Work in progress: Not for citation or reproduction. Please send comments, criticisms and suggestions to Chad Hansen at chansen(at-sign)hku.hk
Graham speculated that the scattered fragments of one of the remaining sections (traditionally known as The Greater Pick) may have included a more formal treatment of Mozi's ethical utilitarianism. They gave it in axiom form: Morality is utility and utility is what satisfies you when you get it (as opposed to what you desire). Later Mohists gave a weighting account of the original standard of benefit versus harm--one prefers the lesser harm or greater benefit. They differentiated between "thick" and "thin" concern. This may have be a way to address the supposed conflict between utilitarian universalism and our special care to those closest to us. Just as self-care is an efficient means to general well being, so is the care of our relatives and neighbors. Since I know my own father's preferences and we enjoy each others' company, my caring for him and you for your father achieves the good more efficiently than vice versa. So appropriate caring for yourself and your "thick" relations is consistent with a thin moral concern for everyone's well-being.
The Later Mohists probably were first to abandon the authority of tian "nature" and both reference to and reliance on xin "heart-mind." They viewed these as terms used in theories to avoid accountability. Unlike Mozi, they treated ren "humanity" as a kind of Confucian partial love. Their realism presupposes that carving the world "at the joints" promoted utility. One obvious ground was that objectivity in standards of language use, operational or measurement-like interpretation, facilitate wide-spread linguistic agreement and promote coordinated judgment and action.
They worked out an alternative to rectifying names that was consistent with objective or neutral standards for word reference. They proposed to rectify guiding phrases instead of "names." While thieves are humans, the act of killing-thieves (execution) is not the act of killing humans (murder). Making this ethical point led the Mohists to skeptical conclusions about linguistic "stability."
The Mohists did not separate epistemology from their more general theory of language. They were "analyzing" terms like zhi "to know." The analysis did not contrast zhi with believing. They distinguished (1) know how or skill, from (2) knowledge by acquaintance and (3) a rare (perhaps idiosyncratic) use of zhi "know" that strikes us now as a substitute for consciousness (for which there was no rival term). This use also replaces (for the Mohist) xin "heart-mind" as the "locus of knowing." One important form of skill knowledge is the ability to "discourse" on a topic. This arguably sweeps propositional knowledge into the "skill" category.
The main topics of zhi (know) describe a process: we learn names (words) and objects, then how to "combine" them, and finally how to wei "act." The Mohist Canon stands out among classical texts for its emphasis on checking linguistic knowledge against reality. They left the form of that verification vague, however. The thrust appears again to draw a contrast to rectifying names. The standard of correct use of terms should not be mere convention or authority, but actual similarities and differences among things. This arguably gives a theory of language anchor to Mozi's anti-conventional attack on Confucian ethics.
Mozi used an example that can help us fix on the Later Mohists' concept of "knowing." A blind person, he argued, can know to produce utterances like 'black as coal' or 'white as snow' but he cannot distinguish things when placed in front of him. He knows names, but not "stuff" or how to "combine" them. Thus he cannot use language to guide his action.
The Mohists, as we noted above, used no propositional 'belief' analysis and paid scant attention to other sentential contexts. "Knowing how to combine" meant competently assigning terms to things in real contexts. The Mohists accepted that knowing names was conventional knowledge. They stressed, however, that we apply conventions to an external reality, known independently of language. The goal of knowledge remained practical guidance, not representation or picturing.
The most comprehensive discussion in the collection of Later Mohist writings deals with questions about language. The texts give us a plausible general Chinese theory of how words work. A term "picks out" part of reality. When we use one to pick something out, we commit ourselves to using the name to pick out similar things and 'stopping' with the dissimilar. Thus, for each term we learn a skill at judging shi 'is this' and fei 'is not.' The 'is not' generates an opposite for each name and marks the point of distinction or discrimination from the other stuff of the world.
Once we conventionally attach a term to some reality, the inherent similarities and differences determine its subsequent application. Conventions presuppose a world-guided way to mark distinctions. Mohists view name-object relations on a mereological model, that is, talking about distinctions and boundaries. A name applies to a (scattered) reality having some kind of tong "similarity."
The Mohist's pragmatic substitutes for 'reference', ju "pick out" and qu "choose," had a non-abstract, practical tone. A name picks out a stuff from its background. Convention determines which similarities and differences mark the boundary between shi "is this" (what a name picks out) and fei "is not this" (what it excludes). In using a name, we commit ourselves to go to some real limit and then stop.
The Mohists argued against the "one-name-one-reality" theme implicit in the doctrine of rectifying names. Some terms are more general than others and several might pick out the same object. Names, the Mohists argued, could be very general (like 'thing' itself), or based on similarity classes (such as 'horse') or applied to only one thing (such as 'John'). They saw no objection in principle to these overlapping scopes and two names for the same thing.
Their analysis portrays disagreements as arising from different ways of making the distinctions that gives rise to contraries. Translators thus render the word pien as either "distinction" or "dispute." In Mohist use, it came to stand particularly for philosophical dispute--including disputes in ethics. The Mohists argued that, in a "distinction dispute," one party will always be right. For any term, the thing in question will either be shi 'is this' or fei 'is not'.
The central term of assessment in the Mohist study was k'o "assertable," not any counterpart of "truth." They used k'o in several related ways. We can say an expression is "assertable" of some object. One phrase may be assertable of whatever another phrase "picks out." "Assertable" thus became a way of exploring semantic relations between terms. Mohists asked whether we can sometimes, always or never describe things picked out by term X as Y.
The analysis, although it uses assertability rather than truth, yielded a familiar and important conclusion against certain forms of relativism. The Mohists argued that in any dispute involving "distinctions", there will be a 'winner.' If one disputant claimed it was ox and the other that it was not ox, only one could be correct. When one disputant claimed the object was ox and the other that it was horse, it would not count that as a "distinction dispute". This was merely a formal result, but the Mohists took it as confirming that the world, not conventions, determined the right designation. The winner is the one whose description "hit on" it.
The Mohists, as noted above, had the most realistic theory about the relation of language and the world. Real-world similarities and differences should guide our use of words. They "Quined" the apparently common "mystical" claim that language distorts the Dao. (See LAOZI, MENCIUS and ZHUANGZI.) To say anything along these lines is to treat all language as "not acceptable" or "perverse." Regarding all language as 'perverse,' they noted, was itself 'perverse.' They similarly rebutted claims that we should abandon distinctions. To reject distinctions is to fei fei "not-this 'not-this'". To fei fei is also perverse (Quining again that the person who rejects it, does it.) Finally, they similarly dispatched "learning not to learn."
These results are distant cousins of 'All sentences are false.' Unlike the classic liar paradox, the universal form sentence does have a consistent truth value. It is always false. The Mohist conceptual tools, however, lacked both seemingly crucial concepts for the classic paradox--'sentence' and 'truth'. They had a separate, self-condemning analysis of each mistake and explain them all as resulting from self-reference ("one's own language"). They suggest the proposer of such absurdities try harder to find acceptable words. These results undermine the popular anti-language intuitionist positions in Chinese thought--notably Mencius and Laozi. It invalidates any claim that language distorts the Dao ("guidance").
The Mohists, however, uncovered grounds of skepticism in their own system. They argued that the way terms combined was not world-guided, at least not as a straightforward extension of the way the terms themselves worked. Here is a striking case for postulating a contrasting Chinese conceptual structure. The analysis of compound terms makes most sense if we suppose the theorizing was going on against a background assumption of a part-whole or mereological metaphysical picture. This also explains both the assimilation of common nouns and adjectives in the analysis and the tendency to describe all terms as ming "names." (See LANGUAGE)
The paradigm or straightforward compounds, in the Mohist view, pick out the sum of whatever the individual terms pick out. Classical Chinese lacked pluralization and some compound term such as 'ox-horse' worked like "cats 'n dogs". Classical Chinese was rich in similar compounds, e.g., sky-earth = world, boy-girl =child, mountain-water = scenery. Modification compounds (such as 'white horse') worked as similar structures do in English. The Mohist took the former model to pick out a "compound stuff"--the sum of the range of the two component terms ('draft animals'). They called the unit a jian "whole" and its parts ti "substantive parts". Their analysis of such compounds made them analogous to generalization.
The Mohists ask what was assertable of the things picked out by compound terms. In the case of 'ox-horse', the Mohists observe that 'not-ox' is assertable of 'ox-horse' on the same grounds that 'ox' is. The explanation goes that part of ox-horse is non-ox, so 'non-ox' is "assertable". We can understand the idea by reflecting on another example. We may ask someone how many children he has by asking about his "boys n' girls." Suppose the answer is 'three'. Now we may ask how many are boys. The answer may come back, 'none'. This is a case in which we could say 'his boy-girls are not boys.'
However, the Mohist seems to have something stronger in mind. Even if he said 'two girls and a boy,' the Mohist would argue that it would be right to say (some of) his boy-girls were non-boy. Thus the Mohist concludes that, although we cannot say ox is non-ox or horse is non-horse, we can say intelligibly that ox-horse is non-ox-non-horse.
The paradigm contrast is "hard-white." This is also a compound term but it's component stuffs "blend." So the components are inseparable when combined. Wherever you go in the hard-white, they say, you get both. This reflects the more familiar (to the West) semantics of modification: an intersection compound. The scope of combined term is where the scopes of the two components intersect. Ox-Horse, by contrast, is a sum compound. The scope of the combined term is the union of the scopes of the two component terms. The Mohists used 'ox-horse' as a general description of the sum paradigm and 'hard-white' for the "product" or "intersection" model.
The Mohists contrasted ox-horse combining as one in which there was no "interpenetration": the two components remained separate in the compound. In hard-white "penetration", the two things "exhausted" each other. They called the ox-horse separable compounds in contrast to the hard-white inseparable ones. They never used the term ti "substantive part" of the components of the latter.
The Mohists do not give us any rule for distinguishing intersection from union compounds beyond the metaphysical interpretation as 'penetrating' or 'excluding.' They do not explicitly use the language of scope. These results arise partly from their treating both nouns and adjectives as 'names'--terms with a "spread". They share the pragmatic function of "picking out" or "distinguishing" one part of reality from the rest. Absent a focus on the grammatical distinction of noun and adjective, the Mohists are left with a choice. Either the way names form compounds is simply arbitrary or it is explained mainly metaphysically, i.e., by whether or not its "stuffs" or "realities" can "penetrate."
A question lurked behind this treatment. In what sense is a compound really two things? The system acknowledged the flexibility of language. We could view almost anything either as a compound of more basic stuffs or as a part of some greater compound.
The Mohists' realism failed to give any adequate account of what similarities and differences should count in making a distinction. They neither offered a causal criteria nor had a conception of axiomatic science to ground selection among similarities. Though Graham argued that their propositions resembled a deductive scheme of Euclidean definitions, the most common "definitions" were partial synonyms--apparently thought of as terms that could be substituted for the head term in some contexts. This (along with an etymology) seems to be the implicit theory of early Chinese dictionaries, too. The Mohist text exhibits a theory of language with no hint of a concept of meaning.
They noticed many senses in which things can be the "same" or "different." Some reality might differ only in that we use alternative names. Being 'two' was necessarily differentiated even though called by one name. Realities could also be "same" in the sense of being included in some compound object. Conversely, they could be different in not being included in some "substantial part". They could differ or be alike in location. Finally they could be similar in belonging to the same "kind".
The Mohist analyzed "kind", however, in a loose way. Having that with which to "same" was the criteria of being "same kind". Not having "same" was the criteria of not being of a "kind". Although they might initially have intended to limit "kind" to natural kinds, the account generalized it to almost any similarity based grouping of stuffs. Thus the Mohists could refer to oxen and horses as the same "kind". The only clear examples of not-"kind" are things so unlike they are not comparable. 'Which is longer, wood or night?' The Mohists suggest this is an unintelligible question because it compares two different "kinds".
The Mohists rejected "wild pickings out" but did not give any way of identifying them. The examples were of using similarities of distinctions that were unconventional. The looseness of this account of classifying together with the indeterminacy of the result of compounding, buttressed the skeptic's position (see Hui Shi and Zhuangzi below) that the world offered no reliable basis for linguistic distinctions.
Against the Mohist background, we can now make some sense of the previously obscure writings of Gongsun Long. The text that bears his name consists of several apparent dialogues between a "sophist" and an "objector." The sophist typically starts each dialogue with a counter-intuitive paradox. The objector dissents and the sophist defends his thesis. Graham argued that later writers forged at least two of these dialogues using misunderstood fragments of Mohist semantics. They apparently copied the phrases after copyists had shuffled the Canon and mixed the indexing characters into the text.
We will discuss two of the remaining dialogues--'White Horse' and 'Referring and Things'. They pose difficult puzzles for which different scholars have offered speculative, controversial and mutually inconsistent interpretations. The varied readings flow partly from different standards for choosing 'translation manuals.' I discuss two interpretations here both to illustrate that point and to allow us to locate a range of alternative views of Gongsun Long's Dao.
In the (possibly apocryphal) preface to the dialogues, Gongsun Long gives a Confucian motivation for his theorizing. Confucius rectified names. Gongsun Long alleges that he is defending the master's linguistic Dao. Most Confucians would reject the affiliation, but it does make sense on formal grounds. If rectifying was intended to remove ambiguity from a guiding Dao, then it requires that exactly one name from the guiding discourse should refer to the object in the action situation. I either regard the male before me as 'father' or as 'ruler' or as 'person'. He may be in one sense all three, but if I am to extract guidance from a code, I must decide which rule to use here and now. That requires deciding which term is relevant to this situation. The Mohists rejected the one-name-one-thing principle and argued that we should rectify phrases instead--e.g. thieves are men, but killing thieves is not killing men. (See below.)
The Mohist account of compounding also had negative implications for the Confucian maxim. Separable or sum compounds, such as 'ox-horse', technically conform to "one-name-one-thing." The combination of names picks out a sum of the two. Hard-white compounding, by contrast, violates the principle of strict clarity and consistency in naming. We change each term's scope of reference when we compound them. The terms thus pick out different "things" when compounded.
Other sources confirm that Gongsun Long defended two further theses: 'separating the inseparable' and 'separating hard-white.' However, Graham's identification of the spurious source of the dialogue on 'Hard-White' remains convincing. That he had defended the thesis gave the forger an invitation. We cannot, accordingly, rely on the dialogue to explain the slogan. Still, we can plausibly deal with both slogans together since 'hard-white' is the Mohist example of an 'inseparable' or 'interpenetrating' compound. To 'separate' would be to regard them as 'excluding each other' and to treat the compound as a sum. Gongsun Long would, consistently, object to the Mohist's hard-white model.
Gongsun Long's example, "white horse," takes one term from each type of compound. The White Horse dialogue begins with a question in the canonical analytic form: 'Is "white horse not horse" assertable?' followed by the answer, 'assertable.' The sophist's first defense of the paradox is that 'white' names a color and 'horse' names a shape. Shape and color are different so a combination of shape and color is not merely a shape.
The other most familiar argument the sophist gives is 'if you ask for a horse, both a black or yellow horse can "arrive." If you ask for a white horse, a black horse or yellow horse will not arrive.' This illustrates one of the sophist's fall-back threads of argument. 'X is not Y' follows from 'X is different from or distinguishable from Y.' The linking theme of the two arguments is that white horse is a combination of two things and this requires that 'white horse not horse' be assertable. The objector gives the plausible Mohist response that 'asking for a white horse' is indeed different from 'asking for a horse,' but a white horse is still a horse.
So one line of interpretation links the paradox to Mohist semantics and takes ma to "name" its scope. If its scope changes, it is a different name. The other line of interpretation takes the paradox to flow from a novel and technically inexpressible Platonic insight. It takes the term ma (horse) to refer to an abstract or semantic object—horseness. Bai ma (white horse) similarly refers to white-horseness. The opening sentence thus states the true proposition that the two abstractions are distinct entities. Since the connected terms are logically singular, the fei (is not) represents 'non-identity'.
This first line of interpretation is motivated by the principle of humanity and undermined by charity. It makes the paradoxical thesis accessible from the philosophical context, but wrong. The second makes the paradox true but leaves unexplained how the sophist would have had access to the concepts involved. It also lacks consistency. The abstract reading can not apply to when ma is used in the supporting arguments--all of which make more sense as referring to concrete horses.
The first interpretation, where ma refers holistically to horse-stuff, can still motivate the 'distinct-hence-different' line of argument and yet consistently interpret the concrete references in the rest of the dialogue. If we similarly regard white as the mass-substantive--white stuff--rather than the abstract 'whiteness'--we can see a connection to the Mohist theory of compound names. Gong-sun Long regards 'intersection' or 'interpenetrating' compounds as contrary to the one-name-one-thing principle. If white horse consists of two names, each should consistently name (scattered) things. Used in combination, their 'naming' ought to remain consistent. Thus, they should name the sum of the two stuffs and, as in the case of 'ox-horse', 'not-horse' would be assertable of it.
Alternately, we may either deny that 'white horse' consists of two names or that they are the same names as when used separately. 'White horse' must be thought of as having no essential relation to 'horse'. It must be a sui generis term for a new stuff. We could then say 'white horse is horse' is not necessarily true. Its truth is an accident of usage which might have been otherwise. Thus 'white horse not horse' is assertable.
Gongsun Long's argument then becomes a dilemma. Either we regard 'white-horse' as a sum-compound term--in which case the 'ox-horse' result follows--or we regard it as a sui generis non-compound name--in which case the conventions of its use could tie it to anything at all. It need not necessarily be horse. The assumption must be that a name is the same only if it has identical scope (names the same mereological thing). Since 'horse' in 'white horse' does not have that scope it is a different name. Its use in a compound constitutes an distinct name from its single use.
Gongsun Long's other dialogue poses, if possible, even more daunting barriers to interpretation. The first sentence seems to be an explicit contradiction--everything under heaven is zhi (pointing) and yet pointing is not pointing. The rest of the dialogue is content-thin and teeters repeatedly on the brink of explicit syntactic contradiction. The only content words are the puzzling 'pointing' along with 'thing-kind' and 'the world'.
Most interpreters take the issue to be the meaning of zhi (pointing). Most treat it as semantic reference or meaning. It is literally a finger and is the most plausible candidate for a counterpart of "referring." The Later Mohists, recall, used the term ju (picking-out) and qu (choosing) instead. There are reasons for worry about the second interpretation, since we saw no evidence of any intensional account of 'meaning'. Using 'meaning,' however, makes this dialogue support the abstract interpretation of the 'White Horse' paradox. As in Western conceptualism, the abstract object may serve as the semantic "content." Otherwise, we would have no sign of a sense-reference distinction or any indication that it is individual objects rather than mereological wholes or types that we 'point to'.
Graham's speculative interpretation employs the 'reference' reading. Although far from proved, it is philosophically interesting and relevant to issues that emerge in theory of language and metaphysics. Graham treats the crucial first phrase as meaning that although one can refer to things, you ca not refer to everything. In talking about everything, you fail talk about your own act of referring. Zhuangzi later makes a similar argument against assertions of absolute monism--to say everything is one is to have the one and the saying, which makes two! Tempting as it is, it has little theoretical connection to the White-Horse thesis. Graham treats them as dealing with the principle that whole is different from the part. The maxim needs both careful formulation and plausible motivation. There are no other very persuasive interpretive theories.
Although the Mohists proposed a realist account of "picking-out," they embedded it in the theory that language guides action. Thus the final object of knowing is knowing how to "deem act". They treat guiding action as the real point of combining names. Thus words pick out stuff, while strings or "phrases" convey intentions. In Name and Object (Smaller Pick) this led them to analyze compounds that pick out actions. In the most intact long section of their text, the Mohists pursued a new analysis--one that took a superficially logical form.
Premise: X is Y (white horse is horse)
Conclusion: KX is KY (ride white horse is ride horse)
They called this linguistic algebra "matching phrases" and argued that it was not "reliable." We take for granted that we know the appropriate or assertable form of each phrase. A successful outcome would be this: whenever the assertable form with simple terms was positive (an "is this" phrase) then the parallel with compound terms should also be positive (a "so" phrase). Conversely, a negative base (X is not Y--a "not this" phrase) should yield a negative result (KX is not KY--a "not so" phrase).
The Mohists argue for the instability of this ideal of phrase-matching by listing several different kinds of breakdown:
Sometimes an "is this" yields a "not-so".
Sometimes a "not this" yields a "so".
Sometimes a reference is comprehensive and sometimes not.
Sometimes one reference is "is this" and another one is "not this".
The body of the essay consists of examples that illustrate the respective outcomes.
Graham, drawing on his part-of-speech analysis of "is this" (subject) and "so" (verb), treated the chapter as evidence that the Mohists discovered the subject-predicate sentence. He translated the procedure as 'matching sentences' and treated it as a discussion of logical form. The first two models do rely on syntactic complexes (X is Y) which resemble syllogistic premises, but the latter two do not.
(A technical note on grammar: Classical Chinese uses no articles and has no "is" connective. Expressions ending with the particle ye (assertion marker) mark descriptive uses of noun-phrases (predicate nominative). It signals that one is applying a descriptive term to a contextually selected object--not using the word to identify the topic. Translators typically render such structures in English as '(X) is Y.' In Chinese topic-comment structure, the topic term (X) is optional. The comment may stand alone if the context supplies a topic. The assertion marker, in other words, should not be thought of as linking two terms, but as tying a predicate to some reality.)
The "this-so" analysis given by the Mohist does fit the examples in a way consistent with the topic-comment analysis. If, on the other hand, we focus on the examples as sentences and treat the pattern as a form of inference, then the Mohist analysis will resemble a kind of algebraic logic. I so regarded it in my own earlier study. However, consistent with a topic-comment structure, I now regard it as extending the analysis of the conventional semantic effects of combining "names" to form "phrases".
That the analysis focuses on conventional semantics of terms rather than the logic of sentences sheds a new light on how the examples work. The Mohist does not use the model to correct conventional reasoning errors. He depends on "proper" use. What we would conventionally say determines whether a result is a "so" or a "not-so." The most thoroughly illustrated breakdown are those where an "is this" base produces a "not-so". The examples are:
Parents are people; serving one's parents is not serving the people;
[Suppose] a younger brother is a handsome man; loving one's younger brother would not be loving a handsome man.
A carriage is wood; riding a carriage is not riding wood.
A boat is wood; entering a boat is not entering wood.
Robbers are people; abounding in robbers is not abounding in people; lacking robbers is not lacking people.
The Mohist expands on the last example in a way that signals both the ethical importance of the analysis and the nature of the alleged breakdown in parallelism.
Disliking the abundance of robbers is not disliking the abundance of people.
Desiring to be without robbers is not desiring to be without people.
Everyone would agree with these so they should not object if we say 'robbers are people but killing robbers is not killing people.'
We suppose, following Graham, that the Mohists are defending their inherited doctrine of universal love by arguing that it is consistent with the (presumed) practice in Mohist communities of executing thieves.
What the denial amounts to is this: even if naming were objectively constant and reliable, the use of names in descriptions of actions or intentions could not reliably take us from an "is this" to a "so". An execution is not murder. Loving a brother is morally required, loving a handsome man is (presumably) shameful. Serving one's parents is one kind of duty and serving the people another. One does not fulfill the latter merely in doing the former.
What emerges is an alternative strategy for dealing with the problem that Confucius addressed via rectifying names. The Mohists resist the implication that in executing thieves we must deny that thieves are people. They deny instead that executing thieves is murdering. Rectifying takes place at the "phrase" or "so" level rather than at the "name" level.
The next set of examples illustrate the converse case--those where we start with a "not this" base and get a "so" result.
To read books is not books; to like reading books is to like books.
Cockfights are not cocks; to like cockfights is to like cocks.
About to fall into a well is not falling into a well. To stop one about to fall into a well is to stop one falling into a well.
The Mohist here expands on fatalism. 'That there is fate is not fated; to deny that there is fate is to deny fate.' It is harder to reconstruct an ethical problem that is plausibly solved by this analysis.
The algebraic form is abandoned in illustrating the next two breakdowns in parallelism. The first is 'part comprehensive; part not.'
'Loving people' depends on comprehensively loving people. 'Not loving people' does not.
'Rides horses' does not depend on comprehensively riding horses. To have ridden on horses is enough to count as riding horses.
The examples highlight the holistic pattern in reasoning about reference. In one phrase the term-reference is implicitly comprehensive, in the other it is not.
Finally, we come to the examples of 'one "is this" and one is "not this"'.
Fruit of a peach is a peach, fruit of a bramble is not a bramble.
Asking about a person's illness is asking about the person. Disliking the person's illness is not disliking the person.
A person's ghost is not the person. Your brother's ghost is your brother. Offering to a ghost is not offering to a person. Offering to your brother's ghost is offering to your brother.
If the indicated horse's eyes are blind, then we call the horse blind. The horses eyes are large yet we do not call the horse large.
If the indicated oxen's hairs are brown, then we call the oxen brown. The indicated oxen's hairs are many yet we do not call the oxen many.
One horse is horse; two horses are horse. Saying 'horses are four footed things' is a case of one horse and four feet, not a pair of horses and four feet. Saying 'horses are partly white' is two horses and some white, not one horse and partly white.
There is no further analysis or summing up. The moral, we assume, is a negative one. Had we treated the first algebraic model as a kind of logic, the Mohists' argument by example still would show that it was invalid. It is not a reliable form in the sense that a true premise formally guarantees a true conclusion. However, I now argue that it is not about sentences and truth at all. It concerns whether we can draw reliable parallels from terms to longer (guiding) phrases.
The implicit answer is 'no'. The Mohists offer no constant or consistent principles guiding the construction of longer "phrase" out of terms even when the words are consistently applied to external realities. They offer no way systematically to rationalize the conventional patterns of use. They retreat implicitly from Mozi's goal of replacing convention with a 'constant "guide".' If there is such a "guide", then it is not a product of any simple projection from linguistic reference. Moral guidance cannot derive from knowledge of natural kinds. It requires conventional, creative human social activity. Dialectically, the negative result gives ammunition to the Daoists who argue that no constant "guide" exists.
"Graham, Angus (1978) Later Mohist Logic Ethics and Science, London: School of Oriental and African Studies. (The only source in English for the Later Mohist text. Difficult--understanding Graham virtually requires knowledge of classical Chinese.)
------ (1989) Disputers of the Tao: Philosophical Argument in Ancient China, La Salle: Open Court. (An easier but less detailed treatment in the context of Graham’s account of ancient Chinese thought.)
Hansen, Chad (1983) Language and Logic in Ancient China, Ann Arbor: University of Michigan Press. (Difficult--Based on Graham’s reconstruction. A philosophical argument for a radically different interpretation of the linguistic doctrines.)
------ (1992) A Daoist Theory of Chinese Thought, New York: Oxford University Press. (An easier and more extended treatment in an account of ancient Chinese philosophy that emphasizes language.)
Fung, Yu-lan, 1952, History of Chinese Philosophy, Derk Bodde tr., Princeton, Princeton University Press. (A classic account that highlights the abstract interpretation of the ‘White Horse’ dialogue. Good for general purposes.)