What is the Normative Role of Logic?

In making assertions one takes on commitments to the consistency of what one asserts and to the logical consequences of what one asserts. Although there is no quick link between belief and assertion, the dialectical requirements on assertion feed back into normative constraints on those beliefs that constitute one’s evidence. But if we are not certain of many of our beliefs and that uncertainty is modelled in terms of probabilities, then there is at least prima facie incoherence between the normative constraints on belief and the probability-like structure of degrees of belief. I suggest that the norm-governed practice relating to degrees of belief is the evaluation of betting odds