Truth and falsity: what are truth values and why do we need them
DOI:
https://doi.org/10.31812/apm.v27.01Keywords:
truth value, truth, falsity, Gottlob Frege, slingshot argument, abstract objects, extensionality, logical connectives, logic, logical worldsAbstract
The paper offers a systematic analysis of the notion of a truth value and its significance for logic and the philosophy of language. The point of departure is Gottlob Frege’s conception according to which sentences are construed as names of special objects, namely truth values, identified in the classical case with truth and falsity. The paper explicates the role of truth values in Frege’s functional analysis of language and shows their importance for the development of extensional semantics and for the rigorous formalization of logical connectives as truth-valued functions. It is argued that the introduction of truth values makes it possible to dispense with a separate semantic category of sentences and to provide a uniform semantic interpretation of predicates and logical operators within a single functional framework. Particular attention is paid to the problem of the categorial status of truth. Drawing on Fregean considerations and later philosophical developments, the paper defends the view that truth should not be understood as a property but rather as an abstract object. This ontological interpretation allows one to avoid well-known difficulties associated with the identification of truth bearers and with the undesirable “multiplication of truths” across different kinds of entities. A substantial part of the discussion is devoted to the slingshot argument in the versions developed by Church, Gödel, and Davidson, which is examined as a formal and semantically motivated justification of the thesis that all true sentences share one and the same value, whereas all false sentences share another. On this basis, the paper advances an ontological account of truth values as abstract logical objects. In the concluding sections, logic is interpreted as a science concerned primarily with truth values, and the plurality of logical systems is explained by the diversity of possible logical worlds and by different assumptions regarding the number, structure, and status of truth values.
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