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Philosophy of science

The philosophy of science seeks to understand the nature and justification of scientific knowledge, and its ethical implications. It has proven difficult to provide a definitive account of the scientific method that can decisively serve to distinguish science from non-science. Thus there are legitimate arguments about exactly where the borders are. There is nonetheless a set of core precepts that have broad consensus among published philosophers of science and within the scientific community at large. (see: Problem of demarcation)

Science is reasoned-based analysis of sensation upon our awareness. As such, the scientific method cannot deduce anything about the realm of reality that is beyond what is observable by existing or theoretical means. When a manifestation of our reality previously considered supernatural is understood in the terms of causes and consequences, it acquires a scientific explanation.

Resting on reason and logic, along with other guidelines such as Occam's Razor, which states a principle of parsimony, scientific theories are formulated and the most promising theory is selected after analysing the collected evidence. Some of the findings of science can be very counter-intuitive. Atomic theory, for example, implies that a granite boulder which appears a heavy, hard, solid, grey object is actually a combination of subatomic particles with none of these properties, moving very rapidly in space where the mass is concentrated in a very small fraction of the total volume. Many of humanity's preconceived notions about the workings of the universe have been challenged by new scientific discoveries. Quantum mechanics, particularly, examines phenomena that seem to defy our most basic postulates about causality and fundamental understanding of the world around us.
Mathematics and the scientific methodMathematics is essential to many sciences. The most important function of mathematics in science is the role it plays in the expression of scientific models. Observing and collecting measurements, as well as hypothesizing and predicting, often require mathematical models and extensive use of mathematics. Mathematical branches most often used in science include calculus and statistics, although virtually every branch of mathematics has applications, even "pure" areas such as number theory and topology. Mathematics is most prevalent in physics, but less so in chemistry, biology, and some social sciences.

Some thinkers see mathematicians as scientists, regarding physical experiments as inessential or mathematical proofs as equivalent to experiments. Others do not see mathematics as a science, since it does not require experimental test of its theories and hypotheses, although some theorems can be disproved by contradiction through finding exceptions. (More specifically, mathematical theorems and formulas are obtained by logical derivations which presume axiomatic systems, rather than a combination of empirical observation and method of reasoning that has come to be known as scientific method.) In either case, the fact that mathematics is such a useful tool in describing the universe is a central issue in the philosophy of mathematics.
Further information: Eugene Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences

Richard Feynman said "Mathematics is not real, but it feels real. Where is this place?", while Bertrand Russell quipped, in allusion to the abstraction inherent in the axiomatic method, that "Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."
regards:snor