*See integers from 1 to 10 as pronounced in 4,500 languages.
Tibetan:1 chi 2 nyi 3 sum 4 shi 5 nga 6 truk 7 dün 8 gye 9 gu 10 chu
*Link to Greek philosopher-scientist, Archimedes' essay: Naming the Numbers
*Numbers play a significant role in philosophy. ________________________________________________________
Numbers are often used as mnemonic devices [memory aids]. The Buddhist tradition is no different from others in this regard. For example, the Anguttara Nikaya is the largest of the four main collections of the Buddha’s discourses contained in the Sutta Pitaka of the Pali Canon.
Its title which means Further-factored Discourse derives from the way it is arranged: The Book of Ones (Ekaka Nipata) comprises unique or single items; the Book of the Twos (Duka Nipata), items of pairs of opposites, and so on up to the Book of Elevens.
Many examples of this use of numbers, so common to traditional literature of all kinds, will be seen in the Buddhist examples that follow.
Some traditions go further, placing an importance on the alpha-numeric equivalence of words. For example, the Jewish mystical system, Kabbalah, uses a technique called gematria [pron.: ghemahtria] in which each letter of the Hebrew alphabet accords with a number, so that hidden meanings may be derived from words.
This practice was transferred to other languages and alphabets where it is known as numerology.
Read an explanation and an interesting example of ghematria that makes a connection with the diaspora of the Dalai Lama and other Tibetans in exile.
The 34 Sanskrit consonants [kali] and 16 vowels [ali] used for Hindu and Buddhist scriptures are thought to have great powers, too. Tibetan, though, is not an ancient, but an invented script, and perhaps that is the reason why the numerology tradition does not seem to be practiced.
In Tibetan culture, numbers play an important role in astrology which blends the systems of China and India. Contrary to the system used in the West which is the medieval earth-centred one, the Tibetan one places greater emphasis on the phases of the moon using a system that divides a lunar month into 30 equal "days".
This lunar cycle is thought to be derived from the cosmic tortoise of Hindu mythology that is the foundation of the physical world. (Not surprisingly, North American aboriginal peoples also refer to the 13 moons on Turtle's back.)
Click for M. Erlewine's detailed explanation of the role of significant numbers in Tibetan astrology.
In Sanskrit, shunya stands for perfection, Emptiness, Nirvana which translates as extinction. According to Venerable Ato Rinpoche, there is not such a negative connotation in the Sanskrit references to zero as there is in the Western view.
*The Single Syllable Ah which stands for Non-arising can be thought of as an expression of One.
*One Dharma, perfect in the beginning, the middle and the end!
*Pair: yab-yum, mother-father in union; skillful means with discriminating wisdom.
*Halves: The earth is half grass and half water, say Tibetans. It is used to remind someone whose partner has left that there are many other opportunities - there is someone for everyone.
*2 stages of tantra: generation and completion.
*Three Jewels: Buddha, Dharma, Sangha
Some may think that the qualities and attainments of the 3 Jewels (Skt. triratna) are inaccessible, but by using methods that work with real-life experience -- that is, by means of the 3 Roots we can actualize these qualities.
*Three Roots: Guru, Yidam and Dakini/Dharmapala
The Guru (and qualities he or she embodies) represents both aspiration and goal. It is linked to The Buddha.
The Yidam (or deity-practice) is the method we use to get there, like the Dharma.
The Dharmapala (or Dakini) is a companion who may exert an influence, just like the sangha - brothers and sisters in dharma.
*Vajrayana practitioners who choose to take the 3 Inner Refuges: Lung, Tsa and Tigle [winds, channels and bindus or drops] may attain the realization that the 3 Jewels and their qualities are within the physical body.
*3 Negativities: Ignorance; Clinging/Greed/Desire, and Passion/Anger. Also called the poisons. In Vajrayana Buddhism, these are not thought of as 'sins' but qualities which can be transmuted and recognized by sentient beings as three aspects of Tathagathagarbha.
*Three poisons [see also, 3 negativities, 5 poisons] ignorance, attachment, anger as symbolized by the 3 animals or swirls at the hub of the Wheel of Rebirth, and the tines of the khatvanga [trident carried by adepts].
*Three Kayas: 'realities' or 'states of existence'
*3 Realms of samsara: of desire, of form, and formless.
*Three Great Red Deities of the Sakya denomination: Kurukulla, Ganapati & Kamaraja.
*three forms of action: mental, verbal, and physical
*3 trainings: discipline, concentration, and discrimination.
*Fourth Buddha: Shakyamuni.
The previous One was Kashyapa. Before him was Kanakamuni, and before him, Krakucchanda.
*The Four Immeasurables is the title of the following prayer:
May all beings* know happiness and the causes of happiness.
May they be free from suffering and the causes of suffering.
May they never be separate from the highest bliss ...
May they come to rest in the great equanimity free from attachment and aversion.
*strictly translated from this famous Tibetan prayer, all mother beings, since it is believed that every living being has been the parent of every other numerous times over numerous lifetimes.
*Four thoughts that lead the mind to Dharma practice. Read a 1970's teaching by Lama Ganga.
*4 empowerments of tantric initiation: vase, secret, wisdom - knowledge, precious word. [They are variously described/named.]
*Four continents of 4 shapes around Mt. [Su]meru in the mandala of Indian cosmology: They are: 'Superior Body', Jambu the Southern-most which is our world [so-called because it is home to the Jambuvriksha or Rose-apple Tree], 'Cow Utilizing', and 'Unpleasant Sound'.
*Four activities: pacifying, increasing, magnetizing and subjugating.
*Four means of magnetizing: being generous, uttering kind words, giving appropriate teaching, being consistent in word and deed.
*Four Schools (Buddhist philosophy) Vaibhasika, Sautrantika, Madhyamika and Yogacara. [Link is to HH Dalai Lama's brief answer to query by NZ scientists.]
*Four friends in the Jataka story about ethics: Buddha Shakyamuni was a bird in a previous life while his attendant Ananda was his friend the elephant, Shariputra was the rabbit and Maudgalyana was the monkey.
*The Five Wonderful Precepts as applied by Thich Nhat Han:
Aware of the suffering caused by the destruction of life, I vow to cultivate compassion and learn ways to protect the lives of people, animals, plants, and minerals. I am determined not to kill, not to let others kill, and not to condone any act of killing in the world, in my thinking, and in my way of life.
Aware of the suffering caused by exploitation, social injustice, stealing, and oppression, I vow to cultivate loving kindness and learn ways to work for the well-being of people, animals, plants, and minerals. I vow to practice generosity by sharing my time, energy, and material resources with those who are in real need. I am determined not to steal and not to possess anything that should belong to others. I will respect the property of others, but I will prevent others from profiting from human suffering or the suffering of other species on Earth.
Aware of the suffering caused by sexual misconduct, I vow to cultivate responsibility and learn ways to protect the safety and integrity of individuals, couples, families, and society. I am determined not to engage in sexual relations without love and a long-term commitment. To preserve the happiness of myself and others, I am determined to respect my commitments and the commitments of others. I will do everything in my power to protect children from sexual abuse and to prevent couples and families from being broken by sexual misconduct.
Aware of the suffering caused by unmindful speech and the inability to listen to others, I vow to cultivate loving speech and deep listening in order to bring joy and happiness to others and relieve others of their suffering.
words can create happiness or suffering, I vow to learn to
speak truthfully, with words that inspire self-confidence, joy,
and hope. I am determined not to spread news that I do not know to be
certain and not to criticize or condemn things of which I am not
sure. I will refrain from uttering words that can cause division or
discord, or that can cause the family or the community to break. I
will make all efforts to reconcile and resolve all conflicts, however
Aware of the suffering caused by unmindful consumption, I vow to cultivate good health, both physical and mental, for myself, my family, and my society by practicing mindful eating, drinking, and consuming. I vow to ingest only items that preserve peace, well-being, and joy in my body, in my consciousness, and in the collective body and consciousness of my family and society.
I am determined
not to use alcohol or any other intoxicant or to ingest foods
or other items that contain toxins, such as certain TV
programs, magazines, books, films, and conversations. I am aware that
to damage my body or my consciousness with these poisons is to betray
my ancestors, my parents, my society, and future generations. I will
work to transform violence, fear, anger, and confusion in myself and
in society by practicing a diet for myself and for society. I
understand that a proper diet is crucial for self-transformation and
for the transformation of
~Thich Nhat Hanh. For A Future To Be Possible (rev. ed.)
*Five Buddha Families:
In the Gelugpa system, white or blue Vairochana [Illuminator] is the central Buddha seated on a Lion throne holding the Wheel of Dharma [Truth]. In the East is white Vajrasattva [Purity] on the Elephant throne holding the thunderbolt [Determination], or blue Akshobya [Unshakeable]. To the West is red Amitabha [Radiance} on a Lotus throne with peacocks or water fowl and holding a bowl and/or lotus. To the North is green Amoghasiddhi on a throne supported by garudas [shang-shangs, really cf. harpies: part man or woman, part bird] and holding crossed vajras. Yellow Ratnasambhava is in the South on a horse-supported throne, holding a jewel.
These Buddhas may vary in arrangement, somewhat, according to the various traditions or lineages. They are sometimes thought of as being in the embrace of their consorts [Tib. yab/yum]. The corresponding shaktis or female activity-expressions are the central Mother of Space, the eastern Mamaki [All Mine], western Woman in White, the northern Green Tara the Achiever, and the southern Buddha-eyes.
*Five Skandhas: psycho-physical aggregates.
< kapila [Tib. nangchu] vessel,
The nangchu is a container modeled on the skull cup cauldron-on-a-tripod used in tantric rituals for the transformation of the five psychophysical aggregates [skandhas] and the five delusions into the five wisdoms.
*Five chakras in the body-of-light [gyalu] according to the Tibetan Buddhist system with their corresponding colours: white, red, blue, yellow and green.
*Five kayas of fruition. According to Padmasambhava, these aspects of enlightenment are: The perfection of the benefit of oneself (peaceful dharmakaya), the spontaneous present for the benefit of others (unified samboghakaya), the manifold skillful means to tame beings (nirmanakaya), the distinct and unmixed appearance (true bodhikaya)and the unified or one-taste as Emptiness (vajrakaya).
*Five Paths of Buddhism: Shravakayana (Way of the Hearers)
*Five poisons or kleshas [a.k.a. obscurations, contaminants]: anger, desire, greed, sloth, ignorance.
obstacles or Hindrances are:
i. Attraction or desire (Kamachachhanda).
ii. Aversion or hatred (Vyapada)
iii. Slothfulness (Thinamiddha).
iv. Arrogance and suspiciousness (Uddhachcha-Kukuchcha).
v. Doubt or uncertainty concerning the triratna (Vichikichah).
*Five major disasters: war, epidemics, famine, pollution and poverty.
*Five wisdoms: dharmadhatu, the mirror-like, of equality, the discriminating and the all-accomplishing.
*5 major consorts in the long lifetime of Guru Rinpoche.
*5 Forms of Desire or Qualities of Enjoyment (T. dod-yon sna-lnga, Skt. pancha kamaguna) Items symbolic of the senses remind us how subsceptible we are to craving:
Mirror (T. me-long, Skt. adarsha) like our eye, captures form. Lute (T. pi-wang, Skt. vina) whose sweet sound impinges on our ears. Incense Burner (T. spos-snod) as a shell container with smoke rising from it. Fruit (T. shing-tog, Skt. phala) represents sweet taste. Silk (T. dar, Skt. netra) evokes the smooth, cool touch.
*6 paramitas, the "perfections" or virtues: generosity, self-discipline, joyful effort or energy/determination, concentration or insight/mindfulness, patience, compassion. Wisdom can be regarded as their product.
apperception [with the mind, cognition]
*6 realms of rebirth:
ashuras or demi-gods, "titans"
tormented/ "hell" beings
*7 chakras in the body of light/'subtle' body [in the Hindu tantric system] and their corresponding lotuses
*seven precious substances: ruby, emerald, sapphire, diamond, pearl, coral, lapis lazuli. [Sometimes, silver, gold, crystal, turquoise, or amber are substituted.]
Three-Eyed Gem/Triple Gem (T. nor-bu bskor-cha)
Rhino or Unicorn's Horn (T. bse-ru)
Queen's Earrings (T. btsun-moi rna-cha)
Crossed Gems (T. nor-bu bskor-cha)
King's Earrings (T. rgyal-poi rna-cha)
Eight-Branched Corral (T. byu-ru yan-lag brgyad-pa)
Elephant's Tusks (T. glang-chen mche-ba)
"The origins of these symbols seem to be in Chinese art, and no specific meaning is given to them in Tibet other than the understanding that they represent items of value. "
In astrology, Saturn, Venus, Jupiter, Mercury, Mars, and the Moon and Sun are the traditional seven planets. Their respective symbols according to the Tibetan tradition are: a bundle of wood, an arrowhead, a phurba or ritual dagger, a hand, an eye, and a crescent and disk.
*Prayer to the Eight Noble Ones: includes lists of 8's including the Tibetan names of the 8 Bodhisattvas.
*8 auspicious symbols: [Skt: Ashtamangala] conch shell [shankha] , the auspicious seal [endless knot], banner of victory, umbrella of royalty is also a reminder of spiritual and material protection, dharma wheel, pair of happy fish, the flower, the treasure vase.
*See the gestures or mudras for the 8 Auspicious Symbols.
Can you find all 8 symbols? They stand for the Presence of the Buddha:
-Parasol, sign of nobility, stands for his head.
-Golden Fish are his eyes.
-Treasure Vase is his neck.
-Lotus is truth and purity of speech: his tongue.
-Right-Turning Conch announces royalty: his mouth.
-Endless Knot or 'auspicious seal' which links all dharmas and activity is his heart.
-Victory Banner is his torso.
-Wheel, the dharma-chakra, stands for his limbs - the means by which the teaching reaches us.
Newari.com says the 8 auspicious symbols " ... represent the gifts given by celestial beings to Sakyamuni on his attainment of Enlightenment of Buddhahood.
The white parasol protects one from evil desires; it is also a symbol of royalty
the two fish symbolize beings rescued from the ocean of misery of earth existence;
Shankha, the white conch-shell, symbolizes the blessedness of turning to the right and proclaiming the glory of the saints by its humming sound;
Dhvaja, the banner signifies the victory of Buddhism;
Srivatsa, endless knot or mystic diagram, symbolizes the endless cycle of rebirth; also the karmic connection - pull here it tightens there.
Kalasha, the vase, treasury of all spiritual wealth and it also holds amrita, the water elixir immortality;
Padma, the lotus, symbolizes purity;
Chamaru, the fly-whisk, symbolizes tantric manifestations - it is made of a yak tail attached to a silver handle and is used during ritual recitation and for fanning deities in an auspicious religious ceremony. "
They are displayed, marked on paper, cloth or metal, during ceremonies such as the consecration of houses, life's passages, and at elaborate fire offerings.
worldly dharmas are those influences that challenge
To feel happy when you get a reward,
To feel unhappy when you don't.
To feel happy when praised,
To feel unhappy when criticized.
To feel happy when you feel mentally and physically well,
To feel unhappy when you don't.
To feel happy on hearing nice things,
To feel unhappy or worried on hearing unpleasant ones.
More about the 8 influences by Gen Rinpoche.
*8 Chariots of Tibetan Buddhism: "instructional lineages"
*The 8 Common Abilities/powers [resulting from mastery of Vajrayana techniques]:
The sword, the pill, the eye lotion, swift feet, extraction of essences, celestial realm, invisibility and treasures of the earth.
*8 sub-continents [see 4.]
*8 vidyadharas: Manjushrimitra, Nagarjuna, Hungkara, Vimalamitra, Prabhahasti, Dhana Sanskrita, Shantigarbha, Guyachandra.
*8 classes of gods and demons. Regarded as impure manifestations of 8 types of consciousness, in the Tibetan tradition they are: ging [attendants and entertainers], mara [creators of obstacles, eg. Klesha who embodies passion,Yama who is death, Skandha who is war, Ganapati or 'Godly Son'] tsen, yaksha [genii, titans or guardians of 'upper' realms ], rakshasa [elementals], mamo, rahula and naga.
*8 manifestations of Guru Rinpoche
*The Nyingma School of Tibetan Buddhism classifies the tantras as NINE stages on the spiritual path, or the
*Nine Gradual Vehicles [according to Padmasambhava]
*10 bhumis to Buddhahood. [Sanskrit/Pali for plane, storey or level].
In the Mahayana view, there are two systems, one of 6 Paramitas [ways to cross] and one with 10 Paramitas (the 6 plus another 4). These 'virtues' are inter-dependant. There is no true generosity, for instance, without wisdom or prajna: the realization that giver, gift and recipient are all "empty". The bhumis are also viewed as organized to reflect the 3 kayas or levels of "reality".
of Emptiness, shunyata, is the goal. Therefore, the
bhumis are the consequences of virtue-in-action.
Two sutras which discuss the bhumis: Dasabhumi (Sutra of Ten Bhumis) and Samadhi-nirmocana (Explaining Profound Secrets).
Chandrakirti, in the Bodhisattva-Avatara Shastra explains them:
0. The foundation: Beings in samsara [the 6 realms] having generated the aspiration to climb the Bodhisattva Bhumis by practicing the 6 paramitas.
Now we proceed
through 3 stages on the Path of Accumulation and 3 more stages on the Path
1. "The Joyous": Having tasted shunyata [emptiness], we are joyous. Here, the main practice is to perfect the Generosity Paramita. You might be born as a King in the Human Realm and have lots of chances to practice generosity! Now on the Path of Seeing, we can start the Path of Meditation.
2. "The Stainless": At this bhumi, the main practice is the perfection of Shila [discipline of vows] because of which you are free of anxiety and the 3 Poisons [negative tendencies, obscurations]. You might be born as a chakravartin (King bearing the noble marks of an emperor, like Siddartha Gautama Shakya), whose power and enjoyment are challenged by the practice of discipline and precept-keeping.
3. "The Luminous": Here, we try to perfect Patience or equanimity. This is the source of the luminosity. You might be born as Indra, King of gods, who is Shakra - opposer of the Ashuras.
4. "The Radiant": After the 3rd Bhumi, the Nirmanakaya aspect of Buddhahood has been perfected. But there are two more Kayas, therefore, the Paramita to perfect here is that of Exertion. This activity in the service of virtue creates a radiance of wisdom which burns away false conceptions. Here, you might be reborn as Shyama, a deity in the "Continuous Peaceful Realm").
5. "The Unconquerable": Driven by exertion, you perfect
dhyana [meditation] and other skillful means in preparation for the helping of all sentient beings. The word unconquerable refers to both the difficulty of achieving the state of dhyani and the state of the being having now achieved this goal. Now it is possible to be born as a god in the Tushita Heavens where you can observe the Six Realms and the interplay of dharmas.
6. "The Manifest": The intense practice of dhyana and other skills enables you to be reborn as a God-king who can manifest miraculous activity. The Paramita of Prajna is to be perfected.
7. "The Gone-Afar": Having perfected the Six Paramitas, we now possess both wisdom and skill. This is a plateau below which you will not fall, but there is still room for effort.
In the 10 Paramita system, the perfection is that of Skillful Means needed to overcome Mara who provides opportunities for others to act in opposition.
It is said that once the 7th Bhumi is attained, the Buddhas prophesy concerning your achieving Buddhahood, and will indicate your Buddha-Name and circumstances.
In a former
life, Lord Shakyamuni received this prophecy after having presented 4
golden flowers to the Buddha of that aeon .
8. "The Immovable": At the Eighth Bhumi, you can enter Nirvana at the snap of a finger; so Tathagatas come and click you out of it, reminding you of your aspiration and the work still ahead. But they cannot force you to remain, therefore the virtue is that of firmness of Aspiration.
You might be
reborn as Brahma, Lord of the Universe.
9. "The Good-Wisdom": Almost ready for Buddhabood, you practice the acquisition of the Ten Powers and Six Supernatural Powers. You might also be reborn as Brahma.
10. "The Dharma-Cloud": All the Buddhas and Bodhisattvas rejoice in your elation at having attained Buddhahood completely. Primordial awareness [dhyani/jnana] clears away whatever subtle defilements and tendencies might still be retained. You, like Lord Maitreya in the Tushita Heavens, await your turn. This is also the beginning of the Path of Non-Meditation.
~ based upon an interpretation by BBW submitted to the kagyu elist.
*10 Lunar months: correspond to 9 solar months; Mahamaya's pregnancy with the Buddha, Shakyamuni.
*10 Close Disciples of Shakyamuni Buddha:
*10 non-virtuous Actions: Killing, taking what is not given, sexual misconduct [ie. leading to disorder,] the verbal misdeeds of uttering divisive talk/ lying/ gossiping, and speaking harshly, and the mental misdeeds of covetousness, anger and holding wrong views [generally defined as materialist or nihilist views].
*11-headed Chenrezi, see a Japanese version
*12 Links of Causation: segments on the rim of the Wheel of Samsara
misperception due to disposition
names and forms
sensory experience [see 6 senses]
sorrow, sickness, old age, death [cf. the Sights]
*12 Deeds of the Buddha: according to the Kagyu Tibetan Buddhist litany.
He manifests in the world by taking the form of a divine white elephant to enter the womb of Mahamaya.
He is born from her side in the Lumbini Garden at which time the gods rejoice.
As a youth, he demonstrates proficiency in the martial arts of the time, and emerges victorious in competitions.
He lives in the style of a prince at that time and place, conforming to custom and serving his father's kingdom. [That is, not disgracing his family.]
Seeing the uselessness of attachment to material existence, he sets out alone [a Tibetan version recounts how he escaped by flying] and ordained himself. [He cut off his hair and took the vows of a renunciate or sadhu.]
Through the extensive practice of different forms of yoga for six years, he earnestly attempts to achieve enlightenment.
Through his own perseverance, he attains his goal.
Due to his compassion for others, at Varanasi he preaches [Turns the Wheel of the Doctrine, or Dharma ] three different ways for achieving enlightenment.
He overcomes various opponents, philosophical, political and spiritual.
He performs wonders and miracles at Sravasti, transmuting the elements.
Establishing the Sangha, he causes the Dharma to flourish.
He passes away into Nirvana in such a way as to convince people that the Sublime Knowledge he revealed is indestructible.
*12 Deeds of Guru Rinpoche
*12 remati [semo or shvana] sisters: from the legend of Padmasambhava; they are sworn protectors for whom a torma [ritual food offering] is made to this day.
*Thirteen Golden Doctrines central to the Sakya tradition
*13 lunar months in 1 year
*some say there are 13 bhumis (see 10.)
*16 causes of premature death as per Amitayus [sambhogakaya form of Amitabha] practice.
*18 Mahayoga Tantras. The Essence of Secrets is considered by Jamgon Kongtrul to be the greatest of these.
*21 manifestations of Green Tara, consort of Amoghasiddhi.
Her sadhana [liturgy] is referred to as "Homage to the 21 Taras" or the 21 Praises.
*21 disciples of Guru Rinpoche
*21 genyen: sworn [bonded to the dharma] local deities
*28 Ishvaris: 7 for each of the 4 kinds of activity. (See 4 , 58).
*Thirty Pieces of Advice From the Heart is a text by Longchenpa [Longchen Rabjam,] the founder of the Longchen Nyingthig lineage of the Nyingma denomination, concerning the way to conduct oneself in this life.
Some Larger Numbers
Samantabhadra (All-Goodness) and Samantabadhri plus the five male and five female buddhas, the eight male and eight female bodhisattvas, the 6 munis, plus four male and four female gatekeepers. 58 herukas: five male and five female herukas [blood-drinkers, ie. forms of ego-clinging] plus eight yoginis, eight tramen [hybrid, ie. animal-headed] goddesses, four female gatekeepers, and the twenty-eight ishvaris ['ladies'].
64 bodhisattva vows: found in the Highway for Bodhisattvas [Tib.: Jangchub Shunglam] by Je Tsongkapa [1357-1419]
84 Mahasiddhas: legendary tantric Buddhist adepts of India
100 peaceful and wrathful deities.
108 beads in a mala; Brahma lives for 108 Brahma-years. In Tibetan Buddhism, 108 lotsawas [translators of dharma teachings] were predicted.
253 precepts held by an ordained monk [Tib.: gelong]
500-year periods of ten in all in which Buddha-dharma is expected to endure.
1,000 buddhas predicted for this eon, a Good Eon.
160,000 years in an age of a buddha according to one tradition.
Note: Regarding the large numbers, Tibetan tradition prefers rounded numbers of 100,000 [ Tib.: bum, but called a lakh in India,] etc.
4, 320, 000 years in the kalpa according to the Indian cosmological tradition. This is one 'year' in the life of Brahma, who has lived for around 51 years [this time round]. There are 4 kalpas in a yuga.
In the Hindu view, we are currently in the Kali yuga. One etymology has Kali coming from kalaha meaning quarrel.
Pandeya's footnotes refer to W. Windelband's A History of Philosophy, (2nd ed. New York: Macmillan, 1960.) In the philosophy of the Renaissance, numbers played a very important part. "The book of nature is written in numbers; the harmony of things is that of the number-system."
In modern philosophy, the same problem of reality was viewed in terms of monism, dualism, and pluralism. Descartes' mind and matter, Spinoza's one Substance, Leibniz' plurality of monads, and, finally, Hegel's one Absolute show the way in which numbers play a part in the determination of philosophical concepts. Modern logicians like Frege and Russell give a new orientation to number-concept ( B. Russell, An Introduction to Mathematical Philosophy).
In India, the controversy about the number of ultimate reality dates back to the Rig Veda. "Reality is one but described as many." (ekam sad vipraa bohudhaa vadanti--I.164.46), the episode of the twin birds (1.164.20), and the Nasadiya Sukta (RV, X.129), which perhaps thinks in terms of void or zero, give a glimpse of the numerical thinking of the ancient seers.
The Upanishads abound in discussions about the one
and the many. Has the name "Samkhya" anything to do with numbers?
Except [for] the two Mimamsa views, all other systems of orthodox Indian
philosophy proceed with the enumeration of various categories, viz., 24 or
25 categories of the Samkhya-Yoga, six categories of the Vaisheshka, 16
categories of the Nyaya. The Uttara Mimamsa school discusses the relation
between the one (Brahman) and the many (jiva-jagat). That early Buddhism
was fond of categorization and counting is evidenced in Abhidharma
philosophy. The term "`sunya," [shunya-ta] preferred by Madhyamikas to
designate their concept of reality, therefore assumes
ZERO is often used to indicate absence of quantity. "We can define all the natural numbers if we know what we mean by '0' and 'successor'" (Russell, An Introduction to Mathematical Pbilosopby, p. 20). Thus, number 1 can be defined as the successor of O. But 0 itself is nor the successor of any number. All the natural numbers, therefore, proceed from 0 (24, 25). A number is defined as a number of terms in a class; number 0 is the number of terms in a class which has no member. Since a class is not identical with its member, "0 is the class whose only member is the null-class" ( 23). In this light "`sunya" will mean a class having no member; and "ekam" will mean a class having one member. "Ekam" can be explained in terms of "`sunyam," and thus would be inferior to the latter. "`Sunyam advayam" is a higher philosophy than that of "ekam advaitam." But we are emphatically asked not to take shunyas as a notion or concept (d.r.s.ti), because that, being a class, is in no way better than other class-concepts.
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