Metaphilosophical Pluralism and Paraconsistency: From Orientative to Multi-level
Pluralism
Logic and Philosophy of
Logic
Metaphilosophical Pluralism and Paraconsistency:
From Orientative to Multi-level Pluralism
M.E. Orellana Benado, Andrés Bobenrieth, Carlos Verdugo
Universidad de Valparaíso, Chile
Abobenri@rdc.cl
ABSTRACT: In a famous passage, Kant claimed that controversy and the
lack of agreement in metaphysics—here understood as philosophy as a whole—was a
‘scandal.’ Attempting to motivate his critique of pure reason, a project aimed
at both ending the scandal and setting philosophy on the ‘secure path of
science,’ Kant endorsed the view that for as long as disagreement reigned sovereign
in philosophy, there would be little to be learned from it as a science. The success of
philosophy begins when controversy ends and culminates when the discipline itself as it
has been known disappears. On the other hand, particularly in the second half of the
twentieth century, many have despaired of the very possibility of philosophy constituting
the 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.
Introduction
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 Rescher’s 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
philosopher’s 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, OP’s
"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 Rescher’s metaphilosophy dreamt
of.
The MLP metaphilosophical research program outlined here shares OP’s 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
Rescher’s 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
Wang’s perplexing thesis about the scope of metaphilosophy must be considered.
Section 3.0 The scope of metaphilosophy
Following the Oxford English Dictionary’s 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 Wang’s 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, Wang’s claim is true. But it is also trivial.
Wang’s 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, Wang’s
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 philosophy’s. 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, Carlyle’s 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, Wang’s 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 Wang’s 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 OP’s 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:
Intelligible answers
Currently alive answers
Legitimate answers
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). D’Ottaviano, I.: "On the
Development of Paraconsistent Logic and da Costa’s 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).
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