Extinction of Evidence
II. Making an Initial Probable Judgment
Broadly speaking, Hume’s “Of scepticism with regard to reason” tells us that
proportioning our beliefs to all relevant evidence requires at least two steps of reasoning to
account for two bodies of relevant evidence. In an initial step, the evidence we select and
explicitly consider bears directly on whether our initial judgment is right or wrong. In a
corrective step, recalling relevantly similar judgments supplies the contrary evidence for our
reasoning. These recollected judgments bear directly on whether an initial presupposition of
legitimacy is true or false and, thus, indirectly on whether an initial judgment is right or wrong.
Balancing this evidence fixes a degree of less than full assurance for an initial presupposition of
legitimacy, thereby diminishing our assurance for any initial judgment. Thus, to account for all
relevant evidence our initial reasoning must continue with a corrective step that inevitably
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Utilizing this framework, the Degeneration Argument calls on past errors to show that
demonstrative reasoning is a philosophical source of uncertainty. As such, all demonstrations
are subject to the control of a corrective step so that, in practice, all demonstrations are less than certain. With the Diminishment Argument, Hume’s attention shifts to judgments reached by
probable reasoning. To set the stage for this argument, we’ll briefly revisit Hume’s account of
single-event probable reasoning. However, what we say in this chapter applies to matter of fact
reasoning generally. So even where judgments reached by causal reasoning are not explicitly
mentioned, what follows extends to them as well.
The necessary foundation for reasoning about matters of fact is a present impression of
sensation or memory that informs our selection of evidence and supplies the preliminary
assurance for our reasoning (T 1.3.4.2, 1.3.6.2; SBN 83, 87). Depending upon our present aims
and circumstances, we select a set of relevant evidence from past experience (T 1.3.6.2, 1.3.12.8;
SBN 87, 134).3 Our causal judgments are grounded on sets of uniform evidence where the live
possibilities are all of the same type.4 In contrast, our probable judgments are grounded on sets
of non-uniform evidence that include live possibilities of contrary types.
3 To reinforce these last two points, recall the following: “Tho’ the mind in its reasonings from causes or effects
carries its view beyond those objects, which it sees or remembers, it must never lose sight of them entirely, nor reason merely upon its own ideas, without some mixture of impressions, or at least of ideas of the memory, which are equivalent to impressions” (T 1.3.4.1; SBN 82). “’Tis merely the force and liveliness of the perception, which constitutes the first act of the judgment, and lays the foundation of that reasoning, which we build upon it, when we trace the relation of cause and effect” (T 1.3.5.7; SBN 86). “In all those instances, from which we learn the conjunction of particular causes and effects, both the causes and effects have been perceiv’d by the senses, and are remember’d; But in all cases, wherein we reason concerning them, there is only one perceiv’d or remember’d, and the other is supply’d in conformity to our past experience” (T 1.3.6.2; SBN 87). “Probability, as it discovers not the relations of ideas, consider’d as such, but only those of objects, must in some respects be founded on the impressions of our memory and senses, and in some respects on our ideas…’Tis therefore necessary, that in all probable reasonings there be something present to the mind, either seen or remember’d; and that from this we infer something connected with it, which is not seen nor remember’d” (T 1.3.6.6; SBN 89).
4 This is why preliminary assurance is preserved in causal reasoning such that we secure the full assurance of a
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In the first chapter we saw that Hume’s focus is on a type of probable reasoning that
offers a procedure for making judgments about single events (T 1.3.12.11; SBN 134).5 With this
type of probable reasoning our aim is to determine what, if anything, we should presently
believe, judge, or expect in the face of contrary evidence. Suppose my present concern is to figure out what time I’ll arrive home and that an impression of my watch (which reads “5:30”) is
the foundation for my reasoning. To marshal the relevant evidence, I recall relevantly similar
events with respect to relevantly similar circumstances. For the sake of simplicity, suppose this
reflection supplies recollected events of my returning home by 6:00 p.m. in all but one instance.
In that case, past experience affords relevant evidence that I’ll arrive home by 6:00 p.m. and
relevant evidence that I’ll arrive home after 6:00 p.m. So given my present aims and
circumstances, contrary possibilities are presently live possibilities.
With respect to a set of contrary evidence, a probability is a collection of live possibilities
of the same type whose members outnumber the live possibilities of a contrary type(s) (T
1.3.12.14-1.3.12.18; SBN 135-37).6 The live possibilities outnumbered by the probability are
what Hume calls the “opposite possibility,” which I’ve opted to call the rival possibility. So in
our present case, that I’ll arrive home by 6:00 p.m. is a probability and that I won’t arrive home
by 6:00 p.m. is the rival possibility. Since both a probability and its rival are “compos’d” of live
possibilities, Hume says they are “of the same nature”:
5 Recall that this is Hume’s third sense of “probability,” viz., probability as reasoning from conjecture, which refers
to a procedure for resolving the contrariety in a set of contrary evidence.
6 Recall that this is Hume’s second sense of “probability,” viz., probability as a superiority of evidence, which refers
to a collection of live possibilities of the same type that make up a majority of the evidence with respect to a set of contrary evidence.
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To every probability there is an opposite possibility. This possibility is compos’d of parts,
that are entirely of the same nature with those of the probability. (T 1.3.12.17; SBN 136-
37)
Insofar as they are of the same nature, Hume notes that a probability and its rival have “the same influence” over our judgment (T 1.3.12.17; SBN 136-37).
Since therefore each part of the probability contributes to the production of the belief, each
part of the possibility must have the same influence on the opposite side; the nature of these
parts being entirely the same. (T 1.3.12.17; SBN 136-37)
Accordingly, at some point in our reasoning about a single event on the basis of contrary
evidence, we have some degree of assurance for mutually exclusive event-types.
Hume explains this by saying that because live possibilities of contrary types cannot occur simultaneously, the preliminary assurance from a present impression “is broke into pieces”
such that each live possibility “partakes an equal share of that force and vivacity” (T 1.3.12.10;
SBN 134). Collecting live possibilities of the same type together, the distributing of preliminary
assurance gives us some degree of assurance that events of contrary types will presently occur:
The belief, which attends the probability, is a compounded effect, and is form’d by the
concurrence of the several effects, which proceed from each part of the probability. Since
therefore each part of the probability contributes to the production of the belief, each part
of the possibility must have the same influence on the opposite side; the nature of these
parts being entirely the same. The contrary belief, attending the [rival] possibility, implies
a view of a certain object, as well as the probability does an opposite view. In this particular
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So at this stage of my arrival-time reasoning, I have a high degree of assurance that I’ll arrive
home by 6:00 p.m. and a low degree of assurance that I won’t arrive home by 6:00 p.m.
But in a single case, “’tis evident…the contrary views” afforded by the selected evidence
“are incompatible with each other, and ’tis impossible the object can at once exist conformable to
both of them” (T 1.3.12.19; SBN 138). In other words, I recognize that, presently, I cannot both
arrive home by 6:00 p.m. and fail to arrive home by 6:00 p.m. If I’m to make a judgment about a
single event, I need to resolve the contrariety in the evidence. To that end, Hume proposes a
balancing procedure where live possibilities of contrary types and their apportioned assurance cancel so that “the mind is determin’d to the superior only with that force, which remains after
subtracting the inferior” (T 1.3.12.19; SBN 138, my emphasis). Understanding Hume’s
balancing procedure is crucial to understanding his account of probable reasoning in general and corrective reasoning in particular. So it’s worth our time to briefly review Hume’s procedure for
making single-event judgments on the basis of contrary evidence.
In distinguishing between causal judgments and probable judgments it’s convenient to
say something like the following. Because they concern matters of fact, the falsity of any causal
judgment and the falsity of any probable judgment is conceivable. However, causal judgments
are grounded on uniform evidence from past experience. Because past experience supplies no
positive evidence against them, causal judgments are made with the full assurance of proof.
Probable judgments, on the other hand, are grounded on contrary evidence from past experience.
Because past experience affords positive evidence against them, probable judgments must be
made with something less than full assurance. While this is a useful way of distinguishing these different types of judgments, the “less than full assurance” ascribed to probable judgments is
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I’ve argued that less than full assurance follows from balancing and cancelling live
possibilities of contrary types along with their apportioned assurance. So when a probability is balanced against a rival, some portion of the probability’s preliminary assurance is canceled.
This is at odds with an influential interpretation that tells us the assurance for probable
judgments is proportionate to the superior number of live possibilities that make-up the
probability. On this reading, the less than full assurance of a probable judgment follows from the
apportioning of preliminary assurance to live possibilities of contrary types. But revisiting Hume’s description of single-event probable reasoning makes clear that this latter reading paints
the wrong picture.
With respect to a set of contrary evidence, preliminary assurance is apportioned equally
to each live possibility in the set. Given this apportioning, “in 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 and remember” (T
1.3.13.20; SBN , my emphasis). If assurance for a probable judgment was proportionate to the
number of live possibilities that make-up a probability, we would be done at this point. But because a probability and its rival are “of the same nature…[and] have the same influence on the
mind and understanding,” if we don’t resolve the contrariety in the evidence we’re left with
contrary beliefs (T 1.3.12.17; SBN 136-37).
In resolving the contrariety by way of a balancing procedure, Hume remarks that the “contest is at last determin’d to the advantage of that side, where we observe a superior number
of these experiments; but still with a diminution of force in the evidence correspondent to the
number of the opposite experiments” (T 1.3.13.20; SBN 154, my emphasis). Hume is perhaps
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When any phænomena are constantly and invariably conjoin’d together, they acquire such
a connexion in the imagination, that it passes from one to the other, without any doubt or
hesitation. But below this there are many inferior degrees of evidence and probability, nor
does one single contrariety of experiment entirely destroy all our reasoning. The mind
ballances the contrary experiments, and deducting the inferior from the superior, proceeds
with that degree of assurance or evidence, which remains. (T 2.3.1.12; SBN 403)
In short, Hume’s balancing procedure requires canceling live possibilities of contrary types along
with their apportioned assurance. The preliminary assurance apportioned to a probability is
already less than full, and balancing cancels some portion of it. Then strictly speaking, all
probable judgments are made with a diminished degree of less than full assurance. So when I
say that a probable judgment is made with “less than full assurance,” I mean this in Hume’s strict
sense of a diminished degree of less than full assurance.
Given Hume’s balancing procedure, probable reasoning terminates in a probable
judgment about a single event only where the contrary evidence includes a probability and its
rival (T 1.3.12.17-18; SBN 136-37). Because a probability is made up of a superior number of
live possibilities, at least one live possibility of that type and its apportioned assurance will
survive balancing. In our present case, balancing cancels the single live possibility that I won’t
arrive home by 6:00 p.m. along with a single live possibility that I will arrive home by 6:00 p.m.
The type of live possibility that survives balancing fixes the content of my probable judgment,
viz., I’ll arrive home by 6:00 p.m. The total assurance apportioned to the surviving live
possibilities fixes the degree of assurance for my probable judgment. Thus, by selecting and
balancing a set of contrary evidence, I make an initial probable judgment with a degree of less
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