Reason and Religion: Irremediably Incompatible Bedfellows?
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However, we can assert one thing, explicitly, while at the same time we deny some other thing, implicitly. The explicitly asserted thing remains at the focal level of direct attention while we relegate the other to the subsidiary (or peripheral) level of indirect or peripheral attention. The focal level is there for consciousness while the subsidiary level is not, though what is subsidiary can become focal and vice versa in the blink of an eye. Nothing can be both focal and subsidiary, in consciousness, at the same instant; yet scintillating, rippling, oscillating to and fro switches between something that is now focal, now subsidiary, and now back again, is common in everyday perception and conception.
For example, the cube drawing in Figure 1 cannot be seen as both ‘cube-face-down’ and ‘cube-face-up’ at the same moment. It must be either the one or the other. Good enough. Look at it, and it is ‘cube-face-down’ (‘A’). Look at it again and it might have transformed itself into ‘cube-face-up’ (‘Not-A’). But what if it is not seen as a cube at all? What if it is seen as just a bunch of lines on a flat plane instead of a concocted three-dimensional object on a two-dimensional surface? As such, it is no more than the mere possibility of a cube. As a possible cube it contains, within itself, the potential for its realization either as ‘cube-face-down’ or ‘cube-face-up’. Considered as possibly either the one cube or the other, in its unrealized form we can say that it is both ‘cube-face-down’ and ‘cube-face-up’ (‘Both A and Not-A’).
But,… no,… that doesn’t tell the whole tale. Not really. In its unrealized state we can say that the concoction of lines in Figure 1 is either the one cube or the other one. It is possibly many other things besides: it can be a cake of ice, a glass case, or a wire contraption of some sort. In this case the ‘Not-A’ of ‘Both A and Not-A’ can imply an undefined number of possible things. What if someone sees the drawing as a ‘Cube’? Someone might see it at the same moment might as a box, and someone else as a wire construction, and so on. So what is it? It must be ‘Neither A (‘cube-face-down’) nor Not-A (‘cube-face-up’)’ but something else; in fact, a number of something elses. But,… this won’t quite do the trick either. In our considerations we are taking the lines in terms of incompatible existential forms: unrealized cube (‘Both A and Not-A), realized cube (‘One thing, or another, or another’), and the future possibility of undefined alternatives (‘Neither the one thing nor the other but some else’). If we remain true to logical principles, we shouldn’t mix things up in such a manner.
So, let’s say that the proper assertion regarding Figure 1 can be ‘All the above’, if we wish to disregard the incompatibility. And why not? If we are doing a number on traditional logical principles, why shouldn’t we go whole hog? We include all the assertions, ‘A’, ‘Not-A’, ‘Both A and Not-A’, and ‘Neither A nor Not-A’. Then, the more sober side of us abjures. We would prefer the comfortable confines of consistency. So with respect to the above assertions, including ‘All the above’, we proclaim ‘None of the above!’ And we end up with the Tetralemma coupled with its assertion and its negation, no more, no less. We took it all in our stride, as if it were as natural as could be.
In a remotely comparable fashion, we have observed, a subnuclear event of contemporary quantum theory cannot be both a particle and a wave; it must be either the one or the other. And yet, the quantum event can be both particle and wave, if we contemplate the two manifestations of its schizophrenic nature. It can be ‘particle’ as the ‘actualization’ of a ‘wave’ on Mondays, Wednesdays, and Fridays, and it can be ‘wave’ as an ‘unactualized particle’ on Tuesdays, Thursdays, Saturdays. Or it can be considered neither particle nor wave, but something else, perhaps ‘wavicle’, on Sundays. As both ‘particle’ and ‘wave’, we are considering the event in near-simultaneity, but not-quite-exactly at the same instant in time. As neither ‘particle’ nor ‘wave’, it is just that: neither the one nor the other, but something else, something that at some moment or other happened to push its way through the erstwhile Excluded-Middle that has transmuted into the Included-Middle.
Back to Nāgārjuna for a few moments.
Contradictions? No problem!
B. K. Matilal (1971: 162-65) shows how in what is called the Svatantrika strain of the Mādhyamika school of Buddhism, apparent contradictions lose their sting. On this interpretation, negation can be taken in two different ways. Allow me to continue with the ‘wave-particle’ pair of terms for illustration.
Take two sentences, ‘This unactualized particle is a wave function’, and ‘An actualized wave function is this particle’. If we deny the adjective of the first sentence, we have ‘This actualized particle is a wave function’. This won’t do. In effect we denied ‘unactualization’ of the particle. In a roundabout way this is a double negation. But the double negation did not yield negation of the predicate, ‘is this particle’. Actually, ‘this particle’ is not a ‘wave function’. ‘Particle’ and ‘wave function’, are complementary terms, not equivalent terms. As complementary terms, there can be a ‘wave function’ now and ‘this particle’ in the next moment, but the two cannot emerge to meet us in the same moment. Complementarity leaves the Principle of Non-Contradiction intact.
The adjective of the second sentence tells us what the ‘wave function’ is not. It is not ‘actualized’. There is no need of denying the adjective, for the adjective already says what the subject is not. That is, the predicate, as complement of the subject, is what the adjective of the subject is not. The predicate is an ‘actualized wave function’. In other words, if we assert ‘actualization’ of the ‘wave function’, we hold to the complementarity principle: ‘An actualized wave function is this particle’ implies that ‘An unactualized particle is a wave function’. However, it might be the case that ‘this particle’ is neither that particular ‘unactualized wave function’ nor is it not that particular ‘unactualized wave function’. Any ‘unactualized wave function’ is a ‘wave function’. That much is clear. But an ‘actualized wave function’ can take on many faces. It can be ‘this particle’ here, or it can be any one of a virtually unlimited number of other possible ‘particles’ somewhere else. So the two sentences, ‘This unactualized particle is a wave function’ and ‘An actualized wave function is this particle’, are asymmetrical. ‘This particle’ was an ‘unactualized wave function’ but an ‘unactualized wave function’ is not necessarily ‘this particle’. It could be ‘that particle’, or some ‘other particle’. This is because a particular ‘particle’ is one, while the ‘unactualized wave function’ entails many in terms of a range of possible ‘particles’. The Excluded-Middle Principle doesn’t hold with respect to the complementarity principle, since between one ‘wave function’ and a ‘particular particle’ there could have been many ‘alternate particles.
Now, all this might appear as so much word spinning. The Excluded-Middle (neither A nor Not-A) contends with the Bivalent Principle (either A or Not-A), but it virtually ignores the Non-Contradiction Principle (not both A and Not-A). In contrast, if A and Not-A are considered in simultaneity, then Non-Contradiction continues to exercise its force. A quite feasible way to abrogate both the Excluded-Middle and Non-Contradiction is Nāgārjuna’s Middle Way. In one fell swoop, it negates all four sentences of the Tetralemma. Following ‘A’, ‘Not-A’, ‘A and Not-A’, and ‘Neither A nor Not-A’, and in light of our tentative observations of Figure 1, Nāgārjuna, with a few strokes of the quill, writes ‘All of the above’, and then he caps it off with ‘None of the above’. Beautiful, and monstrous.
One might retort: ‘Monstrous, but hardly beautiful, for the only possible response is apathy or nihilism’. But not really. There’s actually nothing to be concerned over when confronting the Tetralemma. You say you don’t like ‘Both A and Not-A’? So, negate it. And you can plod along the narrow path of two-valued classical logical thinking. You like it? Then revel in it to your heart’s desire. ‘Neither A nor Not-A’ throws a bit of fear in you? Take it in your stride or simply forget it. By all means don’t fret over it. It could give you nightmares. You take a liking to it? Kick your heels up and sing praises to the free-wheeling play of the universe. We are free to accept the Principles of Non-Contradiction and Excluded-Middle, but we don’t necessarily have to if we don’t want to. That’s the beauty of it all (Nishitani 1990).
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