Nonfirstorderizability - Wikipedia
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 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)".[1] Quine argued that such sentences call for 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" (properties, sets, etc.). A standard example is the Geach–Kaplan sentence: "Some critics admire only one another." If Axy is understood to mean "x admires y,"
Nonfirstorderizability - Wikipedia Jump to content From Wikipedia, the free encyclopedia Concept in formal logic This article may be too technical for most readers to understand . Please help improve it to make it understandable to non-experts , without removing the technical details. ( March 2016 ) ( Learn how and when to remove this message ) 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
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