De Principiis Non Disputandum . . .Herbert Feigl
Published in Philosophical Analysis, ed. Max Black (Cornell University Press, 1950).
Justitication involving appeal to principles of formal logic.
Justification or criticism of the processes or the results of reasoning may involve, inter alia, questions of meaningfulness, of truth (or of reliability), of consistency, and of formal correctness (or conclusiveness). We shall concentrate on the two last mentioned criteria in the present section.
In appraising the correctness of a deductive argument we confront it with the rules of deductive logic. Conformity with these rules establishes the correctness, violation establishes the incorrectness of our reasoning. In traditional logic we may prove the legitimacy or expose the illegitimacy of some argument by reference to the rules of the syllogism. In the more generalized disciplines of modern logic a much greater wealth of forms and standards becomes available.
A specific deductive argument such as a valid syllogism may then be justified by reference to the well-known rules of the syllogism. And these rules in turn may be justified by reference to definitions and more fundamental principles such as the dictum de omni et nullo or (in modern logic) the rules of substitution and inference. Here the logician qua logician usually rests his case. But if he is philosophically curious in regard to the justification or justifiability of those basic rules of formal deduction, he will involve himself in peculiar perplexities. If he assumes that the laws of logic are the most general laws of nature, he ascribes a factual content to them that, no matter how thin, would require inductive justification. But inductive justification, while irreducible to deductive justification, presupposes the rules of deductive logic and is therefore impossible without reliance upon them. It may be urged that those most general laws of the universe are known by a priori intuition and, thus being self-evident, are neither in need nor capable of validation. This reply, however, is unacceptable for at least three reasons: The difficulties (Kant's heroic efforts not withstanding) of accounting for the possibility of synthetic a priori knowledge are notoriously insurmountable. The reference to self-evidence involves us in the confusions of psychologism. Finally, closer analysis reveals a difference of kind (not merely of degree) between the laws of logic and the laws of nature.
The view (espoused by Mill and others) which construes the laws of logic as psychological laws of thought is merely a variant of the just criticized factualistic interpretation. Thought, as a matter of fact, does not generally conform to the rules of logic. Even if it were impossible to think a simple self-contradiction, it is only too painfully obvious that even a slight degree of complexity in argument often conceals just such an inconsistency to the thinker who then blithely asserts self-contradictions at least by way of implication.
A more promising view construes the rules of logic as the norms of correct reasoning. Leaving the question of the nature and status of rules or norms aside for the moment, we may say that the rules of logic in their totality define what we mean by correct reasoning. This view presupposes that we possess, at least implicitly, a criterion (or a set of criteria) by which we can tell whether reasoning is correct or incorrect. The formulation of the rules then merely explicates these criteria.
But this position provokes the question: What assures us of thc adequacy of our explicandum, i.e., our pre-analytic notion of correct reasoning? The most widely accepted answer here refers us to the analytic character of all implication relations upon which correct deductive inference must be based. Deducibility, logical (or "strict") implication, entailment, or whatever else we may call it can be accounted for by refcrence to the meaning of the terms employed in deductive argument. We are then likely to say that whatever follows from propositions by virtue of the meaning of the terms they contain and by virtue of the meaning the propositions have as structured wholes follows with necessity. But how are we to decide what (if anything) follows from a given set of premises or is implied by given meanings unless we utilize the very rules of logic which we were going to justify? The emergence of circularity, here as well as elsewhere, is symptomatic of the fact that we have reached the limits of justification, that we are at least in the neighborhood of what are called "ultimate presuppositions."
More specifically, what is it that makes a presupposition ultimate? One well known reply to this question maintains that any attempt to deny reject (or replace by alternatives) an ultimate principle involves its reaffirmation. This view appears indeed most plausible in the domain of formal logic; it is much less convincing in other domains of justification. Yet, even in regard to the laws of deductive logic, the argument, if intended as a validation is specious. The denial of the law of noncontradiction leads to contradiction, that is, if we use all terms ("contradiction," "denial," etc.) in their customary sense. This sense is the "customary" one precisely because it conforms with the basic rules of ordinary (two-valued) logic. The argument therefore demonstrates only that a denial (in this sense!) of the laws of logic involves us in inconsistencies. These inconsistencies, however, are such only within the frame of the rules that determine the logic from which we expect to deviate and define the meaning of "denial" by means of which we attempt to deviate.
Let us then examine the widely held claims as to the legitimacy of alternative logics. The three-valued system of Lukasiewicz and Tarski, of Brouwer and Heyting, or the logic for quantum mechanics of von Neumann, etc., are called systems of logic not only because they, like the two-valued systems of Aristotle or of Whitehead and Russell, are capable of axiomatic deductive presentation, but also because (and this is much more important) they too provide us with rules of inference. We shall pass over in silence the rather confused claims of the disciples of Hegel, Marx, or Engels -- not to mention Korzybski -- in favor of a dialectical logic. If there are any tenable insights in these trends of thought, they would have to be first separated from a great deal of outright nonsense or egregious equivocation. Only by the most charitable interpretation can those tenable elements be assimilated to the aforementioned three-valued (or many-valued) systems.
Is it a matter of "arbitrary" decision whether or not to bestow the title of "logic" upon such alternative systems? An adequate discussion of this controversial question would take us too far afield. I can here only sketchily indicate what seems to me to be involved. First there is the question whether "deduction" or "deducibility" as defined in various alternative logics despite vague analogies is not something so radically different from what these terms signify in two-valued logic that the use of these terms without proper qualification is bound to lead to confusion. Secondly, there is the question whether the rules according to which we manipulate the symbols in a three- (or many-) valued calculus must not themselves be applied according to yes-or-no principles which in turn would impose two valued character upon their metalinguistic formulation. No matter what the structure of a language or of a calculus, if we are to proceed according to constant rules at all, if we are to be able to answer questions, solve problems, etc., in a responsible manner, must we not at some level introduce the definiteness which has throughout the ages been regarded as the very essence of the logical? Is not the requirement of unambiguous designation the very root of the regulative principles of semantics? And is not logic as we customarily understand it predicated upon adherence to rules of univocal designation? Can communication from person to person. ,1S well as with oneself, dispense with the principles that ensure self-consistencyT? Are we not continually trying to remove ambiguity and vagueness from our concepts precisely in order to safeguard ourselves against inconsistency?
These questions and their obvious answers seem also to imply a repudiation of a view of logic which has lately gained some currency especially among mathematically oriented philosophers. These thinkers take their cue from the conventionalism of Poincare and from Duhem's views on scientific method. According to this outlook there is no way of justifying laws or principles in isolation. Only the total set of laws, hypotheses, and principles is capable of test by experience. The principles of logic are simply the ones we are unwilling to surrender or modify, except as the last resort if our total system proves inadequate. The principles of logic are thus considered as in no way sharply distinguishable from those that we ordinarily would call "empirical." The advocates of this view then deny thal there is a sharp distinction between the analytic and the synthetic types of propositions, and they deny accordingly also the sharp distinction between the a priori and the a posteriori type of validity. While it is difficult to see how such a position can be maintained wherever analyticity depends upon explicit definitions (as in "All roans are horses" ), it may he grantcd that the distinction between analytic and synthetic propositions within such systems as theoretical physics is more problematic. A given formula may represent an analytic or a synthetic proposition depending upon the context of inquiry. Or, more precisely speaking, it depends upon the specific interpretation (by way of co-ordinating definitions, or semantical designation rules) to which the given formula (or a whole postulate system) is subjected. But the admitted last-ditch-surrender policy in regard to logical principles would seem to indicate that it is the data of experience which have jurisdiction over the factual content of a theory, whereas criteria of a very different kind are relevant for the adoption (or rejection) of the logical principnles. In the customary view of the theories of the factual sciences, the principles of logic and pure mathematics are silent partners, presupposed but not explicitly listed among the postulates of the given theory (geometry, mechanics, electrodynamics, quantum mechanics, etc.). They are, to use a Kantian phrase with greater propriety than we find it used by Kant himself, the necessary conditions for the very possibility of any theory whatsoever. To ensure definiteness of meaning for our symbols, to ensure (the related) conclusiveness of deductive inference we have no choice but to conform to the principles of identity, of noncontradiction, and of the excluded middle. No matter whether we understand these principles as tautologies of the object language (as we do in propositional and functional logic) or whether we understand them as semantical precepts (formulated in the metalanguage), it is impossible to abandon, e.g., the law of the excluded middle, without at the same time abandoning the other two principles (as well as the principle of double negation, or the principles "p V p <--> p," "p . p <--> p," etc.). Only if we allow ourselves to tamper with the implicitly understood meanings of "proposition," "negation," "equivalence," "disjunction," "conjunction," etc., can we responsibly deviate from one principle without affecting the others. And even if, upon modifying some of these meanings, we arrive at an "alternative logic," we shall yet have achieved no more than if, for example, we had perversely decided to replace the numeral "4" by the numeral "5" in arithmetic. That under such conditions "2 + 2 = 5" becomes a true statement is not in the least surprising. Actually, the parallel with arithmetic is (as everybody should have realized, at least since Frege's contributions) not merely a superficial analogy but genuinely a consequence of the fact that arithmetic (in ordinary interpretation) is a branch of logic (in ordinary, i.e., in Frege-Russell-Whitehead interpretation). Even if in some other world putting two and two objects together resulted invariably in a total of five objects, we should need ordinary (good old) arithmetic in order to formulate the rather peculiar natural laws of that world. Thought experiments of this kind reveal that the fundamental principles of logic are indeed independent of the data of experience. They show that these principles are indispensible not because of some pervasive features of the world that is to be symbolized, but because of the requirements of the process of symbolization itself. Every symbolic system has its tautological equivalences, based on conventional synonymities.
What is it then that accounts for the unique and ineluctable character of the principles of logic? If it is not the data of experience or the facts of the universe at large, what is it that makes compliance with them imperative and their violation a sin against the spirit of Reason? Neither the Ten Commandments nor the Law of the Land prescribes any rules of logic or language. What then is the "authority," what are the "sanctions" that dictate conformity with these principles? It will be suggested that at least part of what we mean by "mental sanity" consists precisely in compliance with those laws. Assuredly so, but this merely shows that "mental sanity" is (in part) defined by conformity with logic. The appeal to sanity therefore amounts to begging the question.
It is obvious that we have reached the limits of justification. Justification in the sense of validation involves reliance upon the principles of logic and can thus not provide their validation. Justification in the sense of a pragmatic vindication of the adoption of, and compliance with, the rules of logic would then seem to offer itself as a further opening, if we insist on pursuing our quest to the bitter (because trivial) end. If we wish to give such a justification, it too must be given by reasoning and will thus have to rely upon the very standards whose adoption is now the issue at stake. Will this involve us in a vicious circle? It will not, if we are perfectly clear that we are not seeking a validation of the principles of logic. If pragmatic vindication is sharply distinguished from validation, then all it can provide amounts to a recommendation of a certain type of behavior with respect to certain ends. We may say to ourselves: If we wish to avoid the perplexities and discomforts that arise out of ambiguity and inconsistency, then we have to comply with the rules of semantics and logic. If we wish to derive true propositions from true premises then we must conform to the rules of inference and the rules of substitution. The reasoning concerning these means-ends relations utilizes, as any such reasoning must, the forms of deductive and inductive inference. Perhaps in the extreme case -- the degenerate case, as it were -- only deductive inference is required.
There is only one more question that the dialectical process will finally bring forth: Why should we accept the ends which we took for granted in the vindication of compliance with logical rules? If the end is a means to further ends, then the question merely shifts to those further ends. And just as in the reconstruction of validation we disclose ultimate validating principles, so in the reconstruction of vindication we encounter ultimate ends or purposes. Whether definiteness and conclusiveness of reasoning are to be viewed as ultimate ends or as means to certain other values is a question of psychology. The well known transformation process of means into ends has brought it about that for many persons, especially of the scientific type of mind, the virtues of logicality have become ends in themselves. But for the vast majority of mankind logicality is primarily a means in the struggle for existence and in the pursuit of more satisfactory ways of living. These ends we pursue as a matter of stark fact; they are part of our human nature. The question whether this ought to be our nature, if not altogether prepostetous, falls at any rate outside the domain of logical justification. If there is a meaningful question here at all, it is one for ethical considerations to decide.
Justification involving appeal to principles of methodology.
It is generally granted that consistency and conclusiveness of reasoning are necessary conditions for arguments purporting to substantiate knowledge claims. It is almost equally well agreed that while consistency and conclusiveness may be sufficient in the purely formal disciplines, they are not sufficient in the realm of factual knowledge. The sort of justification that the claims of factual knowledge require leads us then to a consideration of principles outside the domain of formal logic. These principles belong to the field of inductive logic.
One qualification may be in order here. Inductive logic is not required for a justification of factual-knowledge claims that involve no transcendence beyond the completely and directly given. Perhaps a better way to state this contention is in the subjunctive mood: If there were knowledge claims susceptible to complete and direct verification (or refutation), their justification would involve appeal only to immediate data, to designation rules, to definitions, and to the principles of formal logic. We shall not attempt here to clean up this particular corner of the Augean stables of philosophy. In any case the doctrine of immediate knowledge seems to me highly dubious. The very terms in which we formulate observation statements are used according to rules which involve reference beyond the occasion of direct experience to which they are applied. If they involve no such reference then they are not terms of a language as we usually conceive languages. Terms referring exclusively to the data of the present moment of a stream of experience could not fulfill the function of symbols in observation statements that are connected with symbols in other statements (of laws and/or other observation statements). If we are not be be reduced to mere signals indicating the individual occurrences of direct experience, we must formulate our statements regarding these individual occurrences in such a manner that they are capable of revision on the basis of other observation statements and of laws that are confirmable by observation.
Appeal to the justifying principles of inductive logic is inevitably made if the dialectic question "How do you know?" is pursued to the limit. An engineer may rest satisfied with reference to specific physical laws when he justifies his claims as to the efficiency (or inefficiency) of a particular machine. A physicist in turn may justify those specific laws by deduction from very general and basic laws, such as those of thermodynamics or electromagnetics. But when pressed for the reasons of his acceptance of those more (or most ) general laws, he will invariably begin to speak of verification, of generalization, or of hypothetico-deductive confirmation. A researcher in medicine will proceed similarly. In order to justify a particular hypothesis, e.g., one according to which a certain disease is caused by a virus, he will quote evidence and/or will reason by analogy and induction. Justification of knowledge claims in the historical disciplines (natural as well as social) conforms to the same pattern.
A given item of observation is evidence not in and by itself, but only if viewed in the light of principles of inductive inference. On the level of common sense and on the more "empirical" levels of scientific inquiry those principles are simply the accepted laws of the relevant field. Utilizing some items of evidence and some pertinent laws we justify our assertions concerning past events in history, concerning the causes of diseases in pathology, concerning the existence of as yet unobserved heavenly bodies in astronomy, concerning motivations or learning-processes in psychology, and so on. The search for causes generally presupposes the assumption that events do have causes. The investigator of a crime would give us a queer look (if nothing worse) if we asked him how he could be so sure that the death under investigation must have had some cause or causes. He takes this for granted and it is not his business to justify the principle of causality. Philosophers however have felt that it is their business to justify the belief in causality.
We need not review in too much detail the variety of attempts that have been made in its behalf. The assimilation of causal to logical necessity was definitely refuted by Hume. Kant's transcedental deduction of a causal order depends on the premise that the human understanding impresses this order upon the data of the senses. Part of this premise is the tacit assumption that reason will remain constant throughout time and that it therefore can be relied upon invariably to bestow (the same) causal order upon the data. In this psychologistic version of Kant's epistemology we thus find that the lawfulness of the world is demonstrable only at the price of an assumption concerning the lawfulness of Reason. (We shall not press any further questions concerning the credibiliry of this ingenious but phantastic account of the nature of cognition.) Turning to the presuppositional version of the Critique we gladly acknowledge that Kant, more incisively than any of his predecessors, disclosed the frame of justifying principles within which the questions of natural science are raised as well as answered. But the elevation of strict determinism and of Newtonian mechanics to the rank of synthetic a priori principles proved to be a mistake. The development of recent science provides, if not a fully cogent refutation, at least a most serious counter-argument against any such attempt at a rationalistic petrifaction of the laws of science of a given epoch. More crucial yet, Kant did not achieve what he proposed to do: overcome Hume's skepticism. The presuppositional analysis furnishes no more than this: "Knowledge" as we understand this term connotes explanation and prediction. Therefore, if knowledge of nature is to be possible, nature must be predictable. This is true enough. But do we establish in this fashion a synthetic a priori guarantee for the order of nature? Not in the least. All we have attained is an analytic proposition drawn from the definition of "knowledge."
Can intuition justify the belief in causality? Even if we granted that we have an intuitive acquaintance with causal necessity in some of its instantiations, how can we assure ourselves without inductive leap that the intuited samples are representative of the structure of the world at large?
It should scarcely be necessary to point out that the again fashionable attempts to rehabilitate the concept of Real Connections will not advance the problem of the justification of induction. We grant that problems such as those regarding the meaning of contrary-to-fact conditionals show that Hume's (and generally the radical empiricist) analysis of causal propositions is in need of emendation. Indeed, it seems inevitable to establish and clarify a meaning of "causal connection" that is stronger than Hume's constant conjunction and weaker than entailment or deductibility. Perhaps the distinction between laws (nomological statements) and initial conditions will help here. Our world, to the extent that it is lawful at all, is characterized by both: its laws and its initial condition. Counterfactual conditionals tamper with initial conditions. The frame of the laws is left intact in asking this kind of hypothetical question. The "real possibilities" which are correlative to the "real connections" are precisely the class of initial conditions compatible with the laws of our world (or of some other fancied world). These considerations show that the laws of a given world may be viewed as something stronger than can be formulated by means of general implication. Thev are the very principles of confirmation of any singular descriptive statement. They are therefore constitutive principles of the conception of a given world, or rather of a class or family of worlds which are all characterized by the same laws.1
But the reconstruction of laws in terms of modal implications does not alter one whit their status in the methodology of science. Clearly, besides counterfactual hypotheticals we can equally easily formulate counternomological ones. Here we tamper with the laws. And the question of which family of worlds our world is a member can be answered only on grounds of empirical evidence and according to the usual rules of inductive procedure. Upon return from this excursion we are then confronted, just as before, with the problem of induction.
Obviously the next step in the dialectic must be the lowering of our level of aspiration. We are told that it is the quest for certainty that makes the justification of induction an insoluble problem. But we are promised a solution if only we content ourselves with probabilities. Let us see. "Probability" in the sense of a degree of expectation will not do. This is the psychological concept to which Hume resorted in his account of belief, or that Santayana has in mind when he speaks of "animal faith." What we want is a justifiable degree of expectation. And how do we justify the assignment of probability ratios to predictions and hypotheses? That depends on how we explicate the objective concept of probability. But here we encounter the strife of two schools of thought. According to the frequency interpretation chere is no other meaning of "probability than that of the limit of relative frequency. According to the logical interpretation "probability" (in the sense of strength of evidence, weight, degree of confirmation) consists in a logical relation between the evidence which bestows and the proposition upon which there is bestowed a certain degree of credibility. The adherents of this logical interpretation urge that the statistical concept of probability presupposes the logical one. For the ascription of a limit (within a certain interval) to a sequence of frequency ratios is itself an hypothesis and must therefore be judged according to the degree of confirmation that such hypotheses possess in the light of their evidence. Contrariwise, the frequency interpretation urges that locutions such as "degree of confirmation" or "weight," whether applied to predictions of single events or to hypotheses of all sorts, are merely facons de parler. Basically they all amount to stating frequency ratios which are generalized from statistical findings regarding the events concerned (the occurrence of successful predictions).
We shall not attempt to resolve the issue between these two schools of thought. Our concern is with the justification of induction. And here perhaps the divergence of interpretations makes no fundamental difference. Inductive probability in the sense of a degree of confirmation is a concept whose definition renders analytic every one of its specific applications. If we use this concept as our guide, that is if we believe that it will give us a maximum of successes in inductive guessing, then this could be explicated as an assertion about the (statistical) structure of the world. We are thus led to essentially the same rule of induction which the frequentists propose: Generalize on the basis of the broadest background of available evidence with a minimum of arbitrariness. This principle of straightforward extrapolation in sequences of frequency ratios applies to a world which need not display a deterministic order. Statistical regularity is sufficient. Does the application of the rule guarantee success? Of course not. Do the past successes of procedures according to this rule indicate, at least with probability, further successes? No again. Hume's arguments refuted this question-begging argument before Mill and others fell victims to the fallacy. Only if we utilize the logical concept of probability can we achieve a semblance of plausibility in the criticized argument. But for the reasons stated before, mere definitions cannot settle the issue as to whether our world will be good enough to continue to supply patterns of events in the future which will support this definition as a "useful" one.
The presuppositional analysis sketched thus far has merely disclosed one of the ultimate principles of all empirical inference. Any attempts to validate the principle itself involve question-begging arguments. Its ultimate and apparently ineluctable character can be forcefully brought out by considering how we would behave in a world that is so utterly chaotic and unpredictable that any anticipation of the future on the basis of past experience is doomed to failure. Even in such a world after countless efforts at inductive extrapolation had been frustrated we would (if by some miracle we managed to survive) abandon all further attempts to attain foresight. But would not even this yet be another inductive inference, viz., to the effect that the disorder will continue? The inductive principle thus is ultimately presupposed but in turn does not presuppose any further assumptions.
The various attempts (by Keynes, Broad, Nicod, Russell, and others) to deduce or render probable the principle of induction on the basis of some very general assumption concerning the structure of the world seem to me, if not metaphysical and hence irrelevant, merely to begging the question at issue. Assumptions of Permanent Kinds and of Limited Variety, provided they are genuine assertions regarding the constitution of the universe, themselves require inductive validation. To assign to such vast hypotheses a finite initial (or "antecedent") probability makes sense only if "probability" means subjective confidence. But nothing is gained in this manner. Any objective probability (logical or statistical) would presuppose a principle of induction by means of which we could ascertain the probability of such world hypotheses in comparison with the (infinite) range of their alternatives.
We have reached the limit of justification in the sense of validation. Can we then in any fashion provide a "reason" for this acknowlcdged principle of "reasonability"? Obviously not, if "reason" is meant in the sense of validating grounds. What we mean (at least in part, possibly as the most prominent part) by "reasonability" in practical life as well as in science consists precisely in the conformance of our beliefs with the probabilities assigned to them by a rule of induction or by a definition of degree of confirmation. We call expectations (hopes or fears) irrational if they markedly deviate from the best inductive estimates. The attempt to validate one of the major principles of all validation, it must be amply obvious by now, is bound to fail. We would be trymg to lift ourselves by our own bootstraps.
The only further question that can be raised here concerns a justification of the adoption of the rule of induction (or rather of one of the various rules of induction, or one of the various definitions of inductive probability or of degree of confirmation). Such a justification must have the character of a vindication, a justificatio actionis. Our question then concerns the choice of means for the attainment of an end. Our end here is clearly successful prediction, more generally, true conclusions of nondemonstrative inference. No deductively necessary guarantee can be given for the success of such inferences even if we follow some rule of induction. The probability of success can be proved, but that is trivial because we here utilize the concept of probability which our rule of induction implicitly defines. This probability cannot be construed as an estimate of the limit of frequency. We do not know whether such a limit exists. Only if we grant hypothetically that there is such a limit can we assign weights to its various values (i.e., to intervals into which the limit may fall) on the basis of (always finite) statistical samples. What then justifies our optimistic belief in the convergence of statistical sequences toward a limit? Since any attempt at validation would inevitably be circular, we can only ask for a vindication of the rule according to which we posit the existence of limits. Reichenbach's well known but widely misunderstood justification of induction2 consists, as I see it, in a vindication of the adoption of that rule. It amounts to the deductive proof that no method of attaining foresight could conceivably be successful if every sort of induction were bound to fail. Perhaps there are alternative techniques of foresight that might even be more efficient or reliable than the laborious method of scientific generalization. But such alternative methods (let us none too seriously mention crystal gazing, clairvoyance, premonitions, etc.) would themselves have to be appraised by their success; i.e., they would have to be accepted or rejected on the basis of statistical studies of the frequency ratio of correct predictions achieved by them. And our confidence in such "alternative" techniques of foresight would therefore ultimately be justifiable only on the basis of normal induction. If there is an order of nature at all (i.e., at least a statistical regularity), not too complex or deeply hidden, then a consistent application of the rule of induction will reveal it. This statement is of course a tautology. It should not be confused with such bolder and undemonstrable factual assertions as that the inductive procedure is the only reliable one, or that it is our best bet. Reliability and optimal wagering presuppose inductive probabilities and thus cannot be invoked for their justification. We cannot even say that straightforward generalization is a necessary condition (never known to be sufficient) for the success of predictions. The air of plausibility that this statement shares with its close relative, the common-sense slogan "Nothing ventured, nothing gained" arises only if we disregard (logically conceivable) alternative routes to predictive success, such as sheer inspirations, capricious guessing, intuition, premonition, etc. The unique character that the inductive procedure possesses in contrast with those alternatives rests exclusively in this: The method of induction is the only one for which it can be proved (deductively!) that it leads to successful predictions if there is an order of nature, i.e., if at least some sequences of frequencies do converge in a manner not too difficult to ascertain for human beings with limited experience, patience, and ingenuity. This is the tautology over again, in expanded form, but just as obvious and trivial as before. In the more ordinary contexts of pragmatic justification the validity of induction is invariably presupposed. If we want to attain a certain end, we must make "sure" (i.e., probable) that the means to be chosen will achieve that end. But if we ask for a vindication of the adoption of the very principium of all induction, we deal, so to speak, with a degenerate case of justification. We have no assurance that inductive probabilities will prove a useful guide for our lives beyond the prcsent moment. But equally we have no reason to believe that they will fail us. We know furthermore (as a matter of logical necessity or tautology) that if success can be had at all, in any manner whatsoever, it can certainly be attained by the inductive method. For this method is according to its very definition so designed as to disclose whatever order or regularity may be present to be disclosed. Furthermore, since the inductive method is self-corrective, it is the most flexible device conceivable for the adaptation and readaptation of our expectations.
The conclusion reached may seem only infinitesimally removed from Hume's skepticism. Philosophers do not seem grateful for small mercies. In their rationalistic quest for certainty many still hope for a justificatton of a principle of uniformity of nature. We could offer merely a deductive (and trivial) vindication of the use of the pragmatic rule of induction. But for anyone who has freed himself from the wishful dreams of rationalism the result may nevertheless be helpful and clarifying. It is the final point which a consistent empiricist must add to his outlook. We refuse to countenance such synthetic a priori postulates as Russell (perhaps not with the best intellectual conscience) lately found necessary to stipulate regarding the structure of the universe. We insist that no matter how general or pervasive the assumptions, as long as they are about the universe, they fall under the jurisdiction of tho rule of induction. This rule itself is not then a factual assertion but the maxim of a procedure or what is tantamount, a definition of inductive probability. In regard to rules or definitions we cannot raise the sort of doubt that is sensibly applicable to factual assertions. In order to settle doubts of the usual sort we must rely on some principles without which neither doubt nor the settlement of doubt makes sense. The maxim of induction is just such a principle.
1 Cp. W. Sellars, "Concepts as Involving Laws and Inconceivable without Them," Phil. of Science, XV (1948), 287.
2 H. Reichenbach, Experience and Prediction (1938). See also his article "On the Justification of Induction," Jour. of Phil., XXXVII (1940), 101. Also reprinted in H. Feigl and W. Sellars (eds.), Readings in Philosophical Analysis (1949).
Transcribed into hypertext by Andrew Chrucky, June 6, 1999.