|Logic and Philosophy of
Metaphilosophical Pluralism and Paraconsistency:
M.E. Orellana Benado, Andrés Bobenrieth, Carlos Verdugo
In the West, human beings have been doing philosophy for roughly 2,500 years. Eastern traditions are, perhaps, even older. What can we learn about philosophy itself through this experience and practice? This is the initial question of metaphilosophy, the body of discourse that collects and articulates our observations and reflections about philosophy as a human activity. Answers to it are essential in order to address the further issue of what contribution, if any, philosophy has made, or can be hoped to make, toward the education of humanity. For, to be sure, whatever is learnt about the discipline should illuminate, among other things, the significance of our ability to practice it. And, in so doing, metaphilosophy would help us follow the admonition inscribed at Delphi, "Know thyself."(1)
In a famous passage, Immanuel Kant claimed that controversy and the lack of agreement in metaphysics is a "scandal."(2) And metaphysics here stands for philosophy as whole. Attempting to motivate his critique of pure reason, a project aimed at both ending the scandal and setting philosophy in the "secure path of a science."(3) Kant thus endorses the view that for as long as disagreement reigns sovereign within philosophy, there will be little to be learnt from it as a science.
According to Kant, the success of philosophy begins when controversy and disagreement end. And it culminates when the discipline itself as we have known it for twenty-five centuries disappears. On the other hand, particularly in the second half of the 20th century, many have despaired of the very possibility of philosophy constituting a search for truth, that is to say, a cognitive human activity, and constituting thus a source of knowledge. This paper seeks to sketch a research program that is motivated by an intuition that opposes both of these views.
Progress in philosophy is indeed possible. But it is possible precisely because philosophical controversy and disagreement will never end. Philosophy can progress in the sense that the debate itself closes the argumentative routes leading to some positions; they cease to be live options.(4) This closure, however, is not considered progress here because it brings us closer to agreement on the one and only true answer to a given question. On the contrary, it is considered progress because it contributes to determining the range of legitimate answers to it, a concept to which we shall return in section 4.0.(5)
Progress in philosophy is not only possible, but real. And this is also the case for metaphilosophy; to put is bluntly, we are better placed today than the Greeks were to understand what philosophy is. Relying on such improved understanding, the further issue as to what contribution it makes to the education of humanity can be addressed. The disagreements of twenty-five centuries have been fruitful. But in order to see this and embark on answering the initial question of metaphilosophy, we must find ways of doing three things.
First, to reject the temptation to consider all controversy and disagreement as the refutation of the possibility of progress within philosophy. Such temptation stems from scientism, the attempt to conform all areas of cognitive human endeavor to the model of the empirical sciences.(6) But the search for truth in philosophy must not be constructed by analogy with science, that is to say, as the search for the one and only acceptable answer to each question.(7) After twenty-five centuries of philosophical controversy, no self-respecting position in metaphilosophy will cling to the hope that disagreement will disappear. Metaphilosophy owes us an evaluation of the meaning of disagreement; not a hope that it will vanish once philosophy enters "the secure path of a science."
Second, to appreciate the significance for metaphilosophy of the recent developments in paraconsistent logic showing how, within formal systems, contradictory propositions can be held simultaneously without trivialization. The scientificist conception of the search for truth is partly motivated and partly justified by the ancient rejection of all contradictions. But this rejection, as section 2.0 highlights, is no longer a logical imperative. Indeed, it cannot be endorsed without, at least, severe qualifications that rob it from its argumentative bite. Thus the way will be open to adopt a novel understanding of the search for truth. And we shall present a model that conceives it as the determination of the range of legitimate answers to a given question (without precluding answers that, to an extent, contradict each other).
Third, to outline multi-level pluralism (MLP in what follows) in metaphilosophy and its main consequence for the practice of philosophy. In section 4.0, we shall hold that discussions about the conceptions of philosophy, which are philosophical, must be distinguished from both those about its institutions and about its taxonomies, which need not be purely philosophical. Conceived in MLP terms, philosophy continues to present itself as a dialogue. But, and this is the main consequence of MLP at the individual level, it is not exclusively a dialogue with positions or answers different from our own held by others. Also, and crucially, philosophy is a dialogue with ourselves, as defenders of a plurality of legitimate answers, including sometimes, answers that to an extent, contradict each other.
Section 1.0 The meaning of philosophical disagreement
In his Pluralism: against the demand for consensus, Nicholas Rescher rebels against the devaluing of controversy and disagreement. Arguing in terms of our inability to reach it, he concludes that the traditional centrality of consensus for human rationality, truth, and communication as well as social and political order is misplaced.(8) Consensus is understood by him as agreement regarding what is to be thought (belief), what is to be done (action) and what is to be prized (value). According to Rescher, in much of the history of Western philosophy as well as in contemporary philosophy, the search for consensus has been conceived as something desirable to be achieved. But Rescher holds that this is quite wrong.
According to the view presented in his earlier The strife of systems: an essay on the grounds and implications of philosophical diversity, philosophical problems take the form of sets of inconsistent beliefs about the correct answer or solution to a given problem. A principal reason for the emergence of such inconsistent sets of beliefs is that philosophical data overdetermine philosophical theories.(9) Philosophers, as individuals, are bounded by the very nature of rationality to seek to overcome paradoxes by giving up one or another member of such sets, in the light of the cognitive values which orient each individual. But because these cognitive values enter the explanation at the individual level, agreement as to which is the correct solution to a specific paradox will never be reached. And philosophical controversy and disagreement, at the disciplinary level, will not go away.
Section 1.1 Orientative pluralism in metaphilosophy
In The strife of systems, Rescher makes two related distinctions. One of them distinguishes descriptive metaphilosophy from normative metaphilosophy, while the other distinguishes the disciplinary from the individual level. It is in terms of these distinctions, that Reschers views are to be understood.
Descriptive metaphilosophy is not philosophical research at all. It is a historical, perhaps sociological, inquiry into philosophy as a human intellectual endeavor. At the disciplinary level, this boils down to the history, perhaps the sociology, of philosophy as a whole. At the individual level, descriptive metaphilosophy issues in the intellectual biography of each researcher. Normative metaphilosophy, by contrast, is concerned with which are the appropriated problems, the justifiable thesis and the correct methods of philosophy. And, therefore, normative metaphilosophy is a variety of philosophical research.
According to Rescher, the five main options within normative metaphilosophy are doctrinalism, a-rationalism, skepticism, syncretism and his own orientative pluralism (OP, in what follows). Confronting a diversity of philosophical doctrines that rival in their claim to provide knowledge on a given question, their respective views are the following. Doctrinalism asserts that only one of them must be the correct doctrine, and that determining which one is correct is a rational matter. A-rationalism asserts that a philosophers preference for a given doctrine is arbitrary and not a rationally justifiable conclusion. Skepticism rejects the whole lot of rival doctrines and denies the very possibility of philosophical knowledge. Syncretism, to conclude, embraces all doctrines within the diversity.
Rescher presents and works out in detail his OP, making explicit its positions with regards to both the disciplinary and the individual level. At the disciplinary level, OP offers an explanation of the persistence of disagreement within the discipline in the way summarized in the previous section. Strictly speaking, then, OPs "pluralism" is limited to the disciplinary level. For it is only there that OP deems that the diversity of answers to a given question can be rationally justified. However, with regards to the individual level, OP is "doctrinal" because it insists that the very nature of rationality forces each researcher to strive for consistency, and attempt to find the one and only answer which follows from the cognitive values held by the researcher.
Rescher argues in favor of OP by way of highlighting the shortcomings of its four rivals: doctrinalism, a-rationalism, skepticism and syncretism. OP emerges as the victorious position in terms of a cognitive cost-benefit analysis of the kind that OP itself conceives as the appropriated method to overcome philosophical conflicts.(10) This strategy would be sound provided that these five positions exhaust the relevant options. But below we shall argue that it is not. There are more things between the heaven of OP and the earth of the other four options than Reschers metaphilosophy dreamt of.
The MLP metaphilosophical research program outlined here shares OPs evaluation of philosophical diversity: the clash between different answers and values is a basic feature of the discipline. However, our ultimate aim is to suggest (and, given the space, only to suggest) that this not only holds at the disciplinary level but also, and crucially, at the individual level. Only once this point has been properly developed and understood, can the question about what we have learnt from philosophy itself be tackled. For it is only then that a proper understanding of philosophy as a cognitive human activity will become available. And the hope to identify its contribution to the education of humanity is justified. But, before we do that, we need to fulfil the second and third tasks indicated in the introduction.
Section 2.0 Metaphilosophical pluralism and paraconsistency
Reschers objection to syncretism in metaphilosophy stems from his belief that because of its readiness to embrace all different answers to a given question, it is bound to hold contradictory answers. But this, according to Rescher, is not rationally acceptable. It is tantamount to destroying the cognitive nature of philosophy, its aspiration to constitute a search for truth: "To accept a plurality of answers is not to have answers at all; an unending openness to a variety of possibilities, a constant yes-and-no leaves us in perpetual ignorance."(11) The variety of metaphilosophical pluralism here outlined rejects this view. And, in order to understand why it does, we must now evaluate the validity of two logical arguments that have traditionally been used to uphold it.
According to the first, the inclusion of contradictory propositions within the same conceptual space is ruled out by the principle of contradiction. The second is a formal argument known since the Middle Ages (ex absurdo sequitur quodlibet), which in contemporary symbolic logic becomes the proof that from the simultaneous assertion of two contradictory sentences everything can be deduced.(12) During the 20th century, however, a growing body of formal developments called paraconsistent logic, which in the last decade became a leading topic in logico-mathematical research, has critically undermined this view.(13)
Deductive logical systems can incorporate some contradictions. And they can be articulated without thereby necessarily causing the disruption of the inferential structure as a whole. A paraconsistent logical system can serve as the underlying logic that allows the formalization of a theory including some inconsistencies within its postulates (or, indeed, in the consequences derivable from them) without thereby trivializing itself.(14) Although paraconsistent logical systems are as consistent as the classical ones, they can support some contradictions when they formalize a non-purely logical theory.
A recent research line within paraconsistent logic that seeks the unification of mutually inconsistent theories (such as, paradigmatically, classical and quantum mechanics) is especially important for present purposes. The basic strategy of this research line comprises two steps. In the first, the aim is to formalize each theory presenting some extralogical postulates that can characterize them, using a logical system (which can be classical logic) as the underlying logic. In the second step, the aim is to articulate these deductive systems in a global theory that will contain their extralogical postulates, but using as underling logic a paraconsistent system.
Although no attempt will be made here to formalize philosophical theories (we are, after all, merely sketching a research program the development of which would include it), this application of paraconsistent logic to the metatheoretical reflection about science suggests applying a similar strategy to metaphilosophy. The rejection of positions, such as MLP, that are prepared to hold several answers to a question can no longer be sustained on logical grounds alone. Speaking about logical impossibilities requires specifying the logic we are talking about, for such impossibility does not hold for all deductive systems.
In this way, the logical objection to a metaphilosophical pluralism that is prepared to accept a diversity of answers at the individual level is completely dissolved. Pluralism, therefore, becomes equally acceptable both at the disciplinary and the individual level. More, as it will be suggested in section 4.0, we can offer positive considerations that make such option independently attractive. But before embarking on that task, Hao Wangs perplexing thesis about the scope of metaphilosophy must be considered.
Section 3.0 The scope of metaphilosophy
Following the Oxford English Dictionarys definition of metaphilosophy as is a "discourse about (the nature of) philosophy", Wang claims that "a distinguishing characteristic of philosophy is that it properly includes metaphilosophy (indeed, as a major component), while, for instance, chemistry does not include metachemistry."(15) This claim can be interpreted in, at least, three ways: one of them makes it true but trivial, another makes it implausible, while the third makes it outright false.
Wang says that the discourse about, for instance, chemistry does not belong to chemistry while metaphilosophy (i.e. the discourse about philosophy) properly belongs to philosophy. But what is to be understood here by "discourse about" a given discipline? If, by definition, it must be a philosophical one, then Wangs claim is true. Only philosophy includes philosophical discourse about any discipline that it happens to be concerned with, such as chemistry, history and, indeed, philosophy. Under this first interpretation, Wangs claim is true. But it is also trivial.
Wangs claim can be interpreted also as the thesis that discussing the nature of a given discipline must be a purely philosophical enterprise. This second interpretation makes his claim that a distinguishing characteristic of philosophy is that it properly includes metaphilosophy intelligible and not trivial. But why should such a thesis be granted? We cannot hope for a complete answer to the initial question of metaphilosophy without paying due attention to the dimensions of interest associated with other disciplines such as, at least, history, psychology or sociology. Let alone, the issue of what, if anything, philosophy can contribute to the education of humanity.
Philosophers have discussed the nature of their discipline from a philosophical point of view often and intensively. But this goes nowhere toward justifying the claim that a complete metaphilosophical reflection (that is to say, a reflection about the nature of philosophy as a cognitive human activity) can afford to ignore the perspectives on philosophy provided by other disciplines. And in this second interpretation, Wangs thesis is, at best, implausible.
Finally, and this is the third interpretation, if "discourse about" can include those of other disciplines, then at least some disciplines would be in a position equivalent to philosophys. Thus, for example, only history can include its kind of discourse about chemistry. And, of course, only history includes the historical discourse about history, that is to say, metahistory. Surely, we do not want to deny that there is such a thing as the history of history. Nor do we want to deny that discussions about the history of history are a proper part of history. For example, Carlyles claim that "history is the essence of innumerable biographies" is a claim about history, which belongs to the history of history. More, the same will be the case for other disciplines, such as sociology and, perhaps, even, mathematics. Interpreted in this third sense, Wangs claim turns out to be false. The alleged distinguishing characteristic of philosophy is one that it shares with other disciplines.
Section 4.0 Toward multi-level pluralism in metaphilosophy
We may now outline two aspects of MLP in metaphilosophy. One relates to the scope of metaphilosophy. With regard to this issue, MLP builds on the implausibility of the second interpretation of Wangs thesis and includes within metaphilosophy the two non-philosophical components outlined below. The other aspect concerns the model of the search of truth adopted by MLP in the light of the discussion in section 2.0.
According to MLP, if by metaphilosophy is understood "a discourse about (the nature of) philosophy", then, to begin the discussion with reasonable hopes of success, three related but different components should be distinguished within it: the conceptions, institutions and taxonomies of philosophy. Debates about the ambitions, questions, problems and methods of this discipline as well as the specific proposals, theories and systems that have been formulated throughout the history of the subject belong to the conceptions of philosophy component. Controversies about philosophical communities, which are their specific means of production and who are their canonical authors as well as questions about the relations between philosophy and other human activities belong to the institutions of philosophy component. Issues about which are the main thematic areas of philosophy and, if any, what is their relative order of importance as well as those about which have been its main schools of thought, movements and traditions in the past and at present belong with the taxonomies of philosophy component. The MLP research program in metaphilosophy acknowledges that there is work to be done on all three components.(16)
MLP agrees with OP on the cognitive nature of philosophy and, also, on the inevitability of its disagreements. But it parts company with OP on two accounts. First, on the grounds hinted at in section 2.0, it rejects OPs identification of the cognitive nature of an enterprise with the search for the only and one true answer to each question. MLP seeks to preserve part of the Kantian motivation, to make room for talk of progress within philosophy. But it rejects the scientificist assumption shared by Kant and Russell that the search for truth can only be understood as the search for the one and only true answer to a given question.
MLP proposes instead a step by step model for the search for truth that, given a question, distinguishes three stages in the attempt to answer it. They are, the attempts to identify in the debate the ranges of:
Clearly, such model of the search for truth can accommodate subjects, if there are any, in which the third range, the range of legitimate answers, includes only one answer. They would be mere limiting cases of it. But, of course, once fully articulated such model would not license concluding from the failure to converge on only one answer that the search for truth has failed. And here begins to emerge what we have learnt about philosophy itself as a cognitive human activity through its 2,500 years of practice, controversy and disagreement.
We have learnt that human cognitive endeavors (including, of course, philosophy and metaphilosophy) need not conceive of themselves in terms of a search for the one and only true answer to a given question. Alternatively, they can conceive of their task in terms of determining the range of legitimate answers to a given question.
The MLP research program in metaphilosophy here sketched will have to articulate the underlined concepts in each of these three stages. And, also, it will have to develop the three components of metaphilosophy which, according to its perspective, must be distinguished in order to begin addressing its initial question. This, however, is not the place to do so in detail. Instead, to conclude, we will merely gesture toward the leading intuition in terms of which MLP will develop the concept of a "range of legitimate answers." The intuition is that, in philosophy, the range of legitimate answers is constituted by those positions whose very intelligibility constitutively depends on all other members of the range, allowing the fruitful coexistence within it even of mutually inconsistent answers.
What Kant considered a scandal is, on the contrary, according to MLP, a key to any metaphilosophical attempt to elucidate the significance of our ability to do philosophy. Knowing ourselves in philosophical terms is tantamount to knowing which answers to a given question belong to the range of legitimate answers, that is to say, to be sensitive to the mutual argumentative relations of support and refutation holding between them. And the enormous diversity of views about the conceptions, institutions and taxonomies of philosophy are the raw material for this effort. Pluralism within metaphilosophy, thus understood, teaches humanity that, at least in some domains, to conduct a search for truth we must agree to differ. Provided, of course, we understand why we disagree.(17)
NOTES(1) Plato: Charmides 164 d in his The Collected Dialogues (Hamilton, E./ Cairns, H eds; Princeton, New Jersey: Princeton University Press, 1963) p.110.
(2) Cf. Kant, Immanuel: Critique of the Pure Reason (Hong Kong: The MacMillan Press, 1978) p. 29ff (Bxxxiv); (A832, B860).
(3) Kant, 1978, p.17 (Bvii).
(4) "[S]i por progreso entendemos el proceso por el cual se alcanzan perspectivas más complejas y diferenciadas, que por su propia diferenciación hacen imposible una "vuelta atrás", así como un amplio consenso sobre lo más valioso de los resultados obtenidos hasta la fecha, entonces está claro que hay progreso en la filosofía." Moulines, Ulises (ed): La ciencia: estructura y desarrollo (Madrid: Trotta, 1993), p.13
(5) For the argumentative conception of philosophy that underlies this view see Orellana Benado, M.E.: Pluralismo: una ética del siglo XXI (Santiago de Chile: Editorial Universidad de Santiago, 1994), pp 27-36.
(6) For the contrast between empirical and formal questions see Berlin, Isaiah: "The object of philosophy" in his Concepts and Categories (London: Hogarth Press, 1978). For the constrast between empirical and formal questions, on the one hand, and "human"questions on the other, see Orellana Benado, 1994, pp 21-3.
(7) For what is, perhaps, the most significant articulation of this view, see Carnap, Rudolf: Der logische Aufbau der Welt (Hamburg: Felix Meiner Verlag, 1961). On the significance of the failure of logical positivism see, Orellana Benado, M.E.: "Skepticism, humor and the archipelago of knowledge" in Popkin, Richard (ed): Skepticism in the history of philosophy (Utrecht: Kluwer Academic Press, 1996), pp 235-38.
(8) Rescher, Nicholas: Pluralism: Against the Demand for Consensus (Oxford: Clarendon Press 1993).
(9) Rescher, Nicholas: La lucha de los sistemas: un ensayo sobre los fundamentos e implicaciones de la diversidad filosófica (México : UNAM Instituto de Investigaciones Filosóficas, 1995).
(10) Rescher, 1995, p. 326.
(11) Rescher, 1995, p. 350; cf p. 344.
(12) Cf. Hilbert, David / Ackermann, Wilhem: Grundzuege der Theoretischen Logik (Berlin: Julius Spinger Verlag, 1928) p. 29ff.
(13) Cf. Jaskowski, S.: "Propositional Calculus for Contradictory Deductive Systems" Studia Logica t. XXIV (1969) p. 143-157. Da Costa, Newton: "On the theory of Inconsistent Formal Systems" Notre Dame Journal of Formal Logic vol. XV, no. 4 (1974) p. 497-510. Arruda, Aida I. "A Survey of Paraconsistent Logic" in Arruda / Chuaqui / da Costa (eds.): Mathematical Logic in Latin America (Amsterdam: North-Holland Publishing Co., 1980) p. 1-41. Priest, G. / Routley, R. / Norman, J. (eds.): Paraconsistent Logic, Essays on the Inconsistent (Muenchen, Hamden, Wien: Philosophia Verlag, 1989). DOttaviano, I.: "On the Development of Paraconsistent Logic and da Costas Work" The Journal of Non-Classical Logic vol. 7, no. 1 / 2 (1990) p. 89-152. Bobenrieth, A.: Inconsistencias ¿por qué no?: Un estudio filosófico sobre la lógica paraconsistente (Bogota: Colcultuta, 1996).
(14) A system is trivial if and only if the set of theorems becomes equivalent to its set of well-formed formulas.
(15) Wang, Hao: Beyond Analytic Philosophy (Cambridge M.A., London: MIT Press, 1988) p. 10.
(16) For another view that, together with those of Rescher and Wang, restricts the scope of metaphilosophy to philosophy see Double, Richard: Metaphilosophy and Free Will (Oxford : Oxford University Press 1995). For an example of a discussion that falls within the institutions of philosophy component see Mandt, A.J.: "The inevitability of pluralism: philosophical practice and philosophical excellence" in Cohen, A./ Dascal, M. (eds): The Institution of Philosophy (La Salle: Open Court, 1991), pp 77-101.
(17) The authors acknowledge with gratitude the generous support provided to this research through Proyecto 1970613 by Fondo Nacional de Desarrollo Científico y Tecnológico (Chile).