Hume’s Problem of Induction

Hume’s Problem of Induction is a problem about explaining how it is that we correctly reason about future cause–effect relations on the basis of past cause–effect relations.

For example, if I pick up my electric guitar, turn on the amp, and strum an A-chord, I expect an A-chord to sound through the amp. Why am I expecting such a thing? Am I correctly or reasonably inferring that the A-chord will sound? If so, then coming up with a view that shows that such inferences are reasonable is the problem of induction. Hume zeros in on two propositions that constitute the general form of the inferences that we make concerning cause and effect, one which is given by (past) experience, and the other which is concluded on the basis of that experience:

Anyway, it must be admitted that in such a case as [inferring a future cause and effect relation] the mind draws a conclusion; it takes a certain step, goes through a process of thought or inference, which needs to be explained. These two propositions are far from being the same:

•I have found that such and such an object has always
had such and such an effect.
•I foresee that other objects which appear similar will
have similar effects.

The second proposition is always inferred from the first; and
if you like I’ll grant that it is rightly inferred. But if you insist
that the inference is made by a chain of reasoning, I challenge
you to produce the reasoning.

Enquiry Concerning Human Understanding, Section 4 Part 2

Hume then goes on, by process of elimination, to conclude that no reasoning in made from the first proposition to the second. Before noting the absurdity of thinking that the Saturn V rocket—or your smartphone for that matter—was built and expected to work using no reason at all, let’s get to his argument for this. For Hume, there are two kinds of reasoning, demonstrative and matters of fact.

He first eliminates that the reasoning is demonstrative. With similar examples to that of my guitar playing, Hume points out that the expected effects do not necessarily follow, which means that supposing something else occurs is not to suppose a contradiction, unlike the case of supposing that 2 + 3 = 4, or that the square of the hypotenuse does not equal the square of the two sides. It is not a contradiction that I should strum my guitar pressing the strings in the shape of an A-chord and have no A-chord strum (indeed, this sometimes happens, which I will get to shortly). Since demonstrable reasoning involves inferring a conclusion that, if denied, amounts to making a contradiction, I therefore, according to Hume, cannot demonstrably reason that the A-chord will sound after I strum it in the shape of an A-chord.

Hume then argues that neither is such an inference reasoned by matters of fact. For Hume, all arguments about matters of fact are based on the relation of cause and effect. Also,

Our knowledge of that relation is derived entirely from experience; and in drawing conclusions from experience we assume that the future will be like the past. So if we try to prove this assumption by probable arguments, i.e. arguments regarding existence, we shall obviously be going in a circle, taking for granted the very point that is in question.

Enquiry Concerning Human Understanding, Section 4 Part 2

That is, drawing conclusions from experience requires assuming that the future will be like the past, but this is exactly the conclusion to which Hume is trying to reason. So we do not reason that the future will be like the past or that “I foresee that other objects which appear similar will have similar effects”; rather we assume it first in order to then reason about matters of fact. The conclusion that future causes–effect relations will be like past ones, if made through reasoning about matters of fact, will have to rest on the assumption that future causes–effect relations will be like past ones. Since this is circular, no such matters-of-fact reasoning is made. And since these two kinds of reasoning exhaust all kinds for Hume, and concluding that cause–effect relations of the future will be like those of the past involves neither kind, then there is no reasoning to that conclusion.

Hume’s positive picture about how we come to expect or believe in future cause–effect relations is that it comes through custom or the habit of the mind to associate the similar causes with similar effects given many experienced instances. Such a view is perhaps plausible, but it ultimately, I think, fails to account for our everyday understanding of the objective causal reliability of objects, natural and artificial. In general, we understand that the Saturn V rocket worked, and that our smartphones work and will work in the near future, not merely because of a habit of the mind. A habit of the mind cannot explain our understanding of the objective reliability of such things.

Rather, Hume is likely missing some premises, or is assuming that an inference is made that does not quite line up with the inference we actually make. Hume challenges,

If the inference is to be conducted through reason alone, it must be with help from some intermediate step. But when I try to think what that intermediate step might be, I am defeated. Those who assert that it really exists and is the origin of all our conclusions about matters of fact owe us an account of what it is.

Enquiry Concerning Human Understanding, Section 4 Part 2

Let me attempt to take on this challenge here. I think what is missing from Hume’s account is what is another baseline assumption that ought to be made in scientific endeavors: the assumption that the universe is intelligible.

In the context of causes and their effects, this roughly means that if some unexpected effect happens for some cause, then there must be some other cause, which is entirely discoverable, that explains the unexpected effect.

For example, if I strum my guitar with an A-shaped chord, and the A-chord fails to ring through the amp, it is not a conceivable thought I can have that nothing accounts for why this is so. Indeed, I proceed to go through various troubleshooting steps based on what I take the problem to be. I may check my guitar is in tune, that the amp is on, that the cable is secure, and so on. If worse comes to worse, one of my components must be busted and needs to be repaired or replaced. But it cannot be that nothing explains this lack of an A-chord sounding through my amp—what would that even mean? Even if the occurrence is supernatural, then it would be explained by the will of God or something comparable.

In light of these considerations, I think Hume is just wrong about his characterization about how we believe in future cause–effect relations. Let me try a different characterization of the thoughts involved and you can decide for yourself if it is a viable alternative.

Suppose we start with the assumption not only that the universe is intelligible as I mentioned, but that it is also susceptible to our intentions or plans. So if I wanted my A-chord to sound rather like a B-chord, I can accomplish this (most easily by tuning my guitar up a full step). If engineers want a rocket capable of going to the moon, they can make it. And if some clever person wants to make a special set of billiard balls that each react in exactly one of the hundred ways that Hume mentions can be the effect of one billiard ball’s hitting another, then they can also make them. My reasoning of my ability to do this rests on the assumption that the universe is intelligible and susceptible to my plans. Granted these assumptions, I do not reason that the next time I strum my guitar necessitates the sound I expect to ring from my amp, but that, if it doesn’t, I can readily rectify the lack of the sound I want, and that the causes behind the lack of sound I want are transparent to me.

I think that this much better captures the expectations that we do have. We do not generally have such vague notions as “the future will be like the past”, or that “the same cause–effect relations of the past will be the same ones of the future” but rather that the causes that would explain any discrepancy between what is expected and what occurs is completely intelligible and discoverable to us. In general, I don’t think that things will always go as expected, just that what does not go as expected will be transparent as to what caused it to do so.

Let’s again look at the propositions Hume thinks we infer about:

•I have found that such and such an object has always
had such and such an effect.
•I foresee that other objects which appear similar will
have similar effects.

Such a characterization of our thinking now strikes me as absurd. A better way we may inferentially engage with our world is perhaps rather:

•I have found that such and such an object has had such and such an effect, unless prevented by a cause that is readily discoverable
•I foresee that other objects which appear similar will have similar effects, unless prevented by a cause that is readily discoverable

In this version, however, the later proposition does not follow from the former, and this indicates that no inference is made between the two.

Rather the notion of cause–effect relations itself ought be taken to a priori come with assumption of the intelligibility of the universe, or that a lack of an expected cause is itself always for some other cause that is discoverable. Get rid of that assumption, and cause–effect relations cease to be. To briefly show this, obviously that my A-chord sounds at one time but does not sound at another, and not because something else caused it to change (such as the decay of the wires in my guitar), is equivalent with nothing causing the change. There is no cause–effect relation between my guitar going from working to not working. But, again, such a thought seems inconceivable. What would it be for the guitar not to sound an A-chord, for no reason whatsoever? Granted that an object will entail a set of causal capacities, and otherwise would not be an object, then it is to be wondered how my guitar is even singled out as relevant regarding the lack of an A-chord in this case.

Combine this with our ability to realize (many of our) our desires or intentions in how objects causally behave, then objects themselves can be a priori defined by how they conform to our intentions. Indeed, how we immediately use objects is often what is most important to us, and we often define things by their practical functions. A chair is less identified by the number of legs it has and more on whether it is comfortable to sit on, or on the intentions behind it. Mistakes are possible, but a chair that is not capable of being sat on is either broken or not a chair. If broken, this goes back to the intelligibility of a cause that prevents what is expected; if not a chair, then it has, in general, no expected effect of being comfortable for sitting. But this is just how we negotiate with objects generally, and we have no notion that an object must invariably produce some effect it has in the past. Objects are differentiated by their causal capabilities, and having a radically different set of causal capacities proves that the object is rather a different one from what it was initially taken to be. But, if this is so, then the notion that, for Hume’s example, a snowball is hot, is just the very contradiction that Hume believes is lacking in our reasoning. If objects are distinguished solely by their causal capacities, alongside which ones in particular we want or intend, then it will become a straightforward contradiction to ascribe a particular object with a set of causal capacities different from the ones that define it. And if, on the other hand, the chair rather changes in the interim and so is no longer considered to be a chair, this is perfectly explainable and discoverable as to the causes for why this change occurred, and such causes themselves may be prevented in the future.

The sort of thinking I have here outlined regarding the reliability of future cause–effect relations I think much better fits the sort of thinking that helped create the Saturn V and smartphones, and that Hume’s picture does not accurately characterize our thinking about future cause–effect relations. Most prominently, Hume fails to account for the common thoughts held when things do not go as expected, particularly that some other cause must be available to explain the discrepancy. Hume also fails to incorporate that objects are often defined according to our causal expectations, and that a failure to adhere to that expectation casts analytical doubt that it is the object that was thought to be.

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