Global InformationNonfirstorderizability information
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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.).
- ^ Boolos, George (August 1984). "To Be Is to Be a Value of a Variable (or to Be Some Values of Some Variables)". The Journal of Philosophy. 81 (8): 430–449. doi:10.2307/2026308. JSTOR 2026308. Reprinted in Boolos, George (1998). Logic, Logic, and Logic. Cambridge, MA: Harvard University Press. ISBN 0-674-53767-X.