PARADOX AND RIDDLES

PARADOX AND RIDDLES . Although paradoxes can seem enigmatic and riddles paradoxical, they are fundamentally different realities. Riddles are mainly instrumental and performance-oriented, whether used in sacred or secular contexts, whereas paradoxes are rooted in the heart of being and language, touching on the crux of experience and expression. Riddles are to be solved; a paradox is to be transcended, or, rather, lived.

Riddles

A riddle was called griphos (lit., "fishing creel," or something intricate) or ainigma ("dark saying") in Greek and aenigma ("problem") in Latin. The modern meaning of enigma, "that which is unknown and remains obscure," reflects this ancestry. Riddles may or may not have solutions. As the English saying "It remains a riddle" indicates, what cannot be known remains a mystery. In Greek, mustērion meant something beyond the comprehension of human intelligence.

Riddles have been known since antiquity and throughout the world. The oldest recorded riddles are found in Babylonian school textbooks, in which one finds such riddles as: "Who becomes pregnant without conceiving, who gets fat without eating?" The answer, not given in the textbook, is probably a "rain cloud." (Taylor, 1948, pp. 12–13) The Greek poet Pindar called the Sphinx's question a riddle (ainigma ); Plato alludes to the punning riddles common in his time (Republic 5.479). Riddles may be both playful and serious—playful as a humorous diversion or pastime, or serious as in the riddle of the Sphinx, failure to solve which would cost a person's life. German philologists referred to such a riddle as a Halsrätsel (capital riddle). By the same token, Yudhiṣṭhira in the Indian epic of Mahābhārata restored his brothers to life by successfully solving the riddles posed by a yakṣa, a demi-god (chapter 41, "The Enchanted Pool"). Although of modern creation, Bilbo Baggins's interaction with Gollum in The Hobbit by J. R. R. Tolkien preserves the life-staking seriousness of the riddles as a performing act (see ch. 5, "Riddles in the Dark").

In Vedic India, riddles were posed as part of such rituals as the rājasūya (coronation of a king) and the aśvamedha (horse sacrifice). The exchange of questions and answers between the sacrificial priests was highly formalized, as in this pair: "What is it that walketh singly?" "It is yonder sun, doubtless, that walks singly, and he is spiritual luster" (Śatapatha Brāhmaṇa 8.2.6.9ff.). Brahmans competed in jātavidyā (knowledge of the origins) and brahmodya (theological or philosophical discussion about brahman). Cosmological questions were often the topics of riddles, as in the Ṛgveda : "I ask you about the furthest limit of earth. Where, I ask, is the center of the world? I ask you about the Stallion's prolific seed; I ask you about high heaven where abides the Word" (1.164.34). This suggests that philosophical inquiry developed in the form of posing riddles (see Ṛgveda 1.164.46; 10.129; Atharvaveda 9.9–10; 10.7). A verse in the Atharvaveda asks: "How does the wind not cease to blow? How does the mind take no repose? Why do the waters, seeking to reach truth, never at any time cease to flow?" (10.7.37; cited in Bloomfield, 1969, pp. 210–218; Huizinga, 1949, pp. 105–107).

Dealing with the mystery of existence and the universe, riddles were often considered to have a special power. The possession of esoteric knowledge meant the possession of power (Huizinga, 1949, p. 108). Moreover, a magical power was associated with riddles: the idea that a spoken word has a direct influence on the world order is at the heart of the ritualistic use of riddles, such as those used at the time of rice planting and growing (but that were strictly forbidden between harvest and the laying out of new fields), and those used on certain occasions such as funerals.

To the authors of the Hebrew scriptures, riddles were closely connected with wisdom, which the Lord conferred as a blessing (see Samson's riddle in Judges 14:13–18; on the Lord's blessing, see Judges 13:24). Solomon's wisdom, which "God had put in his heart" (1 Kgs. 10:24), was challenged by the queen of Sheba with "hard questions" (1 Kgs. 10:1–13; 2 Chr. 9:1–12). The authors of medieval midrashim elaborated on such questions in detail, as for instance: "Who were the three that ate and drank on the earth, yet were not born of male and female?" "The three angels who revealed themselves to our father Abraham, peace be unto him," and so on (Schechter, 1891, pp. 354–356). Riddles were "most characteristic of Jewish table-amusements in the middle ages" that "great Hebrew poets of the middle ages composed acrostics and enigmas of considerable merit" (Abrahams, 1896, pp. 384–387, 133).

Riddles were actively employed in Christian missionary activities during the middle ages. It was in this context that the bishop Boniface (ca. 675–754) chose ten virtues and ten vices as a theme for riddles (Taylor, 1948, pp. 63–64). Biblical passages often provided allegorical riddles (ibid., pp. 61–65).

KŌan

K'an (Chin., gongʾan, "public document, authoritative statute") are a series of questions that Zen masters give to their students as an aid to their meditation practice. Kōan are still actively utilized to train students in the Japanese Rinzai lineage of Zen tradition, which belongs to Mahāyāna Buddhism. The popularized version of kōan, such as "What is the sound of one hand clapping?" or "What was your original face before your parents were born?", may initially appear to be riddle-like, but they are actually not riddles and have a distinct function to free the mind from its conventional habits beset by the subject-object dichotomy.

The practice of kōan became widespread among the disciples of the Chinese Chan (Jpn., Zen) master Dahui Zonggao (Jpn., Daie Sōkō; 1089–1163). The kōans often consist of questions and answers (known as mondō in Japanese) exchanged between masters and students during the Tang and early Song periods in China, as well as questions put forward by teachers and anecdotes of famous masters.

The kōan traditionally given to the beginners is known as "Zhaozhu and the dog," which is a dialogue between a monk and the master Zhaozhu (Jpn., Jōshū). A monk asked Master Zhaozhu: "Does the dog have a Buddha nature?" The Master replied: "No." A variation of this kōan continues: on another occasion, another monk asked Master Zhaozhu: "Does the dog have a Buddha nature?" The Master replied: "Yes." Baffling it may be, this particular kōan is not about the concept of emptiness or nothingness, nor does it deal with the opposition of existence and non-existence (Izutsu, p. 176). Kōan s point beyond the discursive level of yes and no to the very reality of the world in which all beings are vitally interrelated.

D. T. Suzuki notes that kōan s are intended as themes for meditation, as "the means for opening one's mind to the truth of Zen"; and further: "kōan and zazen [seated meditation] are the two handmaids of Zen; the first is the eye and the second is the foot." Thus without thorough training in seated meditation, Zen students will not attain spiritual awakening (Suzuki, 1964, pp. 101–102).

Zen teaching may appear to deny discursive thinking, but it actually brings the practitioners face to face with the primordial reality that is prior to conceptualization. The following statement by a Chinese master Qingyuan (Jpn., Seigen) illustrates the inner dynamics of Zen/Chan training:

Thirty years ago, before this aged monk got into Chan training, I used to see a mountain as a mountain and a river as a river. Thereafter I had the chance to meet enlightened masters and, under their guidance, I could attain enlightenment to some extent. At this stage, when I saw a mountain: lo! it was not a mountain. When I saw a river: lo! it was not a river. But in these days I have settled down to a position of final tranquility. As I used to do in my first years, now I see a mountain just as a mountain and a river just as a river. (Izutsu, p. 208)

The first stage is characteristic of the ordinary way of looking at the world: the knower (subject) and the known (object) are separated, and the mountain is perceived as a thing standing out there. The second stage is the experience of the oneness of the knower and the known. The third stage is the recognition of the world as is, based on the experience of the oneness (second stage) and overcoming the subject-object dichotomy (first stage) of the knower and the known (Izutsu, pp. 208–209). Riddle-like statements often found in Zen/Chan literature thus have an epistemological foundation.

Paradox

The original Greek meaning of para doxa, "contrary to received opinion or expectation," cuts through various meanings of paradox. In classical Greek, paradoxia meant "marvelousness" and paradoxologeō, "to tell marvels." Thus, paradox was more than just a contradiction; paradoxos meant "incredible"—contrary to one's expectation or a generally held notion (doxa ). This was the sense of the word retained in the New Testament passage about Jesus healing a palsied man: people were "all amazed, and they glorified God, and were filled with fear, saying, we have seen strange things [paradoxa ] today" (Lk. 5:26). In this particular passage, paradoxos thus means "miraculous."

Definitions of paradox

The word paradox has been understood variously as a logical contradiction, absurdity, enigma, or seeming contradiction. Hamlet said, "This was sometime a paradox, but now the time gives it proof" (Hamlet 3.1.114–115). Some define paradox as a unique form of thinking, "a dynamic, bi-polar thought which bespeaks a vital tension involving both the opposition and reciprocation of ideas" (Slaatte, p. 132). Others see paradox, "playing with human understanding," as "primarily a figure of thought, in which the various suitable figures of speech are inextricably impacted" (Colie, pp. 7, 22). Kierkegaard, on the other hand, asserted that the paradox, arising from the "relation between an existing cognitive spirit and eternal truth … is not a concession but a category, an ontological definition" (ed. Bretall, p. 153).

Kinds of paradox

There are logical, visual, psychological, rhetorical, and other types of paradoxes, such as epistemological and existential. Logical paradox has preoccupied logicians and mathematicians since olden times. The paradoxes associated with Zeno of Elea go back to the fifth century bce. Many logical paradoxes are considered solvable by applying different conceptual frameworks as for instance Russell's "barber paradox," which runs: in a certain town the barber shaves everyone who does not shave himself; does the barber shave himself? If the barber does not shave himself, he must shave himself, and if he does shave himself, he cannot shave himself. Some other logical paradoxes are considered antinomies, and still others are mind-twisters. Evaluations as to the kinds of paradoxes are by no means uniform. For instance, Quine considers the paradox by Eubulides of Epimenides the Cretan, who said "All Cretans are liars," untidy and therefore solvable, while Poundstone considers it to be a genuine paradox (Quine, p. 86; Poundstone, p. 18).

Visual paradoxes, such as the picture that presents a duck from one view and a rabbit from another, have come to be regarded more in relation to the psychology of representation (Gombrich, 1960). The rhetorical paradox as a literary genre was extremely popular during the Renaissance. The Praise of Folly (1509) by Erasmus set the tone; the genre was also practiced by the poet John Donne, the satirist Joseph Hall, among others.

Functions of paradox

Fundamentally connected with the problem of language and being, paradoxes function variously. Paradoxes in mathematics or physical science are puzzles to be solved by "putting the conceptual framework in a new perspective," so that "the limitations of the old concept are revealed" (Rapoport, p. 56). Challenging the limits of reason, paradoxes may function as gateways to a new and more comprehensive paradigm of reality. Indeed, "paradoxes have played a dramatic part in intellectual history, often foreshadowing revolutionary developments in science, mathematics and logic" (Rapoport, p. 50). In the field of logic and mathematics the confrontation with paradoxes—such as Russell's paradoxes—greatly stimulated studies of the foundations of mathematics (Quine, p. 84). Contradictions are regarded as a fertile soil for the development of theories in physical science. A. N. Whitehead holds that "in the formal logic, a contradiction is the signal of a defeat: but in the evolution of real knowledge it marks the first step in progress towards a victory" (p. 260).

Some consider paradox as a higher form of expression of truth that defies a logical or linear mode of description as it involves a contradictory juxtaposition of images rather than of logical ideas (Slater, p. 115). Just as metaphor and images point beyond words, so do paradoxes point beyond a logical linguistic construct, and open up the domain of experience itself. They make accessible religious experiences, poetic intuitions, artistic creativities, and much of everyday experience.

Paradox and religious discourse

Heraclitus described God as "day night, winter summer, war peace, satiety hunger" (frag. 67). And the Japanese Zen master Daitō described religious truth as "Separated by an eternity, yet not separated even an instant; face to face the whole day, yet not face to face even an instant." Paradoxical statements are often oxymoronic in style, combining contradictions. Descriptions of the religious reality and religious experience are frequently dressed in contradictory language such as plenum/nihilum, personal/impersonal, immanent/transcendent, affirmation/negation, sin/redemption. Out of the tension between these terms emerges a meaning that is characteristic of religious experiences. Rudolf Otto described the dimension of numinous as "mysterium tremendum et fascinosum," and considered that "these two qualities, the daunting and the fascinating, now combine in a strange harmony of contrasts, and the resultant dual character of the numinous consciousness, to which the entire religious development bears witness, at any rate from the level of the 'daemonic dread' onwards, is at once the strangest and most noteworthy phenomenon in the whole history of religion" (Otto, p. 31).

There is a correlation between types of experience and types of expression. "Between logical contradiction (or seeming contradiction) and certain forms of religious feeling there is a close relation," observes Arthur Lovejoy (p. 279). Some consider paradox to be a more suitable, if not essential, form of expression of religious experience (see Calhoun; Stace). To say God is immanent/transcendent is more than just a simple placing of these two qualities side by side; rather it describes the character of religious experience itself.

In the Christian mystical tradition or in the Zen tradition, linguistic expressions are regarded with suspicion, because of the basic assumption of the limitation of language—or at least of certain forms of statement—and the hierarchy of intelligibility, which is not confined to logical thinking. But all the same the need for affirming the reality beyond human thoughts and language remains strong.

Chinese Chan master Wumen (Jpn., Mumon), whose collection of gong'an (kōan ) is known as The Gateless Barrier (Chin., Wumenguan, Jpn., Mumonkan, 1228), made full use of paradoxical language, as the title of his collection indicates. He wrote in his preface: "The Buddha Mind is the basis, and gateless is the Dharma Gate. If it is gateless, how can you pass through it?" And again: "to cling to words and phrases and thus try to achieve understanding is like trying to strike the moon with a stick, or scratching a shoe because there is an itchy spot on the foot" (Shibayama, p. 9).

Ninian Smart considers "paradoxical pronouncements" to "fulfill such a number of functions that by understanding the gist of them one can penetrate to the heart of the philosophy of religion" (Smart, 1958, p. 20). Citing a passage "It is far, and It is near. It is within all this, And It is outside of all this" (Īśā Upaniṣad 5) as a case in point, Smart notes that the objective, transcendent, numinous, far, brahman, and "wholly other" belong to the strand of worship, whereas the subjective, immanent, mystical, near, ātman, and "within" belong to the strand of mystical experience. Moreover, these two are woven together in a way characteristic of religious experience, as shown by the exhilarating yet self-effacing experience of the mystic (Smart, 1958; see also Austin). Paradoxical expressions may also be considered as rhetorical devices or "therapeutic paradoxes" (Ramsey and Smart, 1959, p. 220).

Coincidentia oppositorum, a paradoxical logic

The expression coincidentia oppositorum or "coincidence of opposites" explains why paradoxical descriptions of themselves belong to the nature of ultimate reality. Although this idea of coincidence of opposites goes back to Proclus and even Heraclitus, it is today generally associated with Nicholas of Cusa (1401–1464), the German churchman, scholar, philosopher, and astronomer. He observed in De docta ignorantia (On Learned Ignorance):

For whatsoever things are apprehended by the senses, by reason, or by intellect both within themselves and in relation to one another—[differ] in such way that there is no precise equality among them. Therefore, Maximum Equality, which is neither other than nor different from anything, surpasses all understanding. Hence, since the absolute Maximum is all that which can be, it is altogether actual. And just as there cannot be a greater, so for the same reason there cannot be a lesser, since it is all that which can be. But the Minimum is that than which there cannot be a lesser. And since the Maximum is also such, it is evident that the Minimum coincides with the Maximum. (1.4; trans. Hopkins, p. 53)

The logic of coincidentia oppositorum presupposes a unifying ground of the many, that is, equality. "Therefore, opposing features belong only to those things which can be comparatively greater or lesser" (ibid.), that is, to the relative world of plurality of things.

Mahāyāna Buddhism also deals with coincidentia oppositorum and maintains the unity of the one and the many. In unity there is multiplicity, and in multiplicity there is unity. A favorite simile is that of the ocean water (the one) and innumerable waves (the many). Paradoxical is the character of the ultimate. The Heart Sutra, the summation of the Prajñāpāramitā corpus, proclaims "all the phenomenal world of experience is empty, and empty is the whole phenomenal world of experience." Suzuki, in discussing this kind of logic of simultaneous negation and affirmation, calls it sokuhi no ronri, or "the logic of prajñā " (Suzuki, 1951, p. 18). Contrasting prajñā ("intuition") with the workings of vijñāna ("reason"), he notes: "Paradoxical statements are characteristic of prajñā -intuition. As it transcends vijñāna or logic it does not mind contradicting itself; it knows that a contradiction is the outcome of differentiation, which is the work of vijñāna. Prajñā negates what it asserted before, and conversely; it has its own way of dealing with this world of dualities" (ibid., p. 24). Such insight into the paradoxical character of reality marks the Japanese Kyoto School of philosophy, of which Nishida Kitarō (1870–1945) was the formative presence.

Docta ignorantia : The paradoxical knowledge of the ultimate

The Socratic tradition of knowledge is a paradoxical mode of knowing: I know that I do not know. Again, "We desire to know that we do not know," wrote Nicholas of Cusa in De docta ignorantia. "If we can fully attain unto this [knowledge of our ignorance], we will attain unto learned ignorance" (1.1). By examining the mode of inquiry and observing that it proceeds by means of a comparative relation and "hence the infinite qua infinite is unknown, for it escapes all comparative relation" (1.1), he concluded that "reason cannot leap beyond contradictories." Moreover, "as regards the movement of reason, plurality or multiplicity is opposed to oneness" (1.24). To recognize reason in this way is to attain "learned ignorance" or "sacred ignorance," which knows that "the precise truth shines incomprehensibly within the darkness of our ignorance" (1.26). Learned ignorance takes people beyond the apprehension of plurality of things, and they also see in their self-knowledge "that there is precise truth which we cannot comprehend" (2, prologue). One also reads in the Kena Upaniṣad : "it is not understood by those who understand it. It is understood by those who understand it not" (11).

Christian mystics also fondly cherished this intuition. John of the Cross held that if it is not by way of reason, then it is by way of non-knowing that one may arrive at what one knows not (The Ascent of Mount Carmel 1.14). In his poem, "I Entered I Knew Not Where," the reader encounters such lines:

I entered I knew not where
and remained without knowing,
transcending all knowledge …

I did not know where I entered,
but when I saw myself there,
not knowing where I was
I understood great things …

The higher one rose,
the less was understood,
for it was the dark cloud
that illuminated the night.…
(Krabbenhoft, pp. 25–29)

The idea of learned ignorance or recognition of the inability of reason to comprehend the ultimate reality has not been foreign to many Western thinkers. Pascal said, "There is nothing so consistent with reason as this denial of reason" (Pensées 182), or, again, "Reason's last step is the recognition that there are an infinite number of things which are beyond it. It is merely feeble if it does not go as far as to realize that. If natural things are beyond it, what are we to say about supernatural things?" (Pensées 188). And Kierkegaard held that "it is the duty of the human understanding to understand that there are things which it cannot understand, and what those things are" (ed. Bretall, p. 153).

The paradox and the via negativa

Dionysius the Areopagite noted that the ultimate reality, the Deity, was beyond human thought and therefore could only be approximated by negative predication. The medieval German mystic Meister Eckhart, a faithful adherent of this method, wrote: "It is God's nature to be without a nature. To think of his goodness, or wisdom, or power is to hide the essence of him, to obscure it with thoughts about him. Even one single thought or consideration will cover it up" (frag. 30). The famous beginning of the Dao de jing echoes this tradition: "The Way that can be spoken of is not an eternal way." In the Upaniṣadic tradition, ātman is "not this, not that [neti, neti ]. It is unseizable, for it is not seized. It is indestructible, for it is not destroyed. It is unattached, for it does not attach itself. It is unbound. It does not tremble. It is not injured" (Bṛhadāraṇyaka Upaniṣad 3.9.26, 4.2.4, 4.4.22, 4.5.15).

The via negativa, or apophatic path, is in fact a paradoxical method of affirming the ultimate, which is considered a superlogical reality. Aquinas pointed out the contradiction inherent in this method: "The meaning of a negation always is found in an affirmation, as appears from the fact that every negative proposition is proved by an affirmative one; consequently, unless the human understanding knew something of God affirmatively, it could deny nothing of God; and such would be the case if nothing of what it says of God could be verified affirmatively" (De potentia Dei 7.5). The approach of mystical theology, however, has a paradoxical rather than a logical interest. Dionysius the Areopagite concluded his Mystical Theology thus: "We can neither affirm nor deny Him [God], inasmuch as the all-perfect and unique Cause of all things transcends all affirmation, and the simple preeminence of His absolute nature is outside of every negation—free from every limitation and beyond them all." One is thus left with the docta ignorantia —one knows that one does not know the divine reality.

The paradox of faith

Referring to the Book of Job, "the paradox of the best man in the worst fortune," G. K. Chesterton wrote that human beings are "most comforted by paradoxes" (p. 237). A. O. Lovejoy explored the psychological need for paradoxical expression in relation to religious salvation in his essay on felix culpa, "the fortunate fall." He argues that Adam's sin was fortunate and as such constitutes the conditio sine qua non of the Christian redemptive drama. This theme "had its own emotional appeal to many religious minds—partly, no doubt, because its very paradoxicality, its transcendence of the simple logic of common thought, gave it a kind of mystical sublimity" (p. 279). His study reveals that this theme in Milton's Paradise Lost actually goes back to du Bartas, Francis of Sales, Gregory the Great, Leo the Great, and Ambrose (pp. 294–295; see also Weisinger, 1953).

The paradox of sin and redemption deeply marks the thinking of religious figures. Luther held that "God conceals his eternal mercy and loving-kindness beneath eternal wrath, his righteousness beneath unrighteousness" (Althaus, p. 279). Again, "If sin is abolished, then Christ has also been done away with for there would no longer be any need for him" (ibid., p. 258). Shinran, the founder of the Japanese True Pure Land school, said: "If the good are saved, how much more the wicked" (Tannishō 3). The paradox of redemption is sustained by faith. The Christian doctrine of the incarnation was for Kierkegaard the paradox par excellence : it is, he wrote, "the 'absolute Paradox,' the paradox of God in time. If one is to believe this paradox, God himself must give him the condition for doing so by giving him 'a new organ' of apprehension—that of Faith" (ed. Bretall, p. 154). The presence of paradox in religious writings can be understood as an integral part of the time-honored question of faith and reason.

Paradox, riddles, and enigma

Both paradox and riddles grapple with the enigma of the universe, of human existence. If something remains a riddle to human intelligence, it remains mysterious or else is understood only paradoxi-cally.

The mystery of existence, the paradox of life, took a concrete expression in an ancient Chinese story. There was an old man living with his son and a very mangy horse near a fortress in a remote border region. One day this horse, the family's only possession, ran away. The villagers all sympathized with the old man for his loss, but he was not a bit perturbed, saying, "This could be a blessing in disguise." The following spring the horse came back with a mare, and they gave the old man many foals. The villagers now congratulated him, but he remained unperturbed. His son broke his leg while riding one of the horses. A war broke out, and nine out of ten men fighting the battle were killed, but his son was spared because he was lame. This Daoist story from the collection of Huainanzi, illustrates the inscrutability of what any event may lead to. This practical wisdom sees a complementary, dynamic interflow of the positive and the negative. It takes the enigma of existence and articulates it in a paradoxical way: It "conceptualizes" it in a "spherical" language. Paradox can be seen as one of the ways in which the human mind rationalizes the nonrational, the inscrutable, the unknown.

Paradoxes are baffling, striking, surprising, or nonsensical to linear thinking. But they are also free, creative, and playful, a form of expression conducive to a "spherical thinking" that expands and contracts freely "across terminal and categorical boundaries" (Colie, p. 7). A host of thinkers have directly or indirectly recognized paradox as an integral aspect of reality. From Heraclitus, Socrates, Plato, ancient sages, numerous mystics, to thinkers such as Pascal, Kierkegaard, Whitehead, Nishida, and Suzuki, the list encompasses seminal thinkers.

See Also

Nishida Kitarō; Transcendence and Immanence; Via Negativa.

Bibliography

For a comprehensive exposition of riddles, see James A. Kelso's "Riddle," in the Encyclopaedia of Religion and Ethics, edited by James Hastings, vol. 10 (Edinburgh, 1918). For close to nine hundred bibliographical entries on riddles, see Archer Taylor's A Bibliography of Riddles (Helsinki, 1939). Taylor's The Literary Riddle before 1600 (Berkeley, 1948) is an invaluable cross-cultural study of riddles with an excellent bibliography on this subject. For an overview of riddles, see Mathilde Hain's Rätsel (Stuttgart, 1966) and Roger D. Abrahams's Between the Living and the Dead (Helsinki, 1980). Johan Huizinga's Homo Ludens: A Study of the Play-Element in Culture (London, 1949) offers a perceptive account of riddles.

For the Jewish and Arab fondness for riddles during the middle ages, see Israel Abrahams's Jewish Life in the Middle Ages (New York, 1896). Solomon Schechter's "The Riddles of Solomon in Rabbinic Literature," Folklore 1 (September 1891): 349–358, gives a full account of fifteenth-century midrash on the Solomon Riddle. Volumes 3, 7, and 9 of James G. Frazer's The Golden Bough: A Study in Magic and Religion, 3d ed. rev. & enl. (London, 1911–1915), contain accounts of riddles. On Vedic riddles, see Maurice Bloomfield's The Religion of the Veda (New York, 1969), pp. 210–218. For the Ṛgveda and other Hindu texts, see Raimon (var. Raimundo) Panikkar's The Vedic Experience (Berkeley, 1977).

On religion and paradox, see I. T. Ramsey and Ninian Smart's "Paradox in Religion," Aristotelian Society Supplementary Volume 33 (1959): 195–232. See also Smart's Reasons and Faiths (London, 1958). William H. Austin's Waves, Particles and Paradoxes (Houston, 1967) applies the principle of complementarity to explaining theological discourse. For the idea of the numinous, see Rudolf Otto's The Idea of the Holy (Oxford, 1928). W. T. Stace's Mysticism and Philosophy (Philadelphia, 1960) has an extensive section on religious discourse and paradox. Religious language and paradox are discussed in Robert L. Calhoun's "The Language of Religion," in The Unity of Knowledge, edited by Lewis Leary (Garden City, N.Y., 1955), pp. 248–262. For Heraclitus's writings, see The Cosmic Fragments, edited by G. S. Kirk (Cambridge, 1954). For a translation of Nicholas of Cusa's De docta ignorantia, see Jasper Hopkins's On Learned Ignorance (Minneapolis, 1981). On John of the Cross, see Kin Krabbenhoft, trans., The Poems of St. John of the Cross (New York, San Diego, London, 1999) (the translation was slightly altered in the text). Pascal's Pensées have been translated by, among others, A. J. Krailsheimer (Harmondsworth, 1966).

On the kōan, see The Kōan: Texts and Contexts in Zen Buddhism, Steven Heine and Dale Wright, ed. (Oxford and New York, 2000); The World of Zen, edited by Nancy W. Ross (New York, 1960); and Daisetz T. Suzuki's An Introduction to Zen Buddhism (New York, 1964). On the Mumonkan (Wumenguan ) text, see Shibayama Zenkei's Zen Comments on the Mumonkan, trans. by Sumiko Kudo (New York, 1974). Toshihiko Izutsu's Toward a Philosophy of Zen Buddhism (Tehran, 1977) provides a philosophical exposition of kōan.

On Buddhism and paradox, see D. T. Suzuki's "Reason and Intuition in Buddhist Philosophy," in Essays in East-West Philosophy, edited by Charles A. Moore (Honolulu, 1951), pp. 17–48; see also Suzuki's "Basic Thoughts Underlying Eastern Ethical and Social Practice," in Philosophy and Culture: East and West, edited by Charles A. Moore (Honolulu, 1962), pp. 428–447. For representative works of the Kyoto School, see Nishida Kitarō, An Inquiry into the Good (New Haven, Conn. 1990) and "The Logic of Topos and the Religious Worldview," trans. by Michiko Yusa, Eastern Buddhist, 19.2 (1986), 1–29 and 20.1 (1987), 81–119, and Nishitani Keiji, Religion and Nothingness (Berkeley, 1982). Robert Slater's Paradox and Nirvana (Chicago, 1951) is a study on the religious ultimate with reference to Burmese Buddhism.

The philosophy of paradox is extensively discussed in Howard A. Slaatte's The Pertinence of the Paradox (New York, 1968). For an accessible coverage of paradox, see William Poundstone, Labyrinths of Reason, Paradox, Puzzles, and the Frailty of Knowledge (New York, London, Toronto, Sydney, Auckland, 1988). On paradox and faith, see The Book of Job, edited by G. K. Chesterton (London, 1916), an introduction to which may be found in The Dimensions of Job, edited by Nahum N. Glatzer (New York, 1969), pp. 228–238. For Kierkegaard's writings, see A Kierkegaard Anthology, edited by Robert W. Bretall (Princeton, 1946). Luther's ideas are studied in Paul Althaus's The Theology of Martin Luther (Philadelphia, 1966). On the idea of felix culpa, see Arthur O. Lovejoy's "Milton and the Paradox of the Fortunate Fall," in his Essays in the History of Ideas (Westport, Conn., 1978), pp. 277–295. See also Herbert Weisinger's Tragedy and the Paradox of the Fortunate Fall (London, 1953).

For logical paradox, see John van Heijenoort's "Logical Paradoxes," in The Encyclopedia of Philosophy (New York, 1967). W. V. O. Quine gives a cogent exposition of the topic in "Paradox," Scientific American 206 (April 1962): 84–96. Anatol Rapoport's "Escape from Paradox," Scientific American 217 (July 1967): 50–56, offers another excellent view of the subject, especially in relation to decision theory. Augustus De Morgan's A Budget of Paradoxes, 2d ed., 2 vols. (Chicago, 1915), presents extensive materials on "paradoxers."

On science and paradox, see Alfred North Whitehead's Science and the Modern World (New York, 1925). Thomas S. Kuhn's The Structure of Scientific Revolutions, 2d ed., rev. (Chicago, 1970), deals with the shift of conceptual scheme in the sciences. Bernard Bolzano's Paradoxes of the Infinite (1851; London, 1950) is one of the classical studies on the topic. On the nature of knowing and paradoxes, see Elizabeth H. Wolgast's Paradoxes of Knowledge (Ithaca, N. Y., 1977).

On the paradoxical tradition of the Renaissance, see Rosalie Littell Colie's Paradoxia Epidemica (Princeton, 1966). Nicholas Falletta's The Paradoxicon (Garden City, N. Y., 1983) gives a concise account while presenting wide-ranging examples of paradoxes with an extensive bibliography. On art and paradox, see Ernst H. Gombrich's Art and Illusion (New York, 1960).

Michiko Yusa (1987 and 2005)