# Radical probabilism

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Radical_probabilism
> Markdown URL: https://mediated.wiki/source/Radical_probabilism.md
> Source: https://en.wikipedia.org/wiki/Radical_probabilism
> Source revision: 1338153150
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

{{Short description|Hypothesis in epistemological philosophy}}
'''Radical probabilism''' is a hypothesis in [philosophy](/source/philosophy), in particular [epistemology](/source/epistemology), and [probability theory](/source/probability_theory) that holds that no facts are known for certain. That view holds profound implications for [statistical inference](/source/statistical_inference). The philosophy is particularly associated with [Richard Jeffrey](/source/Richard_Jeffrey) who wittily characterised it with the ''dictum'' "It's probabilities [all the way down](/source/Turtles_all_the_way_down)."

==Background==
{{main|Subjective probability}}
[Bayes' theorem](/source/Bayes'_theorem) states a rule for updating a [probability](/source/probability) conditioned on other information. In 1967, [Ian Hacking](/source/Ian_Hacking) argued that in a static form, Bayes' theorem only connects probabilities that are held simultaneously; it does not tell the learner how to update probabilities when new evidence becomes available over time, contrary to what contemporary [Bayesians](/source/Bayesian_epistemology) suggested.<ref name="Hacking1967">{{cite journal|last= Hacking|first=Ian|title=Slightly more realistic personal probability| journal=Philosophy of Science|volume=34|issue=4|pages=311–325|year=1967|doi=10.1086/288169|s2cid=14344339 }}</ref>
 
According to Hacking, adopting Bayes' theorem is a temptation. Suppose that a learner forms probabilities ''P''<sub>old</sub>(''A''&nbsp;&&nbsp;''B'')&nbsp;=&nbsp;''p'' and ''P''<sub>old</sub>(''B'')&nbsp;=&nbsp;''q''.
If the learner subsequently learns that ''B'' is true, nothing in the [axioms of probability](/source/axioms_of_probability) or the results derived therefrom tells him how to behave. He might be tempted to adopt Bayes' theorem by analogy and set his ''P''<sub>new</sub>(''A'')&nbsp;=&nbsp;''P''<sub>old</sub>(''A''&nbsp;|&nbsp;''B'')&nbsp;=&nbsp;''p''/''q''.

In fact, that step, Bayes' rule of updating, can be justified, as necessary and sufficient, through a ''dynamic'' [Dutch book](/source/Dutch_book) argument that is additional to the arguments used to justify the probability axioms. This argument was first put forward by [David Lewis](/source/David_Lewis_(philosopher)) in the 1970s though he never published it.<ref name="Skyrms1987a">{{cite journal|year=1987a|last= Skyrms|first=Brian|title=Dynamic coherence and probability kinematics| journal=Philosophy of Science|volume=54|pages=1–20|doi=10.1086/289350|s2cid= 120881078|citeseerx=10.1.1.395.5723}}</ref> The dynamic Dutch book argument for Bayesian updating has been criticised by Hacking,<ref name="Hacking1967" /> [Kyburg](/source/Henry_E._Kyburg_Jr.),<ref>{{ cite journal | last=Kyburg |first=H. | year=1978 | title=Subjective probability: Criticisms, reflections and problems | journal=Journal of Philosophical Logic | volume=7 | pages=157–180 | doi=10.1007/bf00245926| s2cid=36972950 }}</ref> [Christensen](/source/David_Christensen_(philosopher)),<ref>{{ cite journal | year=1991 | last=Christensen |first=D. | title=Clever bookies and coherent beliefs| journal=Philosophical Review | volume=100 | issue=2 | pages=229–47 | doi=10.2307/2185301| jstor=2185301 | url=https://philarchive.org/rec/CHRCBA }}</ref> and [Maher](/source/Patrick_Maher_(philosopher)).<ref>{{ cite book | last=Maher, P | year=1992a | title=Betting on Theories | location=Cambridge | publisher=Cambridge University Press}}</ref><ref>{{ cite journal | year=1992b | title=Diachronic rationality | journal=Philosophy of Science | volume=59 | pages=120–41| doi=10.1086/289657 | last1=Maher | first1=Patrick | s2cid=224830300 }}</ref> It was defended by [Brian Skyrms](/source/Brian_Skyrms).<ref name="Skyrms1987a" />

==Certain and uncertain knowledge==
That works when the new data is certain. [C. I. Lewis](/source/C._I._Lewis) had argued that "If anything is to be probable then something must be certain".<ref>{{ cite book | last=Lewis | first=C. I. | year=1946 | title=An Analysis of Knowledge and Valuation | url=https://archive.org/details/in.ernet.dli.2015.205083 | location=La Salle, Illinois | publisher=Open Court| page=186 }}</ref> There must, on Lewis' account, be some certain facts on which probabilities were [conditioned](/source/conditional_probability). However, the principle known as [Cromwell's rule](/source/Cromwell's_rule) declares that nothing, apart from a logical law, if that, can ever be known for certain. Jeffrey famously rejected Lewis' ''dictum''.<ref>{{ cite book | last=Jeffrey | first=Richard C. | year=2004 | title=Subjective Probability: The Real Thing | chapter-url=https://archive.org/details/subjectiveprobab0000jeff | chapter-url-access=registration | publisher=Cambridge University Press | location=Cambridge | chapter=Chapter 3 }}</ref> He later quipped, "It's probabilities all the way down," a reference to the "[turtles all the way down](/source/turtles_all_the_way_down)" metaphor for the [infinite regress](/source/infinite_regress) problem. He called this position ''radical probabilism''.<ref>{{cite journal|last=Skyrms, B|year=1996|title=The structure of radical probabilism|journal=Erkenntnis|volume=45|issue=2–3 |pages=285–97|doi=10.1007/BF00276795 }}</ref>

==Conditioning on an uncertainty – probability kinematics==
In this case Bayes' rule isn't able to capture a mere subjective change in the probability of some critical fact. The new evidence may not have been anticipated or even be capable of being articulated after the event. It seems reasonable, as a starting position, to adopt the [law of total probability](/source/law_of_total_probability) and extend it to updating in much the same way as was Bayes' theorem.<ref>{{ cite journal | last=Jeffrey | first=Richard | year=1987 | title=Alias Smith and Jones: The testimony of the senses | journal=Erkenntnis| volume=26 | issue=3 | pages=391–399 | doi=10.1007/bf00167725| s2cid=121478331 }}</ref>

: ''P''<sub>new</sub>(''A'') = ''P''<sub>old</sub>(''A'' | ''B'')''P''<sub>new</sub>(''B'') + ''P''<sub>old</sub>(''A'' | not-''B'')''P''<sub>new</sub>(not-''B'')

Adopting such a rule is sufficient to avoid a Dutch book but not necessary.<ref name="Skyrms1987a" /> Jeffrey advocated this as a rule of updating under radical probabilism and called it probability kinematics. Others have named it Jeffrey conditioning.

==Alternatives to probability kinematics==
Probability kinematics is not the only sufficient updating rule for radical probabilism. Others have been advocated including [E. T. Jaynes](/source/E._T._Jaynes)' [maximum entropy principle](/source/maximum_entropy_principle), and Skyrms' [principle of reflection](/source/principle_of_reflection). It turns out that probability kinematics is a special case of maximum entropy inference. However, maximum entropy is not a generalisation of all such sufficient updating rules.<ref>{{ cite journal | last=Skyrms, B | year=1987b | title=Updating, supposing and MAXENT | journal=Theory and Decision | volume=22 | issue=3 | pages=225–46 | doi=10.1007/bf00134086| s2cid=121847242 }}</ref> 

Jaynes has criticised Jeffrey's rule for calculating updated probabilities and dismissed it as an "ad hockery".<ref>{{ cite book | last=Jaynes | first=E. T. | year=2003 | title=Probability Theory. The Logic of Science | url=http://www.cambridge.org/9780521592710 | location=Cambridge, United Kingdom | publisher=Cambridge University Press| page=140 }}</ref>

==References==
{{reflist}}

== Further reading ==
* Jeffrey, R (1990) ''The Logic of Decision''. 2nd ed. University of Chicago Press. {{ISBN|0-226-39582-0}}
* &mdash; (1992) ''Probability and the Art of Judgment''. Cambridge University Press. {{ISBN|0-521-39770-7}}
* &mdash; (2004) ''Subjective Probability: The Real Thing''. Cambridge University Press. {{ISBN|0-521-53668-5}}
*Skyrms, B (2012) ''From Zeno to Arbitrage: Essays on Quantity, Coherence & Induction''. Oxford University Press (Features most of the papers cited below.)

== External links ==
* [http://plato.stanford.edu/entries/bayes-theorem/ Stanford Encyclopedia of Philosophy entry on Bayes' theorem]
{{Authority control}}

{{DEFAULTSORT:Radical probabilism}}
Category:Bayesian inference
Category:Epistemological theories
Category:Probability theory

---
Adapted from the Wikipedia article [Radical probabilism](https://en.wikipedia.org/wiki/Radical_probabilism) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Radical_probabilism?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.