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first-level concept

Subject Philosophy

DOI: 10.1111/b.9781405106795.2004.x


L ogic, philosophy of mathematics, metaphysics Frege distinguished between first-level concepts and second-level concepts, although he sometimes used the expressions “first-order concepts” and “second-order concepts” for the same purpose. Since Frege's distinction between concept and object corresponds to his distinction between predicate and subject, this is also a distinction between first-level predicates and second-level predicates. A first-level concept or predicate is applied to an object to ascribe a property to that object. A second-level concept or predicate is applied not to an object, but to a concept or a predicate. It is a concept of first-level concepts or a predicate of first-level predicates. A first-level concept is also called an nth-level concept, while a second-level concept is called an n+1th-level concept. This doctrine can be traced to Kant 's view that existence is not a real property . Accordingly, existence is a second-level rather than the first-level concept. To say “X exists” means that the concept X is instantiated. Analogously, number is also a second-level concept. When we say that X is a number, we do not mean that X is an object that has the property of being a number, but rather that the concept X has numerous instantiations. Frege's famous doctrine that existence is a second-level concept or predicate is inferred from his doctrine ... log in or subscribe to read full text

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