[This article was published earlier in Alethia, issue 2:3, november 2000]
Logical Meanderings between West and East:
Aristotle, Nagarjuna and Bhaskar.
Jan Straathof
Further, if, whenever an assertion is true, its denial is false and,
whenever a denial is true, the assertion of what it denies is false,
it is not possible truthfully to assert and to deny the same thing.
Aristotle
Everything is real and is not real,
Both real and not real,
Neither real nor not real.
This is the teaching of the Buddha.
Nagarjuna
In this short piece I want to make some remarks on the differences between Western and Eastern logic, focussing
in particular on the difference between the logic of the Greek philosopher Aristotle and that of the Indian philosopher
Nagarjuna. The reason I want to address the issue of logics is because I think this approach could offer a key to the
understanding and appreciation of Roy Bhaskar' s current ontology and epistemology, as elaborated in his latest
book: From East to West.
Aristotle under siege
The two pillars on which the Aristotelian logic rest are: (i) the principium tertii exclusi or principium tertium non
datur, more familiarly known as the principle of the excluded middle or as the principle of the excluded third (PET),
and (ii) the principium contradictionis the so-called principle of non-contradiction (PNC). The latter asserts that one
cannot at the same time have both 'A' and 'not A', and the former states that one has either 'A' or 'not A', and there is
no third possibility. No one will doubt that, via these two guiding principles, Aristotle has fundamentally shaped the
subsequent centuries of development in Western philosophy and especially that of the Western sciences.
In the previous century Brouwer was one of the first mathematicians to notice that Aristotle's principles are not
always completely reliable, and especially not in those parts of the sciences that deal with categories as a 'continuum'
or as 'infinite systems'. Brouwer advocated the view that in mathematics (and maybe also in general) a consequent
deployment of the principle of the excluded third would inevitably lead to illicit ontological mathematical claims.
Brouwer therefore rejected PET and became quite suspicious of the PNC too. On Brouwer' s reading, the PET
"requires that each assumption is either correct or incorrect, mathematically formulated: that for each assumed
incorporation of systems in some way into each other, either the termination [success], or the encounter of an
impossibility can be constructed. The problem of the validity of the principium tertii exclusi is thus equivalent
to the problem of the possibility of unsolvable mathematical problems."
And straight away he offers two examples, viz., 'Is there in the decimal expansion of pi a decimal that in the long
run occurs more often than others?' and 'Are there in the decimal expansion of pi infinitely many pairs of consecutive
decimals which are equal?' (van Dalen 1999, 106-7). In more simple terms, Brouwer' s argument runs as follows: if
one has deduced an inconsistency from the proposition that, for example, there exists no number with the property E,
then one is not (yet) allowed to conclude that such a number (with the property E) really exists; such a claim would
only be legitimate if that number is really constructed. Thus according to Brouwer, to know the meaning of a mathe-
matical object is to know how to perform the practices that lead to its construction (and possibly- inter alia the ability
of reconstruction).
And so the question whether Pierre is or is not in the cafe is easily answered with an Aristotelian 'yes' or 'no', that is,
there is no third alternative. But and this is Brouwer' s point the observation of Pierre' s absence from the cafe,
will not logically allow us to conclude now that Pierre is present somewhere outside the cafe. Because it is possible
that Pierre is physically standing on the threshold of the cafe, and thus he would be neither physically inside nor outside;
and also it is possible, for example in the case where Pierre has died yesterday, that Pierre (as we know him) is actually
absent both inside and outside the cafe. The presence of Pierre can only then be asserted when Pierre is actually found
present (somewhere). This example may seem inconclusive, but let us go to the tennis court, where it may not. Here
too we will notice that it is not always easy (or even possible) to judge conclusively between a 'yes' or a 'no'. If we are
watching a tennis game, quite often it is clear that the ball is in or out, but sometimes there is uncertainty: according to
the linesman the ball was in, but the player is disputing this observation and fiercely claims that the ball was out.
Luckily with modern video equipment it is possible to take a closer look at this situation in slow motion, but even
then it is sometimes not possible to reach an Aristotelian conclusion. And even if we went some steps further and
deeper with our measurements, lets say at the quantum level, the question could still remain inconclusive. [and, by
the way, would (an Aristotelian) God possess an a priori monitor which would reveal whether the ball was really in
or out?] My speculative conclusion here is that Aristotelian logic does not rule on the tennis court. There seem to be
in principle four truth-value possibilities/alternatives, viz.:
(i) the ball is in;
(ii) the ball is out;
(iii) the ball is neither in nor out, i.e. the ball hits, so to speak, an (onto-)logical threshold, viz. that place/space that is
neither in nor out; and
(iv) the ball is both in and out, that is, per the 'quantum effect', viz. the phenomenon that an elementary particle
(electron) can be present in two places at the same time: and thus, exit PET and PNC in tennis.
Brouwer is only one of many modern critics of Aristotelian logic. Its applicability is doubted and contested across a
range of fields, from quantum mechanics to complexity theory, from world systems analysis to neuropsychology.
The main critique is directed against the exclusionism of Aristotle' s twofold logic, which could well be regarded as
a kind of Tina-logic (Bhaskar 1993, 116), in the sense that it offers only two logically acceptable possibilities: there
is no third alternative. Overall, the current state of play seems to indicate that Aristotelian logic is still quite useful
and reliable, but only in (quasi- or artificially) discrete and finite (closed) systems; when we deal with or investigate
ontological realms which lie beyond the discrete and finite, we simply don't know, and have deep suspicions!
Nagarjuna' s four-lane path
It is time to travel East and to take a look at one of the most compelling logical systems that originated there: the
logical dialectics of the buddhist Madhyamika School. Nagarjuna is regarded as the founder of this school, one of the
most important in the Buddhist tradition. The method Nagarjuna and his followers employed could be called a critical
dialectical procedure. It consists in analysing and criticizing the philosophical assumptions and arguments of opponents
by demonstrating their incoherence or internal contradictions, hence their untenability. A notorious characteristic of
Madhyamika dialectics is its purely 'negative' approach with its emphasis on Sunyata (openness, openendedness,
unboundedness, emptiness, indeterminacy, freedom, silence, space or absence (cf. McCagney 1997)) as the sole and
ultimate reality. In his analyses and critiques, Nagarjuna deployed the so called Catuskoti (fourfold) logic, more widely
known as tetralemma logic, which, it is said, was inaugurated by the first buddha Gautama himself.
According to Madhyamika tetralemma logic, every proposition could, or better ought to, be approached via four
different perspectives: (i) the proposition is true, (ii) the proposition is not true, (iii) the proposition is both true and
not true, (iv) the proposition is neither true nor not true. Construing these more ontologically, we could also render
them as the categories of: (i) neither being, (ii) nor not being, (iii) nor both being and not being, (iv) nor neither being
nor not being. There is no better way in my opinion to illuminate the deployment of this tetralemma logic than by
Nagarjuna himself, so below I give a long example from his Mulamadhyamakakarika, the so called Treatise of the
Middle Way. In Chapter 15, which analyses and in the end refutes the reality of Essence (Self-Nature), he writes
(Garfield 1995, 3940):
"1.Essence arising from causes and conditions makes no sense.
If essence came from causes and conditions, then it would be fabricated.
2. How could it be appropriate for fabricated essence to come to be?
Essence itself is not artificial and does not depend on another.
3. If there is no essence, how can there be difference in entities?
The essence of difference in entities is what is called the entity of difference.
4. Without having essence or otherness-essence, how can there be entities?
If there are essences and entities, entities are established.
5. If the entity is not established, a non-entity is not established.
An entity that has become different, is a non-entity, people say.
6. Those who see essence and essential difference, and entities and non-entities,
They do not see the truth taught by the Buddha.
7. The Buddha, through knowledge of reality and unreality,
In the Discourse to Katyayana refuted both 'it is' and 'it is not' .
8. If existence were through essence, then there would be no non-existence.
A change in essence could never be tenable.
9. If there is no essence, what could become other?
If there is essence, what could become other?
10. To say 'it is' is to grasp for permanence, to say 'it is not' is to adopt the view of nihilism.
Therefore the wise person does not say 'exists' or 'does not exist'.
11. 'Whatever exists through its essence cannot be non-existent' is eternalism.
'It existed before but doesn't now' entails the error of nihilism."
This all may sound quite strange and contradictory to the ears of the Western reader, because what happens here, in
this line of argument, is that both the PET and the PNC are cancelled and violated. But before one misunderstands
this as some form of obscure scepticism or nihilism, it is important to bear in mind that the Madhyamika philosopher
is not at all rejecting the existence of the phenomenal or conventional world, s/he only claims that all phenomena in/of
the conventional world lack inherent self-nature (essence). In the final analysis Madhyamika philosophy contends,
again and again, that from whichever or from all of the four logical orientations, all propositions about ultimata and/or
essences (and the apparent ultimate essential realities they refer to) will inevitably be incoherent and untenable, and
thus the only ontological truth that seems acceptable is that all beings are devoid of self-essence: there is only one
ultimate reality Sunyata.
Whatever the ontological or ethical merits of Madhyamika philosophy, the strength of its tetralemma logics lie in its
epistemic range, which offers a considerably wider set of analytical tools than Aristotle' s di(a)lemma logic. To guide
our speculations, investigations and explanations of the dialectical totality of the poly-causal, pluri-temporal, ever
changing, multicultural world-systemic reality we live in today, we seems better off with Nagarjuna than Aristotle.
When Aristotle contends that, for example, 'a cause is prior to its effect', Nagarjuna holds it possible (and even neces-
sary to presume) that, because both lack any inherent self-nature or essence, cause and effect emerged simultaneously
in a united relationship, that is, in one act/event of pratitya samutpada (dependent co-arising, or interdependent origination);
when Aristotle holds that time is essentially linear, Nagarjuna will contend that time is open/empty and certainly without
any essence such as linearity (and inter alia opening up the possibility of backwards causation); where Aristotle would
claim that the substance (ousia) of things/beings is permanent (and therefore affording the logical ground for any ceteris
paribus clause), Nagarjuna would counter with the observation that impermanence and change is ubiquitous, and further,
given the lack of any inherent essence, what substance could be granted permanence?
All in all, this Madhyamika-style reasoning may seem very abstract and too remote from everyday reality to be useful,
but it is not. I think we could easily (and fruitfully) apply this tetralemma method to the superficial dualistic mode of
conflict analysis which currently holds sway in politics and the media. Take as a random example the Middle East
crisis: the conflict ('who started the violence?'; 'whose holy city is this?'; 'whose forefathers are buried here?'; ' who is
making the profit?'; 'who is paying the bills?'; 'who is the master, who the slave?', and so on) is narrowed down to two
parties, the Israelis (Jews?) and the Palestinians (Muslims?), and the blame is either put on one side or on the other.
But according to the Madhyamika philosophy, as long as the conflicting parties fail to consider and analyse the further
possibility that both are to blame and at the same time neither of both are to blame, there is no way to resolution and
peace.
Meandering between Aristotle and Nagarjuna
"The fact that God is unbounded, and in principle consists (also) of infinite (layers of) depth and (zones or
swathes of) extension does not mean that he can have no positive qualities (rather he has infinite qualities) or
that he can only be defined by the via negativa, as not this, not that and so on. It does mean, however, that we
must say that God is both consciousness, love, truth, bliss and so on, and beyond consciousness, love, truth,
bliss and so on. Incidentally the relative absolute (absolute-for-us) may or may not be absolute-in-itself; and
even if it is, it may be characterisable by different degrees of unboundedness, i.e. need not be simple or
undifferentiated ...." (Bhaskar 2000, 47).
It is indeed a great surprise to read Roy Bhaskar's new book. The subject of God, only mentioned and referred to
sporadically in the earlier works, here comes explicitly to the fore and is elaborated into in what could be called
A Realist Theory of God. Whence, one wonders, this seemingly radical turn to an issue and vocabulary which only
had such a minor attention in the previous oeuvre? But my interest here is not in the 'god talk' as such, and if Bhaskar
had mentioned the word 'God' only once in this new book (substituting it by some other suitable container-words),
I would still have enjoyed it as much as I do now. Because what I am interested in here are questions like: what kind
of logic is presumed in the argument of From East to West and is it of an Aristotelian or a Nagarjunian kind, or is
it both, or neither?
The above quote is I think a nice specimen of Bhaskar's current logic. It is a meandering between Aristotelian
exclusionism (exemplified in references to 'zones or swathes', 'positive qualities' and 'absolute-in-itself'), and on the
other hand Nagarjunian inclusionism ('unboundedness', 'both ..., and beyond'). In fact, throughout the whole book
Bhaskar uses a mix of logics to prepare the way for new discourses and to discover/uncover new ontological domains
which will help to make possible further and deeper scientific explanations. Examples of the innovative concepts
Bhaskar is offering include: 'aefficacious', which opts to fuse both affective and effective powers; 'demi-being' (incl.
'demi-real being', 'demi-reality'), which denotes an ontological status that lies between being and not-being; 'ingredient
essence', which incorporates the apparent contradiction of an essence with an ingredient c.q. a non-essence; 'categorial
realism', which postulates among other things the existence of a creative intelligent (epi-)structure that is both dependent
and independent of human being; 'stratified monism', which unites two opposite ontologies, viz. that of stratification
(differentiation) and that of monism (undifferentiation); 'co-presence (co-absence)', the event or emergence of both
the present and the absent at the same time. In all these examples, whatever the other influences, the imprint of
Nagarjuna's logic is clearly visible. Aristotelian motifs are, however, also prevalent, for example in the arguments for
universal causality, dispositional realism, immanent stratification of being, ethical teleology (incl. ethical ceteris paribus),
eudaimonia, the ultimate good, the ultimate god, and so on.
Bhaskar's current logic is a bold and liberating one. (Epistemically, it is remarkably bold in deeming, among other
things, time- and astral travel, mystic experience, angelic messengers, divine whisperings, dreams, reincarnations,
'transcendental identity consciousness', 'spontaneous right action', and so on as possible media of/for knowledge
gathering). It is a logic which meanders freely between Eastern and Western thought, constantly forcing and
challenging us to broaden and deepen our readings of the various cultural traditions of the past, but above all
constructively aimed at furthering genuinely open debate and totalising understanding of the present complex
and chaotic world in which we live.
References
Bambrough, R. et al., 1963. The Philosophy of Aristotle: Introduction with translations. New York, the New
American Library.
Bhaskar, Roy 1993. Dialectic: The Pulse of Freedom. London, Verso.
Bhaskar, Roy 2000. From East to West: Odyssey of a Soul. London, Routledge.
van Dalen, D. 1999. Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer, Volume 1: The Dawning
Revolution. New York and Oxford, Oxford University Press.
Garfield, J. L. 1995. The Fundamental Wisdom of the Middle Way:Nagarjuna' s Mulamadhyamakakarika. New
York and Oxford, Oxford University Press.
McCagney, N. 1997. Nagarjuna and the Philosophy of Openness. New York and Oxford: Rowman & Littlefield.
------------------------------------------------------------------------------
Oktober 2000 - Jan Straathof - janstr@chan.nl
-------------------------------------------------------------------