The chief architect of a universal Inferential Calculus for science is Edwin T. Jaynes. His early contributions are described in a book review of his collected papers.
The culmination of his work is his book Probability Theory: The Logic of Science, which has been under construction for 40 years. This masterpiece should be ranked among the historical great books of science. Sadly, Jaynes passed away in April 1998 before the manuscript was complete, but it has been published posthumously by Cambridge University Press. The first three chapters of the book can be downloaded from http://bayes.wustl.edu, where many other valuable papers can be found. A collection of essays in his honor has been published under the title Physics and Probability (Cambridge University Press, 1993). The concluding essay by Jaynes himself outlines work for the future.
More fine papers by Jaynes and many others can be found in the proceedings to series of conferences on "Maximum Entropy and Bayseian Methods," published mostly by Kluwer. These papers document Jaynes' broad interest and influence on statistical practice in physics, data analysis, signal processing, tomography, economic forecasting, and much more. The yearly MaxEnt conferences are rich in ideas and information about new developments.
The statistical practice of most physicists, not to mention other scientists, is crude and often seriously flawed. It is very important, therefore, to expose undergraduate students to the insights of Jaynes in coherent instruction on probability and statistics. A noteworthy step toward meeting this need is De Sivia's textbook Data Analysis, A Bayesian Tutorial, Oxford University Press (1996).