Editing Nonfirstorderizability (section)

{{Short description|Concept in formal logic}}
{{tech|date=March 2016}}In [[formal logic]], '''nonfirstorderizability''' is the inability of a natural-language statement to be adequately captured by a formula of [[first-order logic]].  Specifically, a statement is '''nonfirstorderizable''' if there is no formula of first-order logic which is true in a [[Model theory|model]] if and only if the statement holds in that model. Nonfirstorderizable statements are sometimes presented as evidence that first-order logic is not adequate to capture the nuances of meaning in natural language.

The term was coined by [[George Boolos]] in his paper "To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables)".<ref name="boolos-to-be">{{cite journal |last1=Boolos |first1=George |author-link=George Boolos |title=To Be Is to Be a Value of a Variable (or to Be Some Values of Some Variables) |journal=The Journal of Philosophy |date=August 1984 |volume=81 |issue=8 |pages=430–449 |doi=10.2307/2026308 |jstor=2026308 }} Reprinted in {{cite book | first=George | last=Boolos | year=1998 | title=Logic, Logic, and Logic | publisher=[[Harvard University Press]] | location=[[Cambridge, MA]] | isbn=0-674-53767-X }}</ref>
Quine argued that such sentences call for [[second-order logic|second-order]] symbolization, which can be interpreted as plural quantification over the same domain as first-order quantifiers use, without postulation of distinct "second-order objects" ([[Property (mathematics)|properties]], sets, etc.).