Why Is a Valid Inference a Good Inference?. (24th July 2015) - Dogramaci, Sinan
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.