Jaina Saptabhaṅgī

Origin. Jaina logicians of classical India. The sevenfold predication (saptabhaṅgī) under the qualifier syāt, the logical arm of anekāntavāda (non-one-sidedness) and of the naya theory of standpoints. First full exposition: Samantabhadra's Āptamīmāṃsā (also Devāgamastotra), 114 verses — traditionally dated to the 2nd century CE, placed in the 6th by most modern scholarship, with proposals from the 4th to the 8th; commented by Akalaṅka's Aṣṭaśatī. Mature treatments in Prabhācandra and in Vādideva Sūri (1086–1169), whose Pramāṇanayatattvālokālaṃkāra is the text the modern formalizations anchor on; Mallisena's Syādvādamañjarī (1292) is the late dedicated treatise. Modern formalizations: Jonardon Ganeri, "Jaina Logic and the Philosophical Basis of Pluralism" (History and Philosophy of Logic 2002); Graham Priest, "Jaina Logic: A Contemporary Perspective" (History and Philosophy of Logic 2008); Fabien Schang, "A One-Valued Logic for Non-One-Sidedness" (International Journal of Jaina Studies 2013).

Models. A logic for judging under standpoints. Ganeri's framing of the problem it answers: what is the rational response to a set of propositions each of which there is some reason to accept, which are jointly inconsistent — the Jaina answer being that one reasons on, with every predication indexed to the standpoint that supports it. Each clause is prefixed by syāt, "in some respect", and a respect is fixed by four parameters: substance (dravya), place (kṣetra), time (kāla), state (bhāva). For any subject and predicate exactly seven syāt-qualified predications are available — the seven non-empty combinations of three basic answers: it is, it is not, it is inexpressible. The entry sits in Many-Valued through its reconstructions, which read the seven predications as a seven-element matrix of values; the Formalism records that the matrix reading is one reconstruction among several, with modal-discussive and question-answer readings as rivals. The method side — anekāntavāda as a procedure for dissolving disagreement — is the sibling collection's Methods entry Anekantavada; this entry is the formal system.

Formalism.

The three basic predications (mūlabhaṅgī, Gokhale's term): asti — it is: true from some standpoint. nāsti — it is not: false from some standpoint. avaktavya — inexpressible: affirmation and denial pressed simultaneously, exceeding expression.

The seven predications:

1. syād asty eva — in some respect, it is.
2. syān nāsty eva — in some respect, it is not.
3. syād asty eva syān nāsty eva — in some respect it is, and in some respect it is not (successively).
4. syād avaktavyam eva — in some respect, it is inexpressible (both at once).
5. syād asty eva syād avaktavyam eva — it is, and it is inexpressible.
6. syān nāsty eva syād avaktavyam eva — it is not, and it is inexpressible.
7. syād asty eva syān nāsty eva syād avaktavyam eva — it is, it is not, and it is inexpressible. Seven is exact: 2³ combinations of the three basic answers, minus the empty one — every sentence receives at least one.

Non-collapse conditions: Each conjunct carries its own syāt: asti and nāsti in predication 3 hold in different respects under the four parameters, so 3 is successive assertion and denial, not a contradiction. Avaktavya is the simultaneous case and does not reduce to 3: both answers at once, in a single respect, is what language cannot carry. The eighth combination — no answer at all — is excluded.

Ganeri's reconstruction (2002): syāt as an operator over standpoints: a predication holds iff there is a standpoint from which the plain sentence is true. Seven values generated existentially; quasi-truth-functional. The move is Jaśkowski's discussive one — truth at some participant's standpoint — anticipated by the Jainas by some two millennia (Priest, "Jaśkowski and the Jains", Studia Logica 2024).

Priest's reconstruction (2008): Many-valued and modal techniques together. Avaktavya assimilated to assertion and denial from one and the same standpoint — a glut, placing the system beside the paraconsistent logics (Schang's report of Priest's reading). Applied to the problematic aspects of the Jaina position, especially its relativism.

Schang's reconstruction (2013): Question-answer semantics: three questions — is α true, is α false, is α inexpressible — each answered yes (1) or no (0). The seven predications are the seven non-zero answer triples ⟨a₁, a₂, a₃⟩; ⟨0,0,0⟩ is excluded. Avaktavya read as silence, carrying no logical value; on Schang's non-Fregean reading the system is one-valued, not seven-valued.

The matrix reading: The seven combinations tabulated as truth values of a seven-element matrix. The ancient texts themselves use two truth values and no connectives beyond the predications (Balcerowicz 2008); the matrix belongs to the reconstruction, not to the sources.

Symbols.

Metatheory. What is proved is proved about the reconstructions; the tradition states the system and defends it dialectically, without metatheorems. The combinatorial claim is exact and elementary: three basic answers give 2³ combinations and the seven predications are all of them except the empty one (Schang 2013 sets this out). Ganeri's interpretation removes the apparent inconsistency: with syāt as existential quantification over standpoints the seven predications hold together, so the system is a logic for reasoning from inconsistent inputs rather than an inconsistent logic, and Ganeri draws from this a logical basis for philosophical pluralism. Priest (2008) built a many-valued and modal semantics; Humberstone (2008, "Modal Formulas True at Some Point in Every Model") took up a consequence relation arising from Priest's treatment. The reconstructions diverge exactly at avaktavya — a glut at a single standpoint for Priest, silence without a value for Schang, simultaneous unsayable affirmation-and-denial in the tradition — and no result adjudicates among them. Balcerowicz (2008) rejects the constructivist programme wholesale: the texts know only truth and falsity, and the formal systems are of independent interest but not interpretations of syādvāda; Schang's 2013 paper is in substantial part a reply. The date of the founding text is open across four centuries.

Applies to. History of paraconsistent and discussive logic, where the syāt device precedes Jaśkowski's. Standpoint and perspective semantics. Pluralism about truth and the rationality of reasoning with inconsistent commitments. Comparative Indian logic: the saptabhaṅgī accepts all seven predications where the Buddhist catuṣkoṭi refuses all four of its corners (Schang, "Two Indian Dialectical Logics", 2010). Jaina studies.

Limitations. The syāt parameter does all the consistency work and the system never adjudicates between standpoints: nothing says which naya is right for a purpose, and Priest presses the resulting relativism as the philosophically weak point. The ancient texts contain no more connective apparatus than Aristotle's logic (Balcerowicz's observation) and fix no values for compounds, so the seven-valued readings are quasi-truth-functional at best, and Schang reports that his own early seven-valued system could not determine the value of a conjunction, disjunction or conditional. The matrix this division requires is the reconstruction's artifact: Balcerowicz's objection that the sources are bivalent stands, and the entry's placement rests on Priest's and the early Schang-Ganeri readings, not on the Sanskrit. Avaktavya is unstable across readings — glut, gap, silence, transcendence — and the choice decides whether the logic is paraconsistent, partial, or neither. The textual base is late: the first full exposition's date is disputed across several centuries, and the developed theory is known through systematizers a half-millennium later still.

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