Is Logic Empirical? Logical 'Conventionalism' from an Empirical Standpoint

Abstract

The laws of classical logic are taken to be logical truths, and logical truths are taken to objectively hold. However, we might question our faith in these truths: why are they true? One often avoided approach is logical conventionalism, because it makes the logical truths dependent on somewhat intersubjective linguistic conventions. Another approach, proposed by Putnam (1975) and more recently Dickson (2001) or Maddy (2007), is to adopt empiricism about logic. On this view, logical truths are true because they are true of the world alone – this gives logical truths an air of objectivity unlike logical conventionalism. Putnam and Dickson both take logical truths to be true in virtue of the world’s structure, and the structure of the world is to be understood to be given by our best empirical theory, quantum mechanics. As it turns out, the structure of quantum mechanics apparently makes true the laws of quantum logic, and falsifies (one half of) the distributive law, something which was taken to be a logical truth under classical logic. Empiricists take this to indicate that the distributive law was not a logical truth to begin with. However, this argument assumes that there is a single determinate structure of the world prescribed by quantum mechanics. In this essay, I argue that this assumption is false, and that the structure of the world is underdetermined in quantum mechanics. Likewise, the choice of ‘true’ logic, as given by the world’s structure, is also underdetermined. This leads to what I call empirical conventionalism: the world alone fails to determine our logical truths. We need something broadly intersubjective, and thus less than objective, to fix our choice of logic even under empiricism. An attempt to avoid one form of conventionalism has thus led us back to another.