New Directions in Austrian Economics

Toward a Program of Research and Development for Austrian Economics

Louis M. Spadaro

Fordham University

I.

Now that Austrian economics has entered its second century, it is both natural and useful—as the subject of the present conference implies—to look to the future and to try to discern, as far as is possible, the most promising directions along which our discipline might develop further. Of course, the anniversary customarily also invites review and evaluation of past experience; it is, in fact, as the result of some reflection on the latter that I venture to make the single underlying suggestion which will be seen to be the point of the present paper.

While the centenary we are celebrating will be thought by many to be that of the start of the “marginalist revolution,” the fact is that the truly seminal insight was not the marginal analysis—valuable as that analytical device admittedly was, and continues to be—but, rather, the strangely belated recognition of the subjective nature of economic value and even of human action in general. It is the special merit of Austrian economics that, while it shares the concept of the margin with its simultaneous1 co-discoverers elsewhere, its distinctive and characteristic contribution has been its insistence on the explanatory power of subjectivism.

For one thing, unlike either of the other branches of marginalism, the Austrians put forward a complete alternative to the cost-of-production concept of economic value which permeated classical analysis (and also its derivatives, including Marxism) and not just the second half of a dualistic explanation.

Moreover, it was precisely this role of subjectivism that caused the early, and subsequently widening, divergences in both theory and policy among the “marginalisms.” The failure on the part of the non-Austrian marginalists to perceive the full explanatory power of the subjective theory of value is, I believe, what led them—each in its own way—away from economic reality and into an increasingly vacuous formalism. On the one hand, English marginalism, perhaps because it was unable to turn its back on its own Classical heritage, chose to supplement rather than supplant it. The result was a “neo-classical synthesis”2 of supply and demand—best illustrated by the Marshallian “scissors” and progressively refined by an almost obsessive preoccupation with the geometry of intersections, which continues unabated—in class and textbook—to the present time.

The French marginalists, on the other hand, misled by both the pretensions of the Enlightenment and their own mathematical prowess—and also lacking the corrective force of a fully subjectivist view—were led to conceive of the economic process as a general equilibrium system (expressible by the algebra of simultaneous equations)—grander, more inclusive (and, alas, more illusory) than the “partial” equilibrium of the English economists. Both have spawned a numerous progeny who have labored mightily, if single-mindedly, in exploring the theoretical and policy implications of their respective paradigms; and though their results have shown more elegance than usefulness, they have given only cursory—and often contemptuous—attention to the Austrian tradition.

Austrians, on the contrary, have spent an inordinately large part of their talents and resources in efforts to deal with the errors of others, including some frivolous and some highly repetitive ones, and correspondingly less on the development and extension of their special insight. It is to this misallocation of our resources that my central suggestion is addressed, as we shall presently see.

Before proceeding, let me hasten to say that there is, of course, no denying the fact that individual Austrian economists have continued to make contributions of great power, clarity, and depth—and this is increasingly recognized outside their own membership. But those of us who are a little older must, I think, also be sadder to realize how much of the efforts of so many of our people—never a numerous company—has gone into encounters with an endless series of egregious errors, and to speculate on what might have been accomplished had all this investment been directed, instead, to refining and extending our own analysis.

For, we have allowed ourselves, time and again, to become embroiled in time-consuming and largely inconclusive controversies: with Marxism, macroeconomics, mathematical economics, and monetary medicine men—just to name an alliterative few. And the end is nowhere in sight, since most of these exhibit the sort of imperviousness that led the scholastic philosophers to coin the term “invincible error.”

Out of many, let us consider briefly two examples, which not only illustrate this resource misallocation, but also serve as reference points later on in our discussion.3 The first concerns the important Austrian insight that a centrally directed economy cannot, of itself, provide the data necessary for effective decision-making (i.e., consistent with the preferences of consumers). Immediately after Mises had called attention to this defect, socialists and other interventionists trained their heaviest analytical artillery on the idea. There ensued a very long and involuted discussion of “shadow-pricing” and other devices, including not a few mathematical models, which would allegedly enable the ministry of production in a socialist economy to allocate resources efficiently.

It is fair to say, I believe, that all the strenuous rebuttals failed to blunt the force of the original criticism of dirigiste planning, though they may have served to obfuscate it somewhat in the minds of the faithful and of the unwary. But the debate engaged a good deal of time and effort by the then relatively few, highly competent advocates of the market system—time and effort which doubtless would have been better spent on refining and extending their own analysis.4 In short, instead of trying to show the inadequacies of every surrogate for calculation that the advocates of central planning saw fit to come up with, our people might have been better advised to stop after one or two of them and devote the time saved to exploring the agencies, channels, and forms through which a market system conveys and utilizes information—and thus how it does calculate. There is reason to believe that if this had been done successfully, some of our present tasks (e.g., the “rehabilitation” of the entrepreneur as an active, motive force) could have advanced earlier and further.

The second instance is the latest—most certainly not the last—resurgence of the advocacy of national economic planning, one of those imperishable errors we mentioned a little earlier. Although Hayek and others had long ago carefully and definitively shown that the real issue is not planning versus chaos, but rather who is to plan and for whom, the current proposal seems to be proceeding as if the earlier corrective work had never been done at all. Already, Hayek has found it necessary to write in reply,5 repeating the distinction, though with a shade less of the “politeness to a fault” noted by Schumpeter and characteristic of this civilized man.

Though it is undoubtedly presumptuous, one cannot resist expressing the hope that no further time be taken from other, more deserving tasks, in order to beat this recycled dead horse. I feel certain that Professor Hayek would be forgiven—even applauded by many—if he decided to limit himself, on this question, to sending to two senators and to a select group of academicians and others simply a card inscribed with the French saying: “On ne dit pas la Messe deux fois pour les sourds,” together with an order blank for The Road to Serfdom.

If there is a lesson in all this, it is that we ought to scale down very sharply the extent to which our future efforts—and especially those of our best young people—are devoted to the refutation of any and every fallacy which others choose to propose. Instead, increased investment should be made in efforts to work out further the implications of subjectivism—the distinctively Austrian contribution—and to increase its impact on contemporary thought and action. It will be the task of much of the rest of the present paper to show that a good deal of this work is still to be done.

There is, then, much more than a simple anniversary occasion to counsel the value of pursuing our own analysis. Furthermore, political and economic developments during the last decade have created a climate in which subjectivist analysis can expect—temporarily, at least—to get a wider and fairer hearing than before. Though one is tempted to think otherwise, the present temper, and opportunity, may be attributable more to the manifest failure of policies based on non-Austrian economic reasoning than to any sudden persuasiveness of our own. In any event, the increasing number of talented young scholars attracted to the Austrian approach deserve, and probably prefer, a more challenging and productive objective than putting out small and recurrent brush fires.

By now, the central suggestion of this paper—that we concentrate our resources on perfecting and extending subjectivism—hardly needs to be stated explicitly. But its implementation is very far from being obvious. Along what lines is further research in Austrian economics needed? In which of these is there more urgency? Are any of these most effectively pursued by enlisting participation and contribution from specialists or practitioners in other disciplines or activities? Answers to such questions probably can emerge only from a continuing, frank, and critical discussion of points of obscurity, difficulty, or controversy among Austrian economists. The present conference promises to give significant initial impetus in this direction.

The contribution of this paper, if any, is the modest one of setting out a few of the possibilities—as a tentative frame of reference—and thus getting the discussion under way. It is expected that some (or all) of these will be rejected and that others will be proposed. These possible “new directions” will be listed and discussed very briefly under two headings: The next section will offer a small sampling of theoretical (i.e., analytical, methodological) questions. The final section presents an even smaller sample of interaction between Austrian economics and operations-oriented and other “outside” fields. These two types are treated separately largely for convenience and clarity; it will be obvious that they are ultimately interdependent and mutually reinforcing.

II.

As new implications of subjectivism unfold, the conceptual-analytical-methodological framework of Austrian theory may require extensions, and even revisions, for purposes of consistency and coordination. While the bulk of such changes will almost certainly be made by Austrian economists themselves, others may properly come from people not now considered to be Austrian economists—or even economists at all.

Inasmuch as attempts at discovery are mere gropings, and therefore always run high risk of failure, it is perhaps worth pausing to reflect that—even when they fail—explorations may have useful residue in the form of fresh insights, or in other ways. In the present case, it is highly probable that such efforts will produce—at the very least—a deeper understanding on the part of more people as to just what human action is (and, especially, what it is not).

1. The most obvious and urgent areas needing our attention are those which are causing some disagreement among competent Austrians themselves or those in which theorists, individually or in consensus, feel there is a need for additional analytical support. Since each of us is doubtless aware of a number of such problem areas, a single illustration will suffice.

Some time ago, notice began to be taken of the fact that standard economic analysis tended to make, of the entrepreneurial function, something bloodless—rigid, automatic, and unreal. The present writer, for instance, found it necessary to deplore the fact while received theory had gradually relieved everyone else from the despicable role of “economic man,” the technical requirements of its own equilibrium paradigm led to imposing precisely this role on the entrepreneur.6

Since then, in one of the more exciting recent developments of Austrian analysis—notably in work done by Kirzner7—the function of the enterpriser in a market system is being reformulated and refined in a manner that is both more realistic and more consistent with individual freedom of choice than ever before.

The present case is also useful in demonstrating how, typically, answering one question raises others that need to be dealt with next. There is some difference of opinion as to whether—given uncertainty—this new, much more active concept of entrepreneurship is stabilizing or not. This question, which will be seen as an aspect of the more general problem of convergence8 in a free market system, has already begun to be discussed among a group of Austrian economists from the New York metropolitan area who now meet regularly.

Once the specification of the new entrepreneurial concept has been completed, and its implications worked out, there will still remain the task of getting non-Austrian theorists to take it into account. This will, of course, be difficult; resistance will be all the greater because, as we noted earlier, the new formulation removes an important element in the neatness and automaticity of their models. But any success at all in this direction may ultimately lead to wider recognition of the power and potential of a free market to operate without outside direction.

Accumulating evidence of the failure of recent interventions may, in any event, make others a bit more receptive. Samuelson, for example, in a recent piece9 devoted to Adam Smith on the occasion of the bicentennial of the Wealth of Nations, after quoting two of its best-known passages (one on the self-interest of “. . . butcher, the brewer. . . .”; the other the passage mentioning the “invisible hand”), says, in conclusion:

To know the truth—and the limitations!—of these passages is the ultima Thule of economic wisdom.

There is reason to hope that our efforts, together with the force of events, may eventually persuade him to reduce the qualification.

2. Admittedly, the class of further explorations in subjectivist theory just illustrated have a legitimate first claim in any systematic reallocation of our resources. Beyond these, however, there is another group of needs, whose immediacy is less apparent, but whose ultimate contributions to subjective economic theory might prove to be of considerable importance. As a group, these are indirect—theoretic goods of “higher order,” so to speak—and involve inputs from a wide variety of disciplines different from, but often bordering on, economic theory itself. Let us consider, briefly, a small sample of these possibilities.

(a) Statistical inference, in the form it eventually took and as currently understood and applied, is fundamentally incongruent with subjectivity and therefore of little, if any, use in the treatment of most of the phenomena with which Austrian economics is concerned. The conceptual (even the axiomatic) basis of contemporary statistical theory—and, derivatively, of all of its calculations—is admittedly that of “objective” probability (i.e., the observed, or observable, frequency of independent and random events). It is therefore really inapplicable to any phenomena that are unique, or interactive, or subjective—and inapplicable a fortiori to those that are all three, as is the case with human action, in the sense understood by Austrian analysis. Instead of refraining from such phenomena, objectively derived statistical analysis and inference are applied to them widely—at a very high cost in both realism and validity—on the (largely implicit) assumption that such events are somehow amenable to the same “law of large numbers” applicable to independent, random events.

To this writer’s knowledge, there has been virtually no systematic effort to develop alternative inferential systems more consistent with the inescapable subjectivity of human events, despite the fact that the clear inadequacy of received statistical theory in this connection has been recognized for some time.10 It is the more puzzling in that the possibility and feasibility—if not the primacy—of subjective probability were discussed very early11 in the development of statistical thought and have continued to be mentioned.12

Despite these and other insights concerning the essentially subjective element in probability statements,13 the almost irresistible urge to assign cardinal numbers to degrees of belief has led to the arbitrary restatement (and distortion) of subjective probability in objective terms—to the consequent neglect of the need to search for a viable alternative. What is currently referred to as “subjective probability” is thus nothing more than the usual objective probability analysis broken down into segments: an antecedent (or “prior”) probability and a consequent (“posterior”) one14—a process for which subjective is a manifest misnomer; it is more properly designated as “conditional” or “sequential” probability.

Even here, the crucial problem—and the subject of continuing controversy—is the assignment of some weight to the antecedent (prior) probability segment in the many instances where occurrences are too few to justify reliance on the law of large numbers, which underlies the usual statistical apparatus. The facile device for skirting this difficulty—that of arbitrarily assigning equal probabilities to such events—is disputed, as one might easily guess. Some alternative approaches,15 involving the concept of learning by experience, should be of some interest to subjective theorists in a number of respects, including information theory (to be mentioned briefly below) and the analysis of entrepreneurial decision-making.

(b) The advocacy of a free-market system (as clearly superior to one run by central direction) relies, to an important degree, on the assertion that decentralized (i.e., individual) decisions are made on the basis of much more realistic and accurate information available at the source of human decisions: individual valuations and preferences. But in any complex economy, these elemental (e.g., consumer) choices trigger long sequences of derivative decisions by producers and by suppliers of attendant services (e.g., financial, distributive, etc.) at every level and stage of production. The capability of the market process to transmit highly reliable information along networks of such bewildering complexity—and to do so without undue distortion or loss of information—is impressive and a standing rebuke to the aspirations of central planners. That the process works is evident; but precisely how is only dimly and intuitively understood, though the importance of information in the economic process is recognized.16 More detailed understanding of its operation (e.g., the location and role of linkages, the localization [decentralization] of decision-making through subnetworks of information flow, etc.) could help substantially in validating and extending our theories—and might even cause some rethinking by interventionists.

It happens that—in connection with problems different from, but ultimately not unrelated to, economics—the technical analysis of information processing has made significant strides in the last quarter century.17 The results of studies in “communications theory” (or “information theory”) have proven value in the communications industry and in business management in general. And it is not unlikely that this field may have contributions to make to market theory. For one thing, it may help us understand and explain in a much more precise way how the transmission of information facilitates the convergence of the plans and decisions of large numbers of independent individuals and firms. For another, the basic concepts of this analysis—e.g., the minimum amount of information (a binary unit or “bit”) needed to distinguish between two alternatives (binary choice)—might prove to be as suggestive for the development of new approaches to subjective-choice analysis as they were in the early design of electronic computers.18

Again, it seems unfortunate that no serious attempt has been made to invite the attention—and contribution—of these specialists in the explication of the market system. Although these are primarily engineers, there is reason to believe that more than a few of them would respond to the challenge of adapting portions of their analysis to the needs of economic theory. At the very least, some dialogue with them would not leave the field open for advocates of a contrary economic philosophy to bend communication theory to their purposes.19

(c) One aspect of the above—the concept of entropy—deserves brief, separate mention for at least two reasons. The first is related to the special (technical) use made of this concept in communication theory. “Entropy” in this adaptation is very different from the concept of entropy as employed in physics (though possibly ultimately reducible to it). Here, the term is used to mean a measure of the amount of information that a theory provides and is understood to vary directly with the degree of freedom of choice (or “uncertainty”) on the part of recipients of information20—again, there may be interesting insights and implications here for subjective theory.

The second point is that entropy in its more general sense (i.e., the one more directly consistent with its traditional use in physics) seems to offer a viable alternative to the equilibrium paradigm so pervasive in contemporary economic theory—and one seemingly more adaptive to the analysis of economic activities as processes. It also touches conceptually on a number of questions which should be of some heuristic interest to our theorists. Space here will not permit more than the mere mention of some of these: purposive activity, order and probability, partial processes, irreversibility, etc.21 Some investment in exploring the potentialities, possibly in consultation with specialists in that field, would appear to be worthwhile.

(d) It is apparent that some explorations of the sort touched upon in this section imply that at least some of our students have, or acquire, the ability to follow mathematical argument—perhaps even to initiate it. Many of us who have been involved in the theoretical wars for some time will—quite understandably—be skeptical of any such involvement. For, we are all too familiar with mathematical models of high elegance and small economic content; and with countless instances of the Procrustean torturing of economic reality to make it fit the mathematical bed. It is, moreover, notoriously true that mathematical formulation is often made the end, rather than a means, of economic reasoning; and that (especially graduate) students are coerced into this mode of argument by a labor-intensive route which tends to render them the locked-in victims of their over-investment.

But all these are, after all, outrageous abuses of an essentially formal discipline which, like logic, cannot be presumed in advance to be either wrong or useless. Each of the abuses mentioned can easily be avoided; indeed, all of them are attributable to dilettantes rather than to competent mathematicians—and it is to the latter that reference is made here.

Several considerations deserve attention in this connection. First, the summary rejection of mathematics—root and branch—acts to exclude all mathematicians from our company. Yet, it should be possible for a mathematician to be a libertarian, too—and without schizophrenia. Secondly, it is a fact, however regrettable, that arguments in symbolic form—even when invalid—are held in awe by many. There is no good reason for those who have something valid to say to cede this advantage to their opponents. Thirdly, and more important, the scope of mathematics—as understood by its most able practitioners—is far broader, more humane, and more flexible than it appears to be to others. What Boulding22 calls “the puritanism of mathematics” is likely to be merely in the eye of the casual observer.

This brings us at last to the suggestion of this subsection: that we explore the usefulness, for our purposes, of less numerical and more purely relational branches of mathematics.23 One of these—topology—which seems to have special applicability to discontinuous phenomena (and should therefore have interested us long ago), is currently being utilized by a different group, in conjunction with so-called “catastrophe theory.”24 It is also interesting to note that this branch of mathematics, which is relatively neglected in our general treatises, is given more space in the Soviet texts.25

3. The final point of this section is a suggestion for the implementation of our central recommendation on the allocation of our resources with respect to controversies like those mentioned earlier as examples of “malinvestment” on our part. It is unrealistic—and perhaps unwise—to expect that we shall be able to avoid any involvement at all in recurrent and provocative fallacies. But we can—and should—determine to deal with them on our terms rather than on those of others.

This implies not only setting quantitative limits on our engagement in controversies of high (and increasing) marginal futility, but also on two qualitative ones. The first is that we act to set the conditions and the form of the discourse in which we consent to participate, for the purpose of eliminating both sheer repetition and all the small-minded, often demagogic, stratagems and posturings that one would expect, if at all, of secondary school debates and not of mature academic discourse. The second is that we insist on a fairly frank and clear specification of the context (usually a complex of tacit assumptions and esoteric definitions) of the discussion, since the failure to do so often artificially restricts the full scope of the discussion or otherwise puts one group of discussants, from the start, under unfair burden. It is only prudent to ensure that the terms of discourse, like the terms of trade, are not always unfavorable to the same people.

Let us try to illustrate, briefly, with reference to several of the controversial perennials. The issues of economic planning and mathematical economics have already been discussed and will be passed over here, except to say that we ought to insist at the outset of any further discussion of these that (1) it be recognized that we are not opposed to planning, but only to a special form of it; (2) we reject not mathematics per se, but its irrelevant or distortive application to economic analysis; and (3) we shall not continue in any discussion which does not accept these distinctions.

(a) Although discussion of socialism and capitalism as alternative economic systems long ago ran into diminishing returns, very little has been done about changing the context. From the start, Marxism restricted itself to a detailed exposition of the inner stresses expected to emerge within capitalist systems, which would eventually bring about their collapse and replacement by socialist regimes. Now, over a century later, the latter half of which has seen one major such state in actual operation, together with a number of satellites, expositions of the contradictions of capitalism continue,26 while those of socialism are either very lightly touched upon or are allowed to be buried with obfuscation.

Despite the fact that many crucial predictions of Marxism have failed (e.g., the theory of immiserization, the industrial reserve army, the absorption of the middle class, the withering of the state, etc.), we are still largely defending (or criticizing) the operation of capitalism only. On a more theoretical level, both the “transformation problem” and the calculation critique will illustrate clearly the obfuscation mentioned above.

We should therefore cease acceding to discussions of the problems of one system only, or those which compare the actual operation of one with only putative weaknesses in the other. Instead, there ought to be some insistence on the use of some common denominator for comparison—preferably a set of performance standards capable of empirical verification. The designing of such standards admittedly would be difficult—given the incommensurabilities of economic organization and, in particular, the differing degrees of coyness with which data are made available—but the task is far from an impossible one with which to challenge young scholars.

In fine, the burden of proof should shift in part, so that socialists, too, would have to defend their system against the charge that it is failing. Nor should an ideological “detente” be permitted to take the place of the rapidly evanescing political-military one; their “drift” toward capitalism is not on the same road as ours toward socialism—so we may never meet. They are backing slightly away from socialist arrangements which did not work; while in the West we never really got to trying a really free market system.

(b) In our differences with macroeconomic analysis, we have been once again too accommodating in our willingness to accept its context and definitions. By this context, macroeconomics is taken to be a system of causal and other relationships among aggregative economic entities and consequently an alternative to microeconomics—and, indeed, often in sharp conflict with it. As such, it has been vigorously resisted and opposed by free-market economists. But suppose this conception of macroeconomics is neither the only—or correct—one?

It is by now virtually forgotten that it was the intention of the pioneers of national income estimates to set up the equivalent of a profit-and-loss statement for the whole economy—like its prototype, ex post and evaluative. Indeed, Kuznets (a founder and leading architect of national income statistics) states this fact unequivocally:27

. . . national income is the end product of a country’s economic activity, reflecting the combined play of economic forces and serving to appraise the prevailing economic organization in terms of its returns. Being thus a summary and appraisal notion rather than an analytical entity, national income demands statistical measurement. [Emphasis added.]

In this case, as before, we can insist on the recognition of the distinction between macroeconomics as a set of ex post data on the outcomes in the economy and as a distinct explanatory theory—emphasizing that taken in the former sense we accept, and even welcome, it as a valuable supplement to any explanation of the working of the market economy. If this is done, we may be able to avoid becoming enmeshed in a host of wasteful efforts of which the following are illustrations.

One is the frequently-heard wish that some way be sought to coordinate macro- and micro-models of analysis—presumably as separate parts of an even grander, more inclusive explanatory model. This appears to be at least improbable, given their mutually contradictory explanations, and would comprise an inexcusable waste of time and talent if the correct disposition of the conflict turns out to be not the coordination of the two, but the subordination of one to the other as serving very different but complementary functions.28

Another is the interesting—and generous—offer recently voiced by Lachmann:29 that we undertake to “subjectivize” the macro-entities by some process of disaggregation until they are consistent with subjective choice. One suspects that this arduous effort will merely lead us back out of the looking glass and into the familiar micro-economic world. Fortunately, this travail will prove unnecessary if the subordination we have mentioned turns out to be the correct relation between micro- and macroeconomics.

III.

If it is to be taken seriously, any body of theories about the real world must eventually take its own measure against that reality. To fail to do so may avoid, for a time, the risk of disconfirmation, but also forgoes the opportunity for potent reinforcement.

It is often claimed, in defense of delay, that the particular and accidental forms in which actual events present themselves are different and incongruent with those of abstract, systematic thought—and this, of course, is true in part. But, while the most general propositions of a theory may not lend themselves to direct observation, the deductive working out of their implications should tend to produce subsidiary statements whose form and content lend themselves to some form of comparison with empirical reality—if not by the structured methods of positivistic “science,” then by informed subjective judgment (“verstehen”).

The need for some sort of outside confirmation is especially important for those theoretical systems which, like Austrian economics, make the claim that they are axiomatic and apodictically true—and are therefore open to the facile criticism that they are purely formal (i.e., devoid of real content) and are merely internally consistent circularities.

When, in addition to all this, the central propositions of a theory have great generality in their frame of reference, they “vector” out to touch hands with other areas of analysis or of activity not normally subsumed within the domain of the theory itself. This certainly appears to be the case with Austrian economics on at least two grounds: (1) it purports to deal with all human action and not just one aspect or subset (economic activity); and (2) it insists on the categorical primacy of individual choice.

In turn, this generality of Austrian theory implies both an obligation and an opportunity; the obligation, on the one hand, to make whatever contributions it can to other areas to which its principles apply, and, on the other, the opportunity to invite and receive contributions from people with special competence in such areas.

The “field” for such mutuality of interest extends not only to other theoretical disciplines, but also to “applied” areas. Several examples of the former have already been mentioned in another connection (i.e., statistics and mathematics); others will readily occur to the reader (consider, for example, the continuing interest in Austrian theory on the part of philosophers, political theorists, legal scholars, et al.) and will not be discussed here.

The specific task of the final section of this paper will be to offer illustrations of more practical, operational areas which bear this sort of interface with Austrian analysis. Space—and the patience of the reader—will permit only a very small sampling of these; their selection should not be taken to indicate their importance relative to the many omitted, but merely as an attempt to show range and diversity.

A. Business operations and management should be the most obvious—and easiest—of the applied areas with which to establish the sort of two-way communication we are discussing. Yet, the exchange between economists and businessmen continues to be very disappointing both in extent and quality. (The many historical, institutional, and other factors behind this puzzling and complex state of affairs—and the possibilities for changing it—are clearly beyond the scope of this paper.)30 Nevertheless, the relatively realistic nature of its concept of the economic process, together with its emphasis on the power of individual action, gives Austrian economics a special opportunity to explore some proximate and straightforward possibilities for mutual contributions.

(1) Business organizations offer a vast theater for testing the advantages of reliance on the motivation and responsibility of individuals. Indeed, management theorists31 have presented a compelling case for moving away from traditional centralized and authoritarian organizational designs of decision-making responsibility (“Theory X”) and toward more reliance on decentralized, individually oriented initiatives (“Theory Y”). Experimentation with changes along these lines has had to be cautious and marginal (since firms must operate within the constraints of the cost-recouping “imperative”), and the results thus far have not been uniformly conclusive. Detailed and frank analysis of instances of success and failure in such experiments would appear to offer interesting opportunities for practitioners to confer with theorists, to the benefit of both.

(2) Regular consultation with businessmen would not only acquaint the latter with the often esoteric language and concepts of economic theory, it would also tend to reduce the risks that theorists run when they depart from realism. To use one of the points already familiar to the reader as illustration: It is inconceivable that the prevailing conception of the entrepreneurial function in traditional economic theory would appear to actual entrepreneurs as accurate. If this conception is in serious error, a very long sequence of theorizing—as well as costly policies deriving from it—could have been averted by the simple process of identifying the picture of the entrepreneur which was implicit in the early analysis and making it explicit so that experienced practitioners could evaluate it.

Even now, it would be useful to do this. For any revision of the role of the enterpriser will involve radical changes in the traditional models of the operation of the economy and will therefore not be embraced immediately or with enthusiasm. The cooperation of businessmen will not only help confirm that the revision is realistic, but they can help flesh it out further.

(3) The subjective view of human action necessarily puts a great deal of reliance on the concept of “verstehen”—a composite of experience, intuition, and other qualities not adequately conveyed by the word “understanding.” The prevailing positivist temper of our age is apt to dismiss so subjective a notion as being simply vague (if not worse) unless it is buttressed by practical and highly realistic examples. These are best and most influentially to be provided by those experienced in a variety of management decisions in which the “objective” data had to be evaluated and supplemented by human judgment.

(4) Finally, this very subjectivity has important implications for the proper role of present managers in the education of those who will follow them.32 For, if the essence of what they do is subjective, it cannot be conveyed adequately either by rigid sets of rules or by abstract models devised largely without reference to the realities of actual performance. There is reason to think that just such a deficiency now exists and is being dealt with by on-the-job remedial action. The prevalence and extent of management training programs in so many of our large corporations may thus be a tacit—and very costly—criticism of the adequacy of programs in the formal education of young business managers.

B. This brings us to the second illustrative area—and one very close to home. Quite apart from its content—one aspect of which we have just now touched on—the organization of formal education on the collegiate and even on the graduate level is deeply inconsistent with subjectivism. In this respect, we in education have lagged far behind industry, where, as we saw a little earlier, there has been at least some attempt to give greater scope to individual initiative and provision. But where, in our own house, is the application of the same “Theory Y” which we have been urging on others? The fact is that education remains—as it has long been—essentially paternalistic and authoritarian. Persisting patterns of sanctions and rewards are hardly conducive to—or even tolerant of—the exercise of independent judgments and valuations by the individual student. True academic freedom (that is, in its original meaning and intent) has more the appearance of a class privilege reserved to the faculty than an intellectual right that extends to students—or even to applicants for faculty positions.

A little reflection by anyone who has attended college, and especially graduate school, will suggest many examples of this perverse state of academic affairs—and the point will not be pursued here. But it should be obvious that subjective theorists have here a special obligation to establish a dialogue with educational administrators and others and to seek ways in which students can be encouraged—certainly not discouraged—in the exercise of independent judgment.

C. The third and final example, literature, is illustrative of a large class of pursuits or professions whose essence and practice depend significantly on individual effort and on subjective values. The history of literatures from Milton to Solzhenitsyn exhibits real concern for individual freedom of expression and of action33—often defended courageously and at great personal cost. Moreover, as the case of the Fabian Society illustrates all too well, it is possible for people of great literary talent to become interested in social and economic issues and to present these to the reading public with great potency and effect. Here, again, Austrian theorists would seem to have the opportunity and the obligation to establish and maintain communication with all those—however distant from strict economy theory—who share their insight on the nature and significance of human action.

 

REFERENCES

34. Although it was published three years after the others, the work of Leon Walras (Éléments d’économie politique pure, 1874) is now generally accepted as independently developed.

35. Unfortunately, this term is currently being used for things very different from this, its original meaning, resulting in unnecessary confusion. Cf.,e.g., P. A. Samuelson, Economics: An Introductory Analysis, 7th ed. (New York, 1967), pp. 351–52; and also, Newsweek, May 12, 1975.

36. Were it not for this double purpose and the related need to save space, an excellent example would be provided by the extended discussion by so many Marxists and their opponents of the so-called “transformation problem” since Böhm-Bawerk (Karl Marx and the Close of His System, London, 1898).

37. This may also apply to extended discussions with less antagonistic critics. For example, as Ludwig Lachmann observed at a recent conference on Austrian economics (Milwaukee, March 1976), the long discussions following Knight’s criticism of Austrian capital theory took time which was needed elsewhere.

38. F. A. Hayek, “The New Confusion about Planning,” Morgan Guaranty Survey, January 1976.

39. L. M. Spadaro, The Present State of Profit Theory: Asset or Liability? (Philadelphia, 1963).

40. I. M. Kirzner, Competition and Entrepreneurship (Chicago, 1973).

41. See Gerald O’Driscoll, “Spontaneous Order and the Coordination of Economic Activities,” elsewhere in this volume.

42. Newsweek, March 15, 1976.

43. Cf., e.g., L. J. Savage, The Foundations of Statistics (New York, 1954); also, L. M. Spadaro, “Averages and Aggregates in Economics,” in M. Sennholz, ed., On Freedom and Free Enterprise (Princeton, 1956).

44. Both Laplace (Théorie analytique des probabilités, Paris, 1814) and De Morgan (An Essay on Probability, London, 1838) regarded probability as the degree of belief in a proposition and as referring to a state of mind.

45. Cf., e.g., E. Nagel, “The Meaning of Probability,” in J. R. Newman, ed., The World of Mathematics (New York, 1956), vol. 2, pp. 1398–1414; F. J. Anscombe and R. J. Aumann, “A Definition of Subjective Probability,” Annals of Math. Stat., vol. 34 (1963), pp. 199–205. It is interesting, too, to note that J. M. Keynes, in an early work on this subject (A Treatise on Probability, London, 1921), treats probability as a directly intuitable relation which, while capable of varying in degree, is not analyzable by the calculus of probability.

46. One of the earliest and most able of those interested initially in the truly subjective aspect of probability, Thomas Bayes, also emphasized its relation to degrees of belief (cf., his two memoirs in Philosophical Transactions, 1763 and 1764). Nowadays, however, his name is almost exclusively associated—because of a theorem of his (Bayes’s Theorem)—with conditional probability.

47. E.g., S. B. Richmond, Operations Research for Management Decisions (New York, 1968),passim, espec. pp. 129–33,148–52, and 541–47.

48. Cf., e.g., R. Carnap, “What is Probability,” Scientific American (September 1953), pp. 128–36.

49. Cf. F. A. Hayek, “Economics and Knowledge,” in Individualism and Economic Order (Chicago, 1948), pp. 33–56; also, G.J. Stigler, “The Economics of Information,” Jour. Pol. Econ. (June 1961), pp. 213–25.

50. The modern resurgence of interest in the analysis of information begins with a seminal paper by Claude Shannon (C. E. Shannon, “A Mathematical Theory of Communication,” Bell Syst. Tech. Jour. [1948]. For more general implications, see N. Wiener, Cybernetics [New York, 1948]).

51. For comprehension of various aspects of this area, see: C. Cherry, On Human Communication, 2nd ed. (Cambridge, Mass., 1966); J. R. Pierce, Symbols, Signals and Noise: The Nature and Process of Communication (New York, 1961); and espec. H. Theil, Economics and Information Theory (Chicago, 1967).

52. One interesting example is an attempt to use communication theory to buttress what is essentially a variant of many inflationist schemes: S. Bagno, The Angel and the Wheat: Communication Theory and Economics (New York, 1963). Unfortunately, space does not permit an extended analysis of the inflationism involved, but its dedication is revealing:

“Dedicated to
Claude Shannon and Norbert Wiener
Whose Theorems are the Foundations of a Consistent Economic Doctrine
and to John Law
Whose Methods Enabled Us to Learn Our True Potential”

53. Cf., e.g., Pierce, op. cit., chap. 5.

54. For a detailed exposition, see N. Georgescu-Roegen, The Entropy Law and the Economic Process (Cambridge, Mass., 1971).

55. K. E. Boulding, Economics As a Science (New York, 1970), p. 101.

56. The writer had occasion to make this same suggestion some time ago in another context: L. M. Spadaro, “The Heuristic Value of Simulation in Business and Economic Research,” Proceedings, Amer. Stat. Assoc., 1966, pp. 73–79.

57. Newsweek, January 19, 1976.

58. Cf., e.g., A. D. Aleksandrov, A. N. Kolmogorov, and M. A. Lavrent’ev, eds., Mathematics: Its Content, Methods, and Meaning, Eng. transl., 2nd ed. (Cambridge, Mass., 1969), espec. vol. 3, chap. 18.

59. The most recent example known to the writer is D. P. Bell, The Cultural Contradictions of Capitalism (New York, 1975).

60. S. S. Kuznets, “National Income,” Encycl. Soc. Sci. (1933) and reprinted in Amer. Econ. Assoc., Readings in the Theory of Income Distribution (Philadelphia, 1949), pp. 3–43. The quotation here is from p. 3.

61. For discussion of some of the difficulties and errors resulting from attempts to establish causal relationships among macro-quantities directly, cf., H. Theil, “Alternative Approaches to the Aggregation Problem,” in E. Nagle, P. Suppes, and A. Tarski, eds., Logic, Methodology, and Philosophy of Science (Stanford, 1962).

62. Also in his remarks at the Milwaukee conference cited in note 4.

63. The writer is planning a monograph which is expected to include a detailed analysis of this situation.

64. Cf., e.g., D. McGregor, The Human Side of Enterprise (New York, 1960); A. H. Maslow, Eupsychian Management (Homewood, I11., 1965); and P. F. Drucker, Management: Tasks, Responsibilities, Practices (New York, 1973).

65. For a literate and cogent discussion of this role, cf., H. M. Boettinger, “Is Management Really an Art?” Harvard Bus. Rev., (January-February 1975), pp. 54–63.

66. For one suggestive example from literary criticism, cf., L. Trilling, The Liberal Imagination (New York, 1950).

• 1. F. A. Hayek, The Counter-Revolution of Science (Glencoe, 1952), p. 31.
• 2. J. A. Schumpeter, History of Economic Analysis (1954), p. 847, footnote 8.
• 3. G. L. S. Shackle, Epistemics and Economics (Cambridge, 1972), p. 245.
• 4. A. C. Pigou, “The Value of Money,” Quarterly Journal of Economics (November 1917), pp. 42–43.
• 5. J. M. Keynes, A Treatise on Money (1930), Volume I, Chapter 15.
• 6. John Hicks, Critical Essays in Monetary Theory (Oxford, 1967), pp. 61–82.
• 7. Tjalling C. Koopmans, Three Essays on the State of Economic Science (McGraw-Hill, 1957), pp. 146–47.
• 8. K. J. Arrow, “Limited Knowledge and Economic Analysis,” American Economic Review (March 1974), pp. 1–10.
• 9. F. H. Hahn, On the Notion of Equilibrium in Economics (Cambridge, 1973).
• 10. Shackle, op. cit., p. 72.
• 11. John Hicks, A Theory of Economic History (Oxford, 1969).
• 12. Carl Menger, Problems of Economics and Sociology (Urbana, 1963), pp. 151–59.
• 13. My phrase “abstract logic of preference” is obviously modelled after Hayek’s “Pure Logic of Choice,” but fits my purpose better.
• 14. See especially: Mises, Human Action, pp. 350–57; Rothbard, Man, Economy, and State, pp. 277–80.
• 15. George Stigler, Production and Distribution Theories (New York: Macmillan, 1946), p. 181.
• 16. Kirzner, Competition and Entrepreneurship, p. 68.
• 17. Some of the following is based upon Ayn Rand, “Introduction to Objectivist Epistemology,” which appeared in various issues of The Objectivist between July 1966 and February 1967.
• 18. Gerard Debreu, Theory of Value (New York: Wiley, 1959).
• 19. Bertrand Russell, Principles of Mathematics (New York: Norton, n.c.d.), p. 3. Originally published in 1903.
• 20. Morris R. Cohen, A Preface to Logic (New York: Holt, 1944), pp. 9–11.
• 21. I have been informed both by a philosopher and by a mathematician that Russell failed in his lifelong attempt to prove the identity between logic and mathematics.
• 22. W. Stanley Jevons, The Theory of Political Economy, 5th ed. (New York: Kelley & Millman, Inc., 1957), p. 3.
• 23. James R. Newman, The World of Mathematics, 4 vols. (New York: Simon and Schuster, 1956), III, p. 1830.
• 24. Jevons, op. cit., pp. 4–5.
• 25. Several critics of this paper have pointed out that words are symbols which represent concepts. Of course I accept this, and urge that my “symbols” in the following be interpreted as “second-order symbols,” standing for words.
• 26. One or more of these advantages have been claimed by many economists. For one example, see Josef Hadar, Mathematical Theory of Economic Behavior (Reading, Mass.: Addison-Wesley, 1971), pp. 5–7.
• 27. Mr. Roger Garrison points out that the verbal phrase expresses causality while the symbolic expression does not. His observation is absolutely correct, and it strengthens all of my subsequent points about the relative natures of mathematical and verbal analyses.
• 28. Rand, op. cit., passim.
• 29. Hayek, “Economics and Knowledge,” p. 33, passim.
• 30. Richard von Mises, Probability Statistics and Truth (London: George Allen and Unwin Ltd., 1961), first published in 1928.
• 31. See Mises, Human Action, op. cit., pp. 105–18; also, G. L. S. Shackle, Expectation in Economics (Cambridge: University Press, 1952), pp. 5, 109–27.
• 32. See, for example, J. Hadar and W. R. Russell, “Rules for Ordering Uncertain Prospects,” American Economic Review, LIX, No. 1 (1969), pp. 25–34.
• 33. Karl Popper, The Logic of Scientific Discovery (New York: Harper and Row, 1968), p. 40.
• 34The first, and most prominent, feature of Austrian economics is a radical subjectivism, today no longer confined to human preferences but extended to expectations. It found its perfect expression many years ago in Hayek’s statement, “It is probably no exaggeration to say that every important advance in economic theory during the last hundred years was a further step in the consistent application of subjectivism.”
• 35Secondly, Austrian economics displays an acute awareness of the many facets of time that are involved in the complex network of interindividual relations. Time, as the dimension of the interval between input and output, is important, but it is not all-important. Menger’s rejection of Böhm-Bawerk’s theory of capital was largely, if not solely, prompted by the latter’s disregard of all those economically relevant aspects of time that do not fall under the headings “time preference” and “period of production.” To Menger, time was, in the first place, the dimension in which the complex network of interindividual relations presents itself to us. Austrian economics has retained and cultivated this Mengerian perspective. Time is the dimension of all change. It is impossible for time to elapse without the constellation of knowledge changing. But knowledge shapes action, and action shapes the observable human world. Hence it is impossible for us to predict any future state of this world.
• 36To acting man time is no continuum. The future is uncertain, the past alone known, or at least knowable. “We cannot have experience of actuality at two distinct ‘moments’. The moment of actuality, the moment in being, ‘the present’, is solitary. Extended time, beyond the moment, appears in this light as a figment, a product of thought.” As time is continuously flowing across the threshold of the present, it is undergoing a change of quality. With regard to our knowledge, then, time is heterogeneous, comprising the unknowable and the knowable. Hence Austrian economists, compelled by their commitment to subjectivism to view all problems in the perspective of the actor, cannot but look askance at all theories employing the mathematical notion of time as a continuum and will cast a suspicious eye on expressions such as dY/dt. To acting man, time means something different.
• 37The following year, Mises took the first step in the direction of subjectivism by stressing the important role of individual cash balances. In Cambridge, Pigou tried to subjectivize the rigors of the Quantity Equation by means of the “Cambridge k.” The discovery of the variability of bank credit played its part. While commodity money “exists” in a physical form, the creation and maintenance of a volume of credit requires acts of choice. An element of subjectivism entered into the supply of money.
• 38In 1930 Keynes, in the Treatise, introduced the distinction between the industrial and the financial circulation, later called active and idle money. We have here a clear case of a dissolution of a macroaggregate (M) into smaller aggregates amenable to choice, the choice between money to use and money to hold. And in 1934, for a fleeting moment, a few economists even became aware of what was happening, viz. that night in November 1934 when young Dr. Hicks read his paper, “A Suggestion for Simplifying the Theory of Money,” with its emphasis on subjectivism, to a baffled London Economic Club most of whose members felt that something important had been said, but could not quite make out what.
• 39In 1930 Keynes, in the Treatise, introduced the distinction between the industrial and the financial circulation, later called active and idle money. We have here a clear case of a dissolution of a macroaggregate (M) into smaller aggregates amenable to choice, the choice between money to use and money to hold. And in 1934, for a fleeting moment, a few economists even became aware of what was happening, viz. that night in November 1934 when young Dr. Hicks read his paper, “A Suggestion for Simplifying the Theory of Money,” with its emphasis on subjectivism, to a baffled London Economic Club most of whose members felt that something important had been said, but could not quite make out what.
• 40To our knowledge, Professor Koopmans first launched the attack in 1957, criticising what he called “the overextended belief of the liberalist school of economic thought in the efficiency of competitive markets as a means of allocating resources in a world full of uncertainty.” He continued, “To my knowledge no formal model of resource allocation through competitive markets has been developed, which recognizes ignorance about all decision makers’ future actions, preferences, or states of technological information as the main source of uncertainty confronting each individual decision maker, and which at the same time acknowledges the fact that forward markets on which anticipations and intentions could be tested and adjusted do not exist in sufficient variety and with a sufficient span of foresight to make presently developed theory regarding the efficiency of competitive markets applicable. . . . In particular, the economics profession is not ready to speak with anything approaching scientific authority on the economic aspects of the issue of individual versus collective enterprise which divides mankind in our time.”
• 41In a similar vein Professor Arrow, in a recent Presidential Address to the A.E.A., told his listeners, “Even as a graduate student I was somewhat surprised at the emphasis on static allocative efficiency by market socialists, when the nonexistence of markets for future goods under capitalism seemed to me a much more obvious target.”
• 42In February 1973, Professor Hahn, in his well-known Inaugural Lecture in Cambridge, employed the same argument to show that general equilibrium theory has its practical uses in providing a sophisticated critique of the market economy. “The argument will here turn on the absence of futures markets and contingent futures markets and on the inadequate treatment of time and uncertainty.” He continued, “Practical men and ill-trained theorists everywhere in the world do not understand what they are claiming to be the case when they claim a beneficent and coherent role for the invisible hand” (p. 14).
• 43Following what was said above, we have to distinguish between the unknowable future and the knowable past. In neoclassical thought this problem does not arise, since one is ostensibly engaged in finding “laws” applying as much to the one as to the other. But there are the well-known puzzles among which the problem of ceteris paribus, our inability to specify all the conditions under which the laws are to hold, takes prominence. Austrians simply have to face the fact that the autonomy of the mind precludes determinism: If knowledge shapes action and action shapes the human world, the future is unpredictable. “But if theory pretends only to give an account of particular, peculiar and special moments (such as may be scarcely ever attained in fact) and repudiates any hope of connecting them by any intelligible, permanent mechanism allowing prognosis, then the theory ought explicitly to be a classificatory one, putting situations in this box or that according to what can happen as a sequel to it. Theories which tell us what will happen are claiming too much.”
• 44Above all, Austrian economists will want to trace market processes of the past. To identify economic history with the evolution of the market economy is a bold idea at the application of which Sir John Hicks tried his hand a few years ago. A good deal might be done within this framework.
• 45As the heirs of Menger, Austrian economists will take a particular interest in how the market evolves those “organic institutions” it needs. But the degeneration of these institutions is a subject that no less deserves our attention. It might be worth our while to attempt to find out when exactly, and in what circumstances, the downward inflexibility of money wage rates became the prominent feature of the Western world it today unfortunately is. It would be even more interesting to link it to the evolution of the institutions of collective bargaining. History offers many instances of institutions which, created for one purpose, came to serve another. The parallel with malinvestment is obvious.
• 46Concentration upon this latter set of issues constitutes the Austrian differentia. The distinction cannot be appreciated from a simple statement removed from the context of the above remarks, but it appears correct to argue that: whereas most contemporary microtheory focuses upon the abstract logic of preferences, the Austrian School focuses upon action.
• 47The above comments may help to clarify some of the claims made by the Austrian School writers: although the “abstract logic of preferences” can employ the technique of mutual determination via the solution of sets of simultaneous equations, an analysis of the plans underlying these preferences and how plans are modified must incorporate the concepts of purpose and learning. “Purpose” in this sense cannot refer simply to the a prioristic universal goal of “utility maximization”; it refers to some specific goal the individual wishes to achieve and consequently to how his actions and plans are likely to be modified when he learns that the economic environment is going to be different from that which he anticipated when he developed his initial plans. Simultaneous determination may govern the logical analysis of preferences, but the “older concept of cause-and-effect” is the only technique appropriate to the study of learning and the modification of inconsistent plans. The “cause,” of course, is the individual’s subjective perception of an opportunity to improve his situation, and the “effect” is a change in his way of acting, or in his plans.
• 48The above comments may help to clarify some of the claims made by the Austrian School writers: although the “abstract logic of preferences” can employ the technique of mutual determination via the solution of sets of simultaneous equations, an analysis of the plans underlying these preferences and how plans are modified must incorporate the concepts of purpose and learning. “Purpose” in this sense cannot refer simply to the a prioristic universal goal of “utility maximization”; it refers to some specific goal the individual wishes to achieve and consequently to how his actions and plans are likely to be modified when he learns that the economic environment is going to be different from that which he anticipated when he developed his initial plans. Simultaneous determination may govern the logical analysis of preferences, but the “older concept of cause-and-effect” is the only technique appropriate to the study of learning and the modification of inconsistent plans. The “cause,” of course, is the individual’s subjective perception of an opportunity to improve his situation, and the “effect” is a change in his way of acting, or in his plans.
• 49Professor Kirzner’s important work refers to the “alertness to information” as entrepreneurship. But the importance of the Austrian viewpoint is more clear if we realize that this ability is precisely what differentiates man from other living beings, that “entrepreneurship” in general is indistinguishable from use of the rational faculty, from the ability to conceptualize, from thinking.
• 50Professor Kirzner’s important work refers to the “alertness to information” as entrepreneurship. But the importance of the Austrian viewpoint is more clear if we realize that this ability is precisely what differentiates man from other living beings, that “entrepreneurship” in general is indistinguishable from use of the rational faculty, from the ability to conceptualize, from thinking.
• 51If we are to analyze the function of mathematical terminology in economics, we must analyze it at its best. The difficulties associated with the use of differential and integral calculus are well-known (e.g., the requirements that products and factors be infinitely divisible, that individuals consider infinitesimal changes relevant, that all preference orderings be representable by a total utility function and production relations by a total product function), so analyses using differentiable and integrate objective functions are no longer at the frontiers of mathematical economics, except perhaps in the study of uncertainty. The more general approach of set theory has been developed largely since Debreu (1959), and it is a real and significant improvement over differential calculus in economics. Those who wish to criticize mathematical economics must take on its best.
• 52Bertrand Russell contends that “pure mathematics is the class of all propositions of the form ‘p implies q’ . . . .” The claim of equivalence between pure logic and pure mathematics is sometimes attributed to Russell and Whitehead’s Principia Mathematica (1910–13), but the same idea is presented forcefully in the first few pages of Russell’s 1903 work. Russell was led to this conclusion by the discovery that numbers are sets, that ordinary algebra is therefore an application of set theory, and that any statement of implication can be rewritten in set-theoretic terms: e.g., “p implies q” is identical to “q is a subset of p.” Venn diagrams even give us pictures.
• 53Bertrand Russell contends that “pure mathematics is the class of all propositions of the form ‘p implies q’ . . . .” The claim of equivalence between pure logic and pure mathematics is sometimes attributed to Russell and Whitehead’s Principia Mathematica (1910–13), but the same idea is presented forcefully in the first few pages of Russell’s 1903 work. Russell was led to this conclusion by the discovery that numbers are sets, that ordinary algebra is therefore an application of set theory, and that any statement of implication can be rewritten in set-theoretic terms: e.g., “p implies q” is identical to “q is a subset of p.” Venn diagrams even give us pictures.
• 54Bertrand Russell contends that “pure mathematics is the class of all propositions of the form ‘p implies q’ . . . .” The claim of equivalence between pure logic and pure mathematics is sometimes attributed to Russell and Whitehead’s Principia Mathematica (1910–13), but the same idea is presented forcefully in the first few pages of Russell’s 1903 work. Russell was led to this conclusion by the discovery that numbers are sets, that ordinary algebra is therefore an application of set theory, and that any statement of implication can be rewritten in set-theoretic terms: e.g., “p implies q” is identical to “q is a subset of p.” Venn diagrams even give us pictures.
• 55Jevons felt that economics was by nature mathematical because it deals with numbers. Modern mathematicians prefer to identify the roots of their subject with the theory of sets. A set is a collection of undefined “elements,” which may represent any property we wish to attribute to them, and the theory of sets consists of the logical relations among them. Because of the completely general nature of these sets and elements, we can embrace a much wider view of the nature of mathematics than can those who restrict themselves to, say, functional notation; James R. Newman’s cursory sampling of a few modern mathematicians’ views of their own subject indeed suggests that the boundary between logic and mathematics is becoming increasingly blurred.
• 56Jevons felt that economics was by nature mathematical because it deals with numbers. Modern mathematicians prefer to identify the roots of their subject with the theory of sets. A set is a collection of undefined “elements,” which may represent any property we wish to attribute to them, and the theory of sets consists of the logical relations among them. Because of the completely general nature of these sets and elements, we can embrace a much wider view of the nature of mathematics than can those who restrict themselves to, say, functional notation; James R. Newman’s cursory sampling of a few modern mathematicians’ views of their own subject indeed suggests that the boundary between logic and mathematics is becoming increasingly blurred.
• 57Furthermore, either logical relations or mathematics—whatever the distinction may be—is capable of expression in either verbal or abstract symbolic terms. Jevons was correct in this regard: one cannot identify the basically mathematical or nonmathematical nature of a discipline according to whether or not it is expressed verbally.
• 58From this viewpoint it appears as if Austrian School writers’ criticisms of mathematics in general—rather than of crude mathematics, or of symbolic mathematics—are, in essence, criticisms of pure logic, which is not always (sometimes, perhaps, but not always) what they intend. The real issue is: are there advantages to be gained from the substitution of symbols for words in economics?
• 59The advantages claimed for this substitution include economy, precision, and rigor. The economy arises simply from the fact that a symbol (e.g., x) is more brief than the set of words it denotes (e.g., “the number of oranges he buys per week”). The precision and rigor follow from the abstract nature of symbols: once a set of symbols is appropriately defined (i.e., related verbally to the problem of interest) the entire corpus of the formal theory of relations among these symbols becomes applicable to one’s problem. The ability to draw on the pure, abstract theory of logic (or mathematics) provides the rigor, and the exactness required in the definition of symbols forces the precision.
• 60It is clear enough that representation with symbols is always possible: by defining f() and x appropriately we can represent “absence makes the heart grow fonder” by “f1(x)>0.” The question is, why bother? What advantages might such symbolism offer? There will be advantages—economy, precision, rigor—only if the symbols will be used repeatedly in the course of some logical analysis.
• 61To evaluate the process of symbolic analysis outlined above, we must consider the epistemological significance of language. Words are concrete audiovisual representations of the abstractions called concepts, in which form all knowledge is retained. As a consequence, any mathematically derived symbolic propositions which are to be meaningful must be translated into words. (If they are merely translatable then they are merely potentially meaningful.) Thus, the long sequence of intermediate steps in a logical derivation must be expressed verbally if it is to be related to human experience. But without subsidiary hypotheses about how people learn, these intermediate steps are not meaningful as guides to the comprehension of behavior and cannot be related directly to human experience. Only the conclusion can, in the sense that it describes an “equilibrium” state toward which actions are headed. Equilibrium theorists who make extensive use of mathematical symbolism are, in fact, saving a great deal of paper and time. The fact that causality is lost is irrelevant to one concerned only with descriptions of equilibria.
• 62Those who perceive economic theory as a set of propositions which are logically implied by initially hypothesized preference sets and production possibilities understandably find symbolic logic and mathematics a powerful tool: economical, precise, rigorous. But the analysis of the conditions specific to an equilibrium presupposes that the conditions necessary for equilibrium exist. This is hardly much to ask if one restricts his viewpoint to static conditions, in the sense discussed earlier in this paper—that is, to search for a price vector logically consistent with the individuals’ preferences at a specific moment. If one sees the central purpose of economics as the analysis of action, however, the relevant equilibrium is the dynamic one, and its preconditions—interpersonally consistent future plans or expectations—cannot be merely hypothesized. One must attempt to examine the ways in which this interpersonal consistency of expectations can be brought about. This requires the introduction into one’s analysis of empirical (nondeduced) statements about what reactions individuals are likely to have when confronted with unexpected developments. If these reactions were implicit in the initial propositions and therefore could be logically derived from them using their symbolism, they would not be reactions to unexpected developments at all: they would simply be preprogrammed behavioral changes in accordance with perfectly foreseen changes in data and would be empty of learning.
• 63The relative-frequency concept of probability is not applicable to human action with its unique events. For discussion I will simply assume here something which I am by no means convinced is legitimate: that there is an appropriate subjective probability concept according to which future states can be ordered by cardinal degrees of belief.
• 64The relative-frequency concept of probability is not applicable to human action with its unique events. For discussion I will simply assume here something which I am by no means convinced is legitimate: that there is an appropriate subjective probability concept according to which future states can be ordered by cardinal degrees of belief.
• 65Modern analyses using this approach are, like their deterministic counterparts, inevitably static. Even the most sophisticated of the techniques, that of “stochastic dominance,” which permits the entire subjective distribution (rather than only its mean and variance) to be considered, necessarily involves the reduction of an alternative to a “certainty equivalent,” an ordinal which can be value ranked against other alternatives. Essentially, a hypothetical and certain alternative is manufactured—one which has the same value as the uncertain state—and preferences are constructed on the basis of this hypothetical alternative. For example, a man may be indifferent to the choice between $40 and a 50–50 chance at $100 or nothing. In determining preferences he will act as if $40 were actually the alternative; market prices of lottery tickets, for example, will be determined in this manner.
• 66What implications do the foregoing comments have for methodology? How are propositions about economics to be developed? The formal study of patterns of consistent preferences—which I have called the “abstract logic of preference”—may employ the techniques of formal logic and mathematics, particularly set theory. The study of consistent plans, and how inconsistencies in interpersonal expectations are eliminated through learning, requires a technique (if it may be so called) different from the abstract symbolism of mathematics. It requires that specific nondeduced hypotheses be advanced about how an individual’s plans and preferences change when he is confronted with unexpected events. The fact that these propositions about learning cannot be logically derived from other accepted statements may make the analysis appear unscientific, because of course it renders the conclusions dependent upon the accuracy of the empirical hypotheses. But if one accepts Popper’s terminology, the possibility of falsification is precisely that which makes a proposition scientific rather than unscientific.