 Although pursuit of the logicist program produced a great many insights into the nature of mathematics, there emerged a number of serious difficulties with it. Right from the start there was, of course, the problem of the logical truths themselves. Simply saying, as Frege had, that they are “Laws of Truth” doesn’t seem to explain how we could know them a priori. But perhaps they, too, are “analytic” involving perhaps some sort of “implicit” acceptance of certain rules merely by virtue of accepting certain patterns of reasoning. But any such proposal has to account for people’s frequent, often apparent violations of rules of logic in fallacious reasoning and in ordinary speech, as well as of disputes about the laws of logic of the sort that are raised, for example, by mathematical intuitionists, who deny the Law of Excluded Middle (“p or not p”), or, more recently, by “para-consistent” logicians, who argue for the toleration even of contradictions to avoid certain  paradoxes.[7]  Moreover, given that the infinitude of logical truths needs to be “generated” by rules of inference, wouldn’t that be a reason for regarding them as “synthetic” in Kant’s sense (see Frege 1884 [1980], §88, Katz 1988, pp. 58–9, and MacFarlane 2002)?