A Possible Rule-Application Error in Probable Reasoning

Interpreters have tended to overlook the importance of identifying particular errors in reasoning for the purposes of Hume’s skeptical arguments. Don Garrett, however, is a notable

exception. On my account, assurance for any matter of fact judgment is naturally and

mechanistically proportioned to the selected evidence such that we make an error only when we

select something other than all and only the relevant evidence. In contrast, Garrett suggests a

kind of rule-application error that causes assurance for probable judgments to be inaccurately

proportioned to the selected evidence. As Garrett (2006) describes it, error-free probable

reasoning yields a “standard degree” of assurance that is accurately proportioned to the

evidence.18 _{When we make an error, our “actual degree” of assurance is something other than}

the “standard degree.” We can describe this as a case where the evidence is mistakenly balanced

to yield a judgment with the wrong degree of assurance.19 On this picture, the mark of an error

18 _{Above I offer a sketch of the proposal, but for Garrett’s (2006) full description see pp. 161-62. For a similar but}

slightly less detailed account, see Garrett (1997) pp. 224-25.

19 _{This could be due to improperly apportioning preliminary assurance or inaccurately balancing and cancelling}

contrary possibilities. However, as I say below, since both the apportioning of preliminary assurance and the balancing and cancelling of contrary possibilities is mechanistic and not under our direct control, it is unclear how

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in probable reasoning is a judgment made with a non-standard degree of assurance that isn’t

proportioned to the evidence.

As I understand it, there are at least three problems with Garrett’s proposal. First, as the examples from the last section make clear, Garrett’s proposal is at least incomplete. After all,

it’s not the case that all evidence selection errors can be explained in terms of the inaccurate

proportioning of assurance. For instance, in the case of my friend’s speaker, my judgment was

the product of illegitimate reasoning but it was accurately proportioned to the selected evidence.

In that case, my judgment was made with a standard degree of assurance.

This points to a second problem in that Garrett’s proposal seems to rule-out the

possibility of errors in causal reasoning, i.e., cases where the selected evidence is uniform such

that the inaccurate proportioning of assurance is not a possibility. However, Hume is clear that even if “the same objects [were] always conjoin’d together,” we would still need to worry about

“the mistakes of our own judgment” (T 1.3.12.4; SBN 131). In other words, even if all matter of

fact reasoning was carried out with respect to sets of uniform evidence, we would still have to

worry about evidence selection errors.

Third, and finally, I’ve argued that both the content and degree of assurance for matter of

fact judgments is determined by the nature of the selected evidence.20 Because assurance

we might make this error or, supposing that we sometimes do, that it should be understood as an error in reasoning.

20 _{There are two passages in which Hume is clearest on this matter. First, from “Of the probability of causes”:}

“When we transfer contrary experiments [or rival possibilities] to the future, we can only repeat these contrary experiments with their particular proportions; which cou’d not produce assurance in any single event, upon which we reason, unless the fancy melted together all those images that concur, and extracted from them one single idea

or image, which is intense and lively in proportion to the number of experiments from which it is deriv’d, and their superiority above their antagonists” (T 1.3.12.22; SBN 139-40, my emphasis). In other words, balancing rival

possibilities cancels rivals and their attendant assurance to yield a judgment with the content given by the type of live possibility that survives balancing, and a degree of assurance diminished by cancellation. Second, from “Of unphilosophical probability”: “[I]n all determinations, where the mind decides from contrary experiments, ’tis first divided within itself, and has an inclination to either side in proportion to the number of experiments we have seen

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“encreases or diminishes according to the number of chances or past experiments,” our assurance

for matter of fact judgments is fixed by the evidence actually selected. So any worry that a

judgment was made with the wrong degree of assurance is actually a worry that it was reached

by selecting and balancing the wrong evidence. While these three points raise serious concerns about Garrett’s proposal, Hume’s discussion of unphilosophical probability appears to provide

support for something like it.

We said that, for Hume, an “unphilosophical probability” is an unphilosophical source of

uncertainty. In the last chapter, we saw that judgments from philosophical probabilities are

uncertain because they are proportioned to contrary evidence.21 We explained this by saying that

the uncertainty of these judgments is attributable to the uncertain nature of the evidence that

grounds them. In contrast, the uncertainty of a judgment from an unphilosophical probability is

attributable to human nature rather than the evidence that grounds the judgment. Accordingly, uncertain judgments from unphilosophical sources of uncertainty aren’t proportioned to the

relevant evidence.

In total, Hume identifies four distinct unphilosophical probabilities: (i) fading memories,

(ii) particularly striking experiments, (iii) especially complicated arguments, and (iv) unreflective

generalizations. At the close of his discussion, Hume suggests that judgments from

unphilosophical probabilities are errors of some kind. What’s more, three out of the four affect

the assurance with which a judgment is made. This is suggestive of something like a rule-

number of these experiments [or live possibilities]; but still with a diminution of the force in the evidence correspondent to the number of the opposite experiments [or live possibilities of a rival type]. Each [live]

possibility, of which the probability is compos’d, operates separately upon the imagination; and ’tis the larger collection of [live] possibilities [of the same type], which at last prevails, and that with a force proportionable to its superiority [over the collection of live possibilities of a rival type] (T 1.3.13.20; SBN 154-5).

21 _{However, as the examples from the last section make clear, a judgment may be proportioned to the selected}

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application error for matter of fact reasoning, which appears to provide support for something like Garrett’s proposal. If that’s right, then I’ve overlooked anywhere from one to four types of

probable errors.

But careful consideration of Hume’s discussion shows that we need to distinguish errors

in reasoning from what I’ll call natural errors. Judgments from philosophical probabilities are

proportioned to sets of contrary evidence. Because probable judgments are proportioned in

accordance with it, contrary evidence is a philosophical source of uncertainty. When the wrong

set of contrary evidence is selected and balanced, a judgment proportioned to that evidence is

mistaken. Accordingly, mistaken judgments from philosophical probabilities are the result of

evidence selection errors. Insofar as they are brought on by our activities as reasoners, evidence

selection errors are avoidable errors in reasoning. On the other hand, mistaken judgments from

unphilosophical probabilities are caused by human nature, e.g., human limitations and

susceptibilities. Insofar as they are forced on us by nature, these natural errors are unavoidable. Because they’re the unavoidable products of nature, it’s a mistake to treat natural errors as

instances where “our understanding has deceiv’d us” (T 1.4.1.1; SBN 180, my emphasis).