Why Is a Valid Inference a Good Inference?

Abstract

True beliefs and truth‐preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth‐preserving, but truth‐preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: (i) the orthodox definition given in terms of interpretations or models, (ii) a metaphysical definition given in terms of possible worlds, and (iii) a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference.