Monday, September 7, 2009

The Justification for Induction--Or Lack of It

‘If we demand a proof for everything, he [Aristotle] had said, ‘we shall never be able to prove anything, since we shall not have a starting point for any proof. Certain things are obviously true and do not require proof.’

‘Prove it,’ his nephew Callisthenes had said. Aristotle was glad Callisthenes had gone off with Alexander. He was not sorry to learn he’d been killed.

Obviously, Aristotle saw, it is impossible to prove that anything is obviously true.

Even that.

He enjoyed the paradox. [Joseph Heller, Picture This, 1988, p. 288]
In my first post, I said that I had two misgivings about whether a theory or method of induction could be successfully presented; the point of this post is to discuss one of these misgivings.

The issue is: does induction need a justification?

A “justification” is a conclusive reason (or a number of such reasons) for believing that something is proper or warranted. So, if there are conclusive reasons for believing that induction (as a cognitive process employed by us) is proper/warranted, does the process of induction need such reasons? Presently, I don’t think that induction needs a justification, and will now explain why.

Perhaps the best way to make my point is through analogy. With that thought in mind, let’s look at a few examples, starting with Aristotle’s “Principle of Non-contradiction.” (Hereafter, “Principle of Non-contradiction” is shortened to PNC.)

Aristotle’s “Principle of Non-Contradiction”

The PNC has several features, among them is that it states that two opposite assertions cannot be true at the same time: that this is impossible. (See Metaphysics Book 4, Chapter 6, 1011b13-20) For instance, one can state that “this bird is looking at me,” and alternatively state that “this bird is not looking at me,” but cannot state both assertions as happening at the same time in some way as to make it true. The combination of both claims would be ascribing a predicate (“looking at a particular person, that is, ‘me’”) and ascribing the very opposite of that predicate (“not looking at me”) to the same subject (the bird) at the same time, which is no different from ascribing nothing at all to a subject; cognitively, it is no different from refraining from making any assertion at all.

Someone, perhaps a skeptic of knowledge or someone unacquainted with Aristotle’s metaphysics or theory of logic, could ask the question: what justifies the PNC? Why is it the case that two contradictory assertions cannot be true at the same time? The attempt to then justify why this is would lead to predicating certain features as belonging to the PNC, like some noteworthy point about “contradictions,” or some fact about the human mind or reason. At the same time, however, in the very attempt of asserting these predicates of the PNC, the person is utilizing the PNC (perhaps unknowingly): in using these predicates to justify the PNC, he does not intend to assert that these predicates are true of the PNC and do not belong to the PNC at the same and in the same respect.

Aristotle regarded the PNC as axiomatic (as a starting point) for our very thoughts, as inescapable for anyone who chooses to think or use reasoning; as he says it, it is a principle which “is necessary for anyone to have who knows any of the things that are.” (Metaphysics Book 4, Chapter 3, 1005b15) Accordingly, he held that we can’t even engage in an argument without first accepting and relying on the PNC (if only tacitly if not explicitly). This reasoning, I’d like to point out, would apply to our purported justification for the PNC, since it, too, would be an argument.

The Justification of Perception

Another helpful example may be perception, whether or not our senses convey anything about reality, specifically about the external world. (Whether seeing, for instance, gives us any awareness of objects being seen, such as dogs, trees, or houses.)

A justification of perception would amount to a defense of our particular sense organs and sense-activities like seeing, hearing, and feeling. While someone could presumably try this, the resulting defense would contain an underlying fraud: it would assume the validity of the senses, even as it tries to justify them. The defense would argue that we should form our ideas of “touch,” “smell,” etc., from particular cases of touching and smelling, but the point at issue is whether we “touch” or “smell” anything at all.

The reason why a justification would be needed is that, for whatever reason, someone is unsure of whether they even have these senses. What the skeptical person needs is not a conceptual argument, which would be circular reasoning as I explained earlier, but perception. Nothing shows us that our senses are valid, besides the fact that they allow us to perceive; in losing senses, we also lose our ability to perceive, as people with normally functioning eyes discover when their eyes are damaged (through disease or some accident) and they become blind.

Now, let’s return to induction.

Can We Justify Induction?

To answer the question proposed by this section’s title, we need to turn once again to Aristotle. It was Aristotle who once aptly remarked that there are principally two ways of coming to have convictions (beliefs), two ways of reasoning or of argumentation: induction and deduction. If we were to suppose that induction required a justification, then the only two ways to provide such would be through inductive or deductive arguments.

The problem with the first approach--an inductive argument--is that it would consist of building from particular observations to piecemeal generalizations, presumably resulting in a universal, general account of induction. But the very issue at hand is whether such generalizing from particulars is valid in the first place. To utilize inductions to justify induction generally is to commit the “petitio principii,” the fallacy of “begging the question.”

On the other hand, defending induction by means of a deductive argument is impermissible because deductions can only justify non-ampliative inferences. Ampliation is our mental power of extending knowledge we already have to new cases, beyond the ones we originally used to gain that knowledge, and often leads to our possessing universal knowledge about some subject. A non-ampliative inference is one that doesn’t extend our knowledge, so to speak, but merely applies it to a new case or makes explicit something that was implicit in our argument’s premises (or thoughts).

An induction is principally an ampliative inference, and the supposed need to justify induction stems from this ampliative character; what justifies our purported knowledge of the future by means of our past knowledge, or our knowledge of the whole by means of our knowledge of some parts? What is the process of ampliation going on here, and how does it allow us to properly reason from observed cases to unobserved cases, from the past to the future, from particular areas of the world to the entirety of the universe? There is no general account of generalizing or of a universal kind of thinking from which one could produce a deductive argument about ampliation and induction--most likely because an account of induction would have to explain the role of “generalization,” “universal thinking,” and “ampliation” before deductions could be produced, and so would be just as questionable as induction, in this context.

So then what are we supposed to conclude?

I’ve maintained that induction can’t be justified through argument or reasoning, whether inductive or deductive. Rather than becoming an inductive skeptic, I ask that we return to Aristotle, specifically his point that our two ways of gaining conviction and reasoning are done by either induction or deduction. Inductions and deductions, we should come to realize, are our methods of justifying things, of coming to reach conclusions about things. By their peculiar nature, they can’t prove or justify themselves; they can’t be used to prove each other, and they can’t prove themselves (except in a trivial manner, such as “This is a man, therefore this is a man”). Rather, they are the starting points of the whole notion of justification: justification assumes the validity of induction and deduction, as these are the principal ways by which things can be justified at all, and this notion cannot be applied to them without sophistic results, such as circular reasoning. (Indeed, any attempt to prove a starting point or axiom must end in a trivial statement or circular reasoning, as Aristotle was the first to notice, see Posterior Analytics, Book 1, Chapter 3.)

I don’t think this reveals any problems with induction, as if the lack of justification reveals some hidden, underlying arbitrariness at the heart of inductive thinking. I’ve reached the conclusion that this isn’t the kind of thing that can be justified. To make the attempt results in either failing miserably, or in assuming that which one is attempting to prove, which amounts to the same thing as failing.


That said, I obviously don’t think that any and all inductions are therefore valid as a result, just as Aristotle’s thinking that there were “first principles” (starting points) of deductions didn’t lead him to conclude that all deductions were valid. There were proper and improper forms of deductions, and of using the syllogistic forms of demonstrations, he held, and carried out the Herculean task of explicating proper deductive thinking. There are proper and improper forms of inductions, of reaching generalizations, and of conducting the process of ampliation and abstraction, I hold. What we need is not a justification for induction, but a full-scale explication of what exactly induction is.


  1. In order to validate, support, and defend the basis of human knowledge -- including the process of concept-formation -- it is necessary to PROVE that induction is valid. I believe I can do so based on two axiomatic concepts on which induction depends: (1) The Law of Non-Contradiction and (2) the validity of the senses.

    Before I can present my proof, however, it is necessary to have a clear understanding, in terms of essentials, of what induction IS.

    Before Ayn Rand presented her ethics, she asked the fundamental question: What ARE values and why does man need them? In ItOE she solved the Problem of Universals by first explaining what concepts ARE and why man needs them.

    Similarly, the first question to ask when seeking an understanding of induction is: What IS induction and why does man need it?

    I will present my answers, but before I do I would like to hear how Roderick Fitts and the readers of this blog would define induction and explain its place in human cognition.

  2. That's an interesting way to approach the issue, and I think it's appropriate. It both offers a sense of the nature of the subject we're dealing with, and motivates learning about it by considering the consequences for lacking the knowledge being sought, and the possibilities that await those who reach a definitive theory.

    I'll put it up as a separate post, since I plan on writing a full essay on it.

    It should be thought of as my introductory essay on what induction is, and why we should even care about it.

  3. Induction is generalizing, inference from some member of a class to all. It is a method of reasoning. Reasoning is the means for proving everything therefore one cannot prove reason, you just show how it is done.

    Dr. Peikoff's own work on induction is available at the ARI Bookstore as "Induction in Physics and Philosophy". My own notes on "Induction in Physics and Philosophy" are available to read at

  4. I disagree with Betsy that induction relies on the PNC and the validity of the senses because aren't they inductive generalizations themselves? Did we not come to the conclusion, for instance, that the PNC was a requirement by inducing that without it no form of argumentation is possible? It seems she has it inverted unless I'm misunderstanding something.