Mohist Logic

Origin. Later Mohist school, c. 300 BCE. The six dialectical chapters of the Mòzǐ (books 40–45): two books of Canons (jīng 經), two of Explanations (jīngshuō 經說), the Dàqǔ 大取 and the Xiǎoqǔ 小取, together the Mòbiàn 墨辯, compiled between the late 4th and mid 3rd century BCE. Transmitted in disorder and badly damaged, the Dàqǔ worst. A. C. Graham, Later Mohist Logic, Ethics and Science (School of Oriental and African Studies / Chinese University Press 1978) is the reconstruction and the only Western-language translation; Chris Fraser's Stanford Encyclopedia entries "Mohist Canons" and "Logic and Language in Early Chinese Philosophy" and Dan Robins, "The Later Mohists and Logic" (History and Philosophy of Logic 2010) carry the current interpretation. The tradition ended with the Qin.

Models. A theory of when names fit things and of when an accepted assertion licenses another. Disputation (biàn 辯) is contending over a complementary pair of claims — this thing is an ox, this thing is a non-ox — where the claims cannot both fit and one necessarily fits: exhaustiveness and exclusiveness of shì 是 and fēi 非, stated as doctrine, which is why the system sits in the Boolean division beside the other historical codifications of classical validity. On that bivalent base the Mohists build a kind-based inference apparatus — sameness in four grades, standards that fix kind-membership, and the Xiǎoqǔ's catalogue of forms for carrying an assertion from one expression to a parallel one, together with the cases where the carrying fails. The disputation practice, the three standards of evidence and the full name taxonomy are the sibling collection's Argumentation and Rhetoric entry Mohist Dialectics; this entry is the formal apparatus, and its terms follow that entry.

Formalism.

Biàn (disputation): Contending over claims that are the converse of one another: ox against non-ox (A74 in Graham's numbering). A thing is either ox or non-ox; the claims do not both fit (dàng 當); one necessarily fits. The winner is the one who fits the fact. B35: the claim "in biàn there is no winner" necessarily does not fit.

Kinds and standards: lèi 類 (kind): a kind name denotes all things relevantly similar; fixed by dubbing things of the kind with the name. fǎ 法 (standard): that in being like which something counts as so; a thing matches (hé 合) the fǎ of its kind. Judging shì or fēi proceeds by comparison with the fǎ.

Sameness (tóng 同), four grades (A86): chóng 重 — identity: two names, one object. tǐ 體 — part and whole: finger and hand. hé 合 — co-location: together in one place. lèi 類 — kind: same in some respect.

The Xiǎoqǔ's forms: huò 或 — some: not all (the contrast term is jìn 盡, all). jiǎ 假 — supposition: not now so. xiào 效 — modeling: setting up a fǎ as the standard of judgment. pì 辟 — illustrating: "bringing up other things and using them to clarify it." móu 侔 — parallelizing: "comparing expressions and jointly proceeding." yuán 援 — citing precedent: "You are so. How is it that I alone cannot be so?" tuī 推 — extending: "using what is the same in that which he refuses to accept and that which he does accept in order to propose the former" (Graham's rendering).

Where parallels proceed and where they break: shì ér rán 是而然, this and so: a white horse is a horse; riding a white horse is riding a horse. shì ér bù rán 是而不然, this but not so: a robber is a person; yet killing a robber is not killing a person (殺盜人非殺人也). The supporting parallels: disliking the abundance of robbers is not disliking the abundance of people; desiring that there be no robbers is not desiring that there be no people. One universal, one not: loving people requires loving all people without exception; riding horses does not require riding all horses. The caution clause: things have respects in which they are similar, yet it does not follow that they are completely similar; parallels between expressions are correct only up to a point; being so is the same, but that by which it is so is not necessarily the same.

Symbols.

Metatheory. What survives is a corrupt text, and Western-language statements of its logic pass through Graham's 1978 reconstruction: he restored the Canons and Explanations, assembled the hybrid texts "Names and Objects" (the Xiǎoqǔ with part of the Dàqǔ) and "Expounding the Canons" (most of the remaining Dàqǔ), and supported the result with an explicit methodology of emendation and an analysis of the grammar; the reconstruction has been largely accepted, contested in part by Jane Geaney (Journal of the American Oriental Society 1999), so claims about the system are claims about Graham's text unless marked otherwise. Within that text, the bivalence results are explicit: a thing is either ox or non-ox, a complementary pair of claims cannot both fit and one must, and B35 turns the machinery on itself — the claim that disputation has no winner necessarily fails to fit. What the Mohists did not do is equally established: Fraser's assessment is that they never investigate formally valid inference or formulate a notion of logical consequence, and Robins argues that móu arguments rest on linguistic parallelism and that, if the Mohists' own argument succeeds, parallelism can never ground a cogent argument — the Xiǎoqǔ's robber passage defends the school's doctrine that killing robbers is not killing people, against the charge that it contradicts inclusive care, by exhibiting accepted parallels of the same shape rather than by stating a rule. The text never says what distinguishes a "this and so" case from a "this but not so" case; the classification is by example, and finding the principle behind it is a modern research problem, not a Mohist result.

Applies to. History of logic. Chinese philosophy of language, against the School of Names and the white-horse sophisms. Theory of analogical and kind-based inference. Fallacy taxonomy, through the catalogue of breaking parallels. Comparative logic beside the Aristotelian and Stoic systems.

Limitations. There are no variables and no schemata: the forms are named procedures illustrated by examples, generality is read off the examples, and no validity criterion is stated — the Xiǎoqǔ marks exactly where parallel inference breaks without saying why it breaks there. The apparatus is about names fitting things, not about compound statements: connectives and quantifying words are used but not theorized, and nothing corresponds to derivation, so there are no metatheorems and no notion of proof. Kind-sameness is primitive and unmeasured, and the Xiǎoqǔ's own caution — same in one respect, proceeding differently — concedes that lèi cannot carry inference alone. The textual damage is severe enough that parts of the system, especially whatever the Dàqǔ held, are unrecoverable, and the reconstructed portions are Graham's conjectures where the manuscripts fail. And the tradition is a terminus: no school transmitted or developed the Canons after the Qin, so the system had no second generation and its gaps were never filled from within.

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