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Posts Tagged ‘black swans’

Quine

In grunbaum, holism, quine on 25/08/2011 at 2:26 pm

Quine’s problem (which is different from the Duhem problem) begins by calling into question ‘the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience.’ (Quine, 39) However it was never Duhem’s intention to save the hypothesis, merely to indicate the element of uncertainty of falsifying evidence. Quine has taken the Duhem problem and extended it so that there is no limit to the set of hypotheses which face a test: “our statements about the external world face the tribunal of sense experience not individually but only as a corporate body.” (ibid, 41)

Of course, Quine is correct in saying that “Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system. Even a statement very close to the periphery can be held true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws. Conversely, by the same token, no statement is immune to revision,” (ibid, 43) but as Grünbaum shows, this is a trivial result.

It’s best not to reduce Grünbaum’s argument too far, but a brief analysis of the paper is necessary: Grünbaum demonstrates that while the Quine problem is trivially true as a matter of following the rules of logic, it leaves us only with no compelling reason to favor any of our auxiliary hypotheses over our scientific theories, and in its non-trivial form is a non sequitur. Anyone interested in examining Grünbaum’s argument fully can read the paper here [.pdf] (alt link).

In a letter dated June 1, 1962 and printed in Harding (1976), Quine responded to Grünbam. It’s interesting to understand Quine in light of this letter. I’ve reproduced it below, bolding specific passages of note.

Dear Professor Grünbaum:

I have read your paper on the falsifiability of theories with interest. Your claim that the Duhem-Quine thesis, as you call it, is untenable if taken non-trivially, strikes me as persuasive. Certainly it is carefully argued.

For my own part I would say that the thesis as I have used it is probably trivial. I haven’t advanced it as an interesting thesis as such. I bring it in only in the course of arguing against such notions as that the empirical content of sentences can in general be sorted out distributively, sentence by sentence, or that the understanding of a term can be segregated from collateral information regarding the object. For such purposes I am not concerned even to avoid the trivial extreme of sustaining a law by changing a meaning; for the cleavage between meaning and fact is part of what, in such contexts, I am questioning. Actually my holism is not as extreme as those brief vague paragraphs at the end of “Two dogmas of empiricism” are bound to sound. See sections 1-3 and 7-10 of Word and Object.

Sincerely yours,

W. V. Quine

After all, if you see something that appears to be a black swan no matter how many tests are conducted, only by the most tortuous steps can one protect the theory “All swans are white.”

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Strevens on Induction

In induction on 04/08/2011 at 4:38 pm

When two theories are empirically equivalent, their likelihoods relative to any given body of evidence are equal. Thus the difference in anyone’s subjective probabilities for the theories must be due entirely to the difference in the prior probabilities that were assigned to the theories before any evidence came in. Bayesian confirmation theory preserves a prior bias towards simplicity, but it implements no additional bias of its own. …

Bayesian confirmation theory does impose an objective constraint on inductive inference, in the form of the likelihood lover’s principle, but this is not sufficient to commit the Bayesian to assuming the uniformity of nature, or the superiority of “non-grueish” vocabulary or simple theories. The first of these failures, in particular, implies that [Bayesian confirmation theory] does not solve the problem of induction in its old-fashioned sense.

If the old-fashioned problem of induction cannot be solved, what can we nevertheless say about [Bayesian confirmation theory]’s contribution to the justification of induction? There are two kinds of comments that can be made. First, we can identify unconditional, though relatively weak, constraints that [Bayesian confirmation theory] puts on induction, most notably the likelihood lover’s principle. Second, we can identify conditional constraints on induction, that is, constraints that hold given other, reasonable, or at least psychologically compelling, assumptions. We can say, for example, that if we assign low priors to grueish hypotheses, [Bayesian confirmation theory] directs us to expect a future that resembles the past. This is, remember, considerably more than we had before we began. (Michael Strevens, Notes on Bayesian Confirmation Theory [.pdf], 66)

Strevens is admirable, for he is upfront about the inadequacies of Bayesianism. That said, Strevens at times overstates his case. For instance, tet me simplify the bolded passages: “The evidence for any particular theory is underdetermined … however, if we reject theories that are incompatible with our assumption that the future will resemble the past, we will expect a future that resembles the past.” At least two problems for Strevens:

(1) The future does not resemble the past in all domains: black swans, white ravens — in fact, all falsified scientific theories — should give us pause before assuming something that is demonstrably false when applied to all domains. Therefore, if the future resembles the past in only some domains, why we should assume that the future will resemble the past in any particular domain?

(2) Even if the future should resemble the past in this particular domain, it does not follow that any theory that assumes a future that resembles the past is true, for while ‘grueish hypotheses’ are ruled out, there may still be an alternative theory that follows from that same assumption that the future will resemble the past that is in fact true. After all, it’s happened in the past (Einstein replacing Newton).

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