Full Text

probability, theories of

BRIAN SKYRMS


Subject Philosophy » Epistemology

DOI: 10.1111/b.9781405139007.2010.x


Extract

Philosophical theories of the meaning of “probability” have dealt with a variety of concepts which may be loosely grouped into three families: degree of belief , relative frequency and chance . The mathematics of probability has been less controversial than its interpretation, largely because all theories treat probability as some kind of proportion. Frequentists treat probability as the proportion of actual cases displaying an attribute. Degree of belief and chance theories treat probability as a proportion of possible cases, with the measure on which the proportions are based reflecting respectively intensities of belief that one has or ought to have or intensities of causal tendency. Proportions add. If I have one half of the pie and you have one quarter of it (and we aren't sharing any) then together we have three quarters of the pie. Proportions are normalized. All of the pie is 100 per cent. Proportions can't be negative. Formally, we can think of a probability as a function mapping elements of a Boolean algebra B (possible pie slices including the null slice and the whole pie) to real numbers in the interval [0, 1] which satisfies: 1.  If b, c are disjoint then pr(b ∪ c) = pr(b) + pr(c) 2.  pr (universal element) = 1 3.  For no b, is pr(b) < o. (It is often assumed that there is an underlying space (the set of pie atoms) such that the Boolean algebra in the foregoing ... log in or subscribe to read full text

Log In

You are not currently logged-in to Blackwell Reference Online

If your institution has a subscription, you can log in here:

 

     Forgotten your password?

Find out how to subscribe.

Your library does not have access to this title. Please contact your librarian to arrange access.


[ access key 0 : accessibility information including access key list ] [ access key 1 : home page ] [ access key 2 : skip navigation ] [ access key 6 : help ] [ access key 9 : contact us ] [ access key 0 : accessibility statement ]

Blackwell Publishing Home Page

Blackwell Reference Online ® is a Blackwell Publishing Inc. registered trademark
Technology partner: Semantico Ltd.

Blackwell Publishing and its licensors hold the copyright in all material held in Blackwell Reference Online. No material may be resold or published elsewhere without Blackwell Publishing's written consent, save as authorised by a licence with Blackwell Publishing or to the extent required by the applicable law.

Back to Top