Nonfirstorderizability

<p>In <a href="/facts/Formal_logic/SaI7Y3wN">formal logic</a>, nonfirstorderizability is the inability of a natural-language statement to be adequately captured by a formula of <a href="/facts/First-order_logic/lcISqWIg">first-order logic</a>.  Specifically, a statement is nonfirstorderizable if there is no formula of first-order logic which is true in a <a href="/facts/Model_theory/vLWVV8sQ">model</a> 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.
</p><p>The term was coined by <a href="/facts/George_Boolos/K969uIhT">George Boolos</a> in his paper "To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables)".
Quine argued that such sentences call for <a href="/facts/Second-order_logic/C138cGXQ">second-order</a> symbolization, which can be interpreted as plural quantification over the same domain as first-order quantifiers use, without postulation of distinct "second-order objects" (<a href="/facts/Property_(mathematics)/CsKlqNSF">properties</a>, sets, etc.).
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Nonfirstorderizability open-in-new

Nonfirstorderizability