Thursday, November 3, 2011

Week 12: Inference to the Best Explanation

Since we didn’t quite make it through our tour of the different accounts of explanation, I want to start the next class by talking a bit about the Unification and Causal accounts of explanation. We will then slide into a discussion of what seems to me our best hope of putting induction back on a decently secure footing in science: treating inductive inference as a species of explanatory inference — sometimes called ‘abduction’, but more often called ‘inference to the best explanation’ (or ‘IBE’). The basic idea is this: suppose we observe a bunch of green emeralds. What explains this fact (the fact that we’ve observed only green emeralds)? It seems that the best explanation is that all emeralds are green (not just the ones we happened to have observed). IBE tells us to infer that this explanation is correct: that is, to infer that all emeralds are green on the basis of observing many emeralds being green.

As Lipton points out, the IBE picture addresses both the descriptive and justificatory problems of induction. Not too surprisingly it is more obviously successful as a response to the descriptive challenge; Lipton is a little more reticent about its virtues in responding to the justificatory challenge. But even restricting ourselves to the descriptive challenge, IBE has its share of worries and pressing questions. Most obviously: What is the correct view of explanation? Lipton holds a particular version of the causal account that takes on board some the ideas we briefly touched on under the heading of pragmatics. On the justificatory side, I think that we might be able to say a little more than Lipton himself makes out. Some of that will have to wait for our discussion of Scientific Realism in Week 13, but you might start to think about the justification problem of induction again in the context of IBE. I told you it’d return! Make sure you have a look at my earlier FAQ on these issues so that we’re all on the same page about what the issues are.

On Thursday, we will turn our attention to a sort of partner strategy for thinking about induction. It is to think of inductive inference as being sanction by certain features of the world — in particular the existence of natural kinds. Natural kinds are supposed to be categories/groupings that have some sort of independent existence in nature. For example, consider the category emerald. Unlike the category things on my desk, its members seem to share a great deal in common. Moreover, there seems to be a particular reason they share a great deal in common — something to do with their underlying chemical structure, perhaps; something that makes them “natural” (in a bit of a slippery sense). How does this help with the problems of induction?

Start with the descriptive problem. Here I want to quote an important paper by the influential philosopher W.V.O. Quine at some length:
What tends to confirm an induction? This question has been aggravated on the one hand by Hempel's puzzle of the non-black non-ravens, and exacerbated on the other by Goodman's puzzle of the grue emeralds. I shall begin my remarks by relating the one puzzle to the other, and the other to an innate flair we have for natural kinds. Then I shall devote the rest of the chapter to reflections on the nature of this notion of natural kinds and its relation to science.
    Hempel's puzzle is that just as each black raven tends to confirm the law that all ravens are black, so each green leaf, being a non-black non-raven, should tend to confirm the law that all non-black things are, non-ravens, that is, again, that all ravens are black. What is paradoxical is that a green leaf should count toward the law that all ravens are black.
    Goodman propounds his puzzle by requiring us to imagine that emeralds . . . are now being examined one after another and all up to now are found to be green. Then he proposes to call anything grue that is examined today or earlier and found to be green or is not examined before tomorrow and is blue. Should we expect the first one examined tomorrow to be green, because all examined up to now were green? But all examined up to now were also grue; so why not expect the first one tomorrow to be grue, and therefore blue?
    The predicate "green," Goodman says, is projectible; "grue" is not. He says this by way of putting a name to the problem. His step toward solution is his doctrine of what he calls entrenchment. . . . Now I propose assimilating Hempel's puzzle to Goodman's by inferring from Hempel's that the complement of a projectible predicate [that is, the things that are not picked out by that predicate] need not be projectible. "Raven" and "black" are projectible; a black raven does count toward "All ravens are black." Hence a black raven counts also, indirectly, toward "All non-black things are non-ravens," since this says the same thing. But a green leaf does not count toward "All non-black things are non-ravens," nor, therefore, toward "All ravens are black"; "non-black" and "non-raven" are not projectible. "Green" and "leaf" are projectible, and the green leaf counts toward "All leaves are green" and "All green things are leaves"; but only a black raven can confirm "All ravens are black," the complements not being projectible. (Quine 1969, 159-160).
So Quine’s idea here is that the are certain predicates — the ones that refer to natural kinds — which by virtue of their similarity are “projectible”. Howard Sankey — optional reading — is one (very optimistic) philosopher who wants to use this basic thought to solve the justificatory challenge by using natural kinds to rehabilitate the idea of the “uniformity of nature” — understood in a more specific and plausible way. Godfrey-Smith takes this sort of view as a jumping off point. However, he’s a bit more restrictive in how he thinks of the role of natural kinds in inductive inference. There are, he argues, two basic forms of inductive inference. One of them involves random sampling, using the randomness of the sampling as a sort of “bridge” from observed cases to the rest; the other involves natural kinds more explicitly. Here, he suggests, the extent of our sampling is far less important. This observation seems to me to explain a lot of our earlier hesitation/confusion about what was required of our samples/observations (how many, how varied, &c.?) in order for our inferences to seem secure. 

As you will see, however, Godfrey-Smith is less concerned to respond directly to the inductive skeptic. One question we should talk about is whether what he says might be useful to the anti-skeptical project. 

Tuesday (11/8): Inference to the Best Explanation
• Lipton, “Inference to the Best Explanation” [PDF] — on pp. 191–192 he begins assuming familiarity with Scientific Realism that you’ll get next week; read this, but don’t sweat it.
• White, “Explanation as a Guide to Inference” [PDF]* 

(Lots of) Questions: (respond to two)
  1. Describe a case from ordinary life in which you recently used inference to the best explanation.
  2. Thinking back on any of your inferences about the contents of The Box, do any fit well with the IBE model? Describe one in some detail. 
  3. Lipton is a little vague on what he has in mind by “vertical inferences”: try to explain more clearly what kind of inferences he’s referring to.
  4. What does Lipton mean about explanations being judged as “likeliest” vs. “loveliest”?
  5. What’s wrong with taking IBE to be an Inference to the Likeliest Explanation?
  6. Try to explain the “crucial ambiguity” White mentions on p. 7.*
  7. White offers an interesting solution to the Ravens Paradox that stems from explanatory considerations. Give a brief gloss of how his solution works.*
  8. Consider Lipton’s suggestion that explanation is often contrastive. What does this mean? Is he right?
  9. Lipton admits that meeting the “matching challenge” will “exacerbate the guiding challenge”. Why so?
Thursday (11/3): The Role of Natural Kinds in Inductive Inference
• Sankey, “Induction and Natural Kinds” [PDF]* 
• Godfrey-Smith, “Induction, Samples, and Kinds” [PDF] — you may skim §4.

Questions: (respond to one)
  1. In Godfrey-Smith’s first form of inductive inference, how are we supposed to understand “random sampling”? In particular, how would we have to randomly sample emeralds to evade the grue problem? 
  2. In the second form of inference, Godfrey-Smith suggests that numbers become less important and play a different sort of role. Explain clearly why numbers become less important in this form of inference and what role they do play.
  3. How do you suppose that the package of IBE+natural kinds might help us respond to the Humean challenge? If you don’t think they can at all, explain why.

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