Editing Willard Van Orman Quine (section)

==== Ontological commitment ====
The notion of [[ontological commitment]] plays a central role in Quine's contributions to ontology.<ref>{{cite book |last1=Craig |first1=Edward |title=Routledge Encyclopedia of Philosophy |date=1996 |publisher=Routledge |url=https://philpapers.org/rec/BEAREO |chapter=Ontological commitment}}</ref><ref>{{cite web |last1=Simons |first1=Peter M. |title=Ontology |url=https://www.britannica.com/topic/ontology-metaphysics |website=Encyclopedia Britannica |access-date=December 13, 2020 |language=en}}</ref> A theory is ontologically committed to an entity if that entity must exist in order for the theory to be true.<ref name="Bricker">{{cite web |last1=Bricker |first1=Phillip |title=Ontological Commitment |url=https://plato.stanford.edu/entries/ontological-commitment/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=December 13, 2020 |date=2016}}</ref> Quine proposed that the best way to determine this is by translating the theory in question into [[first-order predicate logic]]. Of special interest in this translation are the logical constants known as [[existential quantification|existential quantifiers]] ('{{math|∃}}'), whose meaning corresponds to expressions like "there exists..." or "for some...". They are used to [[First-order logic#Free and bound variables|bind the variables]] in the expression following the quantifier.<ref>{{cite book |last1=Magnus |first1=P. D. |last2=Ichikawa |first2=Jonathan Jenkins |title=Forall X |date=2020 |publisher=Creative Commons: Attribution-ShareAlike 3.0 |url=https://philpapers.org/rec/MAGFXU |chapter=V. First-order logic|edition=UBC }}</ref> The ontological commitments of the theory then correspond to the variables bound by existential quantifiers.<ref>{{cite book |last1=Schaffer |first1=Jonathan |title=Metametaphysics: New Essays on the Foundations of Ontology |publisher=Oxford University Press |pages=347–383 |url=https://philpapers.org/rec/SCHOWG |chapter=On What Grounds What|year=2009 }}</ref> For example, the sentence "There are electrons" could be translated as "{{math|∃''x'' ''Electron''(''x'')}}", in which the bound variable ''x'' ranges over electrons, resulting in an ontological commitment to electrons.<ref name="Bricker"/> This approach is summed up by Quine's famous dictum that "[t]o be is to be the value of a variable".<ref name="Quine">{{cite journal |last1=Quine |first1=Willard Van Orman |title=On What There Is |journal=Review of Metaphysics |date=1948 |volume=2 |issue=5 |pages=21–38 |url=https://philpapers.org/rec/QUIOWT-7}}</ref> Quine applied this method to various traditional disputes in ontology. For example, he reasoned from the sentence "There are prime numbers between 1000 and 1010" to an ontological commitment to the existence of numbers, i.e. [[Philosophy of mathematics#Mathematical realism|realism]] about numbers.<ref name="Quine"/> This method by itself is not sufficient for ontology since it depends on a theory in order to result in ontological commitments. Quine proposed that we should base our ontology on our best scientific theory.<ref name="Bricker"/> Various followers of Quine's method chose to apply it to different fields, for example to "everyday conceptions expressed in natural language".<ref>{{cite book |last1=Inwagen |first1=Peter van |title=Oxford Studies in Metaphysics, Volume 1 |date=2004 |publisher=Clarendon Press |pages=107–138 |url=https://philpapers.org/rec/VANATO-2 |chapter=A Theory of Properties}}</ref><ref>{{cite book |last1=Kapelner |first1=Zsolt-kristof |title=Reconciling Quinean and neo-Aristotelian Metaontology |date=2015 |url=http://www.etd.ceu.hu/2015/kapelner_zsolt-kristof.pdf |chapter=3. Quinean Metaontology}}</ref>