have pacified man's desire to overuse nature. 1950s thru '69. Marcuse, Eros and Civilization, One Dimensional Man. It helps to know some Freud before reading Eros. Anyway, we are now in a situation where, due to our unrestricted will, we must exploit nature while at the same time curing it. This may not be possible. – Gordon Jan 30 '18 at 19:45
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    According to Husserl, phenomenology is science, and its purpose is not the study of nature but of consciousness. According to Aristotle's definition, science is any systematic body of knowledge. Those who proposed alternative to the mainstream approaches to natural phenomena, like Goethe, still typically call them science So you should probably look not for something "other than science" but for a subset of science. Please include what "science" means to you into the post. What exactly do you want "other than"? Currently, it is unclear what you are asking, as PédeLeão pointed out. – Conifold Jan 30 '18 at 22:57
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    Plessner criticised science for being too one-dimensional: Out of the sphere of phenomenological sensation, they single out that which is able to be measured, standardized, fixed. He makes a strong case for philosophy being the one discipline that can work with that which is only accessible through phenomenology (following Husserl: "erschaubar", intuitible (!?)), but not demonstrable ("darstellbar", reappearing in different ways). His philosophy of nature explicitly derives its categories from phenomenology and only deduces (justifies) their reality by means of scientific knowledge and more. – Philip Klöcking Jan 30 '18 at 23:26
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    @Conifold "Feyerabend is not an example of a critic of science, he is a critic of positivist rationalizations of its methodology." It would be hard to deny all of modern science without being an extreme skeptic. – Geremia Jan 31 '18 at 3:39
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    There are critics of methodological naturalism. – Geremia Jan 31 '18 at 3:40
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Of course! You know theologians exist right? They are the biggest critics of 'godless' science.

A big problem though is, how you define science. Several popes have said they accept science. The Dalai Lama says if any of the teachings of hus school of Buddhism are found in conflict with scientific findings, go with science. But these figures also hold many views which cannot be called scientific.

It might seem easy to define science, but I assure you it isn't. Falsifiability, double-blind controlled trials, repeatability, direct observations, and any number of 'hall marks' of science are actually very much discipline dependent. Occam's Razor or Baconian Induction exclude many things now accepted as science or as scientifically true. The idea science is unified in it's methodsvand homogenous is just totally wrong.

Popper developed his ideas on science specifically to stop Marxists saying historical materialism is scientific. It quickly gets political. And Dawkins and his ilk quickly resort to scientism, over truly scientific answers - which are after all very often, we don't and may never know; not a great crowd pleaser.

Critics of science from outside, tend not to have informed enough opinions to be widely listened to, and from inside tend to be reformers. The same holds generally for religions. James Lovelock or Lyall Watson argue passionately for expanded methods and paradigms, but from within, broadly, the community. I can only think of religious figures, and fringe ones, calling for a dismissal of scientific results.

Am thinking about how Foucault reinterpreted science in terms of power structures, and as influenced by and at least partly serving, biology, economics, and linguistics. So he certainly critiqued the idea that there is 'pure' science.

Thomas Kuhn's thinking about science suggested developments within it are at leastbto some extebt subjective and relative, which could be considered a rejection of ideas many scientists have about science.

Plenty of critics of aspects that may or may not be essential to science, like reductionism or positivism.

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    I've studied many different theologians, and none of them are opposed to science. – user3017 Jan 30 '18 at 20:00
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    Thanks :) but I might should've excluded "theologians" from the question. I would like to see answers that are more in the methodological philosophy department, and not in the theology department. And I totally agree with your statement about defining science, and as much as I'd hate to do it, for the sake of the question, let's take the generalized definition of science, and not dwell on the exact definitions (although I would wholeheartedly accept answers which will talk about those definitions). – Yechiam Weiss Jan 30 '18 at 20:01
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    Pé de Leão: you not encountering evidence, is not evidence for absence. In a quick search I found numerous theologians saying religion and science are fundamentally incompatible. – CriglCragl Jan 30 '18 at 20:24
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    It's not just a question of evidence. Any good theologian knows there's no incompatibility between science and the Omniscient. Afterall, God knows about the nature of the universe better than any scientist ever could, so any apparent conflict must be the error of the scientist. – user3017 Jan 30 '18 at 20:33
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    I would have to agree with Pe de Leao, not that I have studied many theologians. However, I would expect the best of them to take into account the findings of science but I wouldn't expect them to focus on science per se. George Ellis, is a cosmologist and he has worked with Stephen Hawking and is something of an amateur theologian. – Mozibur Ullah Feb 1 '18 at 7:58
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Shimon Malin’s “Nature Loves to Hide: Quantum Physics and the Nature of Reality, a Western Perspective” offers Whitehead as a 20th century philosopher that might be what you are looking for. Schrodinger and Heisenberg would be others.

His book attempts to explain the collapse of the wave function by linking fields of atemporal potentiality with the quantum event as an actualization. Science is limited by what Schrodinger considers “objectivation” which removes the subject from the observation. That can lead to what Whitehead calls the “fallacy of misplaced concreteness” where abstractions are confused with facts and are assumed to be valid outside their valid domains. In this way they criticize science.

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