Hume’s Problem of Induction


1.  We naturally reason inductively:  We use experience (or evidence from the senses) to ground beliefs we have about things we haven’t observed.


Hume asks whether this evidence is actually good evidence: can we rationally justify our actual practice of coming to belief unobserved things about the world?  (Hume, pp. 193-4; Salmon, p. 230)


Salmon’s urn example (p. 231):


We have an urn full of balls.  After sampling a few of the black balls, all of which taste like licorice, we infer that all of the black balls in the urn must taste like licorice.


The argument:


(1) Some black balls from this urn have been observed.

(2) All observed black balls from this urn are licorice-flavored.

(3) Therefore all the black balls in this urn are licorice-flavored.


1) This is an inductive generalization: we infer that all the members of a certain class will be similar to those we’ve actually observed.


2) There are also inductive predictions (assumptions about future events, based upon our experience with past events).  Do you, for example, believe that when I jump up in the air, that I might fly off into space?  Why not?


3) There are also causal generalizations.  Hume says that we can’t determine the hidden causal powers of particular things (p. 195 - e.g., the coldness of ice, or the nourishing power of bread) simply by scrutinizing them carefully.  Instead, we infer these capacities from our experience with those kinds of things.



2.  But note that the inductive argument above from the sensory evidence to the general conclusion isn’t logically guaranteed.  It isn’t a “demonstrative” argument (Salmon, p. 232); it’s possible for the conclusion to be false, even if the premises are true (for example, suppose there’s a black marble in the bottom of the urn – or Hume’s examples of eggs, p. 198).


Still we don’t think the argument is logically fallacious; the reasoning here is pretty good – while not guaranteed to be true, the conclusion still seems supported by the evidence, and so seems at least likely to be true.



3.  In order to turn the argument above into one that’s clearly acceptable, it appears that tacitly rely upon some inductive principle – to the effect that similar effects come from similar causes (Hume, p. 197) or that there is a uniformity in nature (Salmon, p. 233).


In the case of the urn-example above, our reasoning seems to rely upon some implicit premise like:


(*) Any two balls in this urn with the same color will have the same taste.


But how, then, can we justify this principle of the uniformity of nature?


1) It isn’t true by definition (what Hume calls a “relation of ideas”).  Its negation – that the truth won’t resemble the past – isn’t a logical contradiction. (p. 197)


2) So if it’s to be true, it must be what Hume terms a “matter of fact.” Our knowledge of such contingent truths could only be grounded in our experience.  But the principle of the uniformity of nature isn’t something that we can just “see” to be true.  As a result, it appears that we could only have inductive evidence to support it.  So it seems that the only way we could justify anything like the inductive principle is through induction.  [That is, inductive reasoning works because it’s always worked.]  But this just seems “flagrantly circular.” (Hume, p. 198; Salmon, p. 233)


So what’s so wrong with this circularity (which Salmon calls “rule circularity” – p. 236)? 


1) It seems that if you could justify inductive reasoning inductively, why then couldn’t psychics gaze into a crystal ball to “justify” the method of using crystal balls to acquire knowledge? (p. 234)


2) Or, using the very same “inductive” evidence that you have that counter-inductive reasoning doesn’t work, why couldn’t a “counter-inductivist” counter-inductively justify the counter-inductive method?  (p. 236)


Note that it is generally agreed that inductive reasoning has a much better track record that counter-inductive reasoning (e.g., the “gambler’s fallacy”).  Just as an inductivist would draw from this the conclusion that inductive reasoning will always work better than counter-inductive reasoning, the counter-inductivist would draw the opposite conclusion: that counter-inductive reasoning is now more likely than ever before to be more successful than inductive reasoning.  Inductive reasoning has simply enjoyed an enormous string of luck so far that’s bound to turn sour.



4.  In the end, Hume despairs.  He sees no way to rationally justify inductive reasoning.


This is a form of skepticism (about inductively acquired beliefs): We don’t have knowledge that we are tempted to think that we do.  Our beliefs that come to us through inductive reasoning are in reality not rationally justifiable.


There are other forms of skepticism (some of which we’ve already encountered, some of which we’ll encounter later).



5.  The significance of the problem (Salmon, pp. 148-50): Much of our everyday beliefs about how the world works, including virtually all of our scientific reasoning, are based upon induction.  Hume shows that all of this so-called “knowledge” is ultimately without foundation (and so possibly not knowledge at all).  This should be somewhat disconcerting, for after all, we would like to think that faith in science and its methods is more than mere superstition, that it’s much better than warranted than, say, gazing into crystal balls.



6.  Hume’s “Skeptical Solution:”


We can’t really help but reason inductively.  A being that was “purely rational” would never form any beliefs based upon induction, and so would never draw any generalizations or make any predictions about the future.  But of course such a being couldn’t possibly make its way around in the world. (Try driving a car without making any inductive predictions – How would you point the steering wheel?)


So nature, through the operation of custom and habit (p. 200), has determined that we draw inductive inferences.


Thus while we cannot really know the true causal powers of things or the course of the future, we can know the customs or habits that our mind has formed through its experiences.


At this point, Hume adopts a “skeptical solution” to the problem: the strategy here is to translate statements about matters the skeptic claims we can’t have any knowledge about into statements about things our knowledge of which is not thrown into question.


So statements about the causal powers of things really should be reconceived as statements about the connections in our minds between the ideas of those things.



Hume is famous for discussing what he took to be the limitations or challenges to reason and for providing skeptical solutions to these challenges.


Another example of this is Hume’s “emotivism”: While we cannot know objective moral facts, what we can know are our reactions to situations.  Thus statements about morality should really be recast as statements about our reactions.