Prediction is impossible in the general case

In his book, FREEFALL (2009, Penguin Books), Joseph Eugene Stiglitz, a professor at Columbia University and a recipient of the Nobel Memorial Prize in Economic Sciences (2001) and the John Bates Clark Medal (1979), states that economics is a predictive science. Now, one must distinguish between predicting a) planetary motion in its scheme of recurrence, and b) this afternoon’s weather vs. next month’s weather, or this afternoon’s prices and quantities vs. next year’s prices and quantities, all subject to to conditions diverging in space and time.

The economic process is an ecology consisting of schemes of recurrence such as crop cycles and manufacturing cycles devised by engineers which can be represented by classical equations.  However, each of today’s recurrent economic schemes once had a probability of emergence and now has a probability of survival.  And economic schemes of recurrence do not exhibit the rigidity of planetary schemes of recurrence.

The economic issue arises in an ecology in which abstract relationships are complemented by concrete probabilities. [CWL 15, 89]

one is led to think of schemes of recurrence, whose several carriers severally follow their own classical laws, whose assembly follows the probability of their emergence, and whose continued functioning follows the probability of their survival.  Such in a nutshell is the evolutionary view that in Insight I sketched out under the name of emergent probability and, earlier in this essay, I have applied to economics. [CWL 15,  92-93]

Our analysis … acknowledged the existence of schemes of recurrence in which a happy combination of abstract laws and concrete circumstances makes typical, further determinations recurrent, and so brings them under the domination of intelligence.  Moreover, it acknowledged that concrete patterns of diverging series of conditions are intelligible; granted both the requisite information and mastery of systematic laws, it is possible in principle to work from any physical event, Z, through as many prior stages of its diverging and scattering conditions as one pleases; and it is this intelligibility of concrete patterns that grounds the conviction of determinists, such as A. Einstein. … However, we agree with the indeterminists inasmuch as they deny in the general case the possibility of deduction and prediction. For while each concrete pattern of diverging conditions is intelligible, still its intelligibility lies not on the level of the abstract understanding that grasps systems of laws but on the level of the concrete understanding that deals with particular situations.  Moreover such concrete patterns form an enormous manifold that cannot be handled by abstract systematizing intelligence for the excellent reason that their intelligibility in each case is concrete. There results the peculiar type of impossibility that arises from mutual conditioning. Granted complete information on a totality of events, one could work out from knowledge of all laws the concrete pattern in which the laws related the events in the totality.  Again, granted knowledge of the concrete pattern, one could use it as a guide to obtain information on a totality of relevant events.  But the proviso of the first statement is the conclusion of the second; the proviso of the second statement is the conclusion of the first; and so both conclusions are merely theoretical possibilities.  For the concrete patterns form a non-systematic aggregate, and so it is only by appealing to the totality of relevant events that one can select the concrete pattern; on the other hand, the relevant totality of events is scattered, and so they can be selected for observation and measurement only if the relevant pattern is known already  [CWL 3, 650/672-3]

To be sure, the economy does not have the rigidities of the schemes of recurrence of planetary motions.  It resembles more the weather.  From time to time innovation and investment opportunities may happen to be greater or lesser; participants may act in unexpected ways and violate norms out of ignorance or malice.  Economic occurrences exhibit randomness.  But the abstract explanation of economic functioning – in classical equations implicitly relating and defining outlays-incomes and receipts-costs – exists always as a current invariant. Its existence is not probabilistic.  One must not confuse the universally-relevant, primary relativities – the laws of Gross Domestic Functional Flows – with the probabilistic secondary determinations, such as coincidental prices and quantities in the non-systematic manifold.

besides the statistical predictions, there exist the fully accurate predictions that are exemplified by astronomy and that rest on the existence of schemes of recurrence.  (See CWL 3, 120-24/ 143-48) Moreover, the intelligent manner of making these predictions is to analyze the schemes into their component classical laws.  Copernicus corrected Ptolemy’s imaginative scheme; Kepler corrected the circles of Copernicus; but it was Newton who worked out the underlying laws and Laplace who revealed the periodicity of the planetary system.  From that discovery of laws the great movement of thought, named modern science, received its most powerful confirmation. [CWL 3, 112/135]

But in the case of events in a non-systematic manifold, deduction and prediction in the general case are impossible; nor, for that matter, would prediction for control be desirable.

For Lonergan, prediction and control are not legitimate ends of science because they are not the same as verified understanding, which is the true aim of science.  Moreover, prediction and control in the area of the so-called applied human sciences conflict with the very nature of the subject matter of human science: on the one hand, prediction and control depend upon and imply the policy of elimination of human freedom; on the other, human freedom is something that may just spring up even in situations in which people have managed practically to eliminate it. [CWL 15, Editors’ Introduction, ftnt 32, xxxvii]

There exist both systematic and non-systematic processes:

… let us divide ideally constructed processes into systematic and non-systematic.  Let us define systematic processes by the already enumerated properties that, other things being equal,

  1. the whole of a systematic process and its every event possess but a single intelligibility that corresponds to a single insight or single set of unified insights
  2. any situation can be deduced from any other without an explicit consideration of intervening situations, and
  3. the empirical investigation of such processes is marked not only by a notable facility in ascertaining in checking abundant and significant data but also by a supreme moment when all data fall into a single perspective, sweeping deductions become possible, and subsequent exact predictions regularly are fulfilled. [CWL 3, 48/71]

Finally, there emerges the rule for constructing non-systematic processes.  For a system is ‘random’ if it is ‘any whatever provided specified conditions of intelligibility are not fulfilled.’.  But non-systematic process results from any basic situation provided it lacks intelligible unity from a definitive viewpoint. Therefore the rule for constructing non-systematic processes is to begin from any random basic situation. [CWL 3, 50-51/74]

Again, science is the verification of understanding.

Still, though both classical and statistical hypotheses need verification, verification has not the same meaning in both cases.  Because the relations between measurements converge on the functional relations that express classical laws, it is possible to substitute the numerical values determined by the measurements for the variables that are functionally related by laws.  In contrast, because relative actual frequencies differ at random from probabilities, it is not possible to deduce the probabilities from any fully determinate mathematical formula by substituting for the variables of the formula the fractions that correspond to relative actual frequencies. [CWL 3, 65-6/89]

The converse to this difference in the meaning of verification appears in the difference between classical and statistical predictions.  Classical predictions can be exact within assignable limits, because relations between measurements converge on the functional relations that formulate the classical laws.  But because relative actual frequencies differ at random from probabilities, statistical predictions primarily regard the probabilities of events and only secondarily determine the corresponding frequencies that differ at random from probabilities.  Hence, even when numbers are very great and probabilities high, as in the kinetic theory of gases, the possibility of exception has to be acknowledged; and when predictions rest on a statistical axiomatic structure, as in quantum mechanics, the structure itself seems to involve a principle of indeterminacy or uncertainty. [CWL 3, 66/88-9]

For in the general case, any event Z, is deducible from antecedent circumstances, Y, provided some P, Q, R, … continue to occur and provided some U, V, W, … do not intervene. ¶It follows that the occurrence of P, Q, R, … and the non-occurrence of the U, V, W, … are similarly deducible. ¶It follows further that the occurrence of, say, P is conditioned by the occurrences A, B, C, … and the non-occurrences, G, H, I, … Similarly, there will be a series of positive and negative conditions for Q, R, … and for U, V, W, … Similarly, each term in these series will have its series of positive and negative conditions, and so forth. ¶Such, then is the diverging series of conditions. [CWL 3, 94-5/118]

Moreover, the conditions of any event, Z, at any nth remove are scattered in space and time.  They are scattered in space, inasmuch as the occurrences and non-occurrences conditioning the event, Z, whether directly or indirectly, proximately or remotely, may be found in any direction and at any distance from the event, Z.  They are scattered in time, inasmuch as the influence from the condition to the conditioned is propagated with a finite velocity and, in different cases, traverses either equal distances with unequal speeds or unequal distances with equal speeds. Evidently this scattering of conditions makes it imperative to know beforehand the aggregate of concrete patterns of diverging series of conditions for events of all kinds; otherwise, one would not know which observations to make and it would be only by luck that one hit upon those that were relevant. [CWL 3, 95/119]

… we set out to indicate an exact meaning for both the indeterminacy of classical laws and the consequent canon of statistical residues.  It has been argued that classical laws are indeterminate because they are abstract and so can become determinate premises for the deduction of determinate events only if sets of positive and negative conditions are fulfilled. Moreover, from this indeterminacy of the abstract there follows a canon of statistical residues because in the general case such sets of conditions are coincidental aggregates and coincidental aggregates can be investigated with scientific generality only by statistical methods. [CWL 3, 97/120]

Also,

Finally, statistical investigations in their turn have no genuine tendency to totalitarian aspirations.  For besides the statistical predictions, there exist the fully accurate predictions that are exemplified by astronomy and that rest on the existence of schemes of recurrence.  Moreover, the intelligent manner of making these predictions is to analyze the schemes into their component classical laws.  Copernicus corrected Ptolemy’s imaginative scheme; Kepler corrected the circles of Copernicus,; but it was Newton who worked out the underlying laws and Laplace who revealed the periodicity of the planetary system.  From that discovery of laws the great movement of thought, named modern science, received its most powerful confirmation. … At the present moment, the profound significance of statistical laws is coming to light.  But if this new movement is not to degenerate into the old talk about what commonly happens, it must retain its contact with the empirically established precision of classical formulations.  For statistical laws are of no greater scientific significance than the definition of the events whose frequencies they determine; unless these definitions are determined scientifically, statistical thought lapses into pre-scientific insignificance. [CWL 3, 112/135]

To resume the argument, deduction and prediction in the general case are impossible.  They are impossible for man’s limited understanding, because limited understanding could master the manifold of concrete patterns of diverging series of scattering conditions, only if that manifold could be systematized; and it cannot be systematized. [CWL 3, 651/673-74]

And,

… even when the laws involved in the process are thoroughly understood, even when current and accurate reports from usually significant centres of information are available, still such slight differences in matters of fact can result  in such large differences in the subsequent course of events that deductions have to be restricted to the short run and predictions have to be content with indicating probabilities. So perhaps it is that astronomers can publish exact times of the eclipses of past and future centuries but meteorologists need a constant supply of fresh and accurate information to tell us about tomorrow’s weather  [CWL 3, 51/74]

Further,

Objective process is not the realization of some blueprint but the cumulation of a conditioned series of things and schemes of recurrence in accord with successive schedules of probabilities. [CWL 3, 445/470]

Also and again, prediction and control are not legitimate ends of science, especially in the human sciences.

For Lonergan, prediction and control are not legitimate ends of science because they are not the same as verified understanding, which is the true aim of science.  Moreover, prediction and control in the area of the so-called applied human sciences conflict with the very nature of the subject matter of human science: on the one hand, prediction and control depend upon and imply the policy of elimination of human freedom; on the other, human freedom is something that may just spring up even in situations in which people have managed practically to eliminate it. [CWL 15, Editors’ Introduction, ftnt 32, xxxvii]

So, as we covered more fully oaths website, Functional Macroeconomic Dynamics constitutes a scientific theory of primary relativities and secondary determinations. The economic process does not possess the rigidity of planetary schemes of recurrence.  While the theory of Functional Macroeconomic Dynamics consists of a set of primary classical equations constituting the formal cause or immanent intelligibility, to reach determinateness these abstract primary relativities must be applied to concrete secondary determinations occurring in a coincidental manifold.   As to the human efficient causes of the economic process, there is both the fact of ignorance and the freedom to do as one will.  While the process has invariant classical scientific laws relating implicitly defined functions among themselves, the process is, nevertheless, fraught with indeterminacy and unpredictability

The following densely-packed paragraph – shown earlier – is worth another slow read, or five slow reads:

Our analysis … acknowledged the existence of schemes of recurrence in which a happy combination of abstract laws and concrete circumstances makes typical, further determinations recurrent, and so brings them under the domination of intelligence.  Moreover, it acknowledged that concrete patterns of diverging series of conditions are intelligible; granted both the requisite information and mastery of systematic laws, it is possible in principle to work from any physical event, Z, through as many prior stages of its diverging and scattering conditions as one pleases; and it is this intelligibility of concrete patterns that grounds the conviction of determinists, such as A. Einstein. … However, we agree with the indeterminists inasmuch as they deny in the general case the possibility of deduction and prediction. For while each concrete pattern of diverging conditions is intelligible, still its intelligibility lies not on the level of the abstract understanding that grasps systems of laws but on the level of the concrete understanding that deals with particular situations.  Moreover such concrete patterns form an enormous manifold that cannot be handled by abstract systematizing intelligence for the excellent reason that their intelligibility in each case is concrete. There results the peculiar type of impossibility that arises from mutual conditioning. Granted complete information on a totality of events, one could work out from knowledge of all laws the concrete pattern in which the laws related the events in the totality.  Again, granted knowledge of the concrete pattern, one could use it as a guide to obtain information on a totality of relevant events.  But the proviso of the first statement is the conclusion of the second; the proviso of the second statement is the conclusion of the first; and so both conclusions are merely theoretical possibilities.  For the concrete patterns form a non-systematic aggregate, and so it is only by appealing to the totality of relevant events that one can select the concrete pattern; on the other hand, the relevant totality of events is scattered, and so they can be selected for observation and measurement only if the relevant pattern is known already  [CWL 3, 650/672-3]

… even when the laws involved in the process are thoroughly understood, even when current and accurate reports from usually significant centres of information are available, still such slight differences in matters of fact can result  in such large differences in the subsequent course of events that deductions have to be restricted to the short run and predictions have to be content with indicating probabilities. So perhaps it is that astronomers can publish exact times of the eclipses of past and future centuries (using “classical laws”) but meteorologists need a constant supply of fresh and accurate information to tell us about tomorrow’s weather  [CWL 3, 51/74 ]

We hope that Professor Stiglitz and others, who make frequent appearances on talk shows to make predictions about the occurrence of events in the intermediate- or longer-term future, will read in either of the two editions of Insight, A Study of Human Understanding, the pages quoted herein plus the surrounding context.

Lonergan, Bernard J. F. (1957 ) Insight, A Study of Human Understanding, LondonLongmans, Green and Co. Ltd.,  [1957 edition, pages 48, 51, 65-6, 94-5, 97, 112, 650-51 ]

or

Lonergan, Bernard J. F. (1997 ) Insight, A Study of Human Understanding, Toronto: University of Toronto Press [CWL 3, 1997 edition,  pages 71, 74, 88-9, 118-20, 135, 672-74]