Editing Probability interpretations (section)

==Philosophy==
The '''philosophy of probability''' presents problems chiefly in matters of [[epistemology]] and the uneasy interface between [[mathematics|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,<ref>[http://www.socsci.uci.edu/~bskyrms/bio/readings/pascal_fermat.pdf Fermat and Pascal on Probability] (@ socsci.uci.edu)</ref> and was formalized and rendered [[axiom]]atic as a distinct branch of mathematics by [[Andrey Kolmogorov]] in the twentieth century. In axiomatic form, mathematical statements about probability theory carry the same sort of epistemological confidence within the [[philosophy of mathematics]] as are shared by other mathematical statements.<ref>Laszlo E. Szabo, ''[http://philosophy.elte.hu/colloquium/2001/October/Szabo/angol011008/angol011008.html A Physicalist Interpretation of Probability] {{Webarchive|url=https://web.archive.org/web/20160304041743/http://philosophy.elte.hu/colloquium/2001/October/Szabo/angol011008/angol011008.html |date=4 March 2016 }}'' (Talk presented on the Philosophy of Science Seminar, Eötvös, Budapest, 8 October 2001.)</ref><ref>Laszlo E. Szabo, Objective probability-like things with and without objective indeterminism, Studies in History and Philosophy of Modern Physics 38 (2007) 626–634 (''[http://philosophy.elte.hu/leszabo/Preprints/lesz_no_probability_preprint.pdf Preprint]'')</ref>

The mathematical analysis originated in observations of the behaviour of game equipment such as [[playing card]]s and [[dice]], which are designed specifically to introduce random and equalized elements; in mathematical terms, they are subjects of [[Principle of indifference|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 had somewhat mundane 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]].

{| class="wikitable" style="text-align: center; "
|+ A summary of some interpretations of probability <ref name="de Elía" />
|-
! scope="col" |
! scope="col" | Classical
! scope="col" | Frequentist
! scope="col" | Subjective
! scope="col" | Propensity
|-
! scope="row" | Main hypothesis
| Principle of indifference || Frequency of occurrence || Degree of belief || Degree of causal connection
|-
! scope="row" | Conceptual basis
| Hypothetical symmetry || Past data and reference class || Knowledge and intuition || Present state of system
|-
! scope="row" | Conceptual approach
| Conjectural || Empirical || Subjective || Metaphysical
|-
! scope="row" | Single case possible
| Yes || No || Yes || Yes
|-
! scope="row" | Precise
| Yes || No || No || Yes
|-
! scope="row" | Problems
| Ambiguity in principle of indifference || Circular definition || Reference class problem || Disputed concept
|}