Hume and the Problem of Induction
Induction is a way of reasoning, according to which the premises of one's argument make the conclusion more or less probable. This is different than deductive reasoning, where one's conclusion follows necessarily from the premises -- that is, the premises, if true, guarantee the truth of the conclusion. Consider the following case of enumerative induction:
1. Thus far, all observed X's have been found to bear property Y.
2. P is an X.
____________________
3. Therefore, P has property Y.
A different scheme could go as follows:
1. Thus far, all observed X's have been found to bear property Y.
__________________
2. Therefore, all X's bear property Y.
In both arguments, the conclusion does not follow necessarily from the premises. Rather, the premises only make the conclusion more or less likely. It's possible, for example, that there is an X that does not have property Y. The fact that all the X's we have observed thus far have had the property Y does not make it necessary that all X's must this property. Regardless, we generally take ourselves to be justified in forming beliefs on this basis (assuming a large enough sample). It seems reasonable to conclude that the sun will rise tomorrow, given that my experience (and that of countless others) testifies to the consistency of this pattern. Although we often reason this way, why think inductive reasoning is actually a reliable method for forming beliefs?
HUME'S CRITIQUE OF INDUCTION
Some propositions, argued David Hume, can be known to be true or false simply on the basis of the relation of ideas expressed in those propositions. Consider the following proposition:
(B) there are no married bachelors.
(B) is necessarily true. What's more, I do not have to find all the bachelors in the world in order to discover whether there are any married ones or not. Rather, I know the truth of (B) simply by knowing what "marred" and "bachelor" mean. If I say that (B) is false, I would would have to affirm that, "there are married bachelors", which is just to say, "there are married people who are not married." This is a contradiction, and contradictions cannot be true [1]. Thus, Hume argues that tautologies, contradictions, and mathematical truths "are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe" [2].
Matters of fact about the physical world, however, are not known in this manner. We come to know what the world is like by experiencing it, by making discoveries and by observing its workings. I did not discover, just from thinking about it, that rocks hurt when thrown at my head. I had to discover this from experience (it was a painful discovery, to be sure). This means, Hume argues, that truth's about the world are contingent -- they could be otherwise [3] -- and, this being the case, one can coherently conceive of the world being different than it is or changing in some manner. He writes,
The same is the case for much of the rest of our knowledge about the world. Our beliefs about laws of nature, how people will behave, and other such beliefs, are based on inductive generalizations, stemming from our experiences.
On the basis of this fact, Hume argues that inductive reasoning is not rationally justified -- we cannot rationally justify the belief that what we experience now (or have experienced in the past) will likely be the same at some future time. The problem can be seen by trying to justify induction via argument. Here's one attempt to justify:
1. We have experienced that the ways things were at some past time are conformable to the way things are at the present.
2. The future will be conformable to the past.
______________
3. Therefore, what we experience (i.e., relations of cause and effect, and the properties of things) at some time, t, will hold true at any future time, t*.
The controversial premise is (2). Why think the future will be conformable to the past. Premise (1) could be cited in support of (2), but why think that 'future futures' will conform to our experience, simply because 'past futures' have seemed to do this? Reasoning as such implicitly assumes premise (3); but that is suppose to be the thing we're arguing for, so we can't assume it in our argument without begging the question. Hume writes,
Why do we think that the properties and relations we observe among things at t will be the same at t*? The uniformity of nature is not demonstrably true and, hence, is not guaranteed. Nonetheless, we may believe that our inductive generalizations will be true at t* because we have a good number of experiences showing that our inductive generalizations have held true over time; that is, in a great number of past cases, we have found that the future has turned out to be like the past. Since the uniformity of nature has held true in the past, it will likely hold true in the future. This, however, is using experience/induction to justify experience/induction. One cannot justify induction with an inductive argument without being guilty of circular reasoning. Consider another attempt:
1. If a practice has been reliable in the past, it will be reliable in the future.
2. In the past, inductive arguments have been reliable.
_________________
3. Therefore, inductive arguments will be reliable in the future.
How do we know that premise (1) is true? It is not analytically true nor demonstrable through deductive reasoning. The only way to justify it is through induction, but that is the very methodology we are trying to justify. Bertrand Russell writes, "All arguments which, on the basis of experience, argue as to the future or the unexperienced parts of the past or present, assume the inductive principle; hence we can never use experience to prove the inductive principle without begging the question" [6].
Neither demonstrative reasoning nor inductive/ampliative reasoning seem capable of justifying induction. We may continue to use induction out of habit, Hume concludes, but we are not able to show that it is a reliable guide to forming beliefs about the future.
__________________________________________________________
Footnotes:
[1] It's not just that the statement "there are no married bachelors" is probably true, it's that it is necessarily true. There is no possible way for it to be false, since, given the meanings and definitions of the words, no bachelors could be married. If you're married, you're not a bachelor.
[2] Hume, David. "Inquiry Concerning Human Understanding." Philosophy of Science: An Historical Anthology. Ed. McGrew, Alspector-Kelly, and Allhoff. N.p.: Blackwell, n.d. Print.
[3] Contrary to this, Saul Kripke has shown that statements like "water is H20" is necessarily true, even though it is known a posteriori. If "water" rigidly designates "H20", then the proposition "water is H20" is necessarily true, and can be known analytically, even if it takes experience to know that water is in fact H20.
[4] McGrew, Ibid.
[5] McGrew, Ibid.
[6] Russel, Bertrand. "The Problems of Philosophy." Philosophy of Science: Contemporary Readings. Ed. Balashov and Rosenberg. New York: Routledge, 2007. Print.
1. Thus far, all observed X's have been found to bear property Y.
2. P is an X.
____________________
3. Therefore, P has property Y.
A different scheme could go as follows:
1. Thus far, all observed X's have been found to bear property Y.
__________________
2. Therefore, all X's bear property Y.
In both arguments, the conclusion does not follow necessarily from the premises. Rather, the premises only make the conclusion more or less likely. It's possible, for example, that there is an X that does not have property Y. The fact that all the X's we have observed thus far have had the property Y does not make it necessary that all X's must this property. Regardless, we generally take ourselves to be justified in forming beliefs on this basis (assuming a large enough sample). It seems reasonable to conclude that the sun will rise tomorrow, given that my experience (and that of countless others) testifies to the consistency of this pattern. Although we often reason this way, why think inductive reasoning is actually a reliable method for forming beliefs?
HUME'S CRITIQUE OF INDUCTION
Some propositions, argued David Hume, can be known to be true or false simply on the basis of the relation of ideas expressed in those propositions. Consider the following proposition:
(B) there are no married bachelors.
(B) is necessarily true. What's more, I do not have to find all the bachelors in the world in order to discover whether there are any married ones or not. Rather, I know the truth of (B) simply by knowing what "marred" and "bachelor" mean. If I say that (B) is false, I would would have to affirm that, "there are married bachelors", which is just to say, "there are married people who are not married." This is a contradiction, and contradictions cannot be true [1]. Thus, Hume argues that tautologies, contradictions, and mathematical truths "are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe" [2].
Matters of fact about the physical world, however, are not known in this manner. We come to know what the world is like by experiencing it, by making discoveries and by observing its workings. I did not discover, just from thinking about it, that rocks hurt when thrown at my head. I had to discover this from experience (it was a painful discovery, to be sure). This means, Hume argues, that truth's about the world are contingent -- they could be otherwise [3] -- and, this being the case, one can coherently conceive of the world being different than it is or changing in some manner. He writes,
"That the sun will not rise tomorrow, is no less intelligible a proposition, and implies no more a contradiction, than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood. Were it demonstrably false, it would imply a contradiction, and could never be distinctly conceived by the mind." [4]
The same is the case for much of the rest of our knowledge about the world. Our beliefs about laws of nature, how people will behave, and other such beliefs, are based on inductive generalizations, stemming from our experiences.
On the basis of this fact, Hume argues that inductive reasoning is not rationally justified -- we cannot rationally justify the belief that what we experience now (or have experienced in the past) will likely be the same at some future time. The problem can be seen by trying to justify induction via argument. Here's one attempt to justify:
1. We have experienced that the ways things were at some past time are conformable to the way things are at the present.
2. The future will be conformable to the past.
______________
3. Therefore, what we experience (i.e., relations of cause and effect, and the properties of things) at some time, t, will hold true at any future time, t*.
The controversial premise is (2). Why think the future will be conformable to the past. Premise (1) could be cited in support of (2), but why think that 'future futures' will conform to our experience, simply because 'past futures' have seemed to do this? Reasoning as such implicitly assumes premise (3); but that is suppose to be the thing we're arguing for, so we can't assume it in our argument without begging the question. Hume writes,
"We have said that all arguments concerning existence are founded on the relation of cause and effect; that our knowledge of that relation is derived entirely from experience; and that all our experimental conclusions proceed upon the supposition that the future will be conformable to the past. To endeavor, therefore, the proof of this last supposition by probable arguments...must be evidently going in a circle, and taking that for granted which is the very point in question" [5].
Why do we think that the properties and relations we observe among things at t will be the same at t*? The uniformity of nature is not demonstrably true and, hence, is not guaranteed. Nonetheless, we may believe that our inductive generalizations will be true at t* because we have a good number of experiences showing that our inductive generalizations have held true over time; that is, in a great number of past cases, we have found that the future has turned out to be like the past. Since the uniformity of nature has held true in the past, it will likely hold true in the future. This, however, is using experience/induction to justify experience/induction. One cannot justify induction with an inductive argument without being guilty of circular reasoning. Consider another attempt:
1. If a practice has been reliable in the past, it will be reliable in the future.
2. In the past, inductive arguments have been reliable.
_________________
3. Therefore, inductive arguments will be reliable in the future.
How do we know that premise (1) is true? It is not analytically true nor demonstrable through deductive reasoning. The only way to justify it is through induction, but that is the very methodology we are trying to justify. Bertrand Russell writes, "All arguments which, on the basis of experience, argue as to the future or the unexperienced parts of the past or present, assume the inductive principle; hence we can never use experience to prove the inductive principle without begging the question" [6].
Neither demonstrative reasoning nor inductive/ampliative reasoning seem capable of justifying induction. We may continue to use induction out of habit, Hume concludes, but we are not able to show that it is a reliable guide to forming beliefs about the future.
__________________________________________________________
Footnotes:
[1] It's not just that the statement "there are no married bachelors" is probably true, it's that it is necessarily true. There is no possible way for it to be false, since, given the meanings and definitions of the words, no bachelors could be married. If you're married, you're not a bachelor.
[2] Hume, David. "Inquiry Concerning Human Understanding." Philosophy of Science: An Historical Anthology. Ed. McGrew, Alspector-Kelly, and Allhoff. N.p.: Blackwell, n.d. Print.
[3] Contrary to this, Saul Kripke has shown that statements like "water is H20" is necessarily true, even though it is known a posteriori. If "water" rigidly designates "H20", then the proposition "water is H20" is necessarily true, and can be known analytically, even if it takes experience to know that water is in fact H20.
[4] McGrew, Ibid.
[5] McGrew, Ibid.
[6] Russel, Bertrand. "The Problems of Philosophy." Philosophy of Science: Contemporary Readings. Ed. Balashov and Rosenberg. New York: Routledge, 2007. Print.
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