An Analysis of Proposed Solutions to Humes Problem of Induction

Written by Andrew Fursman

Monday, 28 January 2008 22:57

In Treatise of Nature and Enquiry Concerning Human Understanding, David Hume raises serious issues with the logic of inductive reasoning. Despite many attempts to address Humes concerns, these issues have remained problematic for philosophers to this day. In The Confirmation of Scientific Hypotheses, John Earman and Wesley C. Salmon examine some of the most historically significant and compelling attempts to resolve Humes problem of induction. While in each case, Earman and Salmon object to the solution given, Hans Reichenbach pragmatic vindication is most promising since it acknowledges Humes concerns without discarding the necessity of induction.Humes argument divides all reasoning into two types: reasoning of ideas and reasoning concerning matters of facts and existence. (Salmon, 55) While the first class, which includes deductive and a priori knowledge, can be vindicated through elementary logical analysis, Hume argued that no such logical support can be found for reasoning of the second class. This second class of inductive reasoning cannot be proven to be logically valid because the conclusion goes beyond the content of the premises. (Salmon, 55) Yet it is only through these ampliative modes of reasoning that one can gain additional understanding of the world, since by definition, deductive reasoning is non-ampliative and therefore gives no information not implicitly contained in the premises. While this may appear trivial and semantic, Hume has successfully argued that there is no logical basis for placing any confidence in any scientific hypothesis. (Salmon, 58) Earman and Salmon conclude that despite numerous attempts to resolve or dissolve Humes problem, no consensus has emerged and it remains to this day a crucial matter of unresolved business for philosophy. (Salmon, 66)Among the attempts to resolve Humes problem examined by Earman and Salmon, Goodmans inductive intuition and Poppers deductivism are inferior to Reichenbachs pragmatic vindication because they attempt to reject one of the two established results of Humes argument.Goodmans inductive intuition can be rejected because it misrepresents the criteria for accepting deductive reasoning, then applies that logic to induction. Goodman suggests that both inductive and deductive logic conform to general rules and that a rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule that we are unwilling to amend. (Salmon, 62) However, Deduction differs from induction in that deduction can be supported by general proofs. Since no general proof exists which illustrates inductive logic as necessarily truth-preserving, Goodmans arguments never successfully overcome Humes core criticism of inductivism. In fact, Goodmans new riddle of induction serves to illustrate that the logical justification of induction requires induction, and is thus rejected as circular reasoning. (Salmon, 63)Poppers deductivism accepts Humes criticisms of induction and attempts to resolve Humes problem by postulating that scientific reasoning does not rely on induction. Popper claims that an explanation of the scientific framework can be constructed appealing solely to deductive logic; however, his argument suffers from a serious limitation. Popper suggests that while confirmation of a scientific hypothesis is impossible without a logical proof vindicating inductive logic, using a criterion of falsifiability scientific theories obtain a level of legitimacy based on their past performance. Popper calls this measure of historical success corroboration. (Salmon, 64) Poppers adherence to corroboration does not allow theoretical science to make predictions since corroboration has no logical connection to future events. Because of this feature, Poppers deductive science it is unable to provide ampliative information and thus does not solve Humes problem.In contrast to Popper and Goodman, Reichenbach accepts both Humes assertion that science requires induction and that there is no strictly logical basis for accepting inductive reasoning. Specifically, Reichenbach acknowledges that inductive reasoning may lead to false predictions since there is no logical basis for assuming that nature will extend uniformly into the future. (Salmon, 64) Following Humes logic, Reichenbach accepts that if nature is uniform, induction will have good predictive power. He concedes that if nature is not uniform, induction will provide no logical basis for predicting future events. Reichenbach goes on to consider the implications of not using the method of induction under the same circumstances. Earman and Salmon summarized Reichenbachs results in the table below: (Salmon, 65)

Since any method of future prediction may occasionally produce successful results, there is no reason to assume that not using induction would logically guarantee an unsuccessful result. However, there is also no logical reason to assume that such a method would succeed. The result is unknown because there is no logical reason to expect consistent results.The crucial point made by Reichenbach is that any method of prediction used successfully to produce consistent results can be harnessed by inductive reasoning to make accurate predictions of the future. If every method of prediction were to cease producing accurate results, then by definition no method of future prediction would be successful. Because of this, Reichenbach concluded that if any method of predicting future events is successful, induction will be successful, and that if induction is not successful, no method can be successful; hence pragmatic vindication.Given that the chart above exhaustively lists all possible methods for predicting the future, the only logical choice for making predictions of the future is induction since no other option can ever yield better results.As stated, Reichenbachs argument appears to give a logical vindication of induction as a method of decision-making while accepting ampliative results from science. Yet Earman and Salmon are quick to point out that the argument as stated is not an accurate representation of reality due to the vagueness of Reichenbachs classifications. This is a just concern, first raised by Reichenbach himself. (Stanford Encyclopedia of Philosophy, 2006) Specifically, Earman and Salmon suggest that the results chart does not exhaustively list all possible outcomes. In their critique they state that past observations suggest that nature is neither strictly uniform nor completely random and further demonstrate that the class non-inductive methods is actually an infinite number of methods which each require individual evaluation. Based on this granularity of natures potential uniformity and the infinity of non-inductive methods available, Earman and Salmon suggest that Richenbachs method vindicates an infinite class of rules. (Salmon, 66) This implies that in practice, pragmatic vindication can be used to justify any rule which converges in the limit to the true limiting frequency (of some type of outcome O in a sequence of events) whenever such a limiting frequency exists and is therefore inappropriate as a general solution to Humes problem of induction. (Juhl, 1994)Despite this shortcoming, Reichenbach has succeeded in creating a logical vindication of induction at a conceptual level and the compelling simplicity of his solution has inspired modern philosophers to search for additional constraints to save the model technically. Specifically, Cory F. Juhls inclusion of a speed-optimality constraint has revived pragmatic vindication as a serious area for academic inquiry and a possible solution to Humes problem of induction. (Juhl, 1994) Even as originally conceived, Reichenbachs method succeeded where Goodman and Popper failed by providing a framework consistent with everyday experience which correctly represents the nature of induction and admits ampliative statements into the realm of science. While Reichenbach may not have solved Humes problem of induction, his argument illustrates key features of the nature of inductive logic. More importantly, Reichenbachs pragmatic vindication provides an excellent model for the human thought process which, as even Earman and Salmon concede, allows us to go on in spite of these troubling philosophical doubts. (Salmon, 66)Works Cited"The Problem of Induction" Stanford Encyclopedia of Philosophy (November 15, 2006), http://plato.stanford.edu/entries/induction-problemEarman, John and Salmon, Wesley C., The Confirmation of Scientific Hypotheses in M. Salmon et al. Introduction to the Philosophy of Science Englewood Cliffs, N.J. : Prentice Hall, 1992.Juhl, Cory F. The Speed-Optimality of Reichenbach's Straight Rule of Induction. The British Journal for the Philosophy of Science 45.3.857 (1994) 857 - 863