We have seen that reasoning in general, including especially scientific reasoning, seems to involve reasoning in which we generalize from cases. There are several puzzles about this sort of reasoning, two of which will discuss here. One is sometimes called “Hume’s Problem” or “The Problem of Induction”. The second is more recent, due primarily to 20^th century philosopher named Nelson Goodman. It is sometimes called “Goodman’s Problem” or “The New Riddle of Induction.” The reading from Russell is about the first problem. The reading from Rosenberg is about both.

 

I. Hume’s Problem

 

Russell begins by asking about our basis for believing that the sun will rise tomorrow. There’s a simple argument:

 

Arg. 1

1. The sun has risen every day in the past.

2. The sun will rise tomorrow.

 

He notes that you might think it’s not just this, but instead something about the laws of motion. And then he notes that there is an “uninteresting” doubt having to do with something interfering with the motion of the earth and the interesting doubt about the status of the regularities concerning motion. And we are in the same position with respect to the laws. That is,

 

Arg. 2

1. Objects have obeyed the (so-called) laws of motion up until now.

2. Objects will obey the laws of motion tomorrow.

 

Note: it’s not really about the future. We could formulate a principle:

 

PF: The future will be like the past. (Regularities that have obtained in the past will continue to obtain in the future.)

 

Note: It’s really about observed and unobserved regularities. Some principle like this seems to be the one that gets us from (1) to (2) in each of the arguments. See p. 65.

 

Russell then notes a difference between the causes of our beliefs and what we have good reason to believe. We do believe in the “uniformity of nature”. The question is whether we have any reason to believe this.

 

In Hume’s formulation of the problem a point gets more emphasis than in Russell’s. It is that there are two ways we might defend (PF): a) It is true a “truth of reason” - a definition, or necessary truth that we can know to be true just by thinking about it. b) We can discover it to be true through experience.

 

Russell deals with (a) in two passages: the example about the chicken on p. 63 shows that it is not true in all cases; the point on the bottom of p. 65 is that there is no demonstrative proof in the inferences above. That is, the arguments from (1) to (2) above are not valid - the premise could be true and the conclusion false. And this shows that (PF) is not true by definition.

 

Russell deals with (b) in the passage on 64-5 about past futures and future futures. He says an argument for PF using past cases “begs the question”. Pretty much the same idea comes back on p. 68. Rosenberg discusses this on p. 115.

 

Here’s a way to represent the most skeptical argument you might get from all this:

 

Arg. 3 (Hume’s Argument)

1. We are justified in accepting the conclusions of inductive arguments (e.g., Arg. 1) only if we are justified in accepting (PF).

2. We are justified in accepting (PF) only if either (a) (PF) is a “truth of reason” or (b) (PF) can be established through experience.

3. But (PF) is not a truth a reason.

4. Any argument for (PF) based on experience assumes the truth of (PF).

5. No argument for a principle establishes that principle if it assumes that very principle.

6. So, (PF) cannot be established through experience. (4), (5)

7. We are not justified in accepting (PF). (2), (3), (6)

8. We are not justified in accepting the conclusions of inductive arguments. (1), (7) 

 

II. Question-Begging Arguments

 

A. Premise 4

The idea behind premise (4) is that inductive arguments for induction are “question-begging”.(Rosenberg., p. 115; Russell, p. 65). Suppose:

 

    D1.   Argument A assumes the truth of its conclusion =df The conclusion of Argument A is also one of the premises of Argument A.

 

Arg. 4

1. Everything I say is true.

2. I say that everything I say is true.

3. So, everything I say is true

 

The inductive argument for induction is something like this:

 

Arg. 5

1. (PF) has been found to be true in the past. (Induction has worked in the past)

2. So, (PF) will be true in the future. (Induction will work in the future.)

 

Arg. 5 does not have (PF) as a premise. So it does not assume the truth of its conclusion in this way. Given D1, premise 4 is false.

 

You might note the following about Arg. 5: the principle it relies on is (PF). Note difference between rule of inference and premise. So,

 

    D2.   Argument A assumes the truth of its conclusion =df The conclusion of Argument A is either one of the premises of Argument A or the principle of inference of Argument A.

 

This makes Pr. 4 of Hume’s Argument true.

 

B. Premise 5

 

    D3.   Argument A establishes the truth of its conclusion =df Argument A has true premises and uses a correct principle of inference.

 

Well, if PF is a good principle, then Arg. 5 does establish its conclusion. So given D3, Pr. 5 is false or at least not justified.

 

You might add to (D3): we have to know that the principle of the inference is a good one. But that runs into trouble since it demands so much. Only people who have actually thought about rules of inference would meet that condition.

 

Maybe Ros. analogy to promising to keep your promise helps clarify. Suppose I first say

 

            Promise 1: I promise to pay back this loan.

 

When asked about this, I say

 

            Promise 2: I promise that I keep all my promises (or: I promise to keep Promise 1.)

 

If you were worried about 1, you shouldn’t feel better now. Promise 2 is pointless - a hearer should be no more confident of Promise 1 after it than before. Maybe Arg. 5 is also pointless in a similar way. If you had doubts - reasonable or not - about PF, then they are not eliminated by this argument.

 

    D4.   Argument A establishes the truth of its conclusion =df Argument A has true premises and uses a correct principle of inference, and consideration of Argument A should eliminate any doubts one might have about its conclusion.

 

Given this, maybe Pr. 5 is ok also. So Hume’s Arg. is looking pretty good.

 

But notice: we did not just say that doubts about PF were reasonable. Cf., the promise case. I might be a trustworthy promise maker. And PF might still be a perfectly good principle of inference. There is a difference between its being a good principle and our proving that it’s a good principle. See last sentence of middle ¶ on p. 69 of Russell. Two ways to take this: i) we are not justified in accepting Arg. 5 unless we (illicitly) assume that PF is generally true; ii) we are not justified in accepting Arg. 5 unless PF is in fact a good principle to use in making inferences. Maybe there is a difference between something being a good way to make inferences and our being able to prove that it’s a good. If induction is a good way, then Arg. 5 does not seem quite so bad.

            We will make use of this idea in developing a slightly different response.

 

III. Responses to Hume’s Arg.

 

There are a variety of solutions to the argument in the literature. Rosenberg mentions one on the top of p. 116. I will present what I think is the most promising reply. It is suggested by a few things Russell says. A few ideas work together to get at the main idea:

 

1) As we’ve noted, (PF) is not true! The chicken example in Russell shows this. We know that it is not true if we are reflective.

2) But Russell’s chicken wasn’t unreasonable (given certain assumptions about what it “knew”).

3) When Russell formulates the principle he’s got in mind more carefully, it differs from (PF). See p. 66 and 67. The principles here are more complex in at least two ways: a) the premise part is more complex - numbers of cases, no counter instances; this allows that positive evidence for a regularity has to be weighed against other evidence. b) More importantly, it talks about what has been “found” and what conclusion is “probable”. But here “probable” means something like “reasonable to believe”. So here’s a revised simplified principle highlighting this aspect of what Russell said:

 

(PF*) A person who has observed that things have been a certain way in the past has good evidence that they will be that way in the future.

  

4) So I think that (1) in Hume’s Arg. is false. What matters is (PF*), not (PF).

 

5) Suppose you replaced (PF) by (PF*) in Arg. 3. You now get as a premise

 

(1*) We are justified in accepting the conclusions of inductive arguments (e.g., Arg. 1) only if we are justified in accepting (PF*).

 

I say that (1*) is false. You do not have to be justified in thinking that the principle is a good one. It just has to be a good one. The chicken illustrates this. The chicken is fully reasonable in its belief. It need not be justified in accepting (PF*). It need not be reflective.

 

6) Here is where things get tricky. But we are reflective. We realize that we are relying on something like (PF*). Maybe that messes things up. Consider:

 

(0) We realize that inductive arguments depend upon (PF*)

 

(.5) If we realize that inductive arguments depend upon (PF*), then we are justified in accepting the conclusions of inductive arguments (e.g., Arg. 1) only if we are justified in accepting (PF).

Therefore, (1*).

 

That is (1*) is true about us, given our sophistication, but not true about everyone.

 

7) My response: (PF*) is something we can see to be true just by thinking about it. It captures what being reasonable is. So if we were to restate Hume’s Arg. to be about (PF*), I would reject premise (3).

 

 

IV. Goodman’s Problem

 

A. The Problem

There’s a second problem about induction. In some ways, it’s harder than Hume’s problem. Some examples seem to show that even (PF*) is false.

 

The fundamental idea is that observed (past) regularities are reasons to believe in future (unobserved) regularities:

 

(PF*) A person who has observed that things have been a certain way in the past has a good reason to believe that they will be that way in the future.

 

We might add by way of clarification that this can’t just be selectively picking out positive instances of a pattern.

 

Examples (details given in class):

 

Ex. 1: Presidential elections - candidate X has never won before. But suppose also, two female candidates and one uses no woman has won before. And also, a major party candidate always wins. There are conflicting patterns. Does one have reasons for conflicting conclusions?

 

Ex. 2: I’ve never been 50 years old before, so ... But, also, everyone who has been 49 has become 50 on his next birthday. So I have reasons for both conclusions?

 

Ex. 3: green/ grue (See Rosenberg, p. 119). So, using PF*, a geologist at the right time has a reason to believe that the next emerald will be green and also a reason to think that the next emerald will be grue.

 

The objection is then:

 

1. The people in Examples 1-3 have observed that things have been a certain way in the past.

2. These people do not have a reason to believe that they will be that way in the future.

3. Therefore, (PF*) is false.

 

B. A Possible Response

There is a possible response to the objection. (2) is false. They do have a reason. It’s just that they have a stronger competing reason. Notice that (PF*) differs from:

 

(PF**) A person who has observed that things have been a certain way in the past is justified in believing that they will be that way in the future.

 

This is surely false. The examples show it. The competing predictions case is especially compelling on this point.

 

So one might defend (PF*) from the objection by saying that in these cases there are reasons, but the person is not justified in the “bad” conclusions. To explain this, one might add to (PF*) another principle. Let’s call it the “No Defeating Evidence Principle”

 

(NDEP) If a person has a reason to believe something, and does not have an equally strong or stronger reason not to believe it, then the person is justified in believing it.

 

You might also say that one is justified in believing the stronger, or better, inductive argument. The overall evidence determines what’s justified, even if you have reasons for all the various conclusions. So, the “green evidence” defeats the “grue evidence” and the fact that everyone goes from 49 to 50 evidence defeats the “I’ve never been 50 before” evidence. (PF*) is ok.

 

C. The Problem Returns

Maybe this is a way to avoid the objection to (PF*). But a hard question remains. Why doesn’t the defeat principle work the other way as well: the “grue evidence” defeats the “green evidence”, and similarly for the other example.

 

This seems to be the situation: we think that “green” is somehow a better basis for prediction than “grue”, and similarly for the other examples. The more general idea: there are all sorts of patterns and regularities we observe. It is overall reasonable to project some of them out into the future, but not all of them. It’s very hard to see what basis we have for this preference. Why are green and blue good in this way but grue and bleen not good?

 

You might think that “grue” is artificial, unlike “green”. But see first full ¶ of p. 120. As the next ¶ says, we don’t have a good response to this puzzle. You might think that it’s obvious that certain patterns are better than others. But it’s extremely hard to say why.

 

Rosenberg concludes this section by saying that we have a hard time saying what counts as a “positive instance” of a generalization. He means by “positive instance” something like “instance that provides evidence of general truth” or “confirming instance” and not just “instance of the generalization which is true”.

 

Rosenberg also connects this to questions about “falsification.” See middle ¶ on p. 121. We will discuss this next time. The questions will be: what is it to “falsify” an hypothesis? what role does this idea play in our thinking about science? why does Rosenberg think that no hypothesis can be falsified?