RÉSUMÉ

On examine le problème de la vérification et de l’application des connaissances en sciences humaines, en considérant successivement trois niveaux : celui des faits, celui des hypothèses et celui des théories. On emprunte des exemples à la science économique. On conclut que la vérification et l’application d’un savoir scientifique consistent fondamentalement à tester la corrélation d’un système d’objets et d’un système d’opérations.

SUMMARY

To examine the problem of verification and application in the social sciences, we consider it on three levels : facts, hypotheses, theories, taking examples from Economics. Our general conclusion is that verifying and applying a piece of scientific knowledge fundamentally consists in testing a correlation between a system of objects and a system of operations.

1. Empirical sciences, if not in themselves applied sciences, have necessarily an applied counterpart which gives precision and achievement to their relationship with the empirical world. My purpose is to lend closer attention to this point in the case of Social Sciences.

But I would like first to dissipate a rather common identification between the predictive power or practical relevancy of a scientific knowledge, and its explanatory value. Successes in the application of a piece of scientific knowledge are usually indeed a positive indication in favour of its explanatory value. Insufficient, however, if we explicit more strictly the meaning of explanation. To explain a phenomena requires, first, representing it into a symbolic system (everyday language or a technical one), second integrating this representation into a larger scheme, in which it appears to be deducible, at least in some sense of the word deduction. It is true that such a determination could apply as well to « explanations » for which we would not willingly claim the character scientific, for example mythical explanations... An adequate restriction should be obtained by giving a more precise meaning to the vague terme « deduction », and by requiring simultaneously canonical processes for verifying the « successes » of applications.

2. In so far, the value of scientific knowledge in the empirical disciplines depends on both exaplanatory power and achievements, both upon an abstract conceptual verification and upon the results of applying the knowledge. It is quite remarkable that, in the realm of Social Sciences, so very seldom are systematically and extensively set up critical processes concerning the second aspect of the evaluation.

Notwithstanding various sociological, political, economical and personal reasons, which conspire to prevent people from disclosing too openly a relative poorness of results, there is an epistemological quite cogent one. It lies in the specific relationship of Social Sciences to the empiric world of human facts, and this is the sole circumstance that I will consider. I’ll try to examine from this point of view of verification and application three levels of scientific knowledge : facts, hypotheses, theories.

Facts

1. A general observation about scientific facts which is of great moment with respect to the true meaning of verification : science does not deal with actual, but virtual facts. Actual facts are unique, and completely determined, either in present time or in the passed. Scientific knowledge necessarily uses counterfactual reasoning, considering alternative situations : explanation requires that any actual fact might be taken as representative of a multiplicity of virtual ones, forming a system. Virtual means here : incomplete, schematic, and undated. From this point of view, History qua science appears as a limit-form, but even in this case, virtuality is reintroduced by the impossibility of acquiring complete knowledge of the passed facts.

Another aspect of virtuality : the « non-observables ». Every science, in some degree, introduces non-observable facts to close a structure.

The case of statistical facts. Paradoxically, probability calculus restores in a way the actuality of virtual facts, substituting for individual, virtual events, some collective events representative of the first, and treated as actual.

2. Concerning particularly facts in Social Sciences, a point must first of all be emphasised : while the facts considered in the sciences of matter have generally an intuitive prototype, on the basis of which the scientific concept is construed, it may not be so for the human fact. Or better, the intuitive prototype, being very pregnant and strong, blocks the construction of adequate concepts. The departure from intuitive images to abstract concepts is difficult, sometime even arbitrary.

An example : the concept of agregated price, or price level in Macro-Economics.

A quantitative artificial notion pt is defined, such that : Pt.Qt=q Ph.Qht. Pht : Price of the commodity h at time t, Qht : Quantity of the commodity h at time t, are directly intuitive notions. Qt is a fictive quantity : level of agregated production, defined in function of reference prices Ph, ponderating the effective quantities of commodity produced : Qt = q Ph.Qht.

Pht is then defined as the quotient :qPht.Qht/qPh.Qht  [1] .

This number has not really the dimension of an intuitive price ; it is a mere index.

3. An important problem, insufficiently considered : to what extent are the data significant in Social Sciences ? In the representative case of Economics, I’ll refer to a devastating critique by Morgenstern (On the accuracy of economic observations, 1961). From a study of the collecting methods Kuznets evaluates the errors for the US national Revenue to be 15 to 30% ; now, a 10% error equals more than three times the total exports of USA... Moreover, such inexactitudes in the estimation of basic data may have spectacular consequences for the determination of derived notions. For instance, let us suppose that the USA PNB has been estimated 550 billions $ ±5% at to and 560 billions $ ±5% at t1. According to the directions of the errors admitted, the estimated growth rate should be -7,9% or +12,5%, and in the hypothesis of a null error, it would be +1,8%...

So, the verification of facts in Social Sciences and their application (that is the passage from virtual to actual facts) encounters considerable essential obstacles. To cope with them, the social scientist is bound to explicitly indicate his conceptual definitions, his processes of collecting data, and to deduce alternative determinations depending upon several possible « real » states of the data.

Hypotheses

1. Hypotheses consist in postulating virtual facts, which distinguishes their status from that of facts proper (virtual but posited) and from conjectures (postulating an actual fact).

An hypothesis is characterised by its function in a system of sentences, which is a theory. Two aspects of this function :

a) « Norm ». A paradigmatic notion fixing a conceptual frame for describing the facts of a science. For instance, the notion of phoneme constitutes an hypothesis about the semiotic structure of sounds in a language.

b) « Axiom ». Hypotheses that determine objects by means of mutual explicit relations. Such a determination is submitted at least ideally to a kind of closure of the system of objects, and is correlative of rules for handling them.

2. What must be the relationship of hypotheses with empirical world, particularly in Social sciences ? The meaning of an hypothesis may be subordinated to conditions impossible to be satisfied empirically (in Thermodynamics : the case of the concept of entropy, originally defined for revertible processes). In Economics, a paradoxical thesis (Friedman, Essays in positive Economics, 1953) :

« Truly important and significative hypotheses will be found to have « assumptions » that are wildly inaccurate descriptive representations of reality », and moreover : « the more significant the theory, the more unrealistic the hypotheses ».

This outrageous paradox brings out an effective feature of hypotheses : they need to be strongly idealized descriptions of virtual facts, lest they should overdetermine ab initio the conceptual scheme. Nevertherless, effective hypotheses are always capable of having derivations, in the theory, susceptible of an approximate comparison with actual facts, the degree of strictness of which beeing a matter of convention.

3. Hypotheses are not properly verified, but confirmed, completely or partially, inside a theory, essentially by considering their consequences. An interesting problem : when an hypothesis is partially disconfirmed, through examination of its consequences, what exactly is to be rejected, how is to be distributed the refutation over the elements of the hypotheses, or even all over the theory ?

An example : in Economics, hypotheses of the « expected utility »  [2] . The system of hypotheses schematizes the behavior of an economic actor in aleatory situation. The abstract objets considered are : « loterry tickets », gains assorted with probabilities. Tickets may be combined. The hypotheses are :

1) Existence of a preorder (transitive and reflexive) on the set of tickets.

2) « Continuity » : if f < h < g, there exists a combination Rf+(1-R)g equivalent to h. Consequently : f < g implies f < af+(1-a)g < g

3) Independence : the same combination of two different tickets with the same ticket does not modify their order (f < g implies : af+(1-a)h < ag+ (1-a)h), and reciprocally.

4) Composed lotteries with the same resulting expected value are equivalent. For instance :

equivalent to

It is important to see that this system of hypotheses has a twofold function : abstract axiomatization, making possible the existence of a numerical rating function on tickets (satisfactions) ; empirical meaning, it can be approximately tested by inquiries among individuals. This dual aspect is characteristic of the function of hypotheses in Social sciences : a kind of intermediary between virtual and actual facts.

But the system of hypotheses may be questioned, considering some paradoxical consequences. Two classical examples :

a) The « paradox of the alpinist ». f= sure death < g= sure survival. The lottery af-(1-a)g is preferred to g (and of course to f) for certain values of a, by the practising alpinist : f < g < a-(1-a)g. Which is contrary to axiom 2. A solution explaining this contradiction : the axiom discards the « amour du risque ». The hypotheses could be preserved at the cost of an explicit restriction of the domain of the facts considered.

b) The Allais paradox   [3] . Between ticket a1 and a2 a subject chooses a1 : the sure thing.

The same subject chooses a3 as against a4, the expected value of which is inferior.

The choices do not violate the hypotheses, but nevertheless are incoherent : impossibility of fixing a satisfaction function. The subject has chosen a1, the expected value of which is indeed superior to that of a2, and yet he has chosen a3 as against a4, albeit the value of a3 is inferior to that of a4. Which of the hypotheses is to be rejected ? Independence, as we may show, introducing ticket a* :

We can now restate the tickets :

Axiom 3 gives : if a1 > a2 : 0,11a* + 0,89a < 0,11a + 0,89a implies a* < a

if a3 > a4 : 0,11a + 0,89.0 < 0,11a* + 0,89.0 implies a < a*

The economists reject hypothesis 3 or, weaken it.

So applying knowledge in the sciences of man admits of a liberal attitude with respect to the empirical meaning of hypotheses. « Verification » of hypotheses consists in a test of coherence and fecundity relative to a complete system of propositions organized as a theory.

Theories

1. I’ll introduce a preliminary distinction between theories proper and « prototheories », for instance econometric models. Prototheories are characterized by their « locality » : describing a strictly isolated field of phenomena ; and the absence of explanatory interpretation. For instance, the Philips curve (1958) : the rate of growth of prices is a decreasing function of the rate of unemployment. Established for England between 1861 and 1957, not confirmed later. Freedom of interpretation : neo-keynesian (salaries adjust themselves to employment) ; or neo-classical (unemployment is a result of prices and salaries).

Such prototheories have to be checked from two standpoints : verified as enunciation of facts, and evaluated in a theoretical context.

2. An example of pure theory : the extreme case of Debreu’s theoretical construction for General economic equilibrium.

a – The objects are highly abstract notions : homogeneous individual consumers and producers ; vectorial space of commodities and dual vectorial space of prices.

The producers and consumers respectively choose points of the space of commodities. This choice is not a function but a correspondence between couples of one price and one initial asset, and sets of vectors in the space of commodities.

An equilibrium is a state in which the excedentary demand is negative or null, and such that there exists a price to which some of the corresponding excedentary demands are contained in the negative quadrant of the space of commodities.

b – Hypotheses of « rationality » : the sets of production are closed and convex. The sets of consumption are under the hyperplan defined by prices and the initial assets of consumers.

c – The purpose of the theory is to establish the abstract conditions that guarantee the existence and stability of an equilibrum. The solution is of a topological and analytical nature : compacity of the subspace of the excedentary demands, superior semi-continuity of the correspondence...

Such a theory is purely explanatory, and on a high level of abstraction where no empirical verification would be meaningful. It ascertains fundamental concepts (equilibrium), as well-construed notions. More concrete theories should build a bridge giving access to micro and macroeconomic mechanisms.

3. Is it possible to completely eliminate « theoretical terms », so that a theory should be reduced to a system of relations between empirical notions, directly accessible to verification ? A nominalistic ideal for Empiricism.

What is a theoretical term ? Sneed : t is theoretic if in every experience of measurement determining its value, the theory must be presupposed valid.

The question is : are the contents of a theory only of empirical nature ? The history of science demonstrates the essential contribution of mathematical (and even purely logical concepts) to the explanation of phenomena. Examples : the contribution of the Calculus to the creation of the fundamental concepts of Mechanics (Leibniz, Lagrange, Hamilton). Mathematics is not a mere language. Formal thought introduces « formal contents » in the representation of phenomena, irreductible to empirical contents.

4. What is the weigh of predictive power in the process of verifying a theory ? At the beginning, I insisted on the difference between predictive power and explanatory value. Especially in Social sciences, what does signify failure of prediction ? Theories concern virtual facts, prediction concerns actual, historically determined facts. To judge a theory on its incapacity to predict, one should make allowance for the reasonable indetermination of actual conditions it admits, and estimate, on the other hand, to which degree its concepts may adequately define virtual facts. The explanatory power of a theory depends on functional deductions inside an abstract system. But its power of prediction depends also on the acknowledgement of strategic factors, reintroducing pragmatically the notion of cause, and moreover of external aleatory conditions.

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In general terms, I would say that verification and application of scientific knowledge both essentially consist in testing the capacity and limitations of a system of operations with respect to a system of objects ; the more abstract the operations and objects, the farther the practical relevancy of the knowledge, but no fundamental difference appears with the different degrees of abstraction, and in this respect every empirical science is virtually an applied science, and this has been one discovery of Galilean and Cartesian age.

In the case of the sciences of man, the difficulty of adequately constructing the objects and determining the correlative operations, conceptual as well as material, is still enhanced by the blinding effect of strong immediate subjective notions. So that the gap persists between very abstract theories, without any direct empirical purport, and local, partial prototheories, reasonably if only weakly, predictive, but without any explanatory power. Are social sciences doomed to stay in this unsatisfactory state ? The advances are very slow and scarce indeed ; nevertheless, the past history of the development of other sciences may cause us to foster better hopes, even if it is hard and disappointing to apply rational knowledge to human facts.

L’auteur

Professeur émérite à l’Université de Provence, professeur honoraire au Collège de France.

Principaux travaux :

Méthodologie économique, PUF, 1955.

Pensée formelle et sciences de l’homme, Aubier, 1956.

Essai d’une philosophie du style, A. Colin 1960 ; 2ème éd. Odile Jacob, 1988.

La théorie aristotélicienne de la science, Aubier, 1976.

Langages et épistémologie, Klincksieck, 1979.

Pour la connaissance philosophique, Odile Jacob, 1988.

Invitation à la lecture de Wittgenstein, Alinea, 1990.

La vérification, Odile Jacob, 1992.

Champs d’intérêt : Epistémologie générale et épistémologie des sciences de l’homme ; Aristote ; Wittgenstein.

* The topics sketched in this paper have been developped later in a book : La vérification, Odile Jacob, 1992.

** Collège de France (Paris

[1] . Cf. Malinvaud,  Théorie macroéconomique, 1981.

[2] . Cf. Ph. Mongin, « Problème de Duhem et théorie de l'utilité espérée », in  Fundamenta Scientiae, vol 9, n° 43, 1988, pp. 299-327.

[3] . Cf. Allais, "Le comportement de l'homme rationnel devant le risque",  Econometrica, t. 27, 1953, pp. 503-556; Allais and Hagen,  Expected utility hypothesis and the Allais Paradox, 1979.