Among the so-called six ‘dialectical’ chapters in the Mo Tzu, the last one is unique in being the only surviving treatise of pre-Buddhist China which discusses the forms of reasoning continuously and at some length. This was a product of the later Mohist school of the 3^rd century B. C., which is known to have studied the forms of reasoning for their own sake. Specifically, ‘huo’ is the first one of seven terms listed and defined in the chapter referred to above. The rest are chia, hsiao, pi, mou, yuan, and t’ui. The main purpose of my present paper is to interpret the first three of these terms with reference to their contemporary significance in logical or semantical studies.

Surprisingly, the original text for ‘huo’ (‘some’) is given no more than a very brief characterization: ‘some’ means ‘not all’. Here hsiao is defined in relation to chin, a verb (‘apply to all’, ‘exhaust’), also used adverbially in the sense of ‘all’, ‘exhaustively’. In the canonical chapters of the ‘dialectical’ group, chin itself is defined in relation to mo, ‘none’: "(applying to) all’ is ‘of none not so’."

However, scholars disagreed on the exact meaning and role of huo. Fung Yu-lan, the author of the monumental History of Chinese Philosophy, takes huo as one way of establishing a statement just as the rest of six terms do. Fung maintains that huo in the given definition combines the meanings ‘some’ and ‘possibly’, and his translator Professor Bodde, forced to make a choice, picks the latter: "What is possible is what is not omplete." However, Fung himself continues with some elaboration:

Later on, when we put this Neo-Mohist concept huo in a temporary perspective, it will become more significant. Now let us continue with a survey of other scholars’ view of this concept.

My purpose in this paper is to draw the important implications of huo with regard to our contemporary logical studies.

In the familiar logic of categoricals, ‘some’ and ‘all’ are two basic quantifiers. Combined with the two forms of quality: Affirmative and negative, they yield exactly four categorical forms. For the sake of definiteness, logicians adopt the minimal and necessary meaning of ‘some’ as ‘at least one’. In its ordinary use, however, the word ‘some’ unlike ‘all’, is both vague and ambiguous.

First of all, it is often vague. By ‘some’ we mean ‘a few’; but how many are a few? For example, when a person says that some people are watching T. V. in the next room, is he or she claiming that there is at least one person watching T. V. there, that there are at least two, or perhaps that there are at least three? Such questions have no answer; for the word ‘some’ is vague as it is ordinarily used. For logical use, vagueness of this kind is inconvenient. in order to decide more definitely what meaning the Word ‘some’ hag, it will be best for logicians to assign it the minimum meaning. It is thus stipulated that "Some so-and-so’s are such-and-such’s" is to mean that there is at least one so-and-so that is a such-and-such.

A second difficulty is that the word ‘some’ can give rise to ambiguity as it is ordinarily used. The ambiguity involved with ‘some’ comes to light if we consider a person who says that some people are boring. Is he or she thereby claiming that some people are not boring? In ordinary discourse this may sometimes be part of what his remark means, although more often it is not. For example, a student who says in an acid tone, "Some professors are worth listening to" is strongly suggesting that some are not, and perhaps we should regard his remark as asserting that some are and some are not worth listening to. But usually to say that some so-and-so’s are such-and-such’s is not to say that some are not.

Thus, for the purposes of logic, it is best to choose the minimum meaning of ‘some’. The sentence "Some so-and-so’s are such-and such’s" would be interpreted as meaning merely that there is at least one so-and-so that is a such-and-such. Nearly, the particular negative sentence is to be interpreted as meaning merely that at least one so-and-so is not a such-and-such. This leaves it an open question whether there is any so-and-so that is a such-and such. So too with any particular affirmative sentence.

Here the question of whether terms imply existence is involved. So far as the ‘some’ sort of general statement is concerned, at least the subject class designated by the subject term is understood as not empty. For example, when someone asserts a particular affirmative proposition, say, "Some flowers are annuals", the speaker commits himself to the view that at least one flower exists. Further, he equally commits himself to the belief that there is at least on annual. These consequences are obvious in the Venn diagram, because the marked X is the schematic picture of an existing object which is both a flower and an annual. To sum up, any particular affirmative proposition carries with it the implicit assertion of the existence of at least one member in both the subject and predicate classes.

But when someone asserts a particular negative proposition, say, "Some UFO’s are not flying saucers," it is often used in such a way that it implies the existence of only the members of the subject class. That is to say, the speaker believes there are unidentified flying objects but wants to deny that they are explainable as ‘flying saucers’.

So far all this may seem so obvious as to require no special emphasis. But when someone says: "All dogs are mammals," is he likewise committing himself to asserting the existence of ‘dog’ and ‘mammals’? The answer, like saying "Some flowers are annuals," again seems to be yes. But once we look a little more closely, the Venn diagram as used in the Boolean sense does not carry any such commitment. It contains only a series of lines whose purpose it is to deny membership to the class represented by the left-most area of the diagram. This is certainly against the ordinary usage which does commit us to the existence of both dogs and mammals. But suppose the proposition under discussion were the following: "All mermaids are fictitious animals." It is a fairly ordinary proposition and true, and yet no one would want the assertion of it to imply the existence of such things as mermaids or fictitious animals. Thus, though in ordinary conversations many uses of universal affirmative sentences are existence-committing, still others are meant to be true assertions without such commitment. So far as the goal of logic is the evaluation of arguments involving categoricals, the categoricals must have no vagueness or ambiguity. This is exactly the reason why we assign the minimum meaning ‘at least one’ to the word ‘some’. Similarly, it is very important that we specify which meaning is to be reflected in out universal affirmative categorical proposition.

In modern quantificational logic, the word ‘some’ plays a more important role both in symbolization and calculus when it is accompanied by the notion of identity. The notion of identity is a familiar one. The usual notation for the relation of identity is the ordinary equals sign ‘=’. So, we shall abbreviate the expression ‘x is identical with y’ as ‘x=y’. And we shall also write its negation as ‘x¹ y’. No doubt, the notion of identity is the most important dyadic relation for our present purposes. "Is" also has two uses other than identity — the existential sense and the predicative (or copulative) senses. It is intuitively obvious that the relation of identity is transitive, symmetrical, and reflexive. Symbolically, we may write:

Similarly, sentences continuing the expressions ‘at most’ (or ‘no more than’) may also be expressed using the identity sign. Consider: "At most one spy is in the room." This sentence amounts to: "If here is a spy in the room, he’s the only one. so it may be symbolized as (x)(y) [(Sx • Sy) É x=y]. How about "There is only one deity"? A little reflection will assure us that to say there is exactly one is to say that there is at least one and at most one. Thus the statement becomes (ヨx) [Dx • (y) (Dy É y=x)]. So much for the quantifier ‘some’ as accompanied by the notion of identity in modern quantificational logic. Now I shall consider the notion of chia in its relation to contemporary logic.

Fung admits that he has followed Hu Shih’s interpretation on taking the chia as ‘hypothesis’ or as ‘argument by supposition,’ but Hu’s interpretation, in turn, was inspired by a phrase, chia chih, ‘supposing...’ (literally ‘borrow it’) in the Confucian Hsün Tzu, which introduces fictitious illustrations in the manner of the later chia ru. Graham thinks that this kind of usage is untenable. He offers two objections to such an explanation:

(1) It is incredible that the author of the canon should flatly reject hypothetical illustrations as ‘erroneous’, ‘illegitimate’ (pei). Mo Tzu himself was as fond of them as other Chinese thinkers, and even the later Mohist dialecticians did not scorn them entirely.

In addition, Graham refers to Maspero’s translation of chia as ‘le faux’ in order to show again the difficulties of Fung’s explanation. However, Graham rejects the assumption behind this translation—that chia is opposed to chen, which means ‘genuine’. Maspero’s interpretation is based on the Shuo-wen definition of chia, as the opposite of chen ‘genuine’. All the same, Graham’s rejection is rather interesting in its own right and worth noting:

In what follows, I shall consider further the current logical importance of this Neo-Mohist notion by relating it to truth functions.

No important truth function is so complicated and controversial as the type called hypothetical or conditional. It is even taken as paradoxical in the sense of being counter intuitive. A statement of the form p É q is called a material conditional, a term which indicates that it is a conditional but of a special sort. Its truth conditions are: It is false if p is true and q is false; for all other substitutions of p and q, p É q is true. Thus p É q is tantamount to saying, "It is not the case that p can be true and q can be false, for the only time when ‘P É q is false is when the statement replacing p is true and the one replacing q is false.

In example 1 there is a temporal relation between the antecedent and the consequent. Here the order in which things happen is clearly significant: John must first get his check and then he will pay his debts. But the ‘horseshoe’ does not express this sense. It only says that 1 is false when and only when the antecedent is true and the consequent false—the chronological order is not taken into account.

Example 2 suggests that there is a causal relationship between the events expressed in the antecedent and the event expressed in the consequent. That is to say, lowering the temperature of water causes it to expand. But this causal sense is also lost in the formalization p É q. The ‘horseshoe’ simply asserts a true relation, not a causal relation. simply asserts a truth relation and not a causal relation. To put it another way, the truth relation as defined by our truth table is all what matters. The formal logician’s basic concern is: Does ‘É ’ capture the most significant logical features of most conditional sentences, even if it does ignore many secondary features?

Example 3 illustrates a very important sense of ‘if ... then...’ It is the sense of entailment. In general, to say that ‘p entails q’ is to gay that ‘q is deducible from p.’ Knowing that Smith is a father enables us to deduce that he has child(ren). But this sense of ‘if ... then...’ is not to be identified with É . The confusion between the two is a common one and must be guarded against at all costs.

Now as a truth function, a conditional statement counts as true except when its antecedent is true and its consequent is false. Put another way, it counts as true provided either that the consequent is true or that the antecedent is false. At first sight, this may strike you as odd or even paradoxical because its truth-functional use hardly corresponds to its role in ordinary discourse. This gives rise to the so-called Paradoxes of the Material Conditional. However, once only truth and falsehood are construed to be relevant here, there is nothing paradoxical. As Copi points out, "The alleged paradox arises primarily from treating a technical terms if it were a term of ordinary, everyday language. "

Are there some uses of ‘if ... then...’ which are not amendable to our sense of ‘É ’? The answer is, of course, "Yes." At present, we will consider two kinds of conditional statements which cannot adequately handled by our truth-functional connective. They are the contrary-to-fact conditional and the generalized condition. Each is illustrated below:

1. If Napoleon had not invaded Russia, then he would have main-tained the Empire.
2. If anyone publishes that person is promoted.

Example I is called counterfactual conditional, because the antecedent expresses something that is contrary to the fact. Now a counterfactual conditional such as I cannot be truth-functional. For if it were, the conditional itself would of course be true. But if the falsity of its antecedent sufficed to make a counterfactual true, the all such conditionals automatically would be true. For example:

1. If Napoleon had not invaded Russia, then he would have main-tained the Empire.
2. If Napoleon had not invaded Russia, then he would not have maintained the Empire.

Let us now comment example 2. Conditionals such as 2 involve the element of generality. This feature is indicated by the presence of the word ‘anyone.’ Clearly it cannot serve in the same way, say, "If Smith publishes then he is promoted", as a premise in a truth-functional argument. To "argue" as follows hardly does make sense:

Of course, this does not mean to say that generalized conditionals cannot appear as premises in any argument. For example, the argument:

is surely valid, even though its validity cannot be ascertained by the method available in the truth-functional logic. Arguments like this lie outside the scope of our truth-functional treatment. That is, they need a logic of generality.

Earlier what we said about a generalized conditional such as "If anyone publishes, then that person is promoted" may be restated as follows: Strictly speaking, the ‘if ... then ...’ does not connect two statements. That is, the clause "anyone publishes" is neither true or false. Its function, however, is clear; it refers to an indefinite set of persons who publish. The force of the whole conditional may be brought out with this rendering:

Basically, Graham’s interpretation of the hsiao is similar to what T’ang Chün-i has argued, that is, the hsiao is not a form of inference, but it is one of seven phases concerning the course of resolving doubts. in this connection, Chad Hansen’s brief remark on the compatibility of these two scholars’ interpretations of the hsiao and related definitions in the Hsiao-ch’u is worth our attention:

In the same passage we have just quoted, Hansen thinks that the series of definitions are not plausibly treated as deductive forms because the author of the Hsiao Ch’u is at pains to show that they can "go wrong." Of course, it does not follow that these three scholars are all in perfect agreement. Each, in my opinion, has his own axe to grind. However, they seem to differ about only the extent to which the hsiao must not be treated as a form of reasoning at all.

It is not surprising that there are some other scholars who would not agree with this camp. Janusz Chmielewski probably is the most known scholar in this opposite direction. Basically he returns to what Hu Shih earlier interpreted concerning the role of the hsiao in the Neo-Mohist logic. However, as a sinologist trained in modern symbolic logic, he is quite a different breed in the treatment of early Chinese logic. Since he claims that he improves on Hu Shih’s argument for the hsiao as a non-syllogistic deduction, let us concentrate on how he with the aid of modern symbolic logic interprets this controversial term or concept in the Neo-Mohist logic.

To show that the hsiao must have been a form of reasoning belonging to the calculus of functions, Chmielewski first turns to the main definition of the hsiao given in the Hsiao-Ch’u, which, in his view, must be supplemented by some information collected from ‘canonical’ chapters (40-43).

Here is the main definition of the hsiao as tentatively translated by Chmielewski:

Chmielewski is aware that the bare translation of the definition of the bsiao is by no means illuminating, but it becomes much clearer, he says, if we bear in mind that the ‘norm’ involved in this definition is "whereby then so’." What follows is his interpretation of the hsiao:

(sensu lato)

Furthermore, in connection with Maspero’s dispute with Hu Shih’s interpretation of the hsiao, Chmiciewski argues that, even if we follow Maspero in considering the word ku of the definition as a mere ‘therefore’, we should still interpret the hsiao (sensu lato) as a specific formula of deductive reasoning. Then the corresponding part of the main definition would read: "...therefore if (the reasoning) is ‘conform to the hsiao’, it is correct; and if it is not ‘conform to the hsiao’, it is incorrect." What is more important, he continues, if ku is rendered as ‘therefore’, the condition of ‘being conform to the hsiao’ becomes perhaps clearer, as it then refers to the whole of the ‘hsiao-ised’ (not to its antecedent alone). In other words, even if the ku were rendered as ‘therefore’, his own way of interpreting the hsiao (sensu lato) as a specific formula of deductive reasoning would be more plausible.

Finally. Chmielewski proposes to justify his theory of the hsiao on the basis of a specific semantic value different from the common meaning of ‘imitation’ the character hsiao connotes. Here he finds textual corroboration in the I-Ping P’ien (ch. 15) of the Hsün Tzu. Here he essentially refers to the notion of ‘efficacy’ from which the hsiao in its Neo-Mohist sense can be derived. However, he is aware that the evdence in question is rather indirect and incomplete, since it involves no actual hsiao-reasoning in the Neo-Mobist sense of the term. That is to say, it can only be conceived as referring to what he considers as the hsiao sensu stricto (or ‘general implication’). What follows is the most essential part the passage on which his case relies.

1. I should like to be permitted next to speak of the hsiao of kings and feudal lords as being strong or weak. Of the hsiao of their pre servation or ruin, and of the shih of their being in safety or danger.
2. If the prince is a worthy one, his country is well-governed.

(c) If the prince is without ability, his country is in disorder.

(f) If (the prince’s country) is well-governed, (the prince) is strong.

(g) If (the prince’s country) is in disorder, (the prince) is weak.

As for the merit of the Neo-Mohist notion of hsiao, Chmielewski made three points: First, this hsiao has been theoretically defined as a ‘norm of becoming’ corresponding to our notion of the general implication; second, such an all-statement directly implies any of the specialized statement which are ‘conform’ to the given hsiao; and last, the Neo-Mohists have consequently developed the primary hsiao-notion as a specific form of reasoning by derivation.

The word hsiao of the Hsün Tzu passage earlier quoted was glossed by the T’ang commentator, Yang Liang, as ‘verification, test’ (nien). Chmielewski took this suggestion seriously and thinks that it is precisely in reference to ‘effect’ that Yang Liang glossed the work hsiao as ‘test’. This leads Chmielewski to think that the term hsiao in its specific Neo-Mohist use etymologically derives from ‘effect’ rather than from any other meaning of the charcter. The word shih in the same quoted passage commonly means ‘strength’, but also ‘force of circumstances’. Shih was more specifically meant to stress the antecedents of these implications, while the antithetical term hsiao ‘effect as entailed by ...’ was specifically meant to emphasize their consequents. According to Chmielewski, it is precisely in reference to ‘effect’ that Yang Liang glossed the word hsiao as ‘test’.

In addition, Chmielewski at least cites another term, fan, ‘every’, which is chiefly concerned with the all-operator in the general implication. As he sees it, this single Chinese word is, in fact, the linguistic equivalent of what we call the universal quantifier, ‘(x)’, in modern logic.

These terminological considerations, Chmielewski claims, corroborate his assumption that the Neo-Mohist term hsiao derives from the meaning ‘effect’ rather than from any other meaning of the character. However, the term hsiao can have no exact equivalent in English. No English word both designates a general implication and at the same time emphasizes the consequent of the implication. Therefore he chooses to leave the term untranslated. So have I followed him in being non-com-mitted in this respect.

Toward the end of his discussion of this Neo-Mobist notion of hsiao, Chmielewski sums up as follows:

Now a brief evaluation is in order. From a logical point of view, Chmielewski has certainly improved on Hu Shih’s interpretation of the hsiao as a non-syllogistic form Of reasoning. This has been shown, I think, mainly in his clarification of the two senses of the term hsiao in its main definition. To recapitulate, in his own words, the hsiao is used in its primary sense (stricto sensu) to refer to a general implication or all-statement. The other sense is called sensu lato which also refers to the hsiao-ised as derived from the given hsiao if true. This consequently paves the way for his formal formulation with the aid of the calculus of functions. This new kind of approach to the study of Chinese philosophy in general and Chinese logic in particular is certainly long overdue. As a matter of fact, the same approach had been very fruitful in western philosophy for decades. Of course, it does not follow that logical analysis is an adequate approach to the study of Chinese philosophy. It at least should not be belittled. More positively, it should be put to work if possible, especially on much of classical Chinese philosophical literature.

Second, an appeal to only one passage in the Hsün Tzu to substantiate his theory of the Neo-Mohist notion of hsiao is hardly convincing enough. Linguistically, hsiao hag multiple meanings and its use varies with different associations of other expressions. This is a familiar linguistic fact about Chinese language. In addition, the non-Neo-Mohist philosophers occasionally used the primary hsiao for a purpose different from that of the Neo-Mohist theory, that is, for that of forming a specific form of the chain reasoning, as is actually shown in our Hsün Tzu passage. Actually, Chmielewski himself is aware that he only partially corroborate his theory of the Neo-Mohist hsiao. Since he is conscious of the conjectural nature of his justification, there is not point in me pressing any further.

To conclude, we started with three basic Neo-Mohist concepts of logic more than two thousand years ago in ancient China and now we end with their full-fledged development in modern logic. Of course, we have covered an immense distance. I am not at all saying that something like the quantificational symbolism for ‘some’ or something like the special sort of conditional called ‘material’ is explicitly implied in these Neo-Mohist concepts. For that would be rather far-fetched. Indeed our account has digressed a long way from the Neo-Mohists, but what higher compliment can we pay them than to say that they force us to reflect again on current work on important logical or semantical concepts?