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Being, Unity, and Identity in the Fregean and Aristotelian Traditions

Chapter
Part of the Philosophers in Depth book series (PID)

Abstract

These are some of the things we nowadays learn about the notions of being or existence,1 identity and unity, through being exposed to any standard system of post-Fregean predicate logic and the related philosophical literature. Existence is a second-order concept, meaning that it is a logical connective, what in the Aristotelian tradition used to be called a syncategorematic concept.2 A concept of this sort does not have the function of representing or characterizing some extramental objects, as categorematic or first-order concepts do, such as the concepts of “man” or “horse”; rather, they have the function of operating on these concepts, forming more complex concepts with them. The resulting complex concepts or thoughts, then, will have different functions, determined by the functions of their components. For example, by Fregean lights, if the function of the concept of “horse” is to represent horses in a universal fashion (as opposed to the concept of “Bucephalus” that represents a single horse in a singular fashion), and the function of the concept of existence is to state that the first-order concept with which it is construed has a non-empty extension, then the thought expressed by the sentence “Horses exist” or “There are horses” has the function of denoting the True, just in case the extension of the predicate denoting the concept of horses is not empty. Or, equivalently, but sticking closer to Frege’s original ideas, the concept denoted by the predicate “horse” is nothing but a function from individuals to truth-values (the True and the False), and the thought resulting from the application of the concept of existence to this concept denotes the True, just in case this function yields the True as its value for some individual.

Keywords

Principal Part Partial Identity Existential Quantifier Identity Claim Absolute Identity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Gyula Klima 2013

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