Nelson Goodman: “The New Riddle of Induction”

The Old Problem of Induction [215.1]

Hume: we are not justified in making judgments about unknown or future cases on the basis of experience because such judgments are neither reports of experience nor logical consequences of it. Or, to put it another way, induction is only justified if we can justify the principle of the Uniformity of Nature. But the only way to do so would be inductively, which is circular.

So why is it that we are almost incapable of refraining from making such judgments?

Hume’s answer: repeated experience causes a conditioned response in humans, a “habit of the mind” just like it does in Pavlov’s dogs. If enough times the sound of a bell is followed by the experience of food arriving, the mind will become such that an image of food is triggered by the sound of a bell.

Most people assume that Hume does not take this psychological account of why we believe predictions to justify those predictions, any more than an explanation of why a person is addicted to gambling legitimizes that practice. However, Goodman says:

I think Hume grasped the central question and considered his answer to be passably effective. And I think his answer is reasonable and relevant, even if it is not entirely satisfactory. [216.1]

Dissolution of the Old Problem [216.1]

To get some idea of how to justify inductive inferences, we can look at how we justify deductive inferences.

When a deductive argument has been shown to conform to the rules of logical inference, we usually consider it justified without going on to ask what justifies the rules. Analogously, the basic task in justifying an inductive inference is to show that it conforms to the general rules of induction. [216.2]

But, of course, not just any old rules of inference will do for either kind of –duction. So how do we justify the rules of deduction? Answer: by reflective equilibrium:

Principles of deductive inference are justified by the conformity with accepted deductive practice. Their validity depends upon accordance with the particular deductive inferences we actually make and sanction. If a rule yields inacceptable [sic] inferences, we drop it as invalid. Justification of general rules thus derives from judgments rejecting or accepting particular deductive inferences…

The point is that rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either. [216.2/217.1]

The same applies for induction, and for that reason, Hume was right to address the problem of inductive validity by “dealing with the question of how normally accepted inductive judgments are made” (that is, by giving a psychological account of belief-formation). “The problem of induction is not a problem of demonstration but a problem of defining the difference between valid and invalid predictions.” [217.1]

Now the task is to provide principles of inductive logic on a par with those available in deductive logic.

The Constructive Task of Confirmation Theory [217.2]

Comparison: formulating rules that distinguish between valid and invalid inductive inference with formulating rules of use of the term “tree”. We work from a set of examples of certain trees, formulate rules, then use the rules to settle borderline cases.

Hempel has suggested that, just as deduction has the consequence relation, so induction has the relation of confirmation.

Suggestion: confirmation is simply the same relation as consequence, only in reverse.

Problem: a result of this is that every statement confirms every other.

Explanation: S1 is a consequence of S1 & [any other statement, say] S2

But, of course, S2 is also a consequence of S1 & S2. But that means that S2 is a consequence of a statement confirmed by S1. So, in effect, S1 confirms S2 (because surely a statement confirms all the consequences of something it confirms: if some evidence confirms that Smith and Jones are American, then it certainly confirms that Jones is American). And you can put any statement you like in place of S2, ergo, any statement (S1) confirms any other (S2), because it confirms the conjunction of itself with that other statement, and that other statement is a consequence of that conjunction.

Suggestion 2: “While some statements that confirm a general hypothesis are consequences of it, not all its consequences confirm it.”

To be precise, as Hempel suggested:

A hypothesis is genuinely confirmed only by a statement that is an instance of it in the special sense of entailing not the hypothesis itself but its relativization or restriction to the class of entities mentioned by that statement. [218.2]

That is, a hypothesis about all copper is confirmed by a statement about a particular lump of copper. And S1 & S2 is not confirmed by S1 – only S1 is confirmed by S1.

New Problem: The paradox of the ravens.

A non-black non-raven (e.g. a piece of paper) confirms the hypothesis

“all non-black things are non-ravens”
but by contraposition, this is equivalent to:

“all ravens are black”

Thus, by looking at a piece of paper we can confirm that all ravens are black. This is “indoor ornithology” and therefore very suspect.

Suggestion 3: You can solve the paradox of the ravens by noticing that a non-black non-raven is also a non-raven non-black thing, and therefore confirms the hypothesis:

“all non-ravens are non-black things” and hence “all black things are ravens”, which is patently false. It also confirms the stronger hypothesis: “nothing is either black or a raven” and thus that there are no ravens, and thus that “no ravens are black” is as confirmed as “all ravens are black”.
HOWEVER: while this takes away the possibility of indoor ornithology, it is of small comfort to the idea of confirmation. Nonetheless, it paves the way to a solution that narrows the scope of confirmation

BUT:

The New Riddle of Induction [219.2]

New problem: an instance of conducting copper confirms the claim that all copper conducts, but an instance of a man in the audience being a third son does not confirm the claim that all men in the audience are third sons.

So how do we make sure that the first is a valid instance of confirmation and the second is not?

Suggestion 3: “Only a statement that is lawlike…is capable of receiving confirmation from an instance of it; accidental statements are not.”

So, if we can find a way of distinguishing lawlike generalizations from accidental ones, we will have made progress.

BUT:

THE PROBLEM WITH GRUE:

We have equal confirmation of the claim that emeralds are grue as we do that they are green (and thus we have equal confirmation of any number of alternatives – gred, etc.)

, because the evidence we have gathered up until now confirms equally the claims “all emeralds are green” and “all emeralds are grue”. The trouble is, then, that our past evidence equally confirms two (actually an infinite number of) predicates which warrant incompatible predictions about the future. Thus induction tells us, effectively, nothing about the future (or, by extension, any generalization beyond the immediate particular facts).

If we simply choose an appropriate predicate, then on the basis of these same observations we shall have equal confirmation, by our definition, for any prediction whatever about other emeralds – or indeed about anything else… We are left once again with the intolerable result that anything confirms anything. [220.1]

Objection: “Grue” is complex and artificial, but “green” is simple and natural.

Reply: “Green” is complex and artificial if you are used to “grue” (it is constructed out of “grue” and “bleen”).

Objection: “Grue” makes essential reference to time.

Replies: (a) What (independently of the grue problem) is wrong with making essential reference to time? (That is, to avoid this you would need a cogent understanding of “complete generality”, and this is impossible to clarify [221])

(b) “Green” makes essential reference to time (if it is constructed out of “grue” and “bleen”, which it would have to be for the person who is not a natural user of “green”)

The Pervasive Problem of Projection [222.1]

We prefer green to grue because green is projectible.

It is projectible for us because we have used it in successful inductions in the past. “Green” is entrenched, “grue” is not. (But of course, this is just like saying that it is a “habit of mind”, as Hume did.)