The modern quantitative theory of information provides us with a set of powerful mathematical tools that can be used to develop a quantitative philosophy of science. After all, science is fundamentally a set of effective methods for dealing with information. A quantitative information-theoretic analysis of those methods can provide the key to developing a useful, quantitative philosophy of science.
Quantitative information theory was developed in the twentieth century by theorists including Leo Szilard, Norbert Weiner, Claude Shannon, and Gregory Chaitin. And philosophers in the past who attempted to develop a philosophy of science without using the ideas of quantitative information theory were in a position somewhat analogous to physicists from Thales and Aristotle through Galileo and Huygens: These early physicists lacked the critical mathematical tools contained in Newton’s calculus that were needed to make physics quantitative for the first time. By making philosophy quantitative, information theory plays a role in the philosophy of science analogous to the role of calculus in physics.
Using this quantitative, information-theoretic analysis of scientific methods we can show how a single error by the logical positivists led to absurdities such as relativism and post-modernism, and we will see how the error can be easily remedied. A quantitative philosophy of science will also provide something that Thomas Kuhn lacked in his famous discussion of paradigm shifts. Kuhn was unable to provide a precise quantitative definition of a paradigm because he lacked the quantitative information-theoretic tools that can provide such a definition. Information theory also makes previously difficult topics such as Goedel’s famous incompleteness theorem much simpler and easier to understand.
These matters are discussed in more detail on http://cires.colorado.edu/~doug/philosophy/
