UC Davis

Proponents of model-theoretic logical inferentialism defend the view that the meaning of logical vocabulary, such as the truth functions associated with conjunction or negation, is determined by their inferential use. This position provides a naturalist and empiricist account of the meaning of logical vocabulary, since inferences consist of concrete speech acts that can be observed, such as assertions and denials. As a consequence, model-theoretic inferentialism gives an account of a problem widely discussed in philosophy of language as well as cognitive science for the meaning of logical vocabulary, that is, it provides an account of meaning based on the use of language. In this dissertation, we provide a model-theoretic logical inferentialist account to three-valued Strong Kleene Logics. In particular, we will show various solutions to the categoricity problem regarding these logics in order to show that we can determine the intended models of these logics from their inferences, we will give a model-theoretic logical inferentialist account to Quine [94]'s challenge ``Do proponents of different logics talk past each other, i.e., does the meaning of logical operators change when logics change?", and last we will give an account of Prior [93]'s challenge of tonk to inferentialism.

In Chapter 1, we introduce model-thereotic logical inferentialism, and we introduce the technical machinery to determine the inferential semantics from a logic. In Chapter 2, we show how we can determine the intended semantics of Classical Logic and a class of Strong Kleene logics. In other words, we provide a number of well-motivated solutions to the categoricity problem, also known as Carnap's problem, regarding these logics. In Chapter 3, we provide a model-theoretic logical inferentialist account Quine [94]'s question: Do proponents of different logics talk past each other, i.e., does the meaning of logical operators change when logics change? We argue that model-theoretic inferentialists can provide an alternative account to this problem in comparison to the traditional model-theoretic or proof-theoretic accounts, since model-theoretic inferentialists use the inferential semantics of a logic. Chapter 4, we discuss the problem of tonk from a model-theoretic logical inferentialist point of view. We first introduce different tonk-like logical operators in our metainferential system, and define notions of metainferential existence and metainferential uniqueness. Then, we argue that the solution discussed by Fjellstad [39] is favored by model-theoretic logical inferentialist, given that the non-determinate interpretation of tonk discussed in Teijeiro [126] does not yield a completeness result when tonk-like connectives are introduced to our metainferential systems. Then, we argue that the substructural solution to tonk cannot be generalized to all logical operators.