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I am a student of science (physics) with no formal or informal training in philosophy. However, I'm interested in knowing a very basic question: what kind of questions does a philosopher deal with and what is/was the impact of philosophers on the society and science?

Is there a beginner-level book or online resource which I can read and try to understand the meaning and importance, in terms of how did philosophy shape our society and enriched our knowledge from the time of its birth?

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    This could use a little more focus -- maybe you could clarify this: are you after a book recommendation primarily, or an immediate explanation about what sorts of questions are investigated by philosophers of science? – Joseph Weissman Nov 23 '16 at 18:45
  • An immediate explanation will be extremely helpful. – SRS Nov 23 '16 at 18:51
  • Philosophers developed modern logic, have connections with mathematics, and modern science of the mind (psychology, which developed from philosophy of mind). Is there a less broad section you wish to view? Are you looking for physics? – NationWidePants Nov 23 '16 at 19:09
  • Try reading the short story "The Weapon" by Fredric Brown, if you want to see what they should be thinking. – Rbma12 Nov 23 '16 at 19:58
  • Also a student of science, ms in physics, with no philosophy training. And can't address the "society" part of your question. But by far the most enlightening (to me) philosophy of science book I've read is scribd.com/doc/127985402/Jammer-QUantum-mechanics-philosophy Just start with the first 20-page chapter, "Formalism and Interpretation", to get an understanding of how a theory is a "partially interpreted formal system". Ernest Nagel en.wikipedia.org/wiki/Ernest_Nagel is typically cited for philosophy of science stuff, but I've personally found Jammer much more helpful. – John Forkosh Nov 24 '16 at 12:05
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You are asking several questions here. Firstly, what kind of questions is philosophy of science concerned with? Here are some of the most important:

How does scientific knowledge advance? Is there a distinctive scientific method, and if so how does it work? Is there a clear difference between what counts as science and what does not? Is there a clear way to demarcate good science from bad science? How objective is science? To what extent is scientific knowledge shaped by sociological or ideological considerations? What is the nature of scientific explanation? Or, what does 'explanation' mean in a scientific context? What is the relationship between observation, theory and model? What is the nature of a scientific law? What is the nature of causation? Do we need this concept, and if so what account can we give of it? Is some kind of determinism true, and if so, what are the implications? What is the relationship between different sciences? Is it entirely reductive in nature? Does science have anything specific to say about what kinds of things exist? Do theoretical entities such as electrons or quarks exist or are they just useful fictions? Can evolutionary theory entirely displace the concept of teleology? What do scientific theories such as thermodynamics, relativity and quantum mechanics have to tell us about the nature of time, space and matter? What does the general theory of evolution tell us about human nature and mankind's place in the universe? Are there ethical implications of scientific research? Are there fundamental limits to what scientific investigation is capable of teaching us? Are there truths that science is not capable of reaching?

Secondly, what impact does philosophy of science have on science? This is harder to answer. Some scientists, including Newton, Einstein and Poincaré were very philosophical in their approach to scientific thinking. Some philosophers of science have been widely read by scientists, such as Karl Popper and Thomas Kuhn. Other scientists, such as Feynman, are dismissive of philosophical considerations.

Thirdly, how has philosophy shaped our society and enriched our knowledge? This is a huge question, and you would need to study the whole history of philosophy to answer it. As far as science is concerned, we might say that philosophical thinking historically gave birth to the sciences. In the time of the ancient Greeks, all knowledge was considered philosophy. Once philosophers learned how certain problems could be solved empirically, philosophy gave birth to natural science. As late as the 18th century, the terms natural science and natural philosophy were interchangeable. Philosophical thinking also gave birth to psychology, linguistics, formal logic, economics, etc., so in a sense, everything we know ultimately comes from philosophy.

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The natural order of theory development is from poetic to philosophy, and from philosophy to science; this is exemplified in the Greek antiquity from school of Miletus to that of Aristotle - where one can clearly see the discursive style of the scientist apparent; poetic thinking, here by the way, isn't the kind of thinking neccessarily exemplified by a poet or poetry, but analogous to it - it operates analogically or metaphorically, rather than the through the discursive tendency of philosophy.

It certainly cannot be the reverse order; often the modes intermingle with a certain note predominating and then another; for example, early QM had quite a bit of 'magical' thinking - Diracs sea, atoms that looked like the solar system, spinning that isn't actually spinning.

Super-symmetry and multiverses are recent example of this kind of 'magical' thinking - though they're not labelled as such; these are scientists after all...perhaps we can think of them as hypotheses with magical consequences.

Often, science is presented without the connecting tissue, so one isn't aware of its inner movement; modern science is still fairly recent, and most of the focus has been on its development - and its development has been exponential and explosive, and a lot less effort has gone on its intellectual history; undoubtedly that is changing and will change more in the future. There is a good reason for this, as its already a technically demanding subject - and one has to think of expositary devices and manoevres that can get around these kind of bottlenecks.

As for good general introductory reference, I'm not sure; what I've learnt has come from general omnivorous learning.

Part of the problem here - as identified by Adorno and Arendt is the break of tradition.

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