Hume's Iterative Probability Argument: A Pernicious Reductio

In this essay I want to look afresh at David Hume's iterative probability argument, found in the section entitled "Of Scepticism with regard to Reason" in his A Treatise of Human Nature.¹ Interestingly enough, after years of comparative neglect,² this argument has been basking in the glow of scholarly sunshine lately.³ But to what can we attribute its extended hiatus? The convergence of three major factors seems responsible. First, philosophers have oftentimes flung this argument into the ocean of obscurity because of its perceived inadequacies.⁴ Second, and on a related note, many assume that Hume himself permitted this argument to drown because it never resurfaces again in his writings. Most suspiciously, Hume's Enquiry Concerning Human Understanding, which is his popular (and preferred) presentation of the epistemological sections of the Treatise, does not contain this argument.⁵ Last, but certainly not least, for a long time this argument sat uncomfortably with the naturalist interpretation of Hume⁶ that has gained ascendancy in the twentieth century. For prior to this century, Hume was almost unanimously regarded as a sceptic. Despite a few waves from those who interpreted Hume as a logical positivist earlier in this century, Norman Kemp Smith charted a new course for Humean interpretations with his emphasis on Hume's naturalism.⁷ And this is the current according to which most Hume interpreters set their sails today.

Because the naturalist reading of Hume relies so heavily on the system he attempts to set forth in the Treatise, though, naturalists have come to see the importance of reading this argument in a naturalistically acceptable way. William E. Morris best expresses the significance of this argument from a naturalistic perspective in the following manner:

If we ever are to understand Hume's view of the role of reason, it stands to reason that we should first figure out how to integrate "Of scepticism with regard to reason" into the picture. Only then will we be ready to move to a consideration of Hume's positive views about reason. These views are the least understood of any of Hume's doctrines. Gaining an adequate understanding of them is both the most pressing and the most difficult problem facing Hume studies today.⁸

While I agree with Morris about the importance of getting a clear understanding of the reasoning of I, iv, 1, I will argue that a correct reading of this section reveals the implausibility of major naturalistic interpretations of Hume.

This paper has four major sections. In the first important section, I will highlight the crucial aspects of the iterative argument that will be the focus of this paper and deal with a preliminary but important interpretive issue. In the second section, I will briefly look at Annette Baier's naturalistic reading of Hume's philosophy to show how this particular passage bears on broader interpretive issues. The third main section will focus on explicating Morris' similar but more detailed interpretation. Finally in the last part I will show that while it is legitimate to characterize the argument here as a reductio (as Baier and Morris both do), the argument still yields, contrary to what naturalists have recently suggested, a very sceptical conclusion.

1. The Arguments of Section I, IV, 1 of the Treatise

Hume's "Of Scepticism with regard to Reason" contains at least two important arguments. While Hume agrees that knowledge involves certainty (whereas beliefs based on probability are by their very nature uncertain⁹ ), the conclusion of his first argument is that "all knowledge resolves itself into probability" (Treatise, 181). His point here is simply that all of our beliefs are fallible. That is, nothing is absolutely certain; thus none of our beliefs attain the exalted status of certain knowledge. But once this consequence of our fallibility is recognized, he then argues roughly that the probability that any particular belief...