Book 3 - Pada-kāṇḍa (11): Saṅkhyā-samuddeśa (On Number)

3.11.1 unformalized

संख्यावान् सत्त्वभूतोऽर्थः सर्व एवाभिधीयते ।
भेदाभेदविभागो हि लोके संख्यानिबन्धनः ॥ १ ॥

saṃkhyāvān sattvabhūto'rthaḥ sarva evābhidhīyate |
bhedābhedavibhāgo hi loke saṃkhyānibandhanaḥ || 1 ||

Every meaning that is a substance-entity whatever is expressed as possessing number; for the division of difference and non-difference, in the world, is grounded in number.

The samuddesa's opening claim, and it is unrestricted. Samkhyavan sattva-bhuto 'rthah sarva eva abhidhiyate: *every* meaning that is a *substance-entity* whatever is expressed as *possessing number* — nothing nominal escapes number (3.1.51's na vina samkhyaya kascit sattva-bhuto 'rtha ucyate: nothing that is a substance-entity is spoken of at all without number). And the ground: bheda-abheda-vibhago hi loke samkhya-nibandhanah — the *division of difference and non-difference*, in the *world*, is *grounded in number*. So number is what makes the one/many distinction available at all: without it there is no telling whether we face one thing or several. Nibandhana — the grounding-word since 1.13. The Jati-samuddesa spent forty verses on when number is *meant* (3.1.51-90); this one asks what it *is*, and it begins by making it the ground of the most basic division there is.

3.11.2 unformalized

स धर्मो व्यतिरिक्तो वा तेषामात्मैव वा तथा ।
भेदहेतुत्वमाश्रित्य सङ्ख्येति व्यपदिश्यते ॥ २ ॥

sa dharmo vyatirikto vā teṣāmātmaiva vā tathā |
bhedahetutvamāśritya saṅkhyeti vyapadiśyate || 2 ||

That property is either distinct from them, or is their very self; having resorted to its being the cause of difference, it is designated as 'number'.

The ontology canvassed and declined, in the samuddesa's second verse. Sa dharmo vyatirikto va: that *property* is either *distinct from* them — a real item over and above the things counted (the Vaisesika's samkhya, a quality inhering in substances). Tesam atma eva va tatha: or is *their very self* — nothing but the things themselves. Bheda-hetutvam asritya samkhya iti vyapadisyate: having resorted to its being the *cause of difference*, it is *designated* as 'number'. So whichever it is metaphysically, number is *named* by its office: causing difference. This is 3.7.15 verbatim in structure (the means either distinct from them or their very self; having resorted to separation, constructed as means-hood) — and the same move: the ontology is undecided, the function is definite, and the grammar proceeds identically either way (2.179's licensed double description).

3.11.3 unformalized

समवेता परिच्छेद्ये क्वचिदन्यत्र सा स्थिता ।
प्रकल्पयति भावानां सङ्ख्याभेदं तथात्मनः ॥ ३ ॥

samavetā paricchedye kvacidanyatra sā sthitā |
prakalpayati bhāvānāṃ saṅkhyābhedaṃ tathātmanaḥ || 3 ||

Inherent in what is to be delimited, it stands somewhere else; it constructs the difference of number for entities, and likewise for its own self.

Number's peculiar location. Samaveta paricchedye: *inherent* in what is *to be delimited* — number inheres in what it counts. Kvacid anyatra sa sthita: it stands *somewhere else* — and yet it is elsewhere: the twoness of two pots is not in either pot. Both, and the tension is the point. Prakalpayati bhavanam samkhya-bhedam tatha atmanah: it *constructs* the *difference of number* for *entities*, and *likewise for its own self* — number numbers itself: there are two twos in four, and the numbering of numbers is number's own doing. So number is inherent-and-elsewhere, and reflexive. This is 3.1.28's stratification (the universal of number resting on what rests on the individual) given its structural description — and 3.1.9's regress (universals of universals) reappearing as number's self-application.

3.11.4 unformalized

परत्वे चापरत्वे च भेदे तुल्या श्रुतिर्यथा ।
सङ्ख्याशब्दाभिधेयत्वं भेदहेतोस्तथा गुणे ॥ ४ ॥

paratve cāparatve ca bhede tulyā śrutiryathā |
saṅkhyāśabdābhidheyatvaṃ bhedahetostathā guṇe || 4 ||

As in priority and posteriority the hearing is alike in respect of difference — so is the state of being expressible by number-words, in the quality that is the cause of difference.

A parallel with the directional pair. Paratve ca aparatve ca bhede tulya srutir yatha: as in *priority* and *posteriority* the *hearing* is *alike* in respect of *difference* — 'before' and 'after' sound alike as relational terms, and neither is a property of anything (3.6.4's para-aparatve grounded in difference of place; 3.6.8-9's inversions with standpoint). Samkhya-sabda-abhidheyatvam bheda-hetoh tatha gune: so is the *state of being expressible by number-words*, in the *quality* that is the *cause of difference*. So number-words behave as directional words do: they express a relational condition, not a thing's property. And the parallel is apt because 3.6 already established that direction orders everything and is itself unordered (3.6.6) — which is exactly what 3.11.3 said of number.

3.11.5 unformalized

अस्वतन्त्रे स्वतन्त्रत्वं परधर्मो यथा गुणे ।
अभेद्ये भेद्यभावोऽपि द्रव्यधर्मस्तथा गुणे ॥ ५ ॥

asvatantre svatantratvaṃ paradharmo yathā guṇe |
abhedye bhedyabhāvo'pi dravyadharmastathā guṇe || 5 ||

As independence in what is not independent is another's property, in a quality — so also the state of being differentiable in what is not differentiable is a substance's property, in a quality.

Two properties a quality wears that are not its own. Asvatantre svatantratvam para-dharmo yatha gune: *independence* in what is *not independent* is *another's property*, in a *quality* — a guna is paratantra by nature (3.5.1's gunatvam paratantratvat) and is spoken of as though free-standing (1.64's guna indicated as though independent, svatantryena). Abhedye bhedya-bhavo 'pi dravya-dharmas tatha gune: the state of being *differentiable* in what is *not differentiable* is a *substance's* property, in a quality. So a quality is treated as independent (which is a substance's way) and as differentiable (which is also a substance's way), and neither belongs to it. Number, being a guna, wears both borrowed properties — which is why it can be counted (3.11.3's numbering of numbers) though it is not the sort of thing that comes in ones and twos.

3.11.6 unformalized

स्वबुद्ध्या तमपोद्धृत्य लोकोऽप्यगममाश्रितः ।
स्वधर्मादन्यधर्मेण व्याचष्टे प्रतिपत्तये ॥ ६ ॥

svabuddhyā tamapoddhṛtya loko'pyagamamāśritaḥ |
svadharmādanyadharmeṇa vyācaṣṭe pratipattaye || 6 ||

Having abstracted it by its own intellect, the world too, having resorted to tradition, explains it by another's property rather than its own — for the sake of comprehension.

Why the borrowed properties of 3.11.5 are not an error. Sva-buddhya tam apoddhrtya: having *abstracted* it by its *own intellect* — apoddhrtya: the kanda's constant verb (3.1.1, 3.4.1: word-meanings abstracted from the sentence). Loko 'pi agamam asritah: the *world* too, having resorted to *tradition*. Sva-dharmad anya-dharmena vyacaste pratipattaye: *explains* it by *another's property* rather than its *own* — *for the sake of comprehension*. So the world, not only the grammarians, describes qualities by substance-properties, and does so deliberately, for understanding's sake. This is 2.13's divisions for the avidvan and 3.7.147's separations constructed for instruction — now credited to the loka itself. The borrowing is a teaching-device that everyone uses and nobody invented.

3.11.7 unformalized

परोपकारतत्त्वानां स्वातन्त्र्येणाभिधायकः ।
शब्दः सर्वपदार्थानां स्वधर्माद् विप्रकृष्यते ॥ ७ ॥

paropakāratattvānāṃ svātantryeṇābhidhāyakaḥ |
śabdaḥ sarvapadārthānāṃ svadharmād viprakṛṣyate || 7 ||

The word, which expresses with independence the realities of all word-meanings — whose nature is to assist another — is drawn away from their own property.

The general diagnosis. Para-upakara-tattvanam: of things *whose nature is to assist another* — every padartha is such, on this kanda's showing (3.7.124's all proceeding for their own becoming, and every one of them assisting; 3.3.5's upakara). Svatantryena abhidhayakah sabdah sarva-padarthanam: the *word*, which expresses *with independence* the realities of *all word-meanings*. Sva-dharmad viprakrsyate: is *drawn away* from their *own property*. So language necessarily misdescribes: it presents as independent what is nothing but assisting, because that is what nouns do (3.8.12's paritah paricchinnam: what is delimited on all sides is spoken of as an entity). The verse generalizes 3.11.5 from qualities to everything: nothing has the independence its name confers on it, and naming confers it regardless.

3.11.8 unformalized

यथैवाविषयं ज्ञानं न किञ्चिदवभासते ।
तथा भावोऽप्यसंसृष्टो न कश्चिदुपलभ्यते ॥ ८ ॥

yathaivāviṣayaṃ jñānaṃ na kiñcidavabhāsate |
tathā bhāvo'pyasaṃsṛṣṭo na kaścidupalabhyate || 8 ||

Just as a cognition without an object shines forth as nothing whatever — so an entity, uncommingled, is not apprehended as anything whatever.

The parallel that justifies 3.11.7's necessity. Yatha eva avisayam jnanam na kimcid avabhasate: as a *cognition without an object* shines forth as *nothing whatever* — an awareness of nothing is not an awareness (3.1.106's cognition never grasped apart from its object's form; 1.124's light that would not shine). Tatha bhavo 'py asamsrsto na kascid upalabhyate: so an *entity*, *uncommingled*, is *not apprehended* as anything whatever. Asamsrsta: uncommingled — 3.1.21's word (neither oneness nor manifoldness nor existence nor non-existence is found in the self-realities of things uncommingled). So the uncommingled thing is as unavailable as the objectless cognition, and for the same reason: both are terms of a relation, taken out of it. This is why language must borrow (3.11.7): there is no unrelated thing whose own property could be expressed.

3.11.9 unformalized

भेदेन तु समाख्यानं यल्लोकोऽप्यनुवर्तते ।
आगमाच्छास्त्रसदृशो व्यवहारः स वर्ण्यते ॥ ९ ॥

bhedena tu samākhyānaṃ yalloko'pyanuvartate |
āgamācchāstrasadṛśo vyavahāraḥ sa varṇyate || 9 ||

But that designation by way of difference which the world too follows along — from tradition, that practice is described as resembling the science.

The world's practice given its status. Bhedena tu samakhyanam yal loko 'py anuvartate: that *designation by way of difference* which the *world too* *follows along* — the ordinary way of speaking, which divides everything (3.11.1's division grounded in number). Agamat sastra-sadrso vyavaharah sa varnyate: *from tradition*, that *practice* is described as *resembling the science*. So the world's dividing talk resembles the sastra's — both divide, both do it from tradition, and neither invented it. Sastra-sadrsa: resembling the science. The verse quietly levels the grammarian and the layman (3.3.55's bala and pandita alike on the worldly path): both are running the same inherited apparatus of division, and the scholar's is only more explicit.

3.11.10 unformalized

बुद्धौ स्थितेषु तेष्वेवमध्यारेणो न दुर्लभः ।
परधर्मस्य न ह्यत्र सदसत्त्वं प्रयोजकम् ॥ १० ॥

buddhau sthiteṣu teṣvevamadhyāreṇo na durlabhaḥ |
paradharmasya na hyatra sadasattvaṃ prayojakam || 10 ||

When they thus stand in the intellect, superimposition is not hard to come by; for here the existence or non-existence of another's property is not the occasioner.

Why the borrowing works. Buddhau sthitesu tesu evam adhyaropo na durlabhah: when they thus *stand in the intellect*, *superimposition* is *not hard to come by* — once things are held in mind, laying one's properties on another is effortless (3.1.6's adhyaropa; 3.9.100's superimposition on a contrary meaning). Para-dharmasya na hi atra sad-asattvam prayojakam: for here the *existence or non-existence* of another's property is *not the occasioner*. So the superimposition does not require that the borrowed property really belong to the lender: one may lay on what is not there. This is the mechanism that lets 3.11.5's quality wear independence — nothing needs to be independent for independence to be superimposed — and it is 3.3.42's doctrine (the negated thing granted figurative existence so the negation can operate).

3.11.11 unformalized

सामान्येष्वपि सामान्यं विशेषेषु विशिष्टता ।
सङ्ख्यासु सङ्ख्या लिङ्गेषु लिङ्गमेवं प्रकल्पते ॥ ११ ॥

sāmānyeṣvapi sāmānyaṃ viśeṣeṣu viśiṣṭatā |
saṅkhyāsu saṅkhyā liṅgeṣu liṅgamevaṃ prakalpate || 11 ||

Thus a general is constructed even among generals, particularity among particulars, number among numbers, and gender among genders.

The reflexivity of every category, stated as a rule. Samanyesu api samanyam: a *general* even among *generals* — generality has its own generality (3.1.9's universals of universals). Visesesu visistata: *particularity* among *particulars*. Samkhyasu samkhya: *number* among *numbers* (3.11.3's number numbering itself). Lingesu lingam: and *gender* among *genders* — anticipating the thirteenth samuddesa. Evam prakalpate: *thus* it is *constructed*. So every category applies to itself, and the self-application is a construction — prakalpate, not a discovery. The regress is admitted and defused exactly as 3.3.28 defused all regresses (there is no operation of an operation; therefore do not resort to infinite regress everywhere): the self-applications are postings, and postings do not generate real hierarchies.

3.11.12 unformalized

अतो द्रव्याश्रितां सङ्ख्यामाहुः संसर्गवादिनः ।
भेदाभेदव्यतीतेषु भेदाभेदविधायिनीम् ॥ १२ ॥

ato dravyāśritāṃ saṅkhyāmāhuḥ saṃsargavādinaḥ |
bhedābhedavyatīteṣu bhedābhedavidhāyinīm || 12 ||

Therefore the proponents of commingling call number a thing resting on substance, ordaining difference and non-difference among things that have transcended difference and non-difference.

The samuddesa's own position, and it is stated as a paradox. Atah dravya-asritam samkhyam ahuh samsarga-vadinah: the *proponents of commingling* (3.7.9's samsarga-vadins, for whom all entities are capacities and possessors of capacities) call *number* a thing *resting on substance*. And the paradox: bheda-abheda-vyatitesu bheda-abheda-vidhayinim — *ordaining* difference and non-difference among things *that have transcended* difference and non-difference. The things are beyond the one/many distinction (3.1.21's uncommingled realities, bearing neither); number ordains it anyway. So number confers a distinction on what is incapable of bearing it — which is precisely 3.6.13's direction giving parts to the partless atom, and 3.6.14's things without place receiving places. Vidhayini: ordaining, prescribing. Number does not find ones and manys; it legislates them.

3.11.13 unformalized

आत्मान्तराणां येनात्मा तद्रूप इव लक्ष्यते ।
अतद्रूपेण संसर्गात् सा निमित्तसरूपता ॥ १३ ॥

ātmāntarāṇāṃ yenātmā tadrūpa iva lakṣyate |
atadrūpeṇa saṃsargāt sā nimittasarūpatā || 13 ||

That by which the self of other selves is marked as though of that form — from commingling with what is not of that form: that is the likeness to the occasioning ground.

The mechanism of number's ordaining. Atmantaranam yena atma tad-rupa iva laksyate: that by which the *self of other selves* is *marked* *as though of that form* — one thing taking on another's look. Atad-rupena samsargat: from *commingling* with what is *not of that form* — and the lender does not have the form it lends (3.11.10's sad-asattvam na prayojakam: the borrowed property need not exist). Sa nimitta-sarupata: *that* is the *likeness to the occasioning ground*. So number works by conferring on things a likeness to what conferred it — and neither the conferrer nor the conferred has the property. This is 3.2.9-10's intentionality-structure exactly (cognition established as though having the object for its self, while being utterly not of that self), and its recurrence here shows how general Bhartrhari takes that structure to be: it is how *everything* wears what it did not have.

3.11.14 unformalized

संसृष्टेष्वपि निर्भागे भूतेष्वर्थक्रिया यथा ।
सत्त्वादिषु च मात्रासु सर्वास्वेवं प्रतीयते ॥ १४ ॥

saṃsṛṣṭeṣvapi nirbhāge bhūteṣvarthakriyā yathā |
sattvādiṣu ca mātrāsu sarvāsvevaṃ pratīyate || 14 ||

As, even among the commingled elements, which are partless, effective action is understood — so it is understood among all the measures, in 'sattva' and the rest.

The doctrine confirmed on the elements. Samsrstesu api nirbhage bhutesu artha-kriya yatha: as, even among the *commingled elements*, which are *partless*, *effective action* is understood — arthakriya: the criterion of the real (2.288's asadharanam karyam; 2.33's own vocabulary). The elements are partless and commingled, and they *work*: fire burns, water wets, and neither has parts to do it with. Sattvadisu ca matrasu sarvasu evam pratiyate: so it is understood among *all the measures*, in *'sattva'* and the rest — the gunas of Samkhya, sattva rajas tamas: equally partless, equally commingled, equally effective. So partlessness does not prevent working, and commingling does not require parts. The verse defends 3.11.12's paradox by precedent: if partless elements can act, partless things can be numbered — the ordaining does not need joints to work on (3.6.15's partlessness equal for the atom and for the pot).

3.11.15 unformalized

द्वित्वादियोनिरेकत्वं भेदास्तत्पूर्वका यतः ।
विना तेन न सङ्ख्यानामन्यासामस्ति सम्भवः ॥ १५ ॥

dvitvādiyonirekatvaṃ bhedāstatpūrvakā yataḥ |
vinā tena na saṅkhyānāmanyāsāmasti sambhavaḥ || 15 ||

Oneness is the womb of duality and the rest, since the differences are preceded by it; without it there is no possibility of the other numbers.

The foundation of the number-series. Dvitvadi-yonir ekatvam: *oneness* is the *womb* of *duality* and the rest — yoni: the birth-word (3.1.3's six modifications as the wombs of differentiation; 2.58's samhita as the womb of the words; 3.7.44's case-endings as the wombs of the karaka's differences). Bhedas tat-purvaka yatah: since the *differences* are *preceded by* it — every number is built of ones. Vina tena na samkhyanam anyasam asti sambhavah: *without it* there is *no possibility* of the *other numbers*. So the series rests on one, and one is not itself a member of the series in the way the others are — it is their womb. And this places the samuddesa's central problem: if oneness generates the numbers, what generates oneness? The verses following (3.11.16-17) canvass how duality arises from it, and none of the answers is comfortable.

3.11.16 unformalized

एकत्वे बुद्धिसहिते निमित्तं द्वित्वजन्मनि ।
एकत्वाभ्यां समुत्पन्नमेवं वा तत् प्रतीयते ॥ १६ ॥

ekatve buddhisahite nimittaṃ dvitvajanmani |
ekatvābhyāṃ samutpannamevaṃ vā tat pratīyate || 16 ||

Oneness, accompanied by the intellect, is the occasioning ground in the birth of duality; or duality is understood as arisen from two onenesses in this way.

Two accounts of how two arises. Ekatve buddhi-sahite nimittam dvitva-janmani: *oneness*, accompanied by the *intellect*, is the *occasioning ground* in the *birth of duality* — one thing plus a mind makes two: the counting is the intellect's, and two is one-as-counted-twice. This is the cognitive account (3.7.104's buddhy-avastha; 3.9.78's cognition's own gathering). Ekatvabhyam samutpannam evam va tat pratiyate: *or* it is understood as *arisen from two onenesses* — two real ones make a real two, no mind required. The realist account. So: is duality a fact about the world or an act of counting? The samuddesa canvasses both and 3.11.17 will add a third — and the reason for the care is that number is where the constructivism of the whole kanda is most exposed. If anything were objectively so, it would be that there are two pots.

3.11.17 unformalized

एकत्वसमुदायो वा सापेक्षे वा पृथक् पृथक् ।
एकत्वे द्वित्वमित्येवं तयोर्द्विवचनं भवेत् ॥ १७ ॥

ekatvasamudāyo vā sāpekṣe vā pṛthak pṛthak |
ekatve dvitvamityevaṃ tayordvivacanaṃ bhavet || 17 ||

Or it is a collection of onenesses; or, in oneness taken severally, with mutual dependence, there is duality — thus their dual-ending form would arise.

The third and fourth accounts. Ekatva-samudayo va: or it is a *collection of onenesses* — two is a heap of ones (3.8.4's samuha, the collection whose non-difference the intellect constructs). Sapekse va prthak prthak ekatve dvitvam iti evam: or, in *oneness taken severally*, with *mutual dependence*, there is *duality* — two ones, each depending on the other for its twoness: neither is two, and their mutual reference is. Tayor dvi-vacanam bhavet: thus their *dual-ending* form would arise — and the morphology follows whichever account is taken. Four accounts now: one-plus-mind, two-ones, a collection, mutual dependence. Bhartrhari does not choose, and the not-choosing is 3.11.2's move (distinct or their very self; the ontology undecided, the office definite). Sanskrit's dual has one form and four possible metaphysics behind it.

3.11.18 unformalized

एकोऽपि गुणभेदेन सङ्घो भेद प्रकल्पयेत् ।
आश्रयाश्रयिभेदो हि तदाश्रयनिबन्धनः ॥ १८ ॥

eko'pi guṇabhedena saṅgho bheda prakalpayet |
āśrayāśrayibhedo hi tadāśrayanibandhanaḥ || 18 ||

Even one aggregate, by difference of qualities, would construct a difference; for the difference of substratum and what rests on it is grounded in that substratum.

How one thing can be counted as many. Eko 'pi guna-bhedena sangho bhedam prakalpayet: even *one* aggregate, by *difference of qualities*, would *construct* a *difference* — one herd is many by its cattle's colours; one man is several by his offices (3.9.32's carpenter and cook; 3.8.63's teacher and uncle). Asraya-asrayi-bhedo hi tad-asraya-nibandhanah: for the difference of *substratum* and *what rests on it* is *grounded in that substratum*. So the counting follows the qualities, and the qualities rest on the thing, and the thing is one. Number therefore does not track things: it tracks the aspects under which things are taken (3.7.104's buddhy-avastha carving one thing into agent, instrument and object). One aggregate, many counts, and the counts are all correct.

3.11.19 unformalized

सङ्ख्येयसङ्घसङ्ख्यानसङ्घः सङ्ख्येति कथ्यते ।
विंशत्यादिषु सान्यस्य द्रव्यसङ्घस्य भेदिका ॥ १९ ॥

saṅkhyeyasaṅghasaṅkhyānasaṅghaḥ saṅkhyeti kathyate |
viṃśatyādiṣu sānyasya dravyasaṅghasya bhedikā || 19 ||

The aggregate of the numbering of an aggregate of countables is called 'number'; in 'twenty' and the rest, it is the differentiator of another substance-aggregate.

The higher numbers analysed. Samkhyeya-sangha-samkhyana-sanghah samkhya iti kathyate: the *aggregate of the numbering* of an *aggregate of countables* is called *'number'* — twenty is not twenty things; it is the gathering of the countings of a gathering. Two levels of aggregation: the things are gathered, the countings are gathered, and the number is the second gathering. Vimsaty-adisu sa anyasya dravya-sangha-sya bhedika: in *'twenty'* and the rest, it is the *differentiator* of *another* substance-aggregate — and this second-order number then differentiates a further group. So 'twenty cows' has: the cows, gathered; their countings, gathered into twenty; and the twenty differentiating the herd. This is 3.11.3's number-numbering-itself given its structure, and it explains why the higher numerals behave grammatically as nouns rather than as adjectives.

3.11.20 unformalized

एकविंशतिसंख्यायां संख्यान्तरसरूपयोः ।
एकस्यां बुद्ध्यनावृत्त्या भागयोरिव कल्पना ॥ २० ॥

ekaviṃśatisaṃkhyāyāṃ saṃkhyāntarasarūpayoḥ |
ekasyāṃ buddhyanāvṛttyā bhāgayoriva kalpanā || 20 ||

In the number 'twenty-one', of the two which resemble another number, there is a construction as though of parts, in one number, by a non-repetition of the intellect.

The compound numerals. Eka-vimsati-samkhyayam: in the number *'twenty-one'*. Samkhyantara-sarupayoh: of the *two* which *resemble another number* — 'eka' and 'vimsati' look like the numbers one and twenty, and are not those numbers here (2.169's kupa-supa-yupa: phonetic containment is semantically inert; 2.177's rule: different meaning-behaviour, different base). Ekasyam buddhy-anavrttya bhagayor iva kalpana: in *one* number, by a *non-repetition of the intellect*, there is a construction *as though of parts*. Buddhy-anavrtti: the mind does not go twice — one grasps twenty-one at a stroke, not twenty and then one. So the numeral's parts are apparent (iva) and its grasp is single. This is 2.36's asvakarna-principle (the compound understood whole, its members idle) applied to arithmetic: twenty-one is one number, and its look of composition is the analyst's.

3.11.21 unformalized

असंख्यासमुदायत्वात् संख्याकार्यं विधीयते ।
समूहत्वे तु तन्न स्यात् स्वाङ्गादिसमुदायवत् ॥ २१ ॥

asaṃkhyāsamudāyatvāt saṃkhyākāryaṃ vidhīyate |
samūhatve tu tanna syāt svāṅgādisamudāyavat || 21 ||

From its not being an aggregate of numbers, the number-operation is prescribed; but on its being a collection, that would not hold — as with an aggregate of one's own limbs and the like.

The argument for 3.11.20. Asamkhya-samudayatvat samkhya-karyam vidhiyate: from its *not being an aggregate of numbers*, the *number-operation* is *prescribed* — twenty-one takes number-morphology precisely because it is not a heap of numbers but one number. Samuhatve tu tan na syat: on its being a *collection*, that would *not* hold. And the illustration: sva-anga-adi-samudayavat — as with an *aggregate of one's own limbs* and the like: a body is not a number of limbs; it is a body, and one does not conjugate it as a plural. So collections do not take number-operations, and twenty-one does; therefore twenty-one is not a collection. The argument is from the grammar's own behaviour (2.443's Panini does not legislate vacuously), and it confirms 3.11.20's single grasp: the morphology treats the compound numeral as a unit because it is one.

3.11.22 unformalized

संख्येयान्तरतन्त्रासु या संख्यासु प्रवर्तते ।
आवृत्तिवर्गसंख्येया तां संख्यां तादृशीं विदुः ॥ २२ ॥

saṃkhyeyāntaratantrāsu yā saṃkhyāsu pravartate |
āvṛttivargasaṃkhyeyā tāṃ saṃkhyāṃ tādṛśīṃ viduḥ || 22 ||

That number which operates among numbers dependent on other countables, and whose countable is a repetition-class — such a number they know as of that kind.

Multiplication analysed. Samkhyeyantara-tantrasu ya samkhyasu pravartate: that *number* which operates among *numbers* *dependent on other countables* — a number whose objects are themselves numbers. Avrtti-varga-samkhyeya: and whose *countable* is a *repetition-class* — avrtti-varga: a class of repetitions; 'three fours' counts not four things but the repeating of four. Tam samkhyam tadrsim viduh: *such* a number they know as *of that kind*. So multiplication is the counting of repetitions, and its countables are recurrences rather than things. The analysis is exact and it fits the samuddesa's frame: number ordains difference (3.11.12), and multiplying ordains difference among ordainings — number applying to itself (3.11.3, 3.11.11's reflexivity).

3.11.23-26 unformalized

न संख्यायां न संख्येये द्वौ दशेत्यस्ति सम्भवः ।
भेदाभावान्न संख्यायां विरोधान्न तदाश्रये ॥ २३ ॥
संख्यायेते दशद्वर्गौ द्विदशा इति संख्यया ।
तद्रूपे वापि संख्येये आवृत्तिः परिगण्यते ॥ २४ ॥
संख्या नाम न संख्यास्ति संज्ञैषेति यथोच्यते ।
रूपं न रूपमप्येवं संज्ञा सा हि सितादिषु ॥ २५ ॥
संख्यानजातियोगात् तु संख्या संख्येति कथ्यते ।
रूपत्वजातियोगाच्च रूपे रूपमिति स्मृतम् ॥ २६ ॥

na saṃkhyāyāṃ na saṃkhyeye dvau daśetyasti sambhavaḥ |
bhedābhāvānna saṃkhyāyāṃ virodhānna tadāśraye || 23 ||
saṃkhyāyete daśadvargau dvidaśā iti saṃkhyayā |
tadrūpe vāpi saṃkhyeye āvṛttiḥ parigaṇyate || 24 ||
saṃkhyā nāma na saṃkhyāsti saṃjñaiṣeti yathocyate |
rūpaṃ na rūpamapyevaṃ saṃjñā sā hi sitādiṣu || 25 ||
saṃkhyānajātiyogāt tu saṃkhyā saṃkhyeti kathyate |
rūpatvajātiyogācca rūpe rūpamiti smṛtam || 26 ||

(23) 'Two tens' is not possible either in the number or in the countable — not in the number, from the absence of difference; not in its substratum, from contradiction. (24) The two ten-classes are counted by a number, as 'two tens'; or, in a countable of that form, the repetition is enumerated. (25) 'Number' is not a number; it is a designation, as is said; likewise 'form' is not a form — for that is a designation, in 'white' and the rest. (26) But from connection with the universal 'numbering', a number is called a number; and from connection with the universal 'form-hood', a form is remembered as a form.

A four-verse knot about self-application, and it is the samuddesa's finest technical passage. (23) states the difficulty: 'two tens' can be neither in the *number* — bheda-abhavat, from the *absence of difference*: ten is ten, and two tens are not two different tens; nor in the *countable* — virodhat, from *contradiction*: the twenty things are not two tens, they are twenty. So 'two tens' has no home. (24) offers two resolutions: the two *ten-classes* are counted (the classes, not their members), or the *repetition* is enumerated (3.11.22's avrtti-varga). (25) then makes the deep move: samkhya nama na samkhya asti — '*number*' is *not a number*: the word 'number' does not name a number; samjna esa iti yatha ucyate, it is a *designation*. And the parallel: rupam na rupam api evam — '*form*' is not a *form*; samjna sa hi sitadisu, it is a designation, in 'white' and the rest. So the category-words are names, not instances (3.11.11's reflexivity now qualified: the self-application is nominal). (26) supplies what saves it: samkhyana-jati-yogat tu samkhya samkhya iti kathyate — from *connection with the universal 'numbering'*, a *number* is called a *number*. So 'number' names a number by way of the universal, not by being one — which dissolves the regress of 3.11.11 exactly as 3.3.28 dissolved all regresses: the self-application runs through a jati and does not iterate.
contested: the four verses are compressed and their argumentative joints are hard; we read 23 as the aporia, 24 as two resolutions, and 25-26 as the deeper diagnosis (category-words as designations, saved by jati-connection). Readers who take 25 as a further horn of the aporia will find 26 the sole answer, which the text permits

3.11.27 unformalized

निमित्तमेकमित्यत्र विभक्त्या नाभिधीयते ।
तद्वतस्तु यदेकत्वं विभक्तिस्तत्र वर्तते ॥ २७ ॥

nimittamekamityatra vibhaktyā nābhidhīyate |
tadvatastu yadekatvaṃ vibhaktistatra vartate || 27 ||

In 'one', the occasioning ground is not expressed by the case-ending; but the oneness of what possesses it — there the case-ending operates.

What the singular ending actually says. Nimittam ekam iti atra vibhaktya na abhidhiyate: in *'one'*, the *occasioning ground* is *not expressed* by the *case-ending* — the ending does not name oneness-the-property. Tadvatas tu yad ekatvam vibhaktis tatra vartate: but the *oneness of what possesses it* — *there* the case-ending *operates*. So the singular says: this thing is one — not: here is oneness. The ending predicates number of a bearer and does not name number. This is 3.7.13's doctrine (the karaka-property is not expressed by the noun; the assistance is understood by the case-endings alone) applied to number: the endings mark, and marking is not naming (3.10.9's upalaksana: indication, pointing without describing).

3.11.28 unformalized

एकस्य प्रचयो दृष्टः समूहश्च द्वयोस्तथा ।
निमित्तव्यतिरेकेण संख्यान्या भेदिका ततः ॥ २८ ॥

ekasya pracayo dṛṣṭaḥ samūhaśca dvayostathā |
nimittavyatirekeṇa saṃkhyānyā bhedikā tataḥ || 28 ||

An accumulation of one is seen, and likewise a collection of two; therefore, apart from the occasioning ground, a different number is the differentiator.

The argument for 3.11.27. Ekasya pracayo drstah: an *accumulation of one* is *seen* — one thing, accumulated (many ones); samuhas ca dvayos tatha: and likewise a *collection of two*. So the same oneness appears in accumulations and the same duality in collections — the numbers recur across their instances. Nimitta-vyatirekena samkhya anya bhedika tatah: *therefore*, *apart from the occasioning ground*, a *different number* is the *differentiator*. The number that differentiates is other than the property that occasions it. So there are two things: oneness-the-property (the nimitta) and the number that the ending marks — and the ending marks the second. This confirms 3.11.27: the singular does not name the property; it marks a differentiation the property occasioned.

3.11.29 unformalized

तदेकमपि चैकत्वं विभक्तिश्रवणादृते ।
नोच्यते तेन शब्देन विभक्त्त्या तु सहोच्यते ॥ २९ ॥

tadekamapi caikatvaṃ vibhaktiśravaṇādṛte |
nocyate tena śabdena vibhakttyā tu sahocyate || 29 ||

And that oneness, though one, apart from the hearing of a case-ending, is not expressed by that word; but together with the case-ending it is expressed.

The stem's silence about number. Tad ekam api ca ekatvam vibhakti-sravanad rte na ucyate tena sabdena: that *oneness*, though *one*, *apart from the hearing of a case-ending*, is *not expressed* by that *word* — the bare stem says nothing about number; 'go-' is neither singular nor plural. Vibhaktya tu saha ucyate: but *together with* the case-ending it *is* expressed. So number enters at inflection and not before — which is 3.2.11's finding for the whole word (prior to the case-ending, the meaning of what ends in the suffix does not exist) applied to number specifically. The stem has no number to be transplanted (3.9.97's unmixed stem having no tense), and the ending supplies it. Stem and ending, meaning and number: the division of labour the whole Padakanda has been mapping.

3.11.30 unformalized

अन्वयव्यतिरेकौ च यदि स्याद् वचनान्तरम् ।
स्यातामसति तस्मिंश्च प्रकृत्यर्थो न कल्प्यते ॥ ३० ॥

anvayavyatirekau ca yadi syād vacanāntaram |
syātāmasati tasmiṃśca prakṛtyartho na kalpyate || 30 ||

And agreement and difference would obtain, if there were another number-form; and in the absence of that, the base-meaning is not constructed.

The distributional test applied to number. Anvaya-vyatirekau ca yadi syad vacanantaram: *agreement and difference* would obtain — the method of 2.12 and 2.166 (vary the form, watch the meaning) — *if* there were *another number-form*: one can test the singular's contribution by substituting a plural. Syatam asati tasmims ca prakrty-artho na kalpyate: and *in the absence of that*, the *base-meaning* is *not constructed*. Where no alternative form exists, the method cannot isolate the base's contribution — one cannot subtract what has no contrast. So number's semantic contribution is established by contrast and only by contrast, which is why 3.1.51-52 could find the singular and plural unintended (they are obligatory, hence contrastless in most contexts) and the dual intended (it contrasts). The samuddesa's method and the Jati-samuddesa's result agree.

3.11.31 unformalized

एकत्वमेक इत्यत्र शुद्धद्रव्यविशेषणम् ।
सगुणस्तु प्रकृत्यर्थो विभक्त्यर्थेन भिद्यते ॥ ३१ ॥

ekatvameka ityatra śuddhadravyaviśeṣaṇam |
saguṇastu prakṛtyartho vibhaktyarthena bhidyate || 31 ||

In 'oneness', 'one' — it is the qualifier of the pure substance; but the base-meaning with its quality is differentiated by the case-ending's meaning.

Two levels distinguished. Ekatvam eka iti atra suddha-dravya-visesanam: in *'oneness'*, *'one'* — it is the *qualifier of the pure substance*: the numeral qualifies the bare thing (3.4.3's dravya defined by pronominal referability, with nothing else in it). Sa-gunas tu prakrty-artho vibhakty-arthena bhidyate: but the *base-meaning with its quality* is *differentiated* by the *case-ending's meaning*. So there are two operations: the numeral qualifies the pure substance, and the ending differentiates the qualified base. Number enters twice — once lexically, once inflectionally — and the two are not the same. This is the stratification 3.11.19 found in the higher numerals (the countables gathered, the countings gathered) reappearing between the numeral-word and the ending.

3.11.32 unformalized

द्वयेकयोरिति निर्देशात् संख्यामात्रेऽपि सम्भवः ।
एकादीनां प्रसिद्धा तु संख्येयार्थत्वमुच्यते ॥ ३२ ॥

dvayekayoriti nirdeśāt saṃkhyāmātre'pi sambhavaḥ |
ekādīnāṃ prasiddhā tu saṃkhyeyārthatvamucyate || 32 ||

From the designation 'of two and one', there is a possibility even in mere number; but the well-known state of 'eka' and the rest is said to be having a countable for its meaning.

The samuddesa's close, and it lands on the distinction it has been building. Dvy-ekayor iti nirdesat samkhya-matre 'pi sambhavah: from the designation *'of two and one'* — Panini's own phrase (1.4.22: dvy-ekayor dvi-vacana-eka-vacane, prescribing the dual and singular for two and one) — there is a *possibility even in mere number*: the rule's words could mean the numbers themselves, abstractly. Ekadinam prasiddha tu samkhyeya-arthatvam ucyate: but the *well-known* state of 'eka' and the rest is said to be *having a countable for its meaning* — in established usage, 'one' means one *thing*, not the number one. So the numerals mean countables and could mean numbers, and prasiddhi decides (2.253's currency-doctrine; 3.9.62's schools sorted). The Sankhya-samuddesa ends where the Padakanda always ends: two construals available, usage settling it, and the settling neither arbitrary nor found in the things.