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


This principle is not valid in classical [[modal logic]]. Moreover adding this principle 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 |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}}</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 |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= |journal= Linguistics and Philosophy |volume=37 |issue=4|doi=10.1007/s10988-014-9154-8}}</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|publisher= Palgrave Macmillan |doi=10.1057/9780230210752_4 |pages=71–120 }}</ref>
This principle is not valid in classical [[modal logic]]. Moreover adding this principle 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= |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|pages= 255–290|doi=10.1023/A:1011255819284}}</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 }}</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}}</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==
==See also==

Revision as of 13:36, 11 December 2021

Free choice is a phenomenon in natural language where a disjunction appears to receive a conjunctive interpretation when it interacts with a 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.[1]

  1. You can watch a movie or play video games.
  2. You can watch a movie or you can play video games.

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

  1. Free Choice Principle:

This principle is not valid in classical modal logic. Moreover adding this principle to standard modal logics would allow one to conclude from , for any and . This observation is known as the Paradox of Free Choice.[1][2] 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.[1][3][4] Others have proposed ways of deriving free choice inferences as scalar implicatures which arise on the basis of classical lexical entries for disjunction and modality.[1][5][6][7]

Free choice inferences are most widely studied for deontic modals, but also arise with other flavors of modality as well as imperatives, conditionals, and other kinds of operators.[1][8][9][4] 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.[9][10]

See also

Notes

  1. ^ a b c d e Aloni, Maria (2016). "Disjunction". In Zalta, Edward (ed.). Stanford Encyclopedia of Philosophy. Retrieved 2021-01-14.
  2. ^ Kamp, Hans (1973). "Free choice permission". Proceedings of the Aristotelian Society. 74: 57–74. doi:10.1093/aristotelian/74.1.57.
  3. ^ Simons, Mandy (2005). "Dividing things up: The semantics of or and the modal/or interaction". Natural Language Semantics. 13 (3): 271–316. doi:10.1007/s11050-004-2900-7. S2CID 14338992.
  4. ^ a b Willer, Malte (2018). "Simplifying with free choice". Topoi. 37 (3): 379–392. doi:10.1007/s11245-016-9437-5. S2CID 125934921.
  5. ^ Fusco, Melissa (2014). "Free choice permission and the counterfactuals of pragmatics". Linguistics and Philosophy. 37 (4): 275–290. doi:10.1007/s10988-014-9154-8. S2CID 27379239.
  6. ^ Schulz, Katrin (2007). Minimal models in semantics and pragmatics: Free choice, exhaustivity, and conditionals (Thesis). University of Amsterdam ILLC.
  7. ^ Fox, Danny (2007). "Free choice and the theory of scalar implicatures". In Sauerland, U.; Stateva, P. (eds.). Presupposition and implicature in compositional semantics. Palgrave Macmillan. pp. 71–120. doi:10.1057/9780230210752_4. ISBN 978-1-349-28206-7.
  8. ^ Zimmerman, Thomas Ede (2000). "Free choice disjunction and epistemic possibility". Natural Language Semantics. 8 (4): 255–290. doi:10.1023/A:1011255819284. S2CID 122826485.
  9. ^ a b Aloni, Maria (2007). "Free choice, modals and imperatives". Natural Language Semantics. 15: 65–94. doi:10.1007/s11050-007-9010-2. S2CID 16471990.
  10. ^ Giannakidou, Anastasia (2001). "The meaning of free choice". Linguistics and Philosophy. 24 (6): 659–735. doi:10.1023/A:1012758115458. S2CID 10533949.
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