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Reasonable Acceptance and Explanatory Coherence: Wilfrid Sellars on InductionAuthor(s): Keith LehrerSource: Noûs, Vol. 7, No. 2, Studies in Wilfrid Sellars' Philosophy (May, 1973), pp. 81-103Published by: WileyStable URL: http://www.jstor.org/stable/2214485 .

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Reasonable Acceptance and Explanatory Coherence. Wilfrid Sellars on Induction

KEITH LEHRER

UNIVERSITY OF ROCHESTER

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 explanatory coherence. What is especially significant about Sellars' treatment 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. Some philosophers have stressed the role of the coherence or simplicity of a system in deciding what statements to accept or reject. Others have formulated specific rules for the acceptance of statements to fulfill various cognitive objectives. But 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. I shall raise some objections to Sellars' theory concerning the explanatory coherence of the system obtained from the rules he proposes and subsequently propose a decision theoretic modification. However, the project of artic- ulating a set of rules for the acceptance of statements aiming at the construction of an overall system of accepted statements serving the goals of scientific inquiry is essentially Sellarsian.

Sellars' Theory. Sellars' theory of inductive inference is basically pragmatic. Inductive arguments, as Sellars conceives of them, have conclusions affirming that it is epistemically reasonable to accept some specified statement. The reasonableness of accepting such a statement is explicated in terms of the effectiveness of such acceptance for achieving epistemic objectives relevant to the kind of statement in question. In the case of laws and theories, the goal is to increase explanatory coherence and simplicity,

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while in the case of singular statements it is to insure that a regulated proportion of the statements accepted will be true. These remarks suggest a similarity between Sellars, who conceives of rational acceptance in terms of such epistemic goals, and another group of philosophers, myself included, who conceive of reasonable acceptance in terms of maximizing expected epistemic utility. We shall return to the comparison below. Here we note that Sellars' theory does not rest on the assumption that we can provide any quantitative analysis of our epistemic goals as utilities, nor does it rest on the assumption that we can provide a quantitative analysis of the probability of all statements whose acceptance we consider, while both of these assumptions are essential to theories of reasonable belief based on expected epistemic utility. Sellars' theory is compatible with such theories but does not presuppose them. Thus one source of interest in his theory results from this nonquantitative feature of the analysis combined with a precisely formulated rule of acceptance.

Another feature of Sellars' theory is his analysis of rational acceptance in terms of practical deductive arguments whose conclusions are statements expressing an intention to accept a statement. The question of whether or not to accept a statement p at time t is answered in terms of whether accepting p at t will achieve the relevant epistemic objective. Let us designate this objective by the letter 0. Now to say that it is reasonable to accept p at t, where the subscript indicates the goal determining the reasonableness of acceptance, is to say that there is some good line of reasoning of the following form:

I shall promote 0. Promoting 0 implies accepting p at t if I am in C at t. I am in C at t. So I shall accept p at t.

This is the formal skeleton of Sellars' analysis. It is reasonable to accept a statement for some epistemic objective if and only if there is some good practical deductive argument proceeding from a first premiss stating one's intention to achieve that objective to a conclusion stating one's intention to accept the statement.

Sellars equates the reasonableness of accepting a statement to promote an epistemic goal with the qualitative probability of the statement. For Sellars, the notion of probability is therefore also pragmatic in the sense that it depends on how well a statement furthers some goal. Thus, just as 'reasonable' requires a subscript



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to indicate the goal that makes it reasonable to accept the statement, so the term 'probable' requires a subscript to indicate the goal that makes the statement probable. (I shall, however, omit sub- scripts whenever the objective is obvious from the context.) If 0 is the goal in question, then it is reasonable0 to accept that p if and only if it is probable0 that p. Thus we can speak of the probability or the reasonableness of accepting statements inter- changeably. This account of reasonable acceptance is pragmatic in the sense that such acceptance is the means of obtaining a chosen end. However, the ends in question are those of epistemic rationality concerned with explanation and truth rather than more directly practical concerns. Ultimately, Sellars contends that what it is epistemically reasonable to accept for epistemic ends, it is categorically reasonable to accept as well, because promoting such epistemic ends promotes the general welfare.

In Sellars' theory, the goals appropriate to the acceptance of statements depend on the kind of statements in question. The goals appropriate to accepting theories differs from those appropriate to accepting nomological statements, and the goals appropriate to these differ in turn from those appropriate to accepting singular and other nonlawlike statements. Each of the goals of acceptance is guided by a supervening objective which is to obtain a system of accepted statements in which theories and lawlike statements provide a maximum of explanatory coherence.

Epistemic Goals: The Acceptance of Theories. With this formal scheme before us, let us now consider what Sellars takes to be the relevant goals of rational acceptance. The goal of acceptance for theories, Sellars says, is to accept that theory T which is the simplest available framework which generates new testable lawlike statements, generates acceptable approximations of nomologically probable lawlike statements, and generates no falsified lawlike statements.2 This account of the reasonable acceptance of theories raises some questions. Simplicity is complex. There is ontological, conceptual, and postulational simplicity. One form of simplicity may sometimes be purchased at the cost of another. Moreover, the comprehensiveness of a theory is as important as simplicity in deciding whether to accept the theory. One theory is more comprehensive than another in the sense I have in mind if it explains and predicts in a wider domain. Furthermore, coherence is also as important as simplicity, where one theory is more coherent than another if it systematically connects laws pertaining to more



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diverse domains. Simplicity, comprehension, and coherence are closely related and all demand explication. But again, one may be obtained at the expense of another. The concept of simplicity embodied in the objective of theoretical acceptance which Sellars articulates must therefore cover a multiplicity of potentially conflicting desiderata. The decision to accept one theory rather than others because it is the "simplest" is thus a complex choice based on a variety of the relevant features of theoretical alternatives. Consequently, what we take to be the simplest theoretical framework in the required sense will turn out to be that theoretical framework which, of all those available, is deemed most probable. Hence, I believe it is more promising to explicate simplicity in terms of probability rather than vice versa, though I agree with Sellars that the simplicity and probability of theories are closely linked.

However, while I agree that a theoretical framework satisfying the objective Sellars articulates is more probable than those with which it competes, I deny that such a theory is probable, that is, more probable than its denial. My reasoning assumes that the comparative concept of probability which Sellars employs, though nonmetrical, should be consistent with a metrical assignment of probability in that any theory that is probable (more probable than its denial) should be one to which one would assign a probability greater than 1/2 if one were to assign it a metrical probability. A theory satisfying the objective which Sellars specifies may be one that would have to be assigned a probability less than 1/2 if one were to assign a metrical probability to it. Suppose that we have five rival theories, and, though they are equally satisfactory in other ways and though there is little to choose between them on the basis of simplicity, one of the theories is slightly simpler than the others. If we also suppose that these competing theories are mutually exclusive in pairs, then, though we might say that the simplest theory is more probable than any of the others, we should not say that it is probable. For, since all the theories are mutually exclusive in pairs, if we were to assign metrical probabilities to the theories, the sum of the probabilities of the five theories could be no greater than unity. Consequently, if we were to assign a probability greater than 1/2 to the simplest theory, we would have to assign very much lower probabilities to the other theories, only 1/8 on the average, and that would be unwarranted on our assumption that the simplest theory was only very slightly superior to its competitors. The most probable of competing theories, if the




competition is very close, may be reasonable to accept, but it should not be considered probable, that is, more probable than 1/2 if a metrical probability were to be assigned. Consequently, though I would agree that a theory that is reasonable to accept is more probable than the other theories with which it competes, I would resist concluding that it is probable, or more probable than its denial.

This is not, of course, an important point of disagreement. Indeed, with my reservations concerning the complexity of simplicity, I would agree with Sellars that it is reasonable to accept a theory that is more probable than its competitors. However, in the case in which there is a set of two or more theories that are equally probable though more probable than any theories outside the set, and there is no single theory that is most probable, Sellars' theory leaves us in the dark as to what it is reasonable to accept. I shall later propose a theory telling us that it is reasonable to accept a disjunction of such maximally probable theories.

The Acceptance of Laws. Let us now consider Sellars' account of the probability and reasonable acceptance of universal and statistical lawlike statements. It is a central doctrine of his philosophy that lawlike statements are construed as principles of inference, that is, as affirming that one propositional function implies another. He calls these implications, P-implications. If it is a law that all As are B, Sellars treats this as the implication statement: that x is A P-implies that x is B. He argues that we may treat such implications as a special case of implications of the form: that K is a finite unexamined class of As P-implies that all K is B. For, if all examined As are known to be B, we need only accept the implication for unexamined As to reach the universal conclusion. A statistical lawlike statement, for example that n/m As are B, is interpreted as the implication: that K is a finite unexamined class of As P-implies that approximately n/rm K is B. Both forms of lawlike statements are explicated as principles allowing us to draw inferences about unexamined classes, even counterfactual inferences about what the proportion of Bs in a class would be if it were a class of unexamined As. On this account we conceive of a universal nomological statement as a limiting case of a statistical nomological in which 'all' replaces 'approximately n/m'.3

What sort of epistemic goal is promoted by the acceptance of such principles of P-implication? Again the answer is ex-



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planation. If our only goal were to restrict what we accept to empirically true statements, it would not be reasonable to accept such principles. But, if one considers the advantage of such principles from the standpoint of explanation, one can develop a good argument for accepting them. Suppose that n/m of the As we have observed are B. This fact of observation needs explanation. We can explain it if we accept a principle of inference that approximately n/m As are B. Hence, for the purposes of explanation it is reasonable to accept the P-implication: that K is an unexamined class of As P-implies that approximately n/m K are B, when n/m examined As are B. By accepting such a principle, I shall, as Sellars says, be able to draw inferences concerning the composition with respect to a given property of unexamined finite samples of a kind, x, in a way which also provides an explanatory account of the composition with respect to that property of the total examined sample of X.4 In short, the goal that makes it reasonable to accept lawlike statements is that of accepting principles of inference providing the simplest explanatory account of the evidence of observation. There is a good practical deductive argument from the intention to promote this goal and the premiss that n/m of all examined As are B to the intention to accept the principle of inference: that K is a finite unexamined class of As P-implies that approximately n/m K is B.

Sellars notes the objection that the acceptance of such P- implications can lead from a true premise to a false conclusion. If 3/4 of all examined As are B, then by the argument above, it is reasonable to accept the principle: that K is a finite unexamined class of As P-implies that approximately 3/4 are B. But, if I accept this principle and infer that 3/4 of some class K? are B, I may be wrong; it may turn out to be that only 1/4 of Ki is B. Sellars replies that one can never be directed by the rule of reasonable acceptance to accept a principle of inference one knows to be false at the time one accepts it.5 Once the members of Ki are examined, this becomes part of the examined rather than the unexamined part of A, and we may be required to revise the P-implications we accept in the light of such evidence. But this fails to prove that it was not reasonable to accept the P-implication we did accept under the former evidence of observation. The reason for accepting such P-implications is not to obtain empirical truth, but to be able to draw inferences concerning the unknown that explain what we have observed.

However, I believe that Sellars is mistaken when he says that




promoting the goal of reasonable acceptance in the manner he indicates "can never lead me to espouse a principle which I know to be false at the time of espousal."6 With a little reasoning we can know that it leads to just such espousal. Suppose that I have observed a large sample of class A, 250,000 members for example, and in this sample, 3/4 A are B. I then accept the principle of inference: that Ki is a finite unexamined class of As P-implies that approximately 3/4 Ki are B. Now consider a class U of 1,000,000 unexamined members of A. The principle of inference just listed yields the conclusion that approximately 3/4 U are B. There are 1,000,000!/750,000!(1,000,000 - 750,000)! different randomly selected classes of unexamined members of U equal in size to the observed sample. Again, the principle of inference listed above implies that each of these classes Ki is such that approximately 3/4 Ki are B. But from the conclusion that 3/4 U are B, it follows that for some class Ki containing 250,000 of the unexamined As in U, it will be false that approximately 3/4 Ki are B. This follows from simple arithmetic. If approximately 3/4 U are B, then approximately 250,000 As in U are not B. A subclass K1 containing all those As will be such that approximately 0 Ki are B. Therefore, if we derive all the conclusions that the P-implication formulated above allows, we can know that some of those conclusions are false, and, hence, that the principle of inference leads from true premisses to false conclusions.

I am not supposing that one can know which of the conclusions one derives from the principle are false. Without examining subclasses of U one cannot know which subclass Ki of 250,000 members of U is such that approximately 0 Ki are B. What one can know is that the conclusion that approximately 3/4 U are B is inconsistent with the set of conclusions one can derive from the principle concerning subclasses Ki of U containing 250,000 members. One cannot be correct about the conclusion one draws about U and also be correct about the conclusions one draws about each such subclass. This proves that the P-implication will lead from a true premiss to a false conclusion in some inference, even if one does not know which one. Moreover, since P-implications are supposed to be rules of inference determining the meaning of terms they connect, and, hence, nonformal entailments, it would seem unreasonable to accept such a P-implication knowing that it leads from true premisses to false conclusions.

Sellars might meet the preceding objection as follows. He says that the degree of approximation referred to in the principle should



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be determined by the size of the unexamined sample. So, when we say that approximately 3/4 K? are B, we mean that the percentage of B in K? is in the interval of 3/4 plus or minus m/n, where the value of m/n depends on the size of Ki. Therefore, Sellars could avoid the foregoing result by requiring suitable adjustments in the value of m/n.

However, this strategy would greatly weaken the explanatory power of the conclusions we could draw concerning unexamined samples of the same size as the examined sample. To return to the preceding example, if we were to accept the conclusion that between 3/4 plus 1/10 and 3/4 minus 1/10 of U are B, then to avoid the inconsistency between that conclusion and the conclusions we could draw concerning unexamined samples Ki of U equal in size to the examined sample, we would have to weaken such conclusions to the point of saying only that between 3/4 plus 1/4 and 3/4 minus 7/20 of Ki are B. But what sort of explanatory account would we have given of the fact that 3/4 of the observed sample of As are B by saying that in all samples that size at least 2/5 of the As are B ? It would seem that Sellars must choose between making the degree of approximation so indefinite as to render the principles virtually useless from the standpoint of explaining the composition of the examined sample and making it so precise that the principles will generate an inconsistent set of conclusions. It is my conjecture that he would prefer to accept the second alternative because he proposes to treat reasonable acceptance as nonconjunctive. Sellars' treatment of singular statements raises the same problem of consistency, and there Sellars explicitly appeals to the nonconjunctivity of reasonable acceptance. Hence, we shall postpone our consideration of the problem and the merits of the appeal to nonconjunctivity as a reply until we have examined what Sellars says about the acceptance of singular statements.

The Acceptance of Singular Statements. Sellars' account of the reasonable acceptance of singular statements, statements of the form: a, is B, where ai is an observable entity, 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 membership of ai in B, and we know that a majority of




the members of K are B.7 If we know that ai is a member of such a class, 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. 8

There are a number of objections of detail. In the first place, the restriction concerning class K is too restrictive. Sellars required that membership in K be such that nothing else is known relevant to the question of whether or not ai is a B. This means that ai cannot be a member, or at least not a random member, of any other class C, where we know the percentage of C that is B. For, such knowledge would be relevant to whether ai is a B. We hardly ever lack such a subclass. Consider any large class K where we know the percentage of B. Now consider a proper subclass of K from which one member of K other than ai is deleted. Class C has approximately the same percentage of B as K does, and ai may be a random member of C as well as a random member of K. Hence, if we require, as Sellars does, that "nothing else is known of an individual ai relevant to the question of whether or not it is B other than that it is a member of K,"9 this condition is rarely satisfied. Hence, the method would be almost useless for the purpose of accepting singular statements.

I do not suggest that this problem is insoluble. However, the objection pinpoints the need for some less restrictive choice of the class K which makes it reasonable to accept a singular statement. The need for this restriction shows that there is more than objective relative frequencies involved in determining what singular statements it is reasonable to accept. There is the choice of class K. Our choice will be guided by our goal of being correct more often than incorrect about the singular statements we accept. But this choice is a matter of intuition. Such subjectivity infiltrates inductive reasoning one way or another. This suggests that rational acceptance rests directly on the subjective probabilities of obtaining correct answers. I shall pursue this suggestion subsequently.

Let us waive these difficulties for the moment and consider the results of applying the method Sellars espouses assuming that the relevance condition can be reformulated in some satisfactory way. One important result, from a critical point of view, is that the set of singular statements it is reasonable to accept on Sellars' theory is known to contain false singular statements.



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Suppose we have some large finite class K having n members, we know that 3/4 K are B, K satisfies the relevance condition, and, hence, for each ai (a,, a2, and so forth to an), we accept the statement that ai 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 nonconjunctive.10 However, if we know that 3/4 K are B, that a1, a2, and so forth to an are the members of K, and consequently accept the statements 'a1 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 a1, 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.

This foregoing result does not imply that any single statement that it is reasonable to accept on Sellars' theory is logically inconsistent. By denying the conjunctivity of reasonable acceptance, Sellars can escape that consequence. But the set of statements it is reasonable to accept for various epistemic purposes is logically inconsistent. This inconsistency cannot be avoided by denying the conjunctivity of reasonable acceptance because it does not presuppose that principle. Moreover, within standard deductive logic, the deductive consequences of any finite set of statements are the same as the deductive consequences of a conjunction of those statements. Hence, once we apply deductive logic to the sets of statements which, according to Sellars, are reasonably accepted, we can deduce a contradiction. We do not need to assume this principle of the conjunctivity of reasonable acceptance to derive the contradiction because the application of deductive logic to the sets of reasonably accepted statements suffices for the deriva- tion.

The preceding objection requires some qualification. I am not claiming that it is always unreasonable to accept an inconsistent set of statements. It may not be unreasonable for a man to accept an inconsistent set of statements because it may be reasonable, though incorrect, for him to think that the set is consistent. I am only claiming that it is unreasonable to accept a set of statements one knows to be inconsistent when such inconsistency defeats




the very epistemic objectives one is seeking to promote in accepting those statements. That is precisely the problem here. Sellars is concerned to promote the objectives of truth and explanatory coherence within the system of statements one accepts. But neither the interest in truth nor the interest in explanatory coherence is adequately served by the theory of rational acceptance Sellars articulates.

Consider the matter of explanatory coherence. From the standpoint of explanation, reasonably accepted general statements concerning the composition of populations should explain and be consistent with reasonably accepted statements concerning the composition of samples and reasonably accepted singular statements concerning members of the population. It is clearly Sellars' intent to construct just such a system of accepted statements, and the aim is entirely worthwhile. But he achieves less than he intends. As we noted, the principles of inference which, according to Sellars, it is reasonable to accept as nomologicals lead from a consistent set of premisses concerning unexamined classes of a population to an inconsistent set of conclusions about the composition of unexamined samples of the population.

Now we note that the set of those singular statements which it is reasonable to accept according to Sellars is inconsistent with the general statement concerning the composition of the population on which the acceptance of the singular statements is based. We begin with statement that 3/4 K are B and wind up accepting a set of statements that can only be true if all of K is B. Note that I am not objecting to the idea that the question-is ai B ?-might reasonably be answered in the affirmative when one's only concern is to answer that question or even, as Sellars suggests, to answer all questions of that form in such a way that a regulated proportion of one's answers are correct. But when deciding what statements it is reasonable to accept in order to obtain an overall system of statements with a maximum of explanatory coherence, one cannot decide on the basis of those limited objectives. To do so would fail to promote the explanatory coherence of the system.

In summary, if one were to follow Sellars' methods for the reasonable acceptance of nomologicals and singular statements, the set of singular statements one would accept and the set of statements about samples inferred from true premisses by accepted nomologicals would refute exactly those general statements about the composition of populations intended to explain them. Some- what different methods of reasonable acceptance are required to



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promote explanatory coherence within the overall set of reasonably accepted statements. I shall propose a modification of Sellars' system that I believe promotes that end more effectively, but first let us consider the matter of promoting truth.

Sellars avers that the interests of truth are served by his method for the reasonable acceptance of singular statements, while we have noted that according to his method the set of singular statements we may reasonably accept is inconsistent with the general statements of proportion on which such acceptance is based. What Sellars avers is not inconsistent with what we note. From the inconsistency, it follows only that not all the statements we reasonably accept can be true, but Sellars' method does guar- antee that a majority of the singular statements we reasonably accept are true. However, one suggestion that Sellars makes concerning truth leads to paradox. Sellars points out that it may be reasonable for a man at a given time to accept a statement that is false, and, hence, his actual reasonable acceptance of that statement cannot be equated with the truth of the statement. This shows that truth cannot be equated with actual reasonable acceptance. Sellars then raises the question of whether we might be prepared to endorse something like the equation of truth with ideal reasonable acceptance and say that a statement is true if and only if it is ideally reasonable to accept it.ll He does not repudiate this suggestion. Let us call this theory of truth the epistemic theory of truth.

The epistemic theory of truth combined with the assumption that Sellars' methods for reasonable acceptance are rules for ideal reasonable acceptance is what leads to paradox. If 3/4 K are B and a,, a2, and so forth through an are the members of B, then it follows that the set C of statements whose members are 'a, is B', 'a2 is B', and so forth to 'an is B' is such that 1/4 of its members are false. A method by which each of those statements would be ideally reasonably accepted, assuming K to be appro- priately chosen, would lead via the epistemic theory of truth to the conclusion that each of the statements is true. Hence, we have the contradiction that set C is such that 1/4 of its members are false and is also such that each of its members is true. Thus 1/4 of those statements would be both true and false.

Of course, Sellars may easily escape this paradox by denying that his methods of reasonable acceptance are methods of ideal reasonable acceptance, and I do not suggest the paradox is a serious objection to his system. However, there is a moral to the




paradox. For, if actual reasonable acceptance aims at the ideal, and if ideal reasonable acceptance is truth, then one's methods of actual reasonable acceptance should not render the attainment of the ideal logically impossible. In short, the methods of reasonable acceptance should at least allow for the logical possibility that the statements which it is actually reasonable to accept are also ones which it would be ideally reasonable to accept and, therefore, true. Thus, the epistemic theory of truth provides another argument for concluding that the set of statements we reasonably accept should be logically consistent. Since Sellars does not explicitly endorse the epistemic theory of truth, this argument is not as important as the previous one concerning explanatory coherence. For, though we may doubt that Sellars actually intends to embrace the epistemic theory of truth, there is no doubt that he does affirm the principle that reasonable acceptance should aim at promoting the maximum of explanatory coherence within our system of reasonably accepted statements.

Reasonable Acceptance and Competition Sets. The foregoing objections to Sellars' system arise from one central problem. Sellars' methods of reasonable acceptance are aimed at the acceptance of the best answers to specific questions we raise in seeking to promote the objectives of truth and explanation. Consequently, a statement only competes for acceptance with the set of answers to the question raised. But a set of answers to such specific questions fails to provide a coherent system of accepted statements. The conception of competition is too narrow. For example, in the case of singular statements, the specific question is: Is a* B ? An affirmative answer competes only with a negative one, and if it is more probable than a negative one, Sellars' method tells us to accept the affirmative answer. If our only interest were in following a policy that would yield a set of accepted singular statements with more true members than false ones, this method would be unexceptionable. But if we are concerned to promote the explanatory coherence of the overall system of reasonably accepted statements, then we must construe competition more broadly in order to articulate the more general question of how to best promote that systematic objective.

We may accomplish this within the general framework that Sellars has provided. We may agree that the comparative probability of a statement is determined by the epistemic goals and objectives it serves. We consider one theoretical framework more



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probable than another, one statement of proportion more probable than another, and a singular statement more probable than its denial because it facilitates our epistemic objectives. Moreover, different kinds of statements fulfill different objectives, as Sellars insists. However, we do not, on that account, need to subscript probability to indicate the objective promoted. By so doing, we splinter the concept needlessly. Instead, we may think of these various objectives as determining one general conception of comparative probability. By so doing, we gain an essential advantage, to wit, the possibility of comparing the probabilities of statements of different kinds. This advantage is essential because of the sort of conflict that can arise between statements of different kinds, for example, statements of proportion and singular statements. If we are to avoid such conflict within the set of statements which we reasonably accept, we shall be forced to choose between them. To make that decision, we must be able to compare the probabilities of such statements.

We shall now propose a solution to the problem that we have raised, assuming that we can compare the probabilities of statements that may so conflict and agreeing with Sellars that such probabilities are determined by the epistemological objectives these statements serve. We cannot elaborate this conception of probability further here except to suggest that such generic probabilities are based on the objectives and purposes of a somewhat idealized community of scientific investigators. This conception is, I believe, consistent with Sellars' general outlook. Given this assumption and one additional modification of Sellars' system, we can provide a method of reasonable acceptance that yields a coherent and consistent set of reasonably accepted statements.

Sellars' methods of reasonable acceptance tell us to accept that statement out of a set of competing statements which best promotes some goal. We claimed above that Sellars construes the membership of such competition sets too narrowly. We need some method for the selection of competition sets that makes the membership of such sets broader than Sellars allows, but not so broad as to make every statement compete with totally independent statements.

We can achieve our objective by requiring that competition sets be strongly independent of each other. Each set should rep- resent an independent arena of competition for reasonable acceptance. To insure that competition sets have this kind of independence, let us define the membership of a competition set




in terms of a partition of statements, that is, a set of statements which are logically exhaustive as a set and logically disjoint in pairs relative to the observational evidence.'2 A competition set will be defined by a partition and truth functional combinations of members of the defining partition. Specifying a competition set in terms of a defining partition provides a simple way of formulating the desired requirement of independence.

The requirement is as follows: the total set of competition sets selected must be such that any set constructed by taking one member from the defining partition of each competition set together with a statement of the evidence will be a logically consistent set. If we combine this restriction with a rule for the reasonable acceptance of statements within a competition set insuring that the set of statements accepted from such a set are logically consistent with each other and the evidence, then the entire system of statements reasonably accepted from all competition sets will be logically consistent with each other and the evidence. This follows because the members of a defining partition of a competition set are the strongest consistent statements of a competition set. Consequently, any strongest set of consistent statements that could be accepted from a competition set would be equivalent to such a member relative to the evidence. Hence, any set of consistent sets reasonably accepted from competition sets satisfying the restriction formulated above will itself be consistent and consistent with the evidence.

A Comparative Probability Rule. Adopting the foregoing restriction, we shall now formulate a rule of reasonable acceptance of members of such a restricted competition set based on our conception of comparative probability. Within a competition set, we assume that we can compare probabilities. For any two statements, we can ascertain whether one is more, less, or equally probable to another on the evidence. Given such a competition set and these comparisons, what statements is it reasonable to accept ? For the sake of coherence, the set of statements reasonably accepted from the competition set must be logically consistent. Suppose we have a set of statements from the competition set that is logically inconsistent, but no proper subset is logically inconsistent. Such a set of statements we shall say is minimally inconsistent. Any such set of minimally inconsistent statements is such that not all of the members can be reasonably accepted, and, indeed, for any given statement, if it is reasonable to accept that statement, then there



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must be at least one other statement in any minimally inconsistent set to which it belongs which it is not reasonable to accept. If it is not reasonable to accept such a statement, then it should be less probable than those which it is reasonable to accept.

From these considerations we can obtain the following rule of reasonable acceptance: It is reasonable to accept a statement S from a competition set C if and only if either (i) S is such that for any minimally inconsistent set M of members of C to which S belongs, there is at least one member of M that is less probable on the evidence than S, or (ii) S is a logical consequence in C of a set of statements satisfying (i).13 This rule insures that the set of statements which it is reasonable to accept from a competition set will be logically consistent. For, if such a set of statements were inconsistent, then it would have a minimally inconsistent subset of two or more members each of which would, by the rule, be less probable on the evidence than some other member. But, since the set would be finite and would have at least one member that was not more probable than any other, this is impossible. Hence, the set of reasonably accepted statements from a competition set is logically consistent with the evidence and so, therefore, is the set of all statements reasonably accepted from all competition sets meeting our restriction.

The consequences of adopting the rule just articulated may be expressed most economically in terms of the members of a defining partition of a competition set. The rule tells us that if there is one member of the defining partition that is more probable on the evidence than any other member of the partition, then it is reasonable to accept that member and all statements in the competition set that are logical consequences of that member. If there is a set of two or more members of the defining partition that are equally probable on the evidence but more probable than any members of the partition not in that set, then it is reasonable to accept a disjunction of those members and all statements in the competition set that are logical consequences of that disjunction. If the members of the partition are theories, it is reasonable to accept the most probable, or if there is a tie, then it is reasonable to accept a disjunction of those tied. Similarly for partitions of nomologicals. When we come back to the question of whether it is reasonable to accept singular statements, we find in the example considered earlier that if it is more probable on the observational evidence that 3/4 K are B than it is that some unexamined member ai of K is BA and it is equally probable that each unexamined member is




B, then it would not be reasonable to accept the statement that ai is B. Of course, if one must answer the question: Is ai B? then it would be more reasonable to answer affirmatively rather than negatively. But when it is one's purpose to construct a system of reasonably accepted statements with a maximum of explanatory coherence, then it is not reasonable to accept such statements.

Maximizing Epistemic Utility. Moreover, our rule of reasonable acceptance may be interpreted as a decision theoretic principle telling us to maximize certain epistemic utilities. To obtain this interpretation, we must make a further assumption, namely, that our comparative probabilities are consistent with quantitative probabilities. What I mean is this: there must be some quantitative probability functor, P(S, E), equal to P(S & E)/P(E) and otherwise conforming to the calculus of probability, such that if H is more probable than K on E in terms of our comparative probabilities, then P(H, E) is greater than P(K, E). If this condition is satisfied, then we shall say that the probability functor in question is consistent with our comparative probabilities. There may of course be an infinite set of different probability functors that are consistent with our comparative probabilities in this way. Moreover, we need not assume that any one probability functor is correct, or even that there is any way of choosing among them.

We shall now show that for any arbitrary probability functor consistent with our comparative probabilities, our rule of reasonable acceptance is a precept to maximize certain epistemic utilities. We shall employ a probability functor that may be thought of as any arbitrary probability functor consistent with our comparative probabilities. We require a probability functor to give a decision theoretic formulation. On this approach, a reasonable decision to accept a hypothesis is based on the probability that the hypothesis is true and the probability that it is false as well as on the utility of accepting the hypothesis when it is true and the utility of accepting it when it is false. Letting "Ut(H)" mean "the utility of accepting H when H is true" and "Uf(H)" mean "the utility of accepting H when H is false", we define "E(H, E)", meaning "the expected utility of accepting H on evidence E", as follows: E(H, E) = P(H, E)Ut(H) + P(-H, E)Uf(H). To obtain the rule we seek, we adopt the following definitions of utilities: Ut(H)

P(-H)/P(H) and Uf(H) - -1. A full defense of these definitions would take us too far afield.14

The definition of the utility of accepting a false statement tells us

2



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that the loss resulting from accepting a statement that is false is the same no matter what statement we accept. It is just the constant loss of being wrong when we might have been right instead. We can recoup our loss by rejecting the statement. The definition of the utility of accepting a statement when it is true tells us that if what we accept is true, then our gain is to be measured in terms of the informational content of the statement we accept. One familiar measure of the content of H is P(-H), and P(-H)/P(H) is a quantity that increases greatly as content increases and decreases greatly as content decreases.

By employing these equalities (together with the equalities P(- H) 1 -P(H) and P(- H, E) = 1 -P(H, E)) and substituting in our equation, we obtain through simple algebra the following equality: E(H, E) = [P(H, E)/P(H)] -1. The right hand side of this equation is a quotient measure of the positive relevance of the evidence E to the hypothesis H, or power of E to confirm H. Moreover, [P(H, E)/P(H)] -1 = [P(E/H)/P(E)]- 1. The right hand side of this equation is a measure of the positive relevance of H to E, or the power of H to explain E. Hence, a rule to accept a hypothesis having a maximum of expected utility would result in accepting hypotheses whose probabilities of being true are most enhanced by the evidence and that are the most useful from the standpoint of explanation.

It is a further consequence of this definition of expected utility that one or more members of the defining partition of a competition set will have an expected utility that is maximal. Thus, every statement in the competition set whose expected utility is maximal will be logically equivalent to a member of the partition whose expected utility is maximal or to a disjunction of such members whose expected utility will also be maximal. Therefore, we can formulate a rule of reasonable acceptance that is also a rule to maximize expected utility as follows: If there is one member of a defining partition whose expected utility is maximal, then it is reasonable to accept that member and all statements in the competition set that are logical consequences of it. If there is more than one member of the partition that is maximal, then it is reasonable to accept a disjunction of those members (which will also be maximal) and all statements in the competition set that are logical consequences of that disjunction. This rule will yield the same results as the one formulated above whenever the probability functor is symmetric, that is, when for any two members of the defining partition, Hi and Hj, P(Hi) = P(Hj). When such




probabilities are equal, the comparative expected utilities of the members of the defining partition will be solely determined by the comparative probabilities of the members on the evidence. A member of the partition that is more probable on the evidence will also have a higher expected utility. Hence, any symmetric probability functor consistent with our comparative probabilities will yield the same result. The utilities can also be defined in such a way as to yield equivalent results even when the symmetric condition is not met, but then the connection between expected utility and positive relevance is lost.15 On either definition, what has maximal expected utility, and hence what it is reasonable to accept, is determined by the comparative probabilities.

The preceding results show how Sellars' approach to reasonable acceptance can be modified so as to serve the goal of promoting explanatory coherence within our system of reasonably accepted statements and to insure that reasonably accepted statements have a maximum of expected epistemic utility. The expected utility thus maximized is a measure of the power of the evidence to confirm the statements we accept as well as a measure of the power of the statements accepted to explain the evidence. This modification is very much in line with a good deal of what Sellars has proposed. I differ from him in employing a somewhat more general conception of probability and in construing competition in a broader and more abstract manner. By so doing, we lose specificity. Sellars delineates much more specifically than I do which statements compete for reasonable acceptance. The loss of specificity is a genuine disadvantage. On the other hand, to obtain coherence and consistency within our system of reasonably accepted statements, a more abstract conception of competition seems to be required.

What I have proposed is built on Sellars' system in three fundamental ways. First, the fundamental objective of promoting explanatory coherence in systems of reasonably accepted statements is taken directly from Sellars. Second, Sellars' account of comparative probabilities in terms of the epistemic goals of promoting explanation and truth is assumed as the basis of reasonable acceptance. Third, and perhaps most important, the rule of reasonable acceptance I propose is a precept to accept that statement which, of all the competing alternatives, is more probable in terms of these goals and objectives. Thus, the solution I have proposed to the problems I have raised is motivated by the objectives Sellars has articulated and remains within the general



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framework Sellars has created. However, I shall conclude by raising some problems that may reflect a more radical departure from that scheme.

The Role of Evidence. In Sellars' methodology, nomological statements are accepted because they accord with the observational evidence, and theories are accepted because they generate approximations to such nomologicals and do not generate any nomological statements falsified by the observational evidence. Consequently, laws and theories must always be made to fit the observation evidence. However, there is some stress within Sellars' system on this point. For, he does say that even observation statements may be rejected to increase the explanatory coherence of the system of statements we accept; he only insists that such alterations be kept to a minimum to preserve the ties between the linguistic and the nonlinguistic embodied in the role of observation statements.16 The problem is that Sellars' methodology of reasonable acceptance provides no mechanism for the rejection of observational evidence for the benefit of the overall system.

If we are to allow for the rejection of observation statements for the sake of the greater explanatory coherence of the system, we must expand the methodology of reasonable acceptance so far laid down to include methods for the reasonable acceptance and rejection of statements as evidence. To facilitate this objective, I think we should part with common sense and become sceptics. It is part of our common sense conception of knowledge that if we know something, then, strictly speaking, there is no chance that it is false. So, if we wish to deny that any empirical statement is immune to rejection for the benefit of the whole, we must admit that, strictly speaking, there is some chance that any such statement is false.17 They are evidence, of course, but statements of evidence are probable, not certain. Sellars has espoused a similar position.'8

Consequently, we need a rule for the reasonable acceptance of statements as evidence to be added to those rules employed for the reasonable acceptance of hypotheses by induction from the evidence. Elsewhere I have formulated a rule for acceptance of statements as evidence based on comparative prior probabilities.'9 These probabilities may, like the conditional comparative probabilities considered above, be determined by how effectively the acceptance of those statements would promote the goals of truth and explanation. As these probabilities shift in response to experience and ratiocination, a statement reasonably accepted




as evidence may be subsequently rejected in favor of some other statement that has become comparatively more probable. The rule may also be so formulated as a directive to accept as evidence statements having certain positive and maximal expected utilities, where the utilities are those appropriate to evidence selection.20 Such a proposal is, I think, a needed supplement to the methodology Sellars proposes.

Reasonable Acceptance and Morality. My final comment on Sellars' views concerns a point that is more peripheral to Sellars' epistemology; it concerns the question of when it is categorically reasonable to accept a statement. Sellars notes that his approach to reasonable acceptance yields the conclusion that it is reasonable to accept statements relative to certain epistemic goals. But this leaves open the possibility that one might, by rejecting those ends, repudiate the claim that it is reasonable to accept the statements in question. In response, Sellars says that the intention to promote these epistemic goals is "the intention as a member of a community to promote the total welfare of that community."21 Consequently, the pursuit of those goals is categorically reasonable, indeed, a moral obligation.

These are words of inspiration, but they raise an immediate objection. Sellars' claim that pursuing certain epistemic goals, even that of truth, is "a necessary condition of securing the common good," is clearly an inductive conclusion.22 It may be reasonable to accept that conclusion, as Sellars avers, but whether it is reasonable to accept that statement depends precisely on the goals of such acceptance. To assume that the relevant goals are the epistemic goals in question would be to argue in a very small circle indeed.

Moreover, other thinkers have denied that it is reasonable to accept those statements that promote the epistemic goals Sellars mentions, because they have different beliefs about what will promote the total welfare of the community. Theists like Kierkegaard have thought that the promotion of such epistemic goals would keep one from taking the leap of faith and the attainment of eternal beatitude.23 Neofreudians like Brown think that the promotion of those epistemic goals contributes to the dominance of reason over the id, thus depriving us of the gratification of polymorphous perversity.24 So Kierkegaard and Brown believe that we shall only secure the common good by repudiating the very goals Sellars says we are morally obligated to pursue in order to



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secure the common good. To argue against such philosophers by assuming that it is reasonable to accept the conclusion that promoting these epistemic goals will secure the common good is to beg the question by assuming that it is reasonable to accept conclusions that promote those very goals.

Without demeaning the advantages of eternal beatitude and polymorphous perversity, I side with the goals that Sellars articulates. But those who think that the pursuit of truth and explanation interfere with the attainment of more important objectives are, I believe, guilty of neither intellectual bewitchment nor moral transgression. They have different fundamental prefer- ences. My interest in the pursuit of truth and explanation is, like my interest in Sellars' philosophy, motivated by the illuminating brilliance of the systematic results. I agree with Sellars that such goals serve the common good, but I find no dialectically satisfying argument for that conclusion.

NOTES

1 Wilfrid Sellars' views on induction and rational acceptance are primarily contained in "Induction as Vindication," Philosophy of Science 31 (1964): 197-231, and in "Are There Non-Deductive Logics ?", in Essays in Honor of Carl G. Hempel, N. Rescher and other eds. (Dordrecht: Reidel, 1970): 83-103. Further elaboration of his ideas is to be found in "Counterfactuals, Dispositions, and Causal Modal- ities," esp. Section IV, in Minnesota Studies in the Philosophy of Science, Vol. II, H. Feigl, M. Scriven, and G. Maxwell, eds. (Minneapolis: University of Minnesota Press, 1957): 285-303; "Scientific Realism or Irenic Instrumentalism," esp. Section VII, in Boston Studies in the Philosophy of Science, Vol. II, R. Cohen and M. Wartofsky, eds., (New York: Humanities Press, 1965): 195-204; and in "Some Reflections on Language Games," esp. the section on Induction, in Sellars' Science, Perception, and Reality (New York: Humanities Press, 1963): 352-358. I reviewed the latter book in The Journal of Philosophy 63 (1966): 266-277.

Research for this article was supported by a grant from the National Science Foundation.

2 "Induction as Vindication," p. 209. 3 Ibid., pp. 212-219. 4Ibid., p. 215. 5Ibid., p. 219. 6 Ibid. 7Ibid., p. 214. 8 Ibid., pp. 220-224. "Are There Non-Deductive Logics?", pp. 88-91. 9 "Induction," p. 223. I have changed the notation of the variables. 10"Induction," p. 222. 11 "Non-Deductive Logics," p. 96. 12 A partition may be thought of as a set of statements each of which is con-

sistent with the evidence and none of which is entailed by the evidence such that the evidence entails that at least one but not two of the statements is true.

13 This rule is further elaborated in my "Induction, Rational Acceptance, and Minimally Inconsistent Sets," forthcoming in Minnesota Studies in the Phi- losophy of Science. (Available from the author.)



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14 The defense is given in my "Belief and Error," forthcoming in a volume edited by E. Klemke and M. Gram to be published by Northwestern University Press. (Available from the author.)

15 Such definitions are given in my "Induction: A Consistent Gamble," THIS JOURNAL, 3 (1969): 285-97, and in "Induction, Rational Acceptance, and Minimally Inconsistent Sets." Compare also the definitions of utility in Carl G. Hempel, "Deductive-Nomological vs. Statistical Explanation," in H. Feigl and G. Maxwell (eds.), Minnesota Studies in the Philosophy of Science, Vol. III (Minneapolis: University of Minnesota Press, 1962): 98-169; Jaakko Hintikka and J. Pietarinen, "Semantic Information and Inductive Logic," in Aspects of Inductive Logic, J. Hintikka and P. Suppes (eds.) (Amsterdam: North-Holland, 1966): 96-112; Risto Hilpinen, Rules of Acceptance and Inductive Logic, Acta Philosophica Fennica, Vol. 22 (Amsterdam: North Holland, 1968); and Isaac Levi, Gambling with Truth (New York: Knopf, 1967).

16 Science, Perception, and Reality, p. 356. 17 I defend this thesis in "Scepticism and Conceptual Change," forthcoming

in a volume edited by R. Chisholm and R. Swartz. (Available from the author.) 18 Science, Perception, and Reality, p. 334, and in conversation. 19 Cf. Keith Lehrer, "Induction and Conceptual Change," Synthese 23 (1971):

206-225. 20 I show this in "Evidence and Conceptual Change," forthcoming in Phi-

losophia and in "Evidence, Meaning and Conceptual Change," forthcoming in a volume edited by G. Pearce to be published by Reidel. (Available from the author.)

21 "Non-Deductive Logics," pp. 102-3. Sellars discusses categorical reasonableness in Science andMetaphysics (NewYork: Humanities Press, 1968): 213-222.

22 "Non-Deductive Logics," p. 103. 23 Soren Kierkegaard, A Kierkegaard Anthology, Robert Bretall, ed. (New

York: Modern Library, 1936), "The Task of Becoming Subjective," pp. 207-208. 24 N. 0. Brown, Life Against Death (New York: Vintage Books, 1959): 307-322.

Sellars' Ontology of Categories MURRAY KITELEY

SMITH COLLEGE

"Category," said H. W. Fowler, "should be used by no-one who is not prepared to state 1) that he does not mean class, and 2) that he knows the difference between the two." (Modern English Usage.) I am sure that Fowler did not intend to rob philosophers of this word, that his animus was directed rather at those who use it as an elegant variant of 'class'. Nonetheless, conscientious ob- servance of the rule of his prohibition would eliminate this old technicality from the professional vocabulary of the most confident



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