Induction and Confirmation

What is it?

All good (but not guaranteed) nondeductive arguments.

Induction: Reasoning from lots of cases to a generalization: This raven is black. That raven is black. ... So, All ravens are black.

Projection: Reasoning from lots of cases to a prediction: This raven is black. That raven is black. ... So, the next raven I see will be black.

Explanatory inference (inference to the best explanation): I believe a story (theory) because it connects together lots of things in an illuminating way.

Lots of people would like, and the logical empiricists needed a theory of confirmation desperately.

It seems pretty hopeless.

Problems

Formal

Evidence that "ravens are black" is also evidence that "ravens are black or God exists." Why doesn't that mean that whether God exists is an empirical question? There is no agreement about what to do about that. Indeed, many philosophers think that the success of modern physics, since it uses mathematics, is evidence that numbers exist, while others think that that is just confused.

Hume

Justification: What reason do we have, or could we have, to think that induction works? Hume looked at a particular kind of problem about induction: Why should we think that the future will resemble the past?

Obvious reason: The future always has resembled the past. That is, that has been true for all past futures. Therefore, we should expect it to continue to work.

That is itself an inductive argument.

To make that clearer, consider anti-induction: it something has been happening for a long time, we should expect it to change soon. The gambler's fallacy is very similar to anti-induction, and it makes lots of money for casinos: they provide forms for gamblers to record the outcomes of the roulette wheel, and gambler's use it to bet on the numbers that haven't been coming up, on the basis of the bad argument that all the numbers are equally likely, and so those numbers are due.

Ravens

All ravens are black says

That, is logically equivalent to

The two sentences are true or false together, and so evidence that one is true is evidence that the other is true.

What is going on here? Surely "indoor ornithology" (Goodman) How can we tell what observations are relevant to a conclusion?

Prior information

In the absence of prior information, seeing a black raven seems to be evidence confirming that all ravens are black. If, however, you have good reason to believe

If ravens are rare, they are all black, but if they are common, they are not all black.
then seeing a raven, even a black raven, is evidence that not all ravens are black.

Grue

Nelson Goodman. An object is grue if it is first seen before 2010 and it is green or if it is not seen before 2010 and it is blue.

Every bit of evidence we have that anything is green is equally evidence that it is grue. Thus, every inductive conclusion we have drawn about green is such that we have just as much, exactly as much, evidence that it is grue.

Grass is grue.

Something is wrong, because it can't be the case that both grass is green and grass is grue.

Everyone has the same reaction: grue is a nutty property: it is defined using a future time, and so it shouldn't work for induction to future times.

That obvious reply won't work. Say that something is bleen if it is blue when first seen and first seen before 2010 or it is green.

Note that something is green if it is first seen before 2010 and it is grue, and otherwise it is bleen.

You can draw at least two conclusions.

  1. You can't use induction on all properties, and so a theory of induction needs to specify which properties are ok.
  2. No formal theory of induction is possible, and so the logical empiricist dream is hopeless.

The question of what properties are suitable on which to perform induction is not just an idle one connected with extreme examples:

Gamblers typically do think "being lucky" is inductive, and that gets them into a lot of trouble. No one thinks "total casualties in Iraq after the escalation" is inductive—whatever opinion one might have about withdrawing troops, the reasons are more complicated than the one I just suggested.

Here is an example of a rule of deduction: From A and B, we can conclude A. That is true for any A and B.

Here is an example of a rule of induction: If a is B and G, and b is B and G, and ..., and you know of nothing that is B and not G, then, it is highly confirmed that All Bs are Gs. This does not work for all B and G, since if it works for green, it can't for grue.

There are many theories of inductive inference. Carnap worked on the problem for decades, and produced lots of interesting progress. This is still an industry today. -- ShaughanLavine - 14 Sep 2005 - 12 Sep 2007