# Probability

## Some Applications Of Probability

Probability theory thus continues to be a vigorous area of research. Moreover, its advances have myriad ramifications. Probability is explicitly used in many of our best scientific theories, for example, quantum mechanics and statistical mechanics. It is also implicit in much of our theorizing. A central notion in evolutionary biology is "fitness," or expected number of offspring. Psychologists publish their conclusions with significance levels attached. Agricultural scientists perform analyses of variance on how effective fertilizers are in increasing crop yields. Economists model currency exchange rates over time as stochastic processes—that is, sequences of random variables. In cognitive science and philosophy, probability functions model states of opinion. Since probability theory is at the heart of decision theory, it has consequences for ethics and political philosophy. And assuming, as many authors do, that decision theory provides a good model of rational decision-making, it apparently has implications for even mundane aspects of our daily lives. In short, probability is ubiquitous. Bishop Butler's dictum is truer today than ever.

## BIBLIOGRAPHY

Butler, Joseph. *Analogy of Religion.* 1736. Reprint, New York: Frederick Ungar, 1961.

Carnap, Rudolf. *Logical Foundations of Probability.* Chicago: University of Chicago Press, 1950.

De Finetti, Bruno. "La Prévision: Ses Lois Logiques, Ses Sources Subjectives." *Annales de l'Institut Henri Poincaré* 7 (1937): 1–68. Translated as "Foresight: Its Logical Laws, Its Subjective Sources." In *Studies in Subjective Probability,* edited by H. E. Kyburg Jr. and H. E. Smokler. New York: Robert E. Krieger, 1980.

Feller, William. *An Introduction to Probability Theory and Its Applications.* 3rd ed. New York: John Wiley and Sons, 1968.

Fine, Terrence. *Theories of Probability.* New York: Academic Press, 1973.

Gillies, Donald. "Varieties of Propensity." *British Journal for the Philosophy of Science* 51 (2000): 807–835.

Hájek, Alan. "Probability, Interpretations of." In *The Stanford Encyclopedia of Philosophy,* edited by E. Zalta. Stanford, Calif.: Stanford University, 2002. Available at http://plato.stanford.edu/entries/probability-interpret/.

Howson, Colin, and Peter Urbach. *Scientific Reasoning: The Bayesian Approach.* 2nd ed. Chicago: Open Court, 1993.

Kolmogorov, Andrei N. *Grundbegriffe der Wahrscheinlichkeitrechnung, Ergebnisse der Mathematik.* 1933. Translated as *Foundations of Probability.* New York: Chelsea, 1950.

Laplace, Pierre Simon. *Essai philosophique sur les probabilités.* 1814. Translated as *A Philosophical Essay on Probabilities.* New York: Dover, 1951.

Li, Ming, and Paul Vitanyi. *An Introduction to Kolmogorov Complexity and Its Applications.* 2nd ed. New York: Springer-Verlag, 1997.

Muckenheim, W., et al. "A Review of Extended Probability." *Physics Reports* 133 (1986): 337–401.

Popper, Karl. *The Logic of Scientific Discovery.* London: Hutchinson, 1959.

Ramsey, Frank P. "Truth and Probability." 1926. Reprinted in *Philosophical Papers,* edited by D. H. Mellor. Cambridge, U.K.: Cambridge University Press, 1990.

Venn, John. *The Logic of Chance.* 2nd ed. London: Macmillan, 1876. Reprint, New York: Chelsea, 1962.

Von Mises, Richard. *Wahrscheinlichkeit, Statistik und Wahrheit.* 1939. Translated as *Probability, Statistics, and Truth.* Rev. English ed. New York: Macmillan, 1957.

*Alan* *Hájek*

## Additional topics

Science EncyclopediaScience & Philosophy: *Positive Number* to *Propaganda - World War Ii*Probability - The Formal Theory Of Probability, Interpretations Of Probability, Some Recent Developments, Some Applications Of Probability