The Problem : How to justify propositions in a context of cognitive finitude ?

Ever since the challenging of mathematical and scientific certainties at the beginning of the twentieth century, scientists have realised that they do not for the moment hold any sort of procedure for absolute foundation and that all knowledge is therefore fallible. For example, Einstein stated about physics that “The truth of a theory can never be proven, for one never knows if future experience will contradict its conclusions1.”

Such fallibility is accepted a fortiori in other branches of knowledge. Thus, in economic science, it is acknowledged that even the interpretative models currently used by most researchers – for instance correlation between rise in monetary mass and rise in prices – may be corrected or improved in view of unprecedented social situations2. In constitutional law, specialists have given up on the idea that fundamental rights represented immutable principles – whether “sacred”, “natural” or derived from some “universal reason”–, and they now recognize that such rights may be revised, through the introduction of more demanding procedures, in as legitimate a fashion as in any positive law3. Such a humble approach is now spreading to philosophical studies, gradually undermining the absolutist goals philosophy once aspired to4. Kuhn notes for instance that “few philosophers of science still seek absolute criteria for the verification of scientific theories.5 ”. Habermas’s view is that philosophy “now disposes only over knowledge that is fallible6”.

Despite that general acknowledgment of cognitive finiteness – that is to say the absence of absolute fundament –, scientists and the majority of philosophers keep on upholding their positions against contending views in an effort to “pretend to validity”. While admitting his relativity theory was probably erroneous, Einstein never let up trying to make it more widely known, in spite of many opponents, be it defenders of Galilean kinematics or Newtonian cosmology, holders of the incontrovertibility of Euclidean geometry or of alternative versions of general relativity. In sociology or economy, although the notion of fallibility is perhaps more generally accepted than in other fields, each and every theoretician continues to defend their own interpretative models against contending models. Finally and significantly, although the tenants of fallibility in knowledge in philosophy or epistemology claim the absence of absolute fundament and even the essentially contingent nature of any type of knowledge, they are the very same ones that staunchly resist the objections raised by the so called “dogmatists”, “absolutists” or “metaphysicians.”

Cognitive finiteness is now recognized, yet the claim to validity remains all the same. But are cognitive finiteness and claim to validity compatible notions? How can anyone hold a claim to validity if the only type of knowledge on can reach is fallible, that is possibly false or inadequate? How can any proposition be justified in the context of cognitive finiteness? Can a rationally acceptable conclusion derive from uncertain assumptions?

Solving the problem

The claim to “greater verisimilitude”

Instead of positing absolute validity – which would be acceptable in any given time or space – the claim would be that a held position is better than all the other competing theories known at the time. Such an approach is known as the claim to “greater verisimilitude.”  That way, the risk of positing, on the one hand, an unreachable universal validity or, on the other hand, an all levelling and self contradictory relativism where any competing theories would be equivalent or equate one another, is avoided.

Such an approach is not new. It is often used by epistemologists, such as Popper: “The best we can say of a hypothesis is that up to now [...] it has been more successful than other hypotheses although, in principle, it can never be justified, verified, or even shown to be probable.7” Kuhn’s words follow suit: “Verification is like natural selection: it picks out the most viable among the actual alternatives in a particular historical situation8.” Indeed Einstein claimed that his own theory, although probably erroneous, was still better than Newton’s position9.

The preference criterion

This raises the following question: what makes it possible to claim that a theory is better than another? More specifically: what makes a problematic theory better than another equally problematic theory? Why, for instance, should one favour Einstein’s relativity theory over Newton’s, when both theories have been criticized? In other words, it is necessary to define a preference criterion which would make it possible to set competing theories into a hierarchy.

Epistemologists such as Popper, Kuhn or Lakatos put forward several preference criteria such as the absence of objection, the importance of the problems raised by each contending theory, the partial resolution of the problems raised, etc. The general approach that will be used here can be summarized as follows: let two theories A and B be contending, the B theory is better than A if it solves some or all the problems caused by the A theory, provided the A theory cannot solve any of the problems possibly caused by B. In more simple terms: the B theory is better than A if at least one problem met in A is solved thanks to B, and if no problem caused by B can be solved thanks to A 10.

A learning process

If a given A theory cannot solve any of the problems possibly found in the B theory, it means that the B theory comprises all the improvements already apparent in the A theory, and that the latter is somehow contained within the B theory. Hence the idea that a better theory is one that has integrated a former one, that has learned from it. Whenever two theories are thus compared, it is a learning process that is being looked at.

According to the preference criterion mentioned earlier, a better theory includes the former theories not so much because they comprise their conclusions but because the solved problems within the former theories – and considered as relevant in the newest theory – find themselves equally resolved thanks to the best theory. In view of the preference criterion, Einstein’s relativity theory “includes” Newton’s theory not because the premises of Newton’s theory are integrated within Einstein’s – as though Einstein’s theory would be inferred from Newton’s – but because Einstein’s theory makes it at least possible to come up with the same results, among which the accurate results, as those from Newton’s theory.

If a better theory is one that does not include the conclusions but the solutions found in the former theories, then one can say a better theory includes in a reshaped form the conclusive contents of the former theories.

The learning process deriving from the preference criterion is thus a reconstructive process when each new step reformulates the former stages. It is akin to the definition of a learning process as put forth by Piaget, in L’épistémologie cognitive, according to which “learning” when “between two structures of different levels, there is no one-way reduction, but a mutual assimilation such as the superior can be derived from the subordinate by means of transformations, but also in such a way as the first one enriches this last one by a process of integration11.”

Therefore, in the context of cognitive finiteness, justifying a scientific position consists in showing it is the temporary stage of a learning process. It could be named “comparative demonstration”, or “dialectical demonstration”, insofar as it is about justifying a position from inadequate competing theories, just as Aristotle defined dialectics12.

A model for scientific presentation

If a position is rationally acceptable only if it is better than competing theories, then the rational acceptance of any position will be all the more secure as it was compared with a larger amount of competing theories. In other words, the larger the number of competing theories a presentation will deal with, the better such a presentation will be deemed “scientific”, “serious” and “thorough”, as opposed to simple unsubstantiated opinion. A theory will be considered “scientific” not because it rests on a immutable basis, but because it results from a proceeding in which more positions have been taken into account. That is why there is no radical difference between an opinion and a scientifically based position, it is more a difference of degree depending on the quantity as well as the quality of the competing theories which have been considered. From that point of view, Euclide’s Elements, the Ethics of Spinoza or Tractatus logico-philosophicus of Wittgenstein are insufficient in that they content themselves with setting down axioms and deducting the consequences from it; the possible evocation of competing theories plays no important role in its demonstration. Conversely, Plato’s dialogues, Aristotle’s treaties or Einstein’s presentations are consistent because they allow much room to the examination of competing theories within the demonstration itself, although such an approach does not necessarily reflect on the quality of the analysis itself: a conclusion may be correct although it has been incorrectly demonstrated; on the contrary, a position can be perfectly demonstrated yet invalidated after new data have been brought in.

The range of application of the dialectical demonstration

Application in sciences

Such an approach has often been used by many authors in several fields, which allows us to understand their reasoning better. It is the case of physics. In his Dialogue Concerning the Two Chief World Systems, Galileo justifies the Copernican conception of the world by grounding the bulk of his theory on the inadequacies of the Ptolemaic theory. Similarly, in most of his papers on the theory of relativity, restricted or general, Einstein always starts with the examination of both the contributions and inadequacies of Newton’s physics before he puts forth his own theory. The dialectical demonstration approach is also to be found in logic, especially in justifying new analytical methods and axioms. That is why logic specialists, when devising alternative or complementary, first make sure they have presented the deficiencies of standard logic before they bring forth new axioms. In Intellectual Structures for instance, Robert Blanché criticizes the insufficiencies of Apuleius’s Square of Opposition before he proceeds to introduce his own hexagonal graph. Dialectical demonstrations also prevail in mathematics, even though mathematics is considered to rely mostly on deductive reasoning. In Proofs and Refutations, Lakatos shows that mathematical argumentation sometimes has to be based on confrontation between several contending theories. Such a confrontation proceeds through trial and error, a pattern very similar to that encountered in any learning process, in the manner of a Socratic dialogue such as in Plato’s Meno. Finally, the comparative demonstration is also used in sociology, for instance in Durkheim’s Suicide. The author first looks into all the contending theories dealing with the causes of suicide – from psychological, race-oriented, heredity-based to social theories – before he presents his own position on the issue. Presumably bridging gaps and righting former errors, his theory is presented as being more satisfactory than the previous positions. More recently, Habermas’s chapters in Theory of Communicative Action are mainly concerned with the critical analysis of contending theories. His own position comes only at the end of the important parts of his work, in the “Intermediate Reflections”. The argumentation is used here to justify the dialectical demonstration approach, as well as the preference criterion mentioned earlier, follows a similar process. The dialectical demonstration thus finds itself demonstrated of its own, as it were, since all logical circles are not vicious13.

Daily life applications

It can be wondered whether the dialectical demonstration does not proceed from a spontaneous operation of the human mind. This question is rendered even more legitimate since the authors mentioned so far seem to use that method without ever justifying it, as though it were a perfectly natural intellectual process. It seems that whenever one makes a decision or opts for a solution, one does not merely infer from previously admitted experiences or principles. One makes a comparison between contending propositions, and chooses among a number of possible options. The one choice does not come about just because it is absolutely vindicated, but simply because it seems the best of all the other choices. It goes to prove that the human mind does not operate only according to rules of deduction, induction or association, but following rules of comparison as well. Piaget’s research and other recent experiments in artificial intelligence tend to confirm that pattern14. The dialectical demonstration would not only be used in specific fields such as scientific activities but also in daily life, making the dialectical demonstration process a universal one.

The case of risky reasonings

One of the most remarkable applications of the dialectical demonstration process is in dealing with risky reasoning. In Fact, Fiction and Forecast, Goodman showed that risky reasonings were not only due to inference from the general to the particular or the future from the present – forbidden by deductive logic – but due to the fact that a particular case can confirm a large number of incompatible hypothetical statements, including a statement and its exact counter statement. For example, the empirical statement, “every emerald is green today” will confirm the general statement “every emerald is green” as well as “every emerald is either blue or green” (“grue”), not to mention the statement “every emerald is either blue, green or red”. Goodman’s paradox is quite telling in that it shows that the conclusion of an risky reasoning is always the result of a selection between a wealth of competing theories15. When, for instance, the following assumption is made:  “I could only see black crows, which means all crows are black”, hypothetical statements such as “all crows are black in summer but brown in winter” or  “crows are not naturally black but have a disease that darkens their feathers” are immediately ruled out.

If the results of risky reasoning are those of a comparative process between several contending propositions, it means that those results are considered better than the other positions. Now the dialectical demonstration makes it possible to rationally establish which position is the best among a group of competing theories. Dialectical demonstration therefore makes it possible to justify rationally the results of risky inferences. The use of this method drives away dead-ends such as can be encountered in the so called  “inductive logic”. It does not follow, however, that the dialectical demonstration necessarily “rescues” risky inferences. It does not at all imply that every inductive reasoning –  “A few x are y, therefore all x are y ” – is valid. Dialectical demonstrations only “rescue ” the results of such reasonings by substituting themselves to risky inferences. They provide, to a certain extent, a “non inductive ” use of such inductions. In that respect, dialectical demonstrations are in complete keeping with deductive logic when it considers risky inferences as “erroneous ” or “not rational. ”

A Methodology of the comparative demonstration approach

A dialectical demonstration implies a series of introductory operations, some of which have remarkable epistemological consequences.

Assessing the various competing theories

A dialectical demonstration first presupposes the survey of the various competing theories. Such positions can be gathered in several fields.

First and foremost one ought to take stock of the contending theories currently debated in the field concerned. For instance, if a new gravitation theory is to be put forward, it has to be compared to the other gravitation theories in debate among physicists, such as the general theory of relativity or the various string theories.

However, some subjects cross over several scientific fields. The study of human behaviour, for instance, is the subject matter of biology, psychology and sociology. A survey of the contending propositions must be carried out in a study of other fields. A comparative demonstration thus implies and justifies cooperation in scientific fields, i.e. an interdisciplinary approach.

Nothing, in the end, guarantees that prior theories can resolve certain problems encountered in more recent theories. It is therefore necessary, in order to justify a position, to go beyond the survey of currently contending theories: the theories put forward in the past have to be taken into account as well. Hence the history of a theory cannot be seen as just a scholarly supplement to science, but rather as one of its necessary conditions. There cannot be a rigorous practice of science without a knowledge of the history of science, and there can be no true scientist who is not also a historian of his own subject.

Selecting the competing theories

Nevertheless, the number of competing theories can be so high that it is not always possible to include them all within the demonstrative process. Selecting the various contending theories is therefore a necessity. The question of criteria according to which such a selection is made arises. Epistemologists have suggested several criteria, such as the notoriety of the theory, the solidity of its argumentation or the greater proximity with the adopted preference criterion.

The choice of criteria depends on the intent behind the demonstration. If it only aims at convincing, it is nothing less than a rhetorical tool and in that case the notoriety criterion will be chosen. It is a given fact that a position presented as better than all the previous ones is far more convincing. On the contrary, when scientific validity is the real goal, the greater proximity criterion with the preference criterion will be preferred, since the object of the demonstration is precisely to determine which position best corresponds to the preference criterion.

A rational understanding and reconstructing competing theories

A dialectical demonstration implies the survey and criticism of competing theories. Surveying and criticizing presupposes a thorough understanding of each contending theory. “Understanding ” means not only grasping what the author meant but also identifying the possible errors and inadequacies of a theory. Without the understanding phase, the attribution of characteristics and problems of one theory to another is likely. The survey can then become incomplete or include irrelevant positions. What’s more, the criticism of the selected positions may not successfully reflect the real impact and limitations of the different positions. The methodology of a dialectical demonstration must therefore include a necessary stage of understanding of the various competing theories, which amounts to a hermeneutic stage.

Yet understanding the various contending theories can be awfully complex. Hermeneutic philosophy has tried to list the possible difficulties and bring solutions, which will just be mentioned here, be it the language barrier, the translation problem of a paradigm to another or the issue of the rational reconstruction of relevant yet misread positions.

It is possible to avoid, partly at least, some of those snags: the dialectical demonstration consists in comparing the various competing theories as they are known. In that case, whenever a dialectical demonstration is being carried out, the less known or totally unknown theories should not be taken into account. If a position is not entirely understood or if its understanding is debatable, a survey of the different interpretations of that particular position will suffice.

Implications and limitations of the dialectical demonstration

Consequences of the dialectical demonstration

As is obvious from the paragraphs above, the dialectical demonstration has several epistemological consequences: it introduces new norms of scientism, redefines the limitations between knowledge and opinion, it modifies the traditional conception of human thought. Other important consequences will be now broached.

The dialectical demonstration consists in establishing the validity of positions from the inadequacies of other known competing theories. Since there is no guarantee that relevant new competing theories may arise in the future, the dialectical demonstration does not claim to present an absolute validity. Yet by determining the best of positions among all the existing positions, it establishes a hierarchy between them. It thus avoids the trap of impossible absolutism and the trap of levelling and self-contradictory relativity. In other words, a dialectical demonstration makes it possible to justify positions in the absence of any absolute basis and, at the same time, to organise positions into a hierarchy that are still seen as hypothetical. It thus solves the recurring issue opposing scepticism and dogmatism.

If the comparative demonstration justifies positions in the absence of any absolute basis, hence justifying what appeared as just hypothetical theories, it also justifies the conclusion of risky reasoning – as shown above – as well as the “unprovable premises” of the deductive logic, that is to say the law of identity, the principle of contradiction and the law of excluded middle. It was indeed through the use of such a device – that is, one that undermines the main competing theories – that Aristotle justified the principle of contradiction in chapter IV of book Γ of Metaphysics. The comparative demonstration process thus supplements and completes the insufficiencies of deductive logic and becomes the very basis of it.

Limitations of the dialectical demonstration

Such a process comes with at least two series of difficulties.

First, it does not claim to absolute validity. As it is a self-conclusive process, the remark applies to it as well. It merely brings about the best solution at a given time. Consequently it is likely that a better substitute comes along in the future, after the examination of new data.

Secondly, the methodology of the dialectical demonstration – that is to say assessing, selecting, understanding and rationally reconstructing prior competing theories – implies Hermeneutic skills that have not so far been formalized. Such a process is therefore fallible and leaves room to human error and arbitrary subjective criteria – contrary to deductive logic, for instance.

1 A. Einstein, “Induktion und Deduktion in der Physik”, Berliner Tageblatt, 25 décembre 1919, suppl. 4, p.1.

2 Cf. for example M. Kennedy, Geld ohne Zinsen und Inflation. Ein Tauschmittel, das jedem dient, München, Goldmann, 2005.

3 For instance J. Habermas, Between Facts and Norms: Contributions to a Discourse Theory of Law and Democracy, translated by W. Rehg, Cambridge Mass., MIT Press, 1996, chapter VI “Judiciary and Legislature: On the Role and Legitimacy of Constitutional Adjudication” (Faktizität und Geltung. Beiträge zur Diskurstheorie des Rechts und des demokratischen Rechtsstaats, Frankfurt-am-Main, Suhrkamp, 1992) ; see also J. Habermas, The Inclusion of the Other: studies in political theory, edited by C. Cronin and P. De Greif, Cambridge Mass., MIT Press, 1998, chapter 7 “Kant’s Idea of Perpetual Peace: At Two Hundred Years’ Historical Remove” (Die Einbeziehung des Anderen. Studien zur politischen Theorie, Frankfurt-am-Main, Suhrkamp, 1996).

4 Such absolutist views are still held today, as shown through the various attempts at reaching “the ultimate foundation of reason” by K.-O. Apel, W. Kuhlmann, D. Wandschneider and V. Hösle ; see K.-O. Apel, “Fallibilismus, Konsenstheorie der Wahrheit und Letztbegründung”, in W. R. Köhler, W. Kuhlmann et P. Rohs (dir.), Philosophie und Begründung, édited by The Forum of Philosophy of Bad Homburg, Frankfurt-am-Main, Suhrkamp, 1987, p.116-211 ; W. Kuhlmann, Reflexive Letztbegründung. Untersuchungen zur Transzendentalpragmatik, Freiburg/München, K. Alber, 1985 ; “Reflexive Letztbegründung. Zur These von der Unhintergehbarkeit der Argumentationssituation”, in Zeitschrift für philosophische Forschung n°35, 1981, p.3-26 ; D. Wandschneider, “Letztbegründung und Logik”, in H.-D. Klein (ed.), Letztbegründung als System, Bonn, 1994, p.84-103 ; V. Hösle, Die Krise der Gegenwart und die Verantwortung der Philosophie. Transzendentalpragmatik, Letztbegründung, Ethik, München, G. H. Beck, 1990.

5 Th. Kuhn, The Structure of Scientific Revolution, University of Chicago Press, 1962, 1996, p.145.

6 J. Habermas, Postmetaphysical Thinking: Philosophical Essays, translated by W. M. Hohengarten, Cambridge Mass., MIT Press, 1992 (Nachmetaphysisches Denken. Philosophische Aufsätze, Francfort-sur-le-Main, Suhrkamp, 1988), p.18 ; ibid.,p.38 : “Philosophy has to implicate itself in the fallibilistic self-understanding and procedural rationality of the empirical sciences; it may not lay claim to a privileged access to truth, or to a method, an object realm, or even just a style of intuition that is specifically its own.”

7 K. Popper, “Unended Quest. An Intellectual Autobiography”, in The Philosophy of Karl Popper, coll. The Library of Living Philosophers, published by P. A. Schilpp, vol. I, Open Court Publishing Co., La Salle, p.3-181, 5 ed : London/New York, Routledge, -2002, note 98, p.252.

8 Th. Kuhn, The Structure of Scientific Revolution, op. cit., p.146.

9 See K. Popper, “Unended Quest. An Intellectual Autobiography”, op. cit., p.38-39 : “He [Max Elstein] drew my attention to the fact that Einstein himself regarded it as one of the main arguments in favour of his theory that it yielded Newton’s theory as a very good approximation; Einstein, though convinced that his theory was a better approximation than Newton’s, regarded his own theory merely as a step towards a still more general theory [...].”

10 For a detailed examination of this central issue, see S. Panis, La démonstration dialectique, § 2.4, p.238 sq. ; paper version: S. Panis, La démonstration dialectique, Lille, ANRT, 2008, p.249 sq.

11 J. Piaget, L’épistémologie cognitive, Paris, PUF, 1970, -1996, p.122 : “[...] entre deux structures de niveaux différents, il n’y a pas de réduction à sens unique, mais une assimilation réciproque telle que la supérieure peut être dérivée de l’inférieure par voie de transformations, mais aussi telle que la première enrichit cette dernière en se l’intégrant.” L. Kohlberg proposes a similar definition in his examination of the theory on moral evolution, in “The Claim to Moral Adequacy of a highest Stage of Moral Judgment”, in The Journal of Philosophy, vol.70, n°18, October, 25, 1973, p.630-646, p.632 : “It assumes, that is, that each new (logical or moral) stage is a new structure which includes elements of earlier structures but transforms them in such a way as to represent a more stable and extensive equilibrium.”

12 For readers of Aristotle, the phrase “dialectical demonstration” may sound contradictory. The terms “demonstration” and “dialectic” point to two radically different and incompatible types of discourse: when a demonstration aims at establishing certain conclusions from a deduction from equally certain premises, a dialectic process aims to put forth plausible conclusions from uncertain premises. Our study shows, however, that if the word “demonstration” is to be understood as “evidential discursive proceeding”, the phrase “dialectic demonstration” is not contradictory. What’s more, in the present state of our knowledge, the only possible demonstration is indeed a dialectical demonstration.

13 If a conclusion asserts that such norm or evidential proceeding is valid and necessary whereas the said norm or proceeding is not used in the argumentative movement, it is an implicit recognition that the mentioned norm or proceeding is not necessary and not valid, amounting to a self destructive conclusion. That is why a logical circle becomes necessary in this case, it even becomes a validity criterion.

14 See for instance J. Piaget, Les formes élémentaires de la dialectique, Paris, Gallimard, 1980. Also see – providing artificial intelligence can make a contribution to the cognitive sciences debate –, R. Pfeifer, C. Scheier, Understanding Intelligence, MIT Press, 1999; S. Nolfi, D. Floreano, Evolutionary Robotics. The Biology, Intelligence and Technology of Self-Organizing Machines, MIT Press, 2000.

15 See A. Reboul, J. Moeschler, La pragmatique aujourd’hui. Une nouvelle science de la communication, Paris, Seuil, 1998, p.106 : “Ce que montre Goodman sur l’induction, c’est qu’elle ne conduit pas à des hypothèses valides en elles-mêmes : c’est la comparaison d’hypothèses concurrentes qui importe [...] et le fait que l’une d’entre elles l’emportera sur les autres parce qu’elle sera projectible et n’aura pas encore été falsifiée.” (“What Goodman shows on induction is that it does not lead to valid hypotheses as such : it is the comparison between competing hypotheses that does […] as well as the fact that one of those will prevail over the other because it will be projectible and not falsified yet.”)

 Author: Sylvain Panis ; translation: Johanna Nepote-Cit