Meaning, Truth, and Identity: A Defense of The Significance of Intensional Logic Submitted by: Abstract Logic concerns itself with truth. It is known that the manner in which the truth of an identity statement, interpreted within formal logic, is explicated purely in terms of its logical structure…
However, if we only consider extensions, a problem would arise. For extensional logic fails to provide an adequate analysis of meanings, and an adequate explication wherein intensional contexts are needed as in the case of its treatment of identity statements. Thus, a distinction must accordingly be drawn between intension and extension. The aim of this research paper is to show that an intensional logic can be done, for it seems to be necessary for an adequate analysis regarding the problem of identity statements between singular terms or variables. In doing so, identity statements will be used to serve as the test case for showing that if meaning is what is sought, then extensions will not suffice. The researcher contends that it is indeed possible to establish an intensional logic. And not only is it possible, but is also necessary for interpreting the truth of non-trivial identity statements between singular terms or variables of the form (a = b). Literature Review The review of related literature in this study focuses on the nature of identity statements flanked by the connective “=” between names, which can be represented by the use of variables. The review examines the scope and limitations of my main inquiry, as well as related issues within the field of the philosophy of logic dealing with identity in the context of intensional and extensional logics. This survey is intended to show related studies and works done in the past regarding the logic and nature of identity. A. Frege, Gottlob. “Sense and Reference.”In The Philosophical Review, Vol. 57, No. 3 (May, 1948) : 209-230. Frege begins by questioning the concept of identity. His main claim is that “meaning” is possible between identity statements for it contains two aspects: its sense and its reference. In a nutshell, sense is its mode of presentation and reference, its mode of designation. However significant Frege is in the philosophy of language and logic, my topic will not focus on Frege’s theory of meaning and his take on the logic of identity. My reasons for such is that Frege’s concern is not that of the nature of “=”, which is the symbol used for identity statements, but rather, identity statements itself, that is, the “sense” of what is on the left and right of “=”. However, his contributions are very much useful in dealing with identity as a relation, for he does not take on the path of identity statements as a relation between names or objects, but rather introduces another concept; its sense, that is, its mode of presentation or representation. Although Frege himself did not explicitly say whether or not his take on identity is intensional or extensional, I believe that this is one instance wherein an intensional reading of identity statements is called forth, to have a better understanding of the nature of identity. B. Geach, Peter Thomas. “Quine on Classes and Properties.” In The Philosophical Review, Vol. 62, No. 3 (July 1953): 409-412. Geach’s article emphasizes on Quine’s account on how classes stand in relation to properties, and does so with the attempt to point out Quine’s mistake in identifying properties with classes. Inasmuch as my topic is concerned with both the relation of classes and properties, Geach’s take differs from my main inquiry insofar that he stresses on Quine’ ...
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