A FORTIORI LOGIC
CHAPTER 12 – A fortiori in China and India
Zen logic, as is well known, is no logic, but a sort of anti-logic, an antithesis of logic. It thrives on paradox and even contradiction, at least apparent if not real. A major feature of Zen logic, though this may not be distinctive to Buddhist or even to Indian or Chinese logic, is its belief in the ‘tetralemma’ (or catuskoti). According to this viewpoint, not only a thesis alone (A and not not-A) or alternatively its antithesis alone (not-A and not A) may in fact be true, but there is a real possibility that both the thesis and its contradictory (A and not-A) are true, or neither the thesis nor its contradictory (not A and not not-A) are true – or even, eventually, that two or more of these four compounds are true together or all false together.
For example, the “two truths” doctrine, formulated by the Buddhist philosopher Nagarjuna (India, ca. 150-250 CE), which distinguishes the “relative truth” of conventional minds and the “absolute truth” of enlightened minds may be classified under the tetralemma category of “neither A nor not-A,” since relative truth is neither absolutely true nor untrue, but something in between. Again, the doctrine that “Nirvana and Samsara are one” may be classified under the tetralemma category of “both A and not-A,” since it proposes a mixture of opposites. These two doctrines are paradoxically considered as mutually supportive, but of course that is quite illogical: if truth is twofold, its two aspects cannot be one; you can’t have it both ways. In scientific Western thought, truth is one; if it is merely ‘relative’, it is simply untruth. Again, if two things are opposites, they cannot overlap.
Moreover, Buddhists argue that existents have no identity of their own, being merely aggregates, constantly in flux, and thoroughly dependent on causes and conditions. They apply this idea to mind as well as matter, and deny existence of the self or soul. Such claims are logically patently absurd. To deny the self or soul is to deny the existence of someone doing the denying. If literally everything is aggregated, then the elements that are aggregated must also be aggregated, ad infinitum, in which case there is ultimately nothing to aggregate. There cannot be such a thing as aggregation without something non-aggregated to aggregate; the buck has to stop somewhere. Similarly, to the Buddhist doctrine of impermanence, which claims that literally everything is constantly in flux, we must ask: flux of what? Change must be change of something to something, with an least momentary stationary existence before and after the change. There cannot be such a thing as change without something static that changes or emerges from the change. The same applies to the Buddhist idea of interdependence, or co-dependence of everything: one thing cannot depend on another if that other thing is as devoid of independent existence as itself. Dependence presupposes something more firmly rooted in being, which can be depended on. Simultaneous mutual dependence is unconscionable. Thus, Buddhist discourse is built on stolen concepts, ignoring their conceptual basis.
Such Buddhist beliefs are contrary to the laws of thought discovered by Aristotle, namely the laws of identity, of non-contradiction and of the excluded middle. For Buddhists, all existents are ultimately “empty” of any nature. But the law of identity is that every existing thing has an identity, a specific nature (whatever that happens to in fact be): it is not ‘just anything’ and it is not ‘nothing’. Every existent is something in particular, with features and behavior peculiar to it. Moreover, a fact is a fact: while it occurs, its constituents, its history and its causes and conditions, if any, are irrelevant to the fact of its existence: it just is. Moreover, identities, facts, are mostly objective givens, not products of mind; to claim otherwise is to affirm one’s claim itself to be imaginary and thus untrue. The law of contradiction is that an existent cannot at once have and not-have a particular identity; presence and absence are incompatible. The law of the excluded middle is that an existent cannot at once neither have nor not-have a particular identity; there is nothing besides presence or absence. These laws, properly understood, are absolute; they are not subject to any exceptions, under any circumstances whatsoever.
These laws – which have been foundational for Western logical thought and the source of its successes (although in today’s atmosphere of willful unreason many people do take a perverse pleasure in disowning them) – were never, it seems, very influential further East. The tetralemma was evidently freely used very early on in East Asia and the Far East, since it is so pervasive in later literature. The “reasoning” behind this irrational belief is that all ordinary human cognition is necessarily “dualistic.” According to its proponents, as soon as anything comes to mind, through perception or conception, its negation must also be considered, even if we tend to either ignore it or arbitrarily reject it. Thus, a positive is unthinkable without a corresponding negative. In one author’s words:
“In Buddhist logic, it is said that all concepts are based upon exclusion. As soon as we affirm something by saying ‘It is this,’ we automatically exclude so many other things it might have been. By imposing a conceptual limitation we fabricate an idea. The suggestion here is that it is just an idea – it is not an open experience.”
But of course this ‘reasoning’ is quite fallacious. Knowledge starts with pure perception of positive phenomena; negatives are never pure percepts but are necessarily products of conception. Note well: positives come before negatives; and negatives are inconceivable without positives. I can cognize a positive through perception and therefore without any reference to its contradictory; but I cannot do the same with a negative. In the latter case, I must first have some idea however vague or hypothetical of the positive, before I can even think of, let alone check out, the negative. Thus, though exclusion is indeed eventually part of the knowing process, it is certainly not a primary act: it is only possible after the pure perception of some things and the subsequent imagination of their possible negation.
Some Buddhist philosophers go still further and, appealing to the notion of “emptiness” (shunyata), claim the ontological primacy of negation over affirmation. But here again the question they do not ask is: “negation of what?” If as they suggest there is nothing there at all, then even negatives have no foot to stand on. The negation of a nothing does not produce a something. What needs to be understood by such people is that the word ‘not’ is more akin to a verb than to a noun. It expresses the Subject’s mental act of rejection of a proposed object. It is therefore necessarily conceptual, and never perceptual. Moreover, such claims invariably ignore the positive existence of the claim, and of someone doing the claiming, and of someone receiving the claim. Such people imagine they can speak in a vacuum, without acknowledging the existential context of their speech. This is illogical.
If anything, it is the Buddhist proponents of “paraconsistent” logic who are dualistic and divorced from reality. They fail to take note of the actual order of knowledge development from positive percepts to negative concepts. Indeed, even at the level of perception, one precedes two. Contrary to what many philosophers imagine, we perceive a whole before we mentally divide it into parts. Here, the confusion involved is to conflate a given moment of perception and perception over time. In any given moment, what we happen to perceive is a whole and this is quickly and mostly automatically divided into parts by the conceptual faculty (note that the perception precedes the subdivision, and only the latter involves negation, i.e. saying ‘this part is not the same as that part’); but of course, over time, many such moments of perception, or more precisely their memories, are added together (again by the conceptual faculty) to form a larger whole. These two operations of the conceptual faculty – viz. conceptual dissection of a present perceptual whole and integration of many past percepts into a conceptual whole – should not be confused.
See Appendix 7.3 for more on the topic of the tetralemma.
I did not, unfortunately, note down every use of such deviant logic that I came across over the years in Buddhist literature. But I do still remember one relatively early instance in the Dhammapada, traditionally attributed to the Buddha (India, ca. 563-483 BCE), “He for whom there is neither this nor the further shore, nor both….” The tetralemma plays a very important role in the Madhyamika philosophy of Nagarjuna, regarded as a forerunner of Zen. As for later, specifically Zen writings, in China and then Japan, they are full of it. Consider, for instance, the words of the third patriarch of Zen, Seng Tsan (China, d. 606 CE):
“What is, is not; what is not, is. If this is not yet clear to you, you’re still far from the inner truth. One thing is all, all things are one; know this and all’s whole and complete.” (Italics mine.)
Eihei Dogen (1200-53 CE), who founded the Japanese Soto Zen sect, often seems (to me, at least) maddeningly obscure, if not insane, due to his frequent breaches of the laws of thought. He indulges without hesitation in self-contradictory statements, such as “There is sitting letting go of body-mind, which is not the same as sitting letting go of body-mind.” Likewise, the law of the excluded middle is no obstacle to his way of thinking. Consider, for instance, this statement: “Active buddhas are neither originally enlightened nor enlightened at some particular time, neither naturally enlightened, nor without enlightenment” – what are they, then, I ask? Or again: “practice-realization is neither existence nor beyond existence” – what’s left, I ask? Surely, if all logical possibilities are exhausted (as seems to be the intention, here), then there are no other possibilities! Dogen pays no attention to such obvious restrictions, making his discourse incomprehensible nonsense.
Although Zen discourse is often antinomic, its favorite form seems to be “neither this nor that.” That is to say, although contradictions and exclusions of the middle are both viewed as possible and do occur in practice, the main emphasis is on denying any thesis whatever, and ‘logically’ enough also the contradictory of any thesis whatever. For ultimate reality is considered by Zen philosophers as essentially out of this world (even while in it) – therefore, whether phenomena point to the existence or to the non-existence of something, anything, is irrelevant. No proposition is true, because none is capable of describing reality as it really is. The phenomenal world is inherently paradoxical; only beyond it can all opposites be harmonized.
This is the gist of the argument, however self-inconsistent and unconscionable it seems to us who are not enlightened. Of course, some sense can be made of it by thinking of ultimate reality as the ‘common ground’ of conflicting phenomena – and this sort of explanation is often used (for example, see the above quoted statement by Seng Tsan). So the ‘noumenon’ (i.e. that which is beyond the phenomenon) may be thought of as both transcendent and immanent. But a true Zen master would disdainfully reject all such philosophizing as misleading babble. Any resort to words as a means of rational description or explanation is regarded as useless when it comes to the “matter” of enlightenment. Consider for instance the following remarks in The Blue Cliff Record:
“It’s wrong to say either that he had words or didn’t have words; nor will it do to say that his answer neither had nor didn’t have words. Chao Chou left behind all the permutations of logic. Why? If one discusses this matter, it is like sparks struck from a stone, like flashing lightning. Only if you set your eyes on it quickly can you see it. If you hesitate and vacillate you won’t avoid losing your body and life.”
All the above tends to the conclusion that Zen ‘logic’ is illogical. However, that judgment can be considerably mitigated, if we understand Zen ‘anti-dualistic’ discourse not as theoretical but as pragmatic. Its purpose is not to formulate a true philosophy, in the Western sense, but to push people to a transforming mystical experience. Thus, when a Zen advocate states: “This is neither true nor false” or “This is neither good nor bad” or “This is neither desirable nor repugnant” – his intent is really, respectively: “Do not think or say that this is true and do not think or say that it is false,” “Do not think or say that this is good and do not think or say that it is bad,” and “Do not think or say that this is desirable and do not think or say that it is repugnant.” For example, Seng Tsan says:
“When you assert that things are real, you miss their true reality. But to assert that things are void, also misses reality. The more you talk and think on this, the further from the truth you’ll be.” (Italics mine.)
In other words, the Zen advocate is not really making logical, prescriptive or descriptive judgments, but advocating the suspension of all judgments, all discourse, in order to arrive at the ultimate “truth.” There is no great inconsistency in doing that. We may, of course, point out that in claiming to be free of concepts he is using concepts and that that is an inconsistency. However, he would reply that he is doing that only in order to communicate with us in our language, in an attempt to allude to things beyond its scope. He is able to function in both the phenomenal and noumenal worlds, whereas we are not – so he has to find some way to reach out to us. In that case, we can only criticize him for being rather gauche in his discourse. He should make it more precise, as just demonstrated. It would then be possible to speak of Zen logic, without inverted commas.
Nevertheless, although a statement like “neither claim it is nor claim it is not” is intended as a non-claim, it objectively definitely does contain a factual claim – viz. the claim that following this advice will facilitate or result in enlightenment (“the truth”); and such a claim is, of course, subject to assessment as true or false, whether the Zen advocate admits it or not.
I would say a very representative example of Zen logic is the koan of Te-shan (China, 9th century CE), the Zen master famous for presenting his students with the following predicament: whether they ‘uttered a word’ (i.e. showed some evidence through word or deed of their understanding of Zen) or not, they would get thirty blows. Another master, Lin-chi (the founder of the Rinzai sect), sent one of his own followers to him with specific instructions. He told him to ask Te-shan why someone who said a word would nevertheless get thirty blows; then, when Te-shan struck him, the student was to grab the stick and push Te-shan back with it. When the student did as instructed, Te-shan responded by simply walking away.
What we have here is a logic of action, rather than words. There is, to start with, a seemingly inescapable dilemma – whether you speak (rightly or wrongly) or abstain from speech, the result will be the same: you will be in error and punished by blows. There is, however, a logical possibility of escape – grab the stick as it comes down and push it back. This could be described as a martial arts response to the attempted physical blow. Logically, the dilemma has by this means been effectively dissolved. There seemed to be no way out, judging by Te-shan’s statement; but there was in fact a way out, perceived by Lin-chi. The opponent is neutralized, prevented from producing the threatened consequences (blows) to either antecedent (speech or silence).
Earlier in the present volume, in an attempt to more accurately depict the logic of a fortiori reasoning, I developed the notion of relative terms, say R1 and R2, such that more R1 and less R2 (and vice versa) are logically equivalent. This idea, I showed, can be extended to the special case of complements, say R and not-R. Although complements, taken as absolute terms, are mutually exclusive – if we take them as relative terms, they are compatible, indeed imply each other. That is, we can define R and not-R so largely that each includes the other, in the same continuum but in opposite directions, i.e. in such a way that more R is less not-R and less R is more not-R. This logical artifice of course changes the meaning of R and not-R, but it is useful for the development of a fortiori logic.
After I worked this idea out, it occurred to me that it could help explain Zen logic. It could be that Oriental philosophers who conceive of A and not-A as being compatible are really thinking in relative terms. Perhaps we in the West think of A and not-A in absolute terms, while they in the East think in relative terms. This may explain, at least in part, why the conjunction of A and not-A does not repel the Oriental mind to the same degree as it does the Western mind. Although, to be sure, this theory is somewhat belied by the fact that Orientals also accept the possibility of neither A nor not-A, which this theory cannot explain.
Needless to say, the said insight does not change the fact that A and not-A, taken in their absolute senses, are incompatible; the Aristotelian law of non-contradiction remains true and unassailable. Relative terms are logical artifacts that function consistently within that universal framework – they do not erase it. The law simply changes form, becoming a distinction between ‘more’ and ‘less’: What is more R is less (and not more) not-R, and what is less R is more (and not less) not-R. Moreover, it is interesting to note that when A and not-A are intended as relative terms, everything falls under both of them; there is no further possibility beyond them. That is to say, the law of the excluded middle also remains operative for relative terms, although it too is stated slightly differently.
But we also find in Zen literature some quite ordinary logic. For example, Dogen mentions an earlier master, Guixing, as saying: “… mind arrives, but words do not; … words arrive, but mind does not; … both mind and words arrive; … neither mind nor words arrive”; this saying of course shows awareness of the four logically possible combinations of two propositions and their negations. Zen writings do on occasion, when it suits their purposes, appeal to the law of non-contradiction. Hakuin Ekaku (Japan, 1686-1768) argues against ‘do-nothing’ Zen as follows: “If you are right about ‘being as you are’ in this ‘plain bowl’ suchness of yours, then the stages of Bodhisattva practice that were set forth long ago are mistaken. If the stages passed down from the past are correct, then being as you are like a ‘plain bowl’ is wrong”.
There are also some instances (few and far between) of a fortiori argument. The following is a list of instances found by me by chance. This is of course not a comprehensive list, but some insights can be gained from it. Note that I give a hint as to the form of each argument by using the abbreviations +s, –s, +p, –p, and &, and I summarize the findings at the end.
The argument can already be found in The Dhammapada, an Indian Buddhist document, in the Pali language, traditionally attributed to the Buddha (c. 563-483 BCE): “‘These are my sons. This is my wealth.’ In this way the fool troubles himself. He is not even the owner of himself: how much less of his sons and his wealth!” (–p). The argument also appears quite early in China, judging by its use in Taoist literature, notably in Lao Tzu’s Tao Te Ching (traditionally dated 6th century BCE, though more probably late 4th century or early third century BCE): “If even heaven and earth cannot go on for ever, much less can man” (–s). We can also mention its occurrence in Sun Tzu’s The Art of War (also traditionally dated to the 6th century BCE, but probably of later origin): “Thus do many calculations lead to victory, and few calculations to defeat: how much more no calculation at all!” (+s).
Later, the argument appears in The Diamond Sutra (an important Mahayana Buddhist text, first translated from Sanskrit into Chinese in 401 CE), section 12: “Wherever this sutra or even four lines of it are preached, that place will be respected by all beings… How much more [worthy of respect] the person who can memorize and recite this sutra [for the benefit of others]!” (+s); or again, in section 15: “If someone… on hearing this discourse on Dharma, were to accept it with a believing heart, the merit acquired by the latter would far exceed… How much more the merit of one who would copy, memorize, learn, recite and expound it for others!” (+s &)
Much later, the Chinese Zen masters use a fortiori to reply to queries; thus, Hui Hai (8th cent. CE): “Even idealism is not Mahayanist, how much less so realism!” (–s) and Huang-Po (d. ca. 850 CE): “If solid things do not exist, how much the less can we make use of reflections” (–s). Another Chinese Zen master, Kuei-shan (771-853 CE), when asked for a Buddhist verse responded by means of a fortiori discourse: “To try to express this [i.e. the key to enlightenment] from person to person is foolish, how much more if you try to put it on paper” (+s). A similar argument is used by the Japanese Zen master Bankei (1622-93), in response to a question asked of him through an intermediary: “This matter of Zen is difficult to convey even by direct question and direct answer; it is all the more difficult to convey by messenger” (–p).
I have also found a fortiori arguments in The Blue Cliff Record (a 12th century compilation of koans, some of which date from the 10th century or before). “Gold dust is a cataract on the eye; the jewel in one’s robe is the defilement of the Dharma. Even one’s own spirit is not important; who are the Buddhas and Patriarchs?” (+s) The point here made is that true enlightenment involves relinquishing all trace of ‘self-consciousness’ (in the pejorative sense) – even thoughts of Buddha Dharma (the teaching of the way to enlightenment; here “gold dust”) and Buddha-nature (the substratum of all existence; here “the jewel”). If even one’s spirituality is forgotten, how much more do the teachers (“Buddhas and Patriarchs”) pale into insignificance. Again, “If they [saints, arhats] have themselves cut off the eighty-one kinds (of passion), how much more so the three poisons [greed, hatred and delusion]!” (+p)
Dogen (whom we already mentioned in the previous section) makes the following a fortiori remark in one of his essays: “Such [deluded] people existed in the past; are there not even more today?” (+s &) – inferring, from the common knowledge that some people were deluded in the past, that many contemporaries are deluded. In another essay he says: “Buddha said, ‘if you are to practice giving to yourself, how much more so to your parents, wife, and children’” (+s). In yet another: “What the tenzo told me corresponded with Xuedou’s poem. So I knew all the more that the tenzo was truly a person of the way” (+s). And again: “When you long for enlightenment… even taking sand and offering it to Buddha is beneficial…. How much more so to be in the position of tenzo” (+s).
I can also quote you an a fortiori argument by the current Dalai Lama of Tibet; reflecting on the inevitability of death for all of us, he writes: “Even Buddhas have left their bodies behind, so what can be said of ordinary beings?” (+s)
All these a fortiori arguments are well formed (albeit not fully explicit), showing that the people formulating them were able to be logical as well as illogical. Of the 13 instances here listed, 10 are positive subjectal (marked +s), 3 are negative subjectal (–s), 1 is positive predicatal (+p) and 2 are negative predicatal (–p). Moreover, 13 of these arguments are purely a fortiori, while 2 of them (marked &) seem to have been intended as a crescendo. These statistics show that all forms of a fortiori argument (at least, of the copulative variety) are represented in Zen Buddhist discourse. Of course, these are only isolated uses of the argument form. I know of no philosophical or logical reflection on a fortiori argumentation in Buddhist or Zen literature. They just used it instinctively and took it for granted.
A fortiori argument is called kaimutika or kaimutya nyaya in Indian logic. Kaimutika (कैमुतिक) or kaimutya is derived from the words kim uta which literally mean ‘what to say of’ (i.e. ‘what is to be said of’), and are used like the expression ‘how much more’ (or how much less’); nyaya means inference. In the Vyavahāramayūkha of Nīlankaṇṭha, it is written: “kaimutika nyaya is a maxim used where a conclusion will a fortiori follow as regards certain matters when it is conceded that it does follow in certain other less important or less obvious matters.” This obviously refers to inference from minor to major; but as we shall soon see, there is also inference from major to minor. The following are examples of a fortiori argument in religious Indian discourse that I found in the Internet:
· “It has been said also in SANdilya-smriti: ‘There may be doubts concerning the redemption of those who serve AchArya, but there is absolutely no doubt about the redemption of those who delight in the service of His devotees’ (1-95). So, in the case of those who depend solely on the AchArya, there is no doubt at all concerning the fruition of prapatti, by the principle of ‘kaimutika nyAya’. (Will not the Lord, who saves those who take refuge in His devotees, save those who take refuge in their AchAryas? Will not a benefit, which is got by one who is not qualified, be obtained by one who is qualified?). The intended a fortiori reasoning in this example seems to be: if those who serve mere devotees are meritorious enough to be redeemed (or to attain “the fruition of prapatti,” i.e. of devotional surrender), all the more so those who serve the teachers of the devotees (the “AchArya”); this is positive subjectal (from minor to major) argument.
· “That Prabhu who bestows even upon His most antagonistic enemies a result that is supremely difficult for great yogés to attain must necessarily, according to the logic of ‘inferential partial illustration’ (kaimutika-nyäya), bestow the highest fruit of all upon His devotees who incessantly cultivate favorable activities and moods in His service.” Here again, the argument seems to be negative subjectal (from major to minor) a fortiori: if his enemies are not disqualified enough to be deprived of great benefits from Prabhu, all the more so his devotees. The intent here may even be a crescendo, in which case the benefits for the latter would be greater than those for the former.
· “This Seshatva, being the servant of the Supreme Lord, will automatically be reflected in his character as well as in his appearance. This results by the principle of ‘kaimutika nyAya’. When a greater thing is known, will not the lesser great thing be known? That will be obvious. Here, the knowledge of SEshatvam is the greatest one. When it is known firmly to a person, will it not reflect in his behaviour and appearance? There is no need to mention it separately as it is obvious.” The explanation given within this example points to positive predicatal (from major to minor) a fortiori argument: if someone is high enough to know the greater thing, all the more so a lesser thing.
· “Here an argument a fortiori (kaimutika-nyaya) is advanced. Even in the world, without a knowledge of something to be done (karya), there is no eligibility. It goes without saying, therefore, that this must be so with regard to sacred matters.” This looks like a negative predicatal (from minor to major) a fortiori argument: If one is not sufficiently qualified to be eligible in relation to mundane matters, all the more so in relation to sacred matters.
From the above four examples, we can see that Indian a fortiori reasoning may go from minor to major or from major to minor. Indeed, all four moods of the argument appear to be used – the positive and negative subjectal and the positive and negative predicatal. Moreover, we can say that Indian discourse does not merely use a fortiori argument, but uses it consciously (as evidenced by appeal to “the principle” or “the logic” of kaimutika nyaya) and it seems that some discussion of it has occurred at some time (as the reference to “inferential partial illustration” suggests).
However, it is noteworthy that my Google searches did not yield many more examples than the above four (which are repeated frequently, in different Hindu websites); and as regards reasoned reflections on kaimutika nyaya, or even explanations of the expression “inferential partial illustration,” I have not found any. We might from this surprising paucity of information infer that nowadays a fortiori argument is not very often used in Hindu discourse and the argument is very rarely if at all discussed.
As regards historical conclusions, it is impossible for us to draw any from the above four examples for now, since their original authors are not readily identifiable and dated (though further research might allow us to do that, of course). All we can say at this stage is that Hindu discourse today, whether based of ancient Indian sources or on capabilities more recently acquired from whatever (e.g. perhaps British) sources, includes valid a fortiori reasoning. Nevertheless, a fortiori argument is manifestly present in quite ancient Indian literature, as the following two examples demonstrate.
There is a case in the Pali-language Dhammapada, a collection of aphorisms traditionally attributed to the Buddha: “‘These are my sons. This is my wealth.’ In this way the fool troubles himself. He is not even the owner of himself: how much less of his sons and his wealth!” – meaning: if the fool (S) has insufficient power (R) to claim ownership of himself (Q), all the less has he (S) power (R) enough to own his sons and wealth (P) (negative predicatal, from minor to major).
There are also four cases in the Sanskrit-language Bhagavad-Gita traditionally attributed to a sage called Vyasa: “These I would not consent to kill, though killed myself, even for the kingdom of the three worlds; how much less for the sake of the earth?” (1:35) – meaning: if the three worlds (P) are of value to me (R) not enough to consent to kill these people to gain rule of them (S); all the less, an earthly kingdom (Q) (negative subjectal, from major to minor); “This world is not for him who offers no sacrifice; how, then, any other world?” (4:31) – meaning: a man who offers no sacrifice (S) has merit (R) not enough to have a share in this world (Q); all the more so, in the higher world (P) (negative predicatal, from minor to major); “Those who take refuge in Me, though they are lowly born, women, merchants, as well as workers—they also attain the highest goal—how much more, then, holy Brahmins and devoted royal saints?” (9:32-33) – meaning: the lower castes who take refuge in Me (Q) are wise (R) enough to attain the highest goal (S); all the more, the higher castes who do so (P) (positive subjectal, from minor to major); “None is equal to Thee; how then could there be one greater than Thee in the three worlds? (11:43) – meaning: no one (S) is great (R) enough to be equal to Thee (Q); all the less so, to surpass Thee (P) (negative predicatal, from minor to major).
These are of course only two texts in the long list of classics of Indian religious literature, including the four Vedas, the Vedangas, the Upanishads, the Ramayana and Mahabharata epics, the Sutras, the Puranas, and many more. A full study of the use of a fortiori discourse in ancient India would have to systematically examine all extant texts, looking for and counting all occurrences of the key words and phrases of such discourse in them. I will not do the job here, albeit its importance, but leave it to others.
I have looked through extracts from The Nyaya Sutras of Gotama (namely, 1:1-2, 2:1-2, 5:1-2). There is, there, a definition of comparison or analogy (upamana) as “the knowledge of a thing through its similarity to another thing well known” (1:1:6, p. 359); and it is later stated that knowledge by this means is “right” provided the “comparison is established through similarity in a high degree” (1:2:44-45, p. 368). There is also an apparent reference to syllogism, an example given being “Sound is non-eternal… because sound has the character of being a product; as a matter of fact, everything that is a product is non-eternal” (1:1:32-35, p. 362); and possibly also a reference to generalization (1:1:36-38, pp. 362-3). But I have not in these extracts found use or discussion of a fortiori argument. Of course, this being a very scant research effort it proves nothing.
As regards Indian logic in general, not having studied it in any depth I will not here attempt to discuss it further. But, based on the little I know of it, I can say offhand that while there are of course some ideas and doctrines in it that are open to criticism, it has a great many interesting and instructive features which we in the West would no doubt gain much from studying. An example of interest, found in the above-mentioned Sourcebook, is the understanding in The Padarthadharmasamgraha of Prasastapada that “Negation… is mere inference; just as the appearance of the effect becomes ‘indicative’ of the existence of the cause, so also does the non-appearance of the effect become ‘indicative’ of the non-existence of the cause. (ix.ii.5)” (6:110, p. 415). This very important insight into negation as an inductive product rather than a direct experience is something that many Western logicians have not yet, to this day, realized and assimilated.
 I should reiterate here that though I repeatedly criticize Buddhism for its illogic, my purpose is not to totally discredit it. I greatly respect this philosophy of life, and am myself positively influenced by it daily. However, there is much in its philosophical discourse that needs to be revised. Its cavalier attitude to logic is simply untenable.
 The 12th century CE Islamic philosopher Averroës (or Ibn Rushd) tried to introduce a similar notion of “double truth” (one for common people and one for the élite). Some Christian philosophers, possibly including Boethius, tried to follow suit. But such tendencies were ultimately rejected in both cultures, as it was realized that if religion was cut off from reason, it ultimately implied that religion is irrational and therefore untrue. More recently, most Christians have gradually adapted their beliefs to empirical science and history (though many still resist, e.g. with regard to Darwinism). Islam, on the other hand, is still firmly marooned in the Middle Ages.
 This goes against Descartes’ phenomenological dictum: “I think, therefore I am,” which means that as of the moment one acknowledges the phenomenon of thought by venturing some proposition, one logically must acknowledge the existence of someone having that thought. ‘Consciousness’ presupposes some sort of subject and some sort of object, being a special relation between two things, the conscious one being called ‘subject’ and the one the subject is conscious of being called ‘object’. The difficulty of fathoming this relation, due to its ontological distinctiveness and therefore primacy, does not make it any the less real; there are a great many things we cannot fathom, but must take for granted. Knowledge must start with some irreducible primaries; it cannot be grounded in an infinity of definitions and proofs. To make a demand for endless grounding is to claim that demand as an irreducible primary; it is self-contradictory. Buddhists consider that what we call the self is simply the totality of our sensory and mental experiences at any given moment of time: for them, there is no one having those experiences – they just are, forming a changing bubble of manifest being (which they call ‘consciousness’); this bubble being particular gives the illusion of selfhood. But the question remains: who has this illusory idea of being a self? How can a non-self imagine that it is a self? They have no answer to such questions, and avoid to ask them, being dogmatically attached to the idea of no-self.
 Moreover, how can a human mind go all the way to infinity and observe that aggregation continues there, before making such a bold claim?
 Here again, how can a human mind know the dependence of literally all things on each other? To have such knowledge, of all things past, present and future throughout the universe and their exact relations to each other, is conceivable for God – but how can a mere mortal obtain it?
 Although Buddhists claim that enlightenment brings about omniscience, such a claim is not empirically justified. For a start, Buddhism has made and still makes many claims about the physical world and the history of life and men that are rejected by modern science; e.g. that the world and life have existed forever. More specifically, consider the following blooper: Zen master Dogen, after attaining enlightenment in 1227-8, wrote in an essay dated 1231 that the Buddha was active about 2000 years before, whereas we know that he lived in circa the 6th-5th centuries BCE, i.e. some two to four hundred years later than Dogen thought. See: Beyond Thinking: A Guide to Zen Meditation, Ed. Kazuaki Tanahashi (Boston, MA: Shambhala, 2004), p. 31. Dogen claims having attained enlightenment in another essay (p. 13).
 How the identity of things is to be known is the question the science of logic seeks to answer. The short answer is, of course, by means of our senses and our reason. That is, empirically and logically, inductively and deductively. Not all identities are necessarily knowable; but we must admit that some are, for otherwise we would be involved in self-contradiction (claiming knowledge and denying it at once).
 See Traleg Kyabgon Rinpoche, “The Path of Mahamudra,” in The Best Buddhist Writing 2005, Ed. Melvin McLeod and the editors of the Shambhala Sun (Boston, MA: Shambhala, 2005), p. 98. Although he refers specifically to conception, the implication of such statements is usually taken to be that all affirmation implies negation, i.e. even affirmation based exclusively on perception. Note however, the contrary statement by Eleanor Rosch, in the same collection of essays, p. 114: “According to Buddhist teachings, while all of the interdependent past can be causally gathered into the microcosm of the moment of present experience, that does not mean that the basic mode of apprehending the present moment is somehow filtered or distorted or abstractly representational.” In other words, Buddhists do ultimately admit of unadulterated percepts (if only in the context of the enlightenment experience).
 The Dhammapada was probably compiled in the third century BCE.
 See my book Buddhist Illogic on this subject. It should not be thought that Nagarjuna’s perverse thought has had no equivalent in the West. For example, the Megaric school (founded by Euclides of Megara in 4th century BCE Greece) argued much like him that predication is either wrong (if the predicate “differs” from the subject) or useless (if the predicate is “the same as” the subject), ignoring the fact that such a statement is itself an act of predication. I have over the years spotted many such similarities between Eastern and Western philosophies. This is a topic that still needs extensive study, though there may already be good books on it that I am unaware of.
 In his “Affirming Faith in Mind,” given in full in Roshi Philip Kapleau’s Zen Merging of East and West (New York: Doubleday, 1980), pp. 184-189. It is hard for me to believe that illogic, the suppression of reason, is compatible with enlightenment, let alone conducive or essential to it—just as it is hard for me to believe that idolatry, the worship of inanimate objects, is compatible with enlightenment, let alone conducive or essential to it. Yet these are recurring theoretical teachings within Zen Buddhism. Even so, paradoxically, I do believe that Zen has much good to offer mankind on a practical level!
 Beyond Thinking, pp. 51, 79, 80. I should additionally draw attention to the frequent use of tautology in some Buddhist texts, as if this was informative. For example, Dogen also enjoys tautologies like “sitting is sitting;” he also, I notice, takes pleasure in reversing statements, as in “sitting is buddha-dharma and buddha-dharma is sitting” (p. 51); and reshuffling terms, as in “zazen is invariably the intention to become buddha, and… zazen is invariably becoming buddha with intention” (p. 39). Such discourse may of course be informative, but I suspect the intention is more poetic.
 The Vimalakirti Nirdesa Sutra, a Mahayana text some consider as dating from about 100 CE (although there is no mention of it till after Nagarjuna’s time, i.e. about a century later), is a veritable litany of antinomies.
 Pi Yen Lu, a Chinese Ch’an Buddhist classic. These remarks were made by Yuan Wu K’e Ch’in (1063-1152), relative to Case 59 (p. 339). Boston, MA: Shambala, 2005. Tr. Thomas & J.C. Cleary.
 The Blue Cliff Record. (I forgot to note the page number.)
 See D. T. Suzuki, The Zen doctrine of no-mind (Boston, MA: Weiser, 1972), p. 87.
 Notice that the student did not try to dissuade Te-shan, saying “if you try to hit me, I will grab the stick and push it.” Rather, he waited for Te-shan to actually strike and then grabbed the stick and pushed it.
 Moon in a dewdrop: Writings of Zen Master Dogen, p. 81. Ed. Kazuaki Tanahashi (New York: North Point Press, 1985).
 Wild Ivy: The Spiritual Autobiography of Zen Master Hakuin. Tr. Norman Waddell. Boston: Shambhala, 2010. (P. 56.) It is interesting to compare Hakuin’s writing (18th cent.) with that of Dogen (13th cent.). While the latter’s discourse often seems muddled and incomprehensible, Hakuin’s (at least in this book) seems quite rational and straightforward. Maybe the five centuries separating them explains this – but more likely, I think it just goes to show how much the particular personality of individuals affects their discourse. In other words, each person has a mental framework that he brings to his philosophical discourse; and this must be taken into consideration when judging a school of philosophy as a whole. I do not think that the explanation is to be found in the fact that these two masters were from different Zen sects, because examples can be adduced from each sect that point in the opposite direction (i.e. there have been less irrational Soto masters than Dogen, and less rational Rinzai masters than Hakuin).
 Anonymous. The Dhammapada: The Path to Perfection. Tr. Juan Mascarò. (London: Penguin, 1973), v. 62.
 See Lao Tzu, Tao Te Ching, trans. D. C. Lau (London, UK: Penguin, 1963), p. 80 (23:51a). Regarding the dating of the text, see the translator’s comments on p. 147. I assume this translation is literal and reflects actual use of a fortiori argument in Chinese language. I posed the question to a correspondent, Prof. Minghui Xiong of Sun Yat-Sen University, who replied that “a fortiori language or argument [is] really present in Chinese,” and is indicated by the words “何况 (he kuang).”
 (1:15.) Also: “But if neither time nor place be known, then the left wing will be impotent to succour the right, the right equally impotent to succour the left, the van unable to relieve the rear, or the rear to support the van. How much more so if the furthest portions of the army are anything under a hundred Li apart, and even the nearest are separated by several Li!” (+a) (6:20). Feedbooks (from Paxlibrorum.com, 2008-9).
 See Mu Soeng, The Diamond Sutra (Somerville, MA: Wisdom, 2000), pp. 111 and122.
 See John Blofeld, Trans., Zen Teaching of Instantaneous Awakening (Totnes, Devon, UK: Buddhist PG, 1987), pp. 158-9. First publ. 1962.
 See John Blofeld, Trans., The Zen Teaching of Huang Po (New York: Grove, 1958), p. 60.
 See Audrey Yoshiko Seo, Ensõ: Zen Circles of Enlightenment (Boston, MA: Weatherhill, 2007), p. 9.
 See Thomas Cleary, Trans., Zen Antics: 100 Stories of Enlightenment (Boston, MA: Shambhala, 1993), pp. 17-18.
 The Blue Cliff Record, p. 348. This is from a commentary by Yuan Wu K’e Ch’in (already mentioned), but he is quoting some unstated earlier master. The explanation I here offer is based on those given in the Translator’s Notes. Needless to say, I assume the a fortiori form of the English sentence to be true to the Chinese original.
 The Blue Cliff Record, p. 520.
 Beyond Thinking, p. 18.
 Moon in a Dewdrop, p. 45. I read this a fortiori argument as positive subjectal, because its intention seems to be (knowing Mahayana Buddhism’s preference for altruism) from minor to major: “if giving to yourself is important enough for you to practice, how much more so giving to your parents, wife, and children.”
 Moon in a Dewdrop, p. 60. A tenzo is a monastery cook.
 Moon in a Dewdrop, p. 64.
 The Essential Dalai Lama, p. 119. Ed. Rajiv Mehrotra. (London: Hodder & Staughton, 2006.)
 At: www.sanskritdictionary.com. In modern Hindi, the word for a fortiori is nishchayapurvak (निश्चयपूर्वक), according to: dict.hinkhoj.com/words/meaning-of-A FORTIORI-in-hindi.html.
 Pandurang Vaman Kane, 1933. P. 262. The author, Nīlakaṇṭhabhaṭṭa, was active the second half of the 17th century. In Varanasi.
 However, I do not see the surrounding text as meaning this; it rather seems to be saying that if someone has “knowledge of SEshatvam,” then this knowledge “will automatically be reflected in his character as well as in his appearance.” This is not a fortiori argument, but indicative of a causation.
 The Saṁbandha-vārtika of Sureśvarācārya (University of Madras, 1972), p. 12.
 Actually, I found only more three examples, in Google Books: in The Journal of Oriental Research, Madras, Volume 36, p. 11; in John Muir’s Original Sanskrit texts on the Origin and History of the People of India, their Religion and Institutions, Volume 4, p. 44 (London: Trübner, 1863); and in Gleanings from Vedic to Puranic Age, collected papers of Sadashiv A. Dange, p. 193 (New Delhi, Aryan, 2002). These three examples seem to relate to Hindu law.
 These books may have been compiled as late as the 4th or 3rd cent. BCE, but using material possibly centuries older. I have added the standard symbols P, Q, R, S, so as to clearly indicate the major, minor, middle and subsidiary terms in these two examples.
 Anonymous. The Dhammapada: The Path to Perfection. Tr. Juan Mascarò. (London: Penguin, 1973), v. 62.
 The passages here quoted are drawn from: A Sourcebook of Indian Philosophy, edited by Sarvepalli Radhakrishnan and Charles A. Moore (Princeton, N.J.: Princeton UP, 1957), which contains the whole Gita, translated by S. Radhakrishnan. I have left out words not directly relevant to our purpose, for brevity’s sake. Note the use of ‘how then’ (ht) in two cases to indicate a fortiori argument; this expression is, of course, not reserved for such argument; I have not looked for it elsewhere.
 These are the passages included in the excellent collection, A Sourcebook of Indian Philosophy, already referenced. According to the editors, Gotama’s Nyaya Sutras date from the 3rd century BCE. The translation used here is that by S. C. Vidyabhusana, in “Sacred Books of the Hindus, VIII (Allahabad: The Panini Office, 1930).”
 Note that this example is actually a commentary drawn from Gautama’s Nyayasutras with Vatsyayana’s Bhasya, translated by Ganganatha Jha (Poona: Oriental Book Agency, 1939).
 This text of the Vaisesika school dates from the 4th century CE. Trans. by Ganganatha Jha (Allahabad: E. J. Lazarus & Co., 1916). See also the small print commentary on this passage drawn from the Nyayakandali of Sridhara (991 CE).
 The reader can find more information on Indian logic, to begin with, in the Web. See for a start: en.wikipedia.org/wiki/Nyaya and en.wikipedia.org/wiki/Navya-Ny%C4%81ya. “Nyāya … is the name given to one of the six orthodox or astika schools of Hindu philosophy—specifically the school of logic. The Nyaya school of philosophical speculation is based on texts known as the Nyaya Sutras, which were written by Aksapada Gautama from around the 2nd century BCE.” “The Navya-Nyāya [school] … was founded in the 13th century CE by the philosopher Gangeśa Upādhyāya of Mithila. It was a development of the classical Nyāya darśana. Other influences on Navya-Nyāya were the work of earlier philosophers Vācaspati Miśra (900–980 CE) and Udayana (late 10th century). It remained active in India through to the 18th century.” Look also in Google Books: https://www.google.com/search?tbm=bks&q=indian+logic&btnG=.