Philosophy
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.
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 widespread ranging from Evidence based medicine, through Six sigma, all the way to the Probabilistically checkable proof and the String theory landscape.
Read more about this topic: Probability Interpretations
Famous quotes containing the word philosophy:
“When a bachelor of philosophy from the Antilles refuses to apply for certification as a teacher on the grounds of his color I say that philosophy has never saved anyone. When someone else strives and strains to prove to me that black men are as intelligent as white men I say that intelligence has never saved anyone: and that is true, for, if philosophy and intelligence are invoked to proclaim the equality of men, they have also been employed to justify the extermination of men.”
—Frantz Fanon (1925–1961)
“This philosophy of hate, of religious and racial intolerance, with its passionate urge toward war, is loose in the world. It is the enemy of democracy; it is the enemy of all the fruitful and spiritual sides of life. It is our responsibility, as individuals and organizations, to resist this.”
—Mary Heaton Vorse (1874–1966)
“The philosophy of hedonism means little to lovers of pleasure. They have no inclination to read philosophy, or to write it.”
—Mason Cooley (b. 1927)