The Problem of Induction & Goodman’s Virtuous Circle

Inferences made from a set of observed statements of fact to an unobserved statement of fact, without formal entailment, are referred to as inductive inferences. Inferences may be drawn from particular observations to

a general law or from particular observations to another.

The following are types of inductive inferences:
(1) Induction about periodic events (e.g. the rotation of the earth about it’s axis)
(2) Induction about interaction between external materials (e.g. acid turning blue litmus red)
(3) Induction about interaction between external materials and the self (e.g. bread will provide nourishment, i.e. ingestion of bread will provide ‘feeling’ of nourishment)

All these types of induction conform to the relation of cause and effect. As Hume pointed out in An Enquiry Concerning Human Understanding, all reasoning about matters of fact is governed by the relation of cause and effect. It establishes this relation on the basis of past experience. The human mind observes certain effects from certain kinds of causes and learns to expect the same effects from similar causes in the future. This expectation becomes stronger with repeated observations of the same cause-effect relation. For example, since birth we observe the sun rising every morning and from that knowledge, we infer that it would rise the following morning. With every passing day, our belief in this phenomenon grows stronger because of the satisfaction of the previous expectation.

Skepticism of Induction

Skeptics agree that inductive reasoning is inherent in human nature. But there stance is that we have no justification to believe those beliefs or predictions that we have obtained by employing inductive reasoning. Inherent in an inductive inference, is the assumption that nature will remain consistent, that the future shall conform to the past. The statement:

“It has been found that cause x has always had an effect y in the past”
is not logically followed by:
“In the future, cause x will be followed by effect y.”

The above two propositions are distinct and the second is not a logical necessity, given the first. But based on our above discussion of human inductive reasoning, we know that such inferences are being made all the time. Hume claims that he is unable to ascertain the chain of reasoning by which this inference is made. It is clear that this is not backed by deduction. This inference aims to yield information (conclusions) over and beyond the
semantic content of the premises.

There is no demonstrative argument that explains this kind of inference frequently employed by humans. That there is none is evident from the observation that a denial of the second proposition is not contradictory. Clearly, it is not evident that objects must have a tendency to move towards the earth in the future, even though that has been the case since all of mankind, and billions of years before that, as claimed by scientists.

Since inductive reasoning is not backed by deduction, there must an alternative form of reasoning. One might argue that only those inductive inferences are justified, that are based on causal events, as opposed to the accidental events. Hence, we might say that the occurrence of an accident right after a black cat crosses one’s path is purely coincidental (contrary to what some people would believe), while acid turning blue litmus paper to red is a causal event. Therefore, causal events are justified inferences while non-causal events are not justified, and hence invalid inferences. Therefore, the constant conjunction of the contact of blue litmus paper with acid, and its turning red can be treated as a law.

Here, a skeptic might argue that there is nothing that contradicts the suggestion that the litmus color conversion by the acid is just a coincidence every single time. It would not be contradictory to deny the occurrence of the litmus color conversion the next time it is tested. Therefore, there would be no way to differentiate the coincidences from the actual lawlike events.

Essential to this line of reasoning by the skeptic is that the relation of cause and effect is not based on any reasoning derived from the cause. The cause does not provide any information about the effect in and of itself. The relation between each cause and effect that governs reasoning about matter of fact is arbitrary, at least to the human mind. The mind does not determine the effect from the cause based on any innate feature of the cause.

The use of induction is so inherent and natural in humans that it is difficult to even identify certain facts as being learned from inductive reasoning. It is reasonable to assume that almost all of us take the transfer of momentum from one body to another (i.e. impulse) as granted. But there is nothing in the first body or in its nature of motion that would prompt us to think that it will cause the second body to move on. Hume argues and shows us through an example of a collision between billiards balls that it is purely from experience that we can predict the motion beforehand.

It is significant, though, that Hume is not referring to prior experience of the motion of those particular billiard balls, or even billiard balls in general. Humans use induction to generalize from the observation of motion in some materials to all other materials. To explain this, we must go back to the cause-effect relation. Through experience, we learn that similar causes yield similar effects. For a common phenomenon like impulse, we come to learn that it applies to all kinds of objects that appear solid to us, and by consistent experience of this kind, we are able to predict the same for all things that appear solid to us, irrespective of whether we have previously observed motion in those particular objects.

Ayer’s reply: Descriptive analysis

Ayer responds to the skeptic’s attack by questioning the intent behind the question raised by the skeptic. He agrees that the inductive argument always involves an assumption about the uniformity of nature and that it relies on the belief that the future shall resemble the past. It is clear that there is no demonstrative or deductive reasoning to justify induction. Also, it has been shown that any other reasoning will either be inadequate or will result in a logically circular argument. Inductive inference suggests a belief in instances of which we have no experience, based on instances of which we do.

In view of the above, it seems that the skeptic’s demand is illegitimate. He is asking for a proof which cannot possibly be presented. The only reasoning that can be presented involves logical circularity since it needs inductive inferences to justify them. The question is such that it is clear that there is no comprehensive solution. As Ayer mentioned – “A proof which is formally correct will not do the work, and a proof which does the work will not be formally correct.” So it seems that the endeavor to seek an answer to such a question is futile.

But the skeptics cannot argue that induction is irrational. The scientific method is based on induction, and it defines the standard of rationality. Therefore, induction does not fail to meet the standard of rationality, merely because it defines it. Therefore, by asking the question, the skeptic seems to be questioning the standards of rationality. The skeptic does point out the absence of a proof, but since it is obvious that this demand cannot be met, the question is not troubling anymore, and hence, does not need further consideration. As Ayer pointed out, there is no need for worry as there is logically, no higher court of jurisdiction, so it is allowable for inductive reasoning to decide its own case.

Goodman’s virtuous circle

Goodman approaches the subject along similar lines as Ayer in that he agrees with the shortcomings of induction that what has happened imposes no logical restrictions on what will happen, but disagrees with skeptics in that there is no justification for the employment of induction as a method of inference. He protests against a sharp division between the description/explanation of induction and its justification. Based on the fallacious arguments by other philosophers, the search for a clear argument for justification of induction is fruitless and therefore, Goodman asserts that the skeptic’s query is illegitimate because it asks for answers that are not available, and never will be.

His point of difference with Ayer is that he goes on to analyze the foundations of deduction as a valid method of inference, in order to come up with a justification for induction. An argument is deemed logical (conforming to deduction) if it conforms to the general rules of deductive inference. But these general rules of deductive inference must themselves be justified. Philosophers have tried to justify these rules by asserting that they follow from some basic axiom or by basing the rules in human nature. In either case, the argument seems to be emerging from human intuition. Goodman argues that the answer is simpler, and that the rules of deductive inference are based on, and hence justified by our deductive practice. So, the justification of general rules of deduction is dependent on their acceptance or rejection of accepted deductive inferences.

Deductive inferences are justified by their conformance to valid general rules of deduction, while the general rules themselves are backed by their conformance to accepted valid inferences. Clearly, this is circular. But here, Goodman argues that the logic is circular, but the circle is a virtuous circle, i.e. this is the only method by which we may justify deduction. This mutual adjustment between inferences and rules is the basis for deduction.

Goodman’s virtuous circle applies to induction as well. Therefore, an inductive reference is justified by conformance to generally accepted inductive rules and these rules in turn are justified by accepted inferences. As opposed to deduction, though, these general rules of induction are not well established, and there needs to be a consensus on valid canons of induction. Therefore, the problem of induction is reduced from that of justification to description. With this conclusion, Goodman asserts that questions concerning the justification for induction, as different from an explanation of it, are illegitimate.

Crystal ball justification

Induction is intuitive and is employed by humans naturally. When people reason about matters of fact using induction, they do not think about justifications for their reasoning. It develops naturally as a habit. This was the description or explanation of induction given by Hume and later supported by Goodman. Inductive reasoning (which is happening all the time) tends to predict or expect events that have been most consistent. On the other hand, crystal balls do not come naturally to people, and there is no “crystal ball practice” that is inherent in our nature, as opposed to the inductive practice discussed by Goodman. Also, induction is generally successful with predictions more often that crystal balls, which supports its usage. Hence, crystal ball justification of crystal ball inferences does not undermine induction.