' But I am not simply rejecting this: I am demanding an explanation of how it could be so. How could this intuitive process justify something unless the process is empirical? The a priori is mysterious because we do not have even a hint of a satisfactory answer. It seems like magic that a process in someone-s [SIC] mind can justify her belief in an external worldly fact without that justification arising from some sort of experiential link to that fact."
Although BonJour unarguably demonstrates admirably the inadequacies of empiricism as a means of explaining a priori knowledge, it is not clear, at least not within BonJour's paradigm, that rationalism is more successful. In fact, many would argue that Bonjour's account of rationalism is precisely the one that has led so many to be wary of the a priori in the first place.
Laurence BonJour's Epistemic Justification: Internal-ism vs. Externalism, Foundations vs. Virtues largely recapitulates the main lines of the debate about epistemic justification. Given the fact that in Epistemic Justification: Internal-ism vs. Externalism, Foundations vs. Virtues BonJour defends the more traditional viewpoint, it should be noted that BonJour's conversion to his current ideological position was a relatively recent one. In the section entitled, "A Version of Intemalist Foundational-ism," BonJour begins with the Regress Argument in the first chapter, which is appropriately named, "The Regress Problem and Foundationalism." According to BonJour, the challenge is for foundationalists to offer foundations that are non-arbitrary. He attempts to overcome this challenge in the chapter, "Back to Foundationalism," in which BonJour endeavors to rest all knowledge on awareness of the content of beliefs. The primary obstacle that BonJour is forced to deal with is the Sellers Dilemma: is awareness of content judgmental or not? If it is, then what justifies this judgment? If it is not, how does it justify anything? BonJour maintains that awareness of a belief's content and of its assertive character are constitutive of what it is to have a belief.
Then, in "The Conceptualization of Sensory Experience and the Problem of the External World," BonJour makes every effort to show that this foundation of constitutive awareness of content can bear the weight of all our ordinary knowledge claims, which will obviously involve the thorny issue of inferences from states of our own consciousness to states of the external world; this most crucial issue is addressed in "The Inference to the Physical World." In the tradition of Berkeley and Locke, BonJour offers an inference to the best explanation: the best explanation of the systematic nature of our experience is a world with corresponding properties and causal powers impinging upon our senses.
While that may be, true BonJour fails to address the controversial issue of justifying inference to the best explanation.
Given his strenuous rejection of coherentism, this seems like a major lacuna. He briefly mentions the problem of that technically this leaves most people without justification, since very few of them ever actually perform such an inference; however, BonJour doesn't find the latter too troubling, given "the argument is in principle available to them," yet this is nothing other than a fairly pervasive form of skepticism.
The proponent of a priori knowledge as rational insight into necessary traits of reality faces the insurmountable problem concerning how a mind can come to knowledge of necessary traits of reality. It is a special case for the rationalist-realist of the more general problem of our knowledge of the external world: how can a mind in an a priori fashion come to know necessary traits of putatively extramental reality? BonJour's bold answer consists of definitively outlining and arguing in favor of a theory of mental content that is nonrepresentational and at once both externalist as well as internalist. His ingenious supposition is reminiscent of some of the more notable forms of rationalism: its fervent quest for that which is true and real amidst pure happenstance is akin to Hegelian rationalism, while the sheer harnessing of mental power as a means to achieving only that knowledge which is of the most fundamental truths bears some semblance to certain tenets of Aristotelian rationalism.
BonJour, Laurence. "The Dialectic of Foundationalism and Coherentism." A Companion to Epistemology. Eds. E. Sosa and J. Dancy. Oxford: Blackwell, 1992.
BonJour, Laurence. Epistemic Justification: Internalism vs. Externalism, Foundations vs. Virtues. Malden, MA: Blackwell, 2003.