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Of course, the very first work outlining the principles of scientific investigation was done by the English philosopher Francis Bacon in "Novum Organum", written in the sixteenth century. In more recent times, Bertrand Russell, also an English philosopher, wrote some very great books on the philosophical and logical bases of mathematics, such as "The Principles of Mathematics". Russell also discussed the relation between science and philosophy in "The Problems of Philosophy" (O.U.P., 1959; see, e.g., the chapter "The Limits of Philosophical Knowledge"), and in "Sceptical Essays" (Routledge Classics, 2004; see the chapters "Is Science Superstitious?" and "Can Men Be Rational?"). Even more technical is "Six Not-So-Easy Pieces" by Richard Feynman (look at "Relativity and the Philosophers", pp. 73-77).

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Q: How do philosophers try to bridge the gap between science and philosophy?
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