sellars on induction reconsidered

Sellars on Induction ReconsideredAuthor(s): Keith LehrerSource: Noûs, Vol. 17, No. 3 (Sep., 1983), pp. 469-473Published by: WileyStable URL: http://www.jstor.org/stable/2215261 .

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Sellars on Induction Reconsidered KEITH LEHRER

UNIVERSIY OF ARIZONA

In an article I wrote about Sellars, I remarked

Sellars' theory of induction and rational acceptance is of fundamental philosophical importance. For he articulates a set of rules that aim at producing an overall system of accepted statements with a maximum of explantory coherence. What is especially significant about Sellars' treat- ment of rational acceptance is his attempt to formulate quite specific rules for the acceptance of theories, laws, and singular statements which take account of the different epistemic purposes such statements serve within a system. . . the attempt to elaborate a set of specific rules resulting in a system of accepted statements promoting the goals of explanation and veracity is rare, bold, and paramount. ([1]: 81)

My exposition of Sellars' major contribution contained an objection, the claim his theory was subject to paradox, and I now believe that there is an interpretation of Sellars' theory, suggested to me by Sellars, that avoids paradox. Since the paradox alleged was akin to the lottery paradox, a theory that avoids the paradox in a cogent way has addi- tional interest. Moreover, since the solution Sellars provides is justified by systematic epistemic objectives and is in no way ad hoc, it is especially worth noting. I shall articulate the Sellarsian solution, consider the only objection that occurs to me, formulate a reply and conclude.

Sellars provides us with rules for the acceptance of theory, laws and statistical generalizations which, though of central importance, are not directly germane to the issue to be discussed ([3]). The issue in question concerns the acceptance of singular statements. I wrote,

Sellars' account of the reasonable acceptance of singular statements... is based on a goal of accepting a majority of true statements of a specified kind. The goal at this level is truth rather than explanation. Suppose we raise the question: is ai B? If our goal is to answer this question in such a way that a majority of our answers are correct, then, Sellars affirms, we need only ascertain that ai is a member of some class K such that membership in K is the only relevant knowledge we have concerning the

469



470 NOOS

membership of ai in B, and we know that a majority of the members of K are B. If we know that as is a member of such a classes then it is reasonable to accept the singular statement that ai is B. The reasonableness of accepting each such singular statement is that by accepting all such singular statements, we shall obtain a preponderance of correct over incorrect answers to the question: is ai B? The latter is the goal, and such acceptance promotes it. ([1]: 88-89)

This interpretation was motivated by Sellars' remarks,

69. Thus the meaning of the metrical functor is logically tied to the basic concept of probability as 'reasonable-to-accept-ness'. Over and above the tie between

prob (h,e)>?/2

and

e makes it probable that h

and hence between the former and

I it is probable that h

as well as

I shall accept h

the apparatus of statistical and proportional probability is largely the logic and mathematics of combinations, and the chief philosophical interest concerns the ends-in-view and entailed policies which support the apparatus.

70. The above remarks take on a more concrete meaning when applied to a simple case of the so called 'statistical' or 'proportional' syllogism,

7 of these 8 objects are Sp

therefore it is probables that a randomly selected one is (p where this, of course, presupposes that we know nothing else about these objects which is relevant to the question 'is one of these objects sp?'

71. To understand this reasoning, suppose that without acquiring any more knowledge of the objects in question, we assign them names '? ,' '02,' ..... '' with reference to an individuating character, thus location in space and/or time. Consider now the class of questions Qi

is Ospo?

Clearly this class of questions is so related to the set of objects that if each Qi is answered in the affirmative, then the number of true answers must equal the number of objects belonging to the set which arep.



SELLAR'S RECONSIDERED 471

72. Obviously one might get more true answers by guessing, but, equally obviously, one might get fewer. The only way one can know how many true answers he has given is by answering all of the questions in the affirmative. If he does so, he knows that 7 of his 8 answers are correct. ([3]: 400-401)

I then went on to make the following objection:

... suppose we have some large finite class K having n members, we know that 3/ K are B, K satisfies the relevance condition, and, hence, for each ai(ai, a2, and so forth to an), we accept the statement that al is B. From the conclusion that it is reasonable to accept 'ai is B' and reasonable to accept 'aj is B,' it does not follow that it is reasonable to accept the conjunctive statement 'ai is B and aj is B.' According to Sellars, reasonable acceptance is non-conjunctive. However, if we know that 3/4 K are B, that al, a2, and so forth to anare the members of K, and consequently accept the statements 'a, is B,' 'a2 is B,' and so forth to 'an is B,' then we know that not all the statements we accept are true, indeed, at least 25% of these statements are false. Thus, assuming that we accept not only these singular statements but also the statement '3/4 K are B, and a,, a2, and so forth to an are the members of K' which we employ as a premiss in our argument for the acceptance of those singular statements, then the total set of statements we accept will be logically inconsistent. The statement about K entails that not all of the singular statements are true. ([1]: 90)

There is, however, an interpretation suggested by other remarks of Sellars that avoids the inconsistency of the total set of accepted statements. Sellars remarks,

. . .let me therefore emphasize, once again, that my concern in this chapter is with "pure cases" of each of the modes of probability which I shall discuss. It is as though in ethics I were to limit myself to a discussion of a plurality of prima facie obligations (in Sir David Ross' sense) and postpone the topic of "toti-resultant obligation" or obligation sans phrase. ([3]: 403-404)

The consequence of this remark is as follows. If one is only concerned with getting a maximum of true observation statements, then it is reasonable to accept all of the statements 'a1 is B ,"a2is B,' and so forth to

'an B.' In the interest of accepting true observation statements, this policy is warranted when the probability that an ai is B is greater than

?2. But, and this is the heart of the new interpretation, such acceptance is only prima facie reasonable. When we ask, not what is prima facie reasonable, but what is reasonable sans phrase, the answer will be different. For then we must be concerned, not only with accepting as many true observation statements as possible, but also with maintaining coherence among statements of different types, for example, observation statements and generalizations about the population, and this will



472 NOUS

preclude us from accepting all the observation statements mentioned so as to avoid inconsistency.

Thus, according to the new interpretation, this way to combine the objectives of accepting true observation statements and at the same time maintaining explanatory coherence is to accept the percentage of the observation statements, provided it is greater than 50%, that corre- sponds to the percentage of members of K that are known to be B in the total population. For example, if we know that 3/4 K are B and K satisfies the pertinent relevance conditions, then we accept 75% of the statements of the form 'ai is B.'

There are other refinements to the principle of acceptance that might be added, but the general proposal is now clear. We can avoid paradox by fitting the percentage of observation statements accepted to the percentage of such statements that are known to be true, provided the percentage is greater than 50%. I have argued elsewhere that rational acceptance must satisfy a nonarbitrariness condition formulated as follows:

... nonarbitrariness. One should not be arbitrary in what one accepts, that is, if one accepts a statement, then one should accept every other statement that is not known to differ from it in any relevant respect. ([2]: 183)

The question is whether the new interpretation of Sellars satisfies this condition. If not, then assuming the cogency of the condition, this would be an objection to Sellars' proposal.

Suppose I have accepted 3 of the statements of the form 'ai is B,' have proceeded in numerical order and reached number a3. I now consider whether to accept aj+i. I cannot accept it because I have already accepted as many such singular statements as my knowledge of the population allows. I might reflect, however, that the statement 'aj isB,' which I havejust accepted, is not known to differ from 'aj+ 1is B' in any relevant respect, the only difference being the lexical ordering of the randomly selected member.

The consequence is that the nonarbitrariness condition is violated. Is the objection decisive? The case against the condition is readily formulated. It is that we may have a set of different alternatives each of which are maximal with respect to obtaining our objectives, and, though there is no relevant difference between them, it is reasonable to choose any one of those alternatives. In practical action, this is standard decision theoretic policy. It is reasonable to choose any maximal action from among a set of maximal alternatives. The proposal is that there are many different sets of singular statements we may accept to fulfill the objective of accepting the percentage of singular statements that



SELLAR'S RECONSIDERED 473

are known to be true for the population. When no other relevant knowledge is available, the choice of one of those sets will be arbitrary. The justification for choosing one such set is that the choice of any such set is maximal with respect to the goals of accepting true observation statements while maintaining explanatory coherence. This interpretation of Sellars' theory, which he suggested, thus avoids paradox while remaining within standard conceptions of rational decision making.

REFERENCES

[1] K. Lehrer, "Reasonable Acceptance and Explanatory Coherence: Wilfrid Sellars on Induction," Nous 7(1973): 81.

[2] , "Coherence and the Racehorse Paradox," Midwest Studies in Philosophy 5(1980), p. 183.

[3] W. F. Sellars, Chap. XVI Essays in Philosophy and Its History (Dordrecht: Reidel, 1974). Chapter XVI was originally published as "Induction as Vindication," Philoso- phy of Science3l(1964): 197-23 1.

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sellars on induction reconsidered

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