Philosophy of probability

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The philosophy of probability presents problems chiefly in matters of epistemology and the uneasy interface between mathematical concepts and ordinary language as it is used by non-mathematicians. Probability theory is an established field of study in mathematics. It has its origins in correspondence discussing the mathematics of games of chance between Blaise Pascal and Pierre de Fermat in the seventeenth century, and was formalized and rendered axiomatic as a distinct branch of mathematics by Andrey Kolmogorov in the twentieth century. In its axiomatic form, mathematical statements about probability theory carry the same sort of epistemological confidence shared by other mathematical statements in the philosophy of mathematics.^{[1] [2]}

The mathematical analysis originated in observations of the behaviour of game equipment such as playing cards and dice, which are designed specifically to introduce random and equalized elements; in mathematical terms, they are subjects of indifference. This is not the only way probabilistic statements are used in ordinary human language: when people say that "it will probably rain", they typically do not mean that the outcome of rain versus not-rain is a random factor that the odds currently favor; instead, such statements are perhaps better understood as qualifying their expectation of rain with a degree of confidence. Likewise, when it is written that "the most probable explanation" of the name of Ludlow, Massachusetts "is that it was named after Roger Ludlow", what is meant here is not that Roger Ludlow is favored by a random factor, but rather that this is the most plausible explanation of the evidence, which admits other, less likely explanations.

Thomas Bayes attempted to provide a logic that could handle varying degrees of confidence; as such, Bayesian probability is an attempt to recast the representation of probabilistic statements as an expression of the degree of confidence by which the beliefs they express are held.

Though probability initially may have had lowly motivations, its modern influence and use is wide-spread ranging from medicine, through practical pursuits, all the way to the higher-order and the sublime.

Philosophy of statistics

Considerations regarding the meaning and justification for deductions of propositions regarding the probability of observations, data, and results of testing hypotheses is the subject of the philosophy of statistics.

Degrees of certainty

Rudolph Carnap and others tried to formulate a mathematical framework for evaluating objective degrees of certainty of propostions, with properties of probability, but differing from probability as used in statistical inference, and differing from the subjective quality of Bayesian inference.

Bayesian analysis

Bayesian Analysis produces a probability-like number which measures the subjective degree of belief in a proposition (including conjunctions of propositions).

Quantum physics

Aspects of probability as it relates to determinism and the structure of the physical world, were discussed in quantum physics. The discussion came to the attention of the general public with Einstein’s quote “God does not play dice” (paraphrase).^[3]

Shuffling and random number generation

Persi Diaconis has debated the possibility of randomness in the macroscopic (non-quantum) world, as well as in random number generation.^{[citation needed]}

References

1. ^ Laszlo E. Szabo, A Physicalist Interpretation of Probability (Talk presented on the Philosophy of Science Seminar, Eötvös, Budapest, 8 October 2001.)
2. ^ Laszlo E. Szabo, Objective probability-like things with and without objective indeterminism, Studies in History and Philosophy of Modern Physics 38 (2007) 626–634 (Preprint)
3. ^ [1]

External links

• Stanford Encyclopedia of Philosophy: "Interpretations of Probability" by Alan Hajek.

Further reading

• Laurence Jonathan Cohen (1989) An Introduction to the Philosophy of Induction and Probability. Oxford Univ. Press.
• Donald A. Gillies (2000) Philosophical Theories of Probability. London: Routledge.
• Hacking, Ian (1975) Emergence of Probability.
• Humphreys, Paul, ed. (1994) Patrick Suppes: Scientific Philosopher, Synthese Library, Springer-Verlag.
  • Vol. 1: Probability and Probabilistic Causality.
  • Vol. 2: Philosophy of Physics, Theory Structure and Measurement, and Action Theory.
• Jackson, Frank, and Robert Pargetter (1982) "Physical Probability as a Propensity," Noûs 16(4): 567–583.
• David Lewis (1986) Philosophical Papers, Vol. II. Oxford Univ. Press.
• Brian Skyrms (2000) Choice and Chance, 4th ed. Wadsworth.
• Von Plato, Jan (1994) Creating Modern Probability. Cambridge University Press.