No solution to the problem of induction first raised by Hume seems to have any consensus among philosophers. Any inference that uses past events to infer future events is inductive and depends on the assumption that nature will remain uniform. However, it is not logically inconceivable that nature may change so to justify induction we need to show that it will stay regular. To argue it will because it has in the past is an inductive inference, the thing we are trying to justify. In this essay, I describe the basis for the problem in Hume’s Enquiry before considering some possible solutions. I argue they are not solutions either because they change the problem, avoid it or employ circular reasoning. I conclude with my own view that a solution can be found since it is rather implausible that the past success of induction in the natural sciences be attributed to luck and that analysis of Hume’s beliefs about the understanding may be a fractional step towards a non-circular account.
There are two types of human understanding according to Hume, relations of ideas and matters of fact. A priori knowledge is of the former and a posteriori, of the latter. Relations of ideas such as Euclidean geometry, algebra and arithmetic are demonstratively certain (Hume, 1993, p. 15). Their denial implies self-contradictions (Bailey & O’Brien, 2006, p. 47). Matters of fact, however, cannot be known a priori and depend on how things are in the world. Their contrary is always possible because it implies no logical contradiction (Hume, 1993, p. 15). If I suspend a body above the ground and release it, no logical contradiction is implied by its moving upwards. It is just as conceivable as it falling. So, Hume investigates the evidence for matters of fact and argues it is causal relations.
Causal reasoning enables inferences beyond the memory and senses (Hume, 1993, p. 16). If I set the kettle and walk away, although I do not watch, I think it will boil because I infer a causal relation between heat and water. So what justifies this causal reasoning? His answer is experience (Hume, 1993, p. 17). It is only after numerous times I find it has boiled that my mind infers a cause and effect. I think it will boil because it always has. Hume describes this as custom (Hume, 1993, p. 18). It is psychological conditioning (Bailey & O’Brien, 2006, p. 50) by which we infer causal relations. Causal inferences then, cannot be a priori.
Causes and effects are distinct and have no known connection to sensible qualities which makes inferring an effect or justifying the inference seem impossible. Anyone presented with an objected entirely new to them cannot deduce any effects from its sensible qualities (Hume, 1993, p. 17). If I raise a stone, its texture, shape or colour does not tell me it will fall when released. Hence, any effect I infer is arbitrary (Hume, 1993, p. 19). I can conceive of countless effects so I have no guide without experience. Hume pre-empts a tempting counterargument. Mathematics, by assisting science in predictions, assure causal relations because they follow the laws of nature (Hume, 1993, pp. 19-20). If the argument is sound, Hume has taken a wrong turn since mathematics is a priori. However, he uncovers a flaw; mathematical applications to laws of nature, presuppose those laws which presuppose causal relations (Hume, 1993, pp. 19-20). Any justification for causal inferences would justify mathematical models of the laws, not the reverse. Since effects are inferred after experience, he asks what process of thought connects experience with causal reasoning.
Hume proposes a negative answer, even after experience, our conclusions are not grounded in reason (Hume, 1993, p. 21). We assume like sensible qualities to have like secret powers so we expect similar effects to those observed from similar objects (Hume, 1993, p. 21). Secret powers refer to the unknown connection between cause and effect if it exists. Since they are unknown, causal relations are unknown and we only know events are constantly conjoined (Hume, 1993, p. 28). It is not a necessary truth that regular conjunction will persist in the future (Hume, 1993, p. 21). However, we do expect it so Hume explains that it rests on an assumption between two propositions, “I have found that such an object has always been attended with such an effect, and I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects” (Hume, 1993, p. 22). A missing premise is required to validate the inference which he believes does not exist. If experience only tells us about past events, it can only justify causal predictions if the laws of nature remain uniform. Experimental conclusions rest on the assumption that the future will resemble the past. Attempting to prove it by matters of fact is circular (Hume, 1993, p. 23). The only way to show that the laws of nature are uniform is by appealing to experience which begs the question.
Harman believes we confuse two questions when attempting a solution, whether or not it is possible to produce a noncircular justification and whether or not induction is reliable. Noncircular justification is not the issue of inductive reliability (Harman & Kulkarni, 2005, p. 2). The problem is that deduction never goes from true premises to a false conclusion but induction can. The difficulty stems from a category mistake of treating deduction and induction as two species of the same genus (Harman & Kulkarni, 2005, p. 5). This mistake leads to the implication that reasoning means making inferences from propositions you already believe. Contrastingly, it often involves giving up prior beliefs (Harman & Kulkarni, 2005, pp. 3-4). He categorises deduction as arguments, a structure of abstract propositions, and induction as reasoning, a psychological process (Harman & Kulkarni, 2005, p. 5). Since inductive conclusions are probable, new information can undermine their truth and lead to a change in initial beliefs. Hence, contrary to Hume, Harman argues induction is grounded in reason. When making reasoned changes in one’s views (his definition of induction), one looks for positive coherence between their beliefs and avoids negative coherence (Harman & Kulkarni, 2005). This is the concept of reflective equilibrium associated with Goodman (Harman & Kulkarni, 2005, pp. 6-7). Goodman argues we can test inductive conclusions by determining their compatibility with general principles already accepted and testing general principles by conclusions already accepted (Harman & Kulkarni, 2005, p. 7). If they conflict, we can adjust either until they cohere (Harman & Kulkarni, 2005, p. 7). Reflective equilibrium justifies inductive conclusions for the believer, pending new information.
There are problems with this view. The issue with circularity is precisely what leads to the question of how induction can be reliable. It is no solution to describe induction as a reasoned change in beliefs. Hume is not concerned with justifying reasoned changes in beliefs. It is not the distinguishing mark of induction. Every time I set the kettle and infer that the water will boil, and return to find it has, I do not undergo a reasoned change in my original belief. On this view, I did not employ induction. That I infer it will boil because it has in the past, distinguishes this inference as inductive. Harman does suggest another possible solution found in statistical learning theory, a discipline responsible for producing new technology (Harman & Kulkarni, 2005, pp. 12-13). However, this appeal does not help the issue since statistics make predictions based on prior data and Hume wants to know how that justifies predictions. It would have no predictive power should the course of nature lose regularity.
A more common solution is that Hume’s demands are not reasonable. Hume showed we have no rational grounds for believing scientific predictions will be true but that is not a reasonable demand (Salmon, p. 278). We should be content with probable predictions which is to demand they be supported by best available evidence (Salmon, p. 278). It is rational to base beliefs on that so it is rational to believe scientific predictions (Salmon, p. 278). To ask whether it is rational to believe in scientific predictions amounts to asking whether it is rational to be rational (Salmon, p. 278). This argument, however, begs the question, much of Hume’s doubt is concerned with justifying exactly that evidence used in predictions. Scientific investigations would suffer the same consequence as statistical learning theory if the course of nature changed. It is for these same reasons that Popper’s response does not offer a solution. He advocates deductively falsifying inductive hypotheses (Salmon, p. 279). Popper claims science should not attempt predictions, only formulate hypotheses to make sense of present facts (Salmon, p. 279). If it is successful in explaining new facts, the hypothesis is kept, if not, either adjusted or discarded (Salmon, p. 279). The aim is to refute a hypothesis, not confirm it. This adds rigour to the scientific method and avoids confirmation bias. However, deductive logic shows the content of premises without extending it to the knowledge of future consequences (Salmon, p. 279). We cannot deduce future events from premises referring to past events. Inferences that predict future events from past events must be different to deductive inferences (Salmon, p. 279). It does not answer Hume’s question of how we can infer future effects, in fact, it proposes a negative answer, that we should not do it with science.
My own view is that Hume is right in claiming that any experimental conclusions to justify induction beg the question. His arguments that they cannot be justified a priori are compelling since a change in the laws of nature implies no contradiction. I agree with Hume’s negative answer and cannot provide a positive solution however I am inclined to believe one exists. Salmon remarks it would be an extraordinary run of luck for science if induction had no rational justification (Salmon, p. 279). Since I believe no scientific investigation can solve the problem without begging the question, I am led to believe that a solution lies in answering two issues of the metaphysical and epistemological kind “What are secret powers and how can we know them?” but Hume has made it clear that the difficulty in answering either is what is perplexing. Therefore, it may shed light to scrutinise some of Hume’s assertions that sustain the problem. We can ask whether something being conceivable means it really is logically possible or whether only causal reasoning can sustain beliefs about matters of fact. If the answer is no to either of these then the problem of induction may be less perplexing. Perhaps, a solution lies in affirming the antecedent.
Bailey, A., & O’Brien, D. (2006). Hume’s Enquiry concerning Human Understanding Reader’s Guide. London: Continuum International Publishing Group.
Harman, G., & Kulkarni, S. R. (2005). The Problem of Induction. 1-17.
Hume, D. (1993). Sceptical Doubs concerning the Operations of the Understanding. Indianapolis, Indiana: Hackett Publishing Company, Inc.
Salmon, W. (n.d.). An Encounter with David Hume. In Reason and Responsibility (pp. 263-282).