catallaxy files

catallaxy in technical exile

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From time to time anti-intellectual rightwing stirrers complain about some of the research projects that get funded at the universities. Usually it is the soft social sciences that are fingered for this hideous waste of public money because they need to put their hand into someone’s pocket for research assistants, questionnaires, postage, data processing and travel to exotic locations like the outer suburbs or Wagga Wagga.

Philosophers don’t usually get pinged, presumably they get under the radar because they don’t need to apply for research grants, just sitting at their desks using up sheets of A4 and recycled electons.

But you have to wonder. Here is a list of sixty odd (some of them very odd) research reports on projects related to induction and confirmation.

This is the abstract of an interesting one by John D Norton (another relative?), “The Formal Equivalence of Grue and Green and How It Undoes the New Riddle of Induction.”

The hidden strength of Goodman’s ingenious “new riddle of induction” lies in the perfect symmetry of grue/bleen and green/blue. The very same sentence forms used to define grue/bleen in terms of green/blue can be used to define green/blue in terms of grue/bleen by permutation of terms. Therein lies its undoing. In the artificially restricted case in which there are no additional facts that can break the symmetry, grue/bleen and green/blue are merely notational variants of the same facts; or, if they represent different facts, the differences are ineffable, and no account of induction should be expected to pick between them. This still obtains in the more interesting case in which we embed grue/bleen in a grue-ified total science; the grue-ified and regular total sciences are merely equivalent descriptions of the same facts. In the most realistic case, we allow additional facts that break the symmetry and then we can also evade Goodman’s new riddle by employing an account of induction rich enough to exploit these facts. Unaugmented enumerative induction is not such an account and it is the primary casualty of Goodman’s new riddle.


I am not joking, even if it is after lunch on Friday. Honestly, all I had was a salad sandwich.

Some background, first of all on the riddle of induction and then on Goodman’s grue/bleen paradox.

Induction was supposed to be the distinctive method of science, the way that we use evidence to verify theories or to assign a numerical degree of probability to them. Hume pointed out that this would not logically wash, thereby launching many philosophical ships to solve the problem of induction.

What would count as a solution to the problem? There are two types of solutions, say A and B. The A type of solution that is sought by the inductivists would enable them to specify the degree of credibility of a proposition with some greater precision (and logical coherence) than “it just works” or “it stands up to tests”. This is what most of the sixty odd papers are about.

The B type of solution consists of showing how science (and problem-solving efforts at large) can proceed without an A-type solution to the problem. The best-known type B solution is attributed to Karl Popper, following ideas that were anticipated to a greater or lesser extent by others such as Whewell, Peirce and Bernard (a biochemist). The answer, in a nutshell, is to form a critical preference for a theory or a policy that appears to solve the problem and stands up to tests as well or better than the alternatives that are on offer.

Seventy years after Popper’s “Logik der Forschung”, and some decades after the protracted debate between Popper and assorted inductivists, the continued efforts by inductivists look like the philosophical equivalent of the quest for a perpetual motion machine.

I need to finish my salad sandwich so I will tell you about Goodman’s paradox tomorrow.

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Written by Admin

November 11, 2005 at 3:27 pm

Posted in Uncategorized

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