In a footnote to chapter 6 (“Of Probability”) of the first Enquiry, Hume writes,
Mr. Locke divides all arguments into demonstrative and probable. In this view, we must say, that it is only probable all men must die, or that the sun will rise to-morrow. But to conform our language more to common use, we ought to divide arguments into demonstrations, proofs, and probabilities. By proofs meaning such arguments from experience as leave no room for doubt or opposition.
This echoes a similar passage in the Treatise (T 1.3.11.2), where Hume divides “the several degrees of evidence” into knowledge, proof, and probability.
These passages, as well as letters such as the anonymously penned Letter from a Gentleman seem to suggest that Hume divides probable arguments into those that do not produce certainty (probabilities) and those that can or do (proofs). Presumably, proofs produce “moral certainty” in the early modern sense. (Hume appeals to “moral certainty” in the Letter to counter accusations that he undermines demonstrations of the existence of God and is therefore a skeptic and atheist).
I find Hume’s defense in the Letter less than convincing for a number of reasons, but let me offer two here. Hume’s opponents were correct to recognize that Hume doesn’t really have a place for “proofs” in this technical sense. First, Hume is clear in T 1.3.1 that knowledge comes from intuition and demonstration. Other than the passages mentioned, Hume only talks about certainty in connection to knowledge. Furthermore, the reason given in T 1.3.1 for why we can be certain is that intuition and demonstration rely on unalterable relations. (See also T 1.3.3.1-3.) The argument isn’t terribly clear, but it seems that if the relations between our ideas are alterable (“so long as the ideas remain the same”) then we couldn’t be certain on the matter. Because probable arguments (presumably; I don’t see him argue that they must) rely on alterable relations, they could not produce certainty, even moral certainty.
Second, Hume is careful in the Treatise and again in the Enquiry to note that philosophers should only distinguish demonstrations and probable arguments. It is only “to conform our language more to common use” (Enquiry) or when “in common discourse” (Treatise) to separate out a third category of evidence. (Note: he makes no effort to fix the potential misreading in the Enquiry.) Philosophers do and should recognize two categories of arguments. This might disturb the common folk, so we should speak of very high probabilities as “proofs,” but this is only for common use, not when doing philosophy.
I am convinced by these two reasons (and some other, less important ones) that Hume does not have a distinct category of proofs (probable arguments which produce moral certainty) when speaking philosophically; such use is only an accommodation to those common folk worried that it is not certain that the sun will rise tomorrow.
However, this seems to cut against a currently popular reading of Hume, which claims that Hume considers certain many things (such as the causal maxim) that are not established via intuition or demonstration. Often these readers appeal to Hume’s unpublished letters, which I find problematic. On my opponents’ behalf, I wonder if something could be made using different kinds of certainty (epistemic vs. psychological, say), which has some traction in the texts. Hume’s use of the terms is frustratingly inconsistent, so it is difficult to know how to proceed on this point. (One starting point could be Of the Passions, where he separates out two kinds of probability.) Until we have a fuller working out of the notions of certainty and probability, I think we should follow Hume’s suggestion and take talk of “proofs” as an accommodation to common use.
Can moral certainty be defined in terms of strength of belief?
There are large stretches in the Enquiry which seem to turn on a distinction between proofs and probabilities, though.
I am thinking in particular of the argument against miracles, which requires us to make sense of proofs possessing different strengths. It is hard to consistently interpret such passages as simply using the term “proof” to stand in for “maximally probable”, I think.
In the Treatise, on the other hand, Hume seems to think there is something more going on between probabilities and proofs than a mere difference in degrees (sort of..I am not phrasing this right).
While the opening of “Probabilities of Causes” looks like it supports your position (“The probabilities of causes are of several kinds; but are all deriv’d from the same origin, viz. the association of ideas to a present impression. As the habit, which produces the association, arises from the frequent conjunction of objects, it must arrive at its perfection by degrees, and must acquire new force from each instance, that falls under our observation. The first instance has little or no force: The second makes some addition to it: The third becomes still more sensible; and ’tis by these slow steps, that our judgment arrives at a full assurance. But before it attains this pitch of perfection, it passes thro’ several inferior degrees, and in all of them is only to be esteem’d a presumption or probability. The gradation, therefore, from probabilities to proofs is in many cases insensible; and the difference betwixt these kinds of evidence is more easily perceiv’d in the remote degrees, than in the near and contiguous.”), the section on unphilosophical probability seems to suggest otherwise:
“I add, as a third instance of this kind, that tho’ our reasonings from proofs and from probabilities be considerably different from each other, yet the former species of reasoning often degenerates insensibly into the latter, by nothing but the multitude of connected arguments.”
Thanks for the great comments, Shoshana and Lewis. Sorry I’ve been so slow to respond. Serves me right for posting the day before classes begin.
Shoshana,
Strength of belief might be the right way to talk about moral certainty. It might also be strength of evidence. I find Hume and other 17th and 18th century writers very unclear at times on these matters. But that is probably a good starting point.
Lewis,
In addition to the passages to which you direct us, Hume uses “proof” to mean demonstrative arguments in T 1.3.3.3. Frankly I am not sure how heavily we should weigh (1) his actual use of terms against (2) places where he seems to define those terms. I would like all occurrences to line up neatly, but I am worried that they do not. The two passages to which I referred seemed to be his clearest statements on what proofs are. It troubles me that he doesn’t always use the term “proof” in a manner consistent with these definitions (if they are definitions). But such is the history of philosophy. (But I should have noted in my initial post that Enquiry 10 doesn’t clearly follow the definition in the Enquiry 6 footnote. And I still don’t know what to make of it.)
To say a bit more, the passage in T 3.13.3 that you mention seems to foreshadow the argument of T 1.4.1. In that justly famous passage, Hume argues that all knowledge (the result of demonstrative arguments) “degenerates” into probability. And probability, in turn, runs through corrections that lead to “a total extinction of belief and evidence.” One could take this passage to mean that Hume ultimately recognizes no distinction between probable and demonstrative arguments, so wondering whether there is a third category of proofs seems even sillier. However, Hume does not abandon the probable/demonstrative distinction after this point (either in the Treatise or later writings). What we should do with the argument, I’m not sure, but I suspect we shouldn’t let T 1.4.1 or T 3.13.3 (another sorites that runs together two apparently distinct argument kinds) have the only (or even last) say in the matter.
Perhaps I should reconsider my initial position. My initial position was the Hume sides with the philosophers in recognizing two kinds of arguments. It is only to appease the common folk that we should speak of a third class of arguments (“proofs”); really, proofs are are just a subspecies of the first. I now wonder if my mistake was in thinking that Hume sides with the philosophers. I don’t think he sides with the common use, but rather his ultimate position is that there is no distinction between classes of arguments. There is only one kind of argument, even though philosophers have thought there were two. This reading would mean attributing to Hume the conclusions of the sorites-style arguments in T 1.3.13 and T 1.4.1. Is this so bad? Maybe not. I’m hesitant to ascribe to him this position, partly because he assumes the distinction so often and partly because his methodology just absorbs apparent problems (like the missing shade of blue) as if they weren’t problems when he thinks he’s on to a good point.