View source for Free choice inference

{{Short description|Phenomenon in natural language}}
{{redirect-confuse|paradox of free choice|The Paradox of Choice{{!}}''The Paradox of Choice''}}
'''Free choice''' is a phenomenon in natural language where a linguistic [[disjunction]] appears to receive a logical [[logical conjunction|conjunctive]] interpretation when it interacts with a [[linguistic modality|modal]] operator. For example, the following English sentences can be interpreted to mean that the addressee can watch a movie ''and'' that they can also play video games, depending on their preference:<ref name = "alonisep">{{cite encyclopedia |last=Aloni |first=Maria |author-link=Maria Aloni |editor-last1=Zalta |editor-first1=Edward |encyclopedia=Stanford Encyclopedia of Philosophy |title=Disjunction |url=https://plato.stanford.edu/archives/win2016/entries/disjunction/ |access-date=2021-01-14 |year=2016}}</ref>

# You can watch a movie or play video games.
# You can watch a movie or you can play video games.

Free choice inferences are a major topic of research in [[formal semantics (natural language)|formal semantics]] and [[philosophical logic]] because they are not [[validity (logic)|valid]] in classical systems of [[modal logic]]. If they were valid, then the semantics of natural language would validate the ''Free Choice Principle''.

# ''Free Choice Principle'': <math> \Diamond( P \lor Q) \rightarrow (\Diamond P \land \Diamond Q)  </math>

This symbolic logic formula above is not valid in classical [[modal logic]]: Adding this principle as an axiom to standard modal logics would allow one to conclude <math>\Diamond Q</math> from <math>\Diamond P</math>, for any <math>P</math> and <math>Q</math>. This observation is known as the ''Paradox of Free Choice''.<ref name = "alonisep" /><ref>{{cite journal |last1=Kamp |first1=Hans |year=1973 |title=Free choice permission |url= |journal= Proceedings of the Aristotelian Society |volume=74 |pages=57–74 |doi=10.1093/aristotelian/74.1.57}}</ref> To resolve this paradox, some researchers have proposed analyses of free choice within nonclassical frameworks such as [[dynamic semantics]], [[linear logic]], [[alternative semantics]], and [[inquisitive semantics]].<ref name= "alonisep" /><ref>{{cite journal |last1=Simons |first1=Mandy|date=2005 |title= Dividing things up: The semantics of or and the modal/or interaction |url= |journal=Natural Language Semantics |volume=13 |issue=3 |pages=271–316 |doi=10.1007/s11050-004-2900-7|s2cid=14338992}}</ref><ref name = "willertopoi">{{cite journal |last1=Willer |first1=Malte|date=2018 |title=Simplifying with free choice|journal=Topoi |volume=37 |issue=3 |pages=379–392 |doi=10.1007/s11245-016-9437-5 |s2cid=125934921|access-date=}}</ref> Others have proposed ways of deriving free choice inferences as [[scalar implicature]]s which arise on the basis of [[classical logic|classical]] lexical entries for disjunction and modality.<ref name = "alonisep" /><ref>{{cite journal |last1=Fusco |first1=Melissa|date=2014 |title= Free choice permission and the counterfactuals of pragmatics |url= https://philpapers.org/rec/FUSFCP|journal= Linguistics and Philosophy  |volume=37 |issue=4|pages=275–290|doi=10.1007/s10988-014-9154-8|s2cid=27379239}}</ref><ref>{{cite thesis |last=Schulz |first=Katrin |date=2007 |title= Minimal models in semantics and pragmatics: Free choice, exhaustivity, and conditionals |type= |publisher=University of Amsterdam ILLC}}</ref><ref>{{cite encyclopedia |last=Fox |first=Danny |author-link=Danny Fox |editor-last1=Sauerland |editor-first1=U. | editor-last2=Stateva |editor-first2=P. |encyclopedia=Presupposition and implicature in compositional semantics |title=Free choice and the theory of scalar implicatures|year=2007 |publisher= Palgrave Macmillan |doi=10.1057/9780230210752_4 |pages=71–120 |isbn=978-1-349-28206-7 }}</ref>

Free choice inferences are most widely studied for [[deontic modality|deontic modals]], but also arise with other flavors of modality as well as [[imperative mood|imperative]]s, [[conditional sentence|conditionals]], and other kinds of operators.<ref name= "alonisep" /><ref>{{cite journal |last1=Zimmerman |first1=Thomas Ede |date=2000 |title=Free choice disjunction and epistemic possibility |journal=Natural Language Semantics |volume=8|issue=4 |pages= 255–290|doi=10.1023/A:1011255819284|s2cid=122826485 }}</ref><ref name="aloni07">{{cite journal|last1=Aloni|first1=Maria|date=2007|title=Free choice, modals and imperatives|journal=Natural Language Semantics|volume=15 |pages=65–94 |doi=10.1007/s11050-007-9010-2 |s2cid=16471990}}</ref><ref name = "willertopoi" /> [[indefinite article|Indefinite noun phrases]] give rise to a similar inference which is also referred to as "free choice" though researchers disagree as to whether it forms a  [[natural class]] with disjunctive free choice.<ref name="aloni07" /><ref>{{cite journal |last1= Giannakidou |first1= Anastasia |date=2001 |title=The meaning of free choice |url= |journal=Linguistics and Philosophy |volume=24 |issue=6 |pages= 659–735 |doi=10.1023/A:1012758115458|s2cid= 10533949 }}</ref>

==See also==
* [[Deontic logic]]
* [[Disjunction]]
* [[Hans Kamp]]
* [[Modal logic]]
* [[Ross's paradox]]
* [[Simplification of disjunctive antecedents]]
* [[Sluicing]]

==Notes==
{{reflist}}

[[Category:Semantics]]
[[Category:Deontic logic]]
[[Category:Modal logic| ]]
[[Category:Philosophical logic]]
[[Category:Mathematical logic]]
[[Category:Rules of inference]]
[[Category:Formal semantics (natural language)]]

{{Formal semantics}}

{{logic-stub}}
{{semantics-stub}}
{{pragmatics-stub}}