We can think of induction1 as inferring future events from patterns of past events. Lifted from SEP, the reasoning takes this form:
All observed instances of A have been B.
The next instance of A will be B.
Well, that seems eminently plausible. It’s the principle that underlies much of our casual, everyday reasoning and our scientific reasoning. All observed instances of balls dropped have fallen to the ground, so the next ball I drop will fall to the ground. And yet, it’s not so clear that this argument is valid. Certainly we can imagine dropping a ball and it not falling to the ground, but levitating somehow. And we can do more than just imagine cases where the logic doesn’t go through; there are actual, real cases where the inference pattern quoted doesn’t hold. Patterns in real life often admit of exceptions. For example, at one point, it might’ve been true that all observed human infants had one head, but at some point there was a case of siamese twins that broke the rule.
The fact that things need not be as they were means that induction isn’t an a-priori truth, and we can’t prove induction inductively because that would be circular. So it seems like we have to answer how we can justify inductive reasoning, and philosophers of science have tried very hard to do this.
Another famous argument against induction is the example of the Grue Emeralds, due to Nelson Goodman. Essentially, the argument goes like this: we define a new property “grue” where X is grue if it is green prior to the year 21002 and it is blue after that point.
We can check emeralds one by one to see that they are green. Every instance of an emerald being green is evidence of our hypothesis that all emeralds are green. However, each such instance will equally well be evidence of the hypothesis “all emeralds are grue” since, by definition, every such emerald we observe now will be grue. It might seem ridiculous, but this argument furnishes infinitely many competing, mutually exclusive hypotheses to the natural one that all emeralds are green, and all are equally well-justified by our inductive reasoning. Here’s a short post by philosopher Henry Folse summarizing the grue argument. The key quote, I think, is this:
Why do we consider "green" as "reasonable" but "grue" as utterly "absurd"?
The reason seems obvious: no one has ever observed gems changing
color on an arbitrary date in the past, so no one has any grounds
for expecting any gem to change from green to blue in the year
2100.But to say this is just to say that we expect the future
will resemble the past (the principle of the uniformity of nature),
which is of course the heart of Hume's problem of induction. No
doubt science proceeds on this assumption of the uniformity of
nature, but our task is to justify it. Yet the only way to justify
it is to reason from the evidence which we have accumulated from
the past, and that of course is to assume the very point which is
at issue, namely the reliability of inductive inference from the
past to the future. We must conclude that the confirmationist has
not escaped the problem of induction, and so Goodman calls this
"grue paradox" the "new riddle of induction."
So how can we justify inductive reasoning? It seems without it we’re lost at epistemological sea; not only do we lose justification for science, suddenly many, maybe most, of the everyday inferences we make are unjustified if we don’t have it.
Let me digress for a moment to an argument from philosopher Alvin Plantinga against naturalism. He argues that believing in both evolution and naturalism is self-defeating. The argument goes like this:
Plantinga defined:
N as naturalism, which he defined as "the idea that there is no such person as God or anything like God; we might think of it as high-octane atheism or perhaps atheism-plus."[14]
E as the belief that human beings have evolved in conformity with current evolutionary theory
R as the proposition that our faculties are "reliable", where, roughly, a cognitive faculty is "reliable" if the great bulk of its deliverances are true. He specifically cited the example of a thermometer stuck at 72 °F (22 °C) placed in an environment which happened to be at 72 °F as an example of something that is not "reliable" in this sense[10]
and suggested that the conditional probability of R given N and E, or P(R|N&E), is low or inscrutable.
Basically, Plantinga claims that, a-priori, there’s no reason to suppose that evolution furnishes reliable cognitive faculties absent a guiding force like God. But if our cognitive faculties aren’t reliable, then we have reason to be skeptical of our beliefs in evolution and naturalism. Indeed, if our cognitive faculties aren’t reliable—and this is the point I want to emphasize—we have reason to be skeptical of our belief in anything at all. Any argument that can be marshalled against the reliability of our cognitive functions is, therefore, a defeater of any belief at all.
Now, there are a lot of problems with this argument, and I don’t feel like getting into all of them, but I suppose I should mention a few of the responses this argument has gotten.
Jerry Fodor argued that there is a plausible historical scenario according to which our minds were selected because their cognitive mechanisms produced, by and large, adaptive true beliefs.
Evan Fales[30] argued that Plantinga had not demonstrated that the reliability of our cognitive faculties is improbable, given Neo-Darwinism, and emphasizes that "if Plantinga's argument fails here, then he will not have shown that [N&E] is probabilistically incoherent." Also, given how expensive (in biological terms) our brain is, and considering we are rather unremarkable creatures apart from our brains, it would be quite improbable that our rational faculties be selected if unreliable. "Most of our eggs are in that basket," said Fales. Fales argued along the same as Robbins: take a mental representation, of heat, for example. Only so long as it is really caused by heat can we call it a mental representation of heat; otherwise, it is not at all a mental representation, of heat or of anything else: "so long as representations [semantics] are causally linked to the world via the syntactic structures in the brain to which they correspond [syntax], this will guarantee that syntax maps onto semantics in a generally truth-preserving way."[31] This is a direct response to one of Plantinga's scenarios where, according to Plantinga, false-belief generating mechanisms may have been naturally selected.
In 2020 a philosophy paper was published called "Does the Evolutionary Argument Against Naturalism Defeat God's Beliefs?" Which argued that if the EAAN provides the naturalist with a defeater for all of her beliefs, then an extension of it appears to provide God with a defeater for all of his beliefs.
It seems to me Plantinga is underselling the possibility that evolution genuinely ought to result in reliable cognitive faculties; it’s very easy to imagine how, if our cognitive faculties were unreliable, we might die or fail to reproduce or both. It seems like Plantinga is also ignoring the idea that our beliefs interact in ways that propogate like waves. He gives the following example of how evolution might furnish unreliable cognitive faculties:
Perhaps Paul very much likes the idea of being eaten, but when he sees a tiger, always runs off looking for a better prospect, because he thinks it unlikely the tiger he sees will eat him. This will get his body parts in the right place so far as survival is concerned, without involving much by way of true belief. ... Or perhaps he thinks the tiger is a large, friendly, cuddly pussycat and wants to pet it; but he also believes that the best way to pet it is to run away from it. ... Clearly there are any number of belief-cum-desire systems that equally fit a given bit of behaviour.
But it seems clear that such a set of beliefs must be evolutionarily maladaptive. Beliefs and actions are not totally separable, and ne’er shall the twain meet, in the way Plantinga is trying to insinuate. Why is Paul not eventually learning that running away from a tiger isn’t an effective mechanism for getting to pet them? If a tiger happens upon his camp in the night, will he run away or allow himself to get eaten? If Paul is to survive and pass on his genes, he must run; but then why is he not allowing himself to get eaten? Beliefs motivate actions and the results of actions inform beliefs; Plantinga refuses to grapple with that and tries to insist each one operates in its own isolated domain.
This all aside, it occurs to me that we can marshal a Plantinga-style argument for induction.
Charles Cassini already did something like this which I want to expand upon. He argues that Hume’s argument against induction is self-defeating:
We now get to the crux of Hume’s critique—namely that inductions lead to epistemic claims that are highly problematic as they all presume the ‘constancy of natural laws’ principle (CoNLP). But how does Hume know this? According to his epistemic limitations, he can acquire this knowledge in only one of two exclusively distinct ways. It is either the result of an acquired matter (truth) of fact or a relation (truth) of reason.
Now in no way can it be a truth of reason. What is there about the term ‘induction’ that requires necessarily relating the idea of CoNLP to it? Furthermore, if it were a truth of reason, then it would perforce be necessary and self-evident and there would be no arguing about the matter. That so much ink has been spilled in doing just that is an irrefutable objection to the obviousness of the claim.
While it might be true (we will stipulate for the sake of argument that it is) that every instance of an induction that Hume examined was found to contain the CoNLP, does it follow that all inductions, past, present and, especially future ones, must of necessity do the same? Within the limitations of Humean epistemic the answer to that question is obviously not. First, he in no way claims (and it would be ridiculous to do so) that he has examined each and every actual as well as every and all possible instances of induction leading to some general or universal conclusion as to the nature of things and found the CoNLP embedded in them in some way. It is possible, then, that an induction can come to occur that would not contain the CoNLP assumption within it?
The only way Hume could have come to his conclusion is by inducing from the several examples he examined to making a universal claim about them all. The only way he has of defending his claims against a charge of inconsistency is to hold that his induction about inductions is uniquely licit and valid in some way that is not the case with all other inductions about all other matters because of the inherent flaw he claims the inductive process to contain. Unfortunately it seems that neither he nor any of his supporters have admitted to his employment of the induction process in this case much less defended the legitimacy of him employing this approach. One can, perforce, accuse him of trying to have it both ways. When it suits Hume to treat induction as a truth ascertaining method about the questionable validity of all other inductions, he does so. When he seeks to cast suspicions and doubts about the achievements of other thinkers in the realms of their expertise, he attacks their use of the very same process on the grounds of its inherent structural flaw.
I think we can actually prove a stronger result than just refuting Hume’s argument against induction. I think we can marshall a Plantinga-style argument to show that any argument against the validity of induction is self-defeating.
My argument goes like this:
Let A be an argument that inductive reasoning is not valid.
Suppose A is sound.
Then inductive reasoning is not valid.
Inductive reasoning is the only possible justification for the belief that our cognitive faculties are such that they can reliably judge the soundness of arguments.
Then in particular we have no reason to believe we are correct in our judgement of the soundness of A.
In other words, A is self-defeating. If A is sound then we have no reason to believe A is sound.
The crux of my argument and the only potentially controversial premise of this argument is (4), namely that inductive reasoning is the only potential justification for the belief that our cognitive faculties are reliable. But the reliability of our cognitive faculties surely isn’t an analytic truth. There are people whose cognitive faculties are decidedly unreliable. It must be, then, that the reason we are justified in believing we can reliably judge the soundness of arguments is that we have, for the most part, done so in the past. But that sounds suspiciously like induction—and it is!
If we give up induction, we give up everything. I’ll keep induction.
Not to be confused with mathematical induction, which as it happens is deductive.
Note that the time we pick here is perfectly arbitrary.
Hey, Chef - thanks for this. Great stuff. I'm gate-crashing here because of some philosophical problems I've seen in my (former) neck of the academic woods. So I'm behind and unsophisticated, but trying to learn nonetheless.
Two questions.
(1) Isn't Plantinga's original argument (the N. E. R. one) slightly different in what it wants to achieve compared with Cassini's and yours?
So, if I shorten (or caricature[?]) the two last-named, can we say they come to something like pragmatic self-refutation regarding induction? (So, for Cassini, the absolute heart of the matter is, How can Hume himself have no epistemic limits in order to say that we all have epistemic limits. And then for your argument, doesn't premiss 4 say this, again, at its core?)
By contrast, in Plantinga's original argument, it's not so much about induction as it is about the two doctrines clashing when their fundamental principles are put in touch with one another, is it?
(2) Of course I agree with you that there are problems with P.'s argument, and of course you're right to note that it bears on induction regardless of what I've said in (1).
What I'm interested in here is that, when P.'s original argument is combined with 'Paul', I think there's something more here about evolution. Couldn't it be that Paul is a better example of evolution at work, so to speak, in a 'modern' human. For example, Paul's seeming confusion may be that he just doesn't see, and so 'know', as many tigers nowadays as Paul's ancestors did - ancestors who would not be so confused and who would adhere to what you've written here.
In short, and this is an unfair and vast question for a blog-post, but isn't there something to the notion that there is some historical variance in evolution? eg, where evolution is working on us in different ways according to different epochs? And if so, then would it mean that evolution's workings are not quite as static as they might need to be in order to polish off P.'s original argument regarding the conflicting doctrines?
Sweet. Thanks again for the posts! Much appreciated.