Using Contemporary Logic to Analyze Pre-Qin Logic*

Thierry Lucas

Abstract. The aim of this article is to sketch how some notions arising from notions or techniques mainly due to contemporary logic and some elements of the theory of argumentation may allow us to reach a better understanding of the logical contributions of the great thinkers of China’s past.It is proposed to extend the usual notion of logic to include some elements of the theory of argumentation,hoping thus to create an open space where“Western logic”and“Chinese logic”may meet(sections 1 and 2).This is exemplified by a detailed study of some important pre-Qin contributions to logic.Sections 3 to 5 analyze some logical contributions in the traditional sense of“logic”:later Mohists and the basic laws of logic;definitions in theory and in practice;classification of names,interdefinability of quantifiers and contemporary explanations of the mou(侔)type of reasoning in the Mohist texts.Section 6 analyzes the phenomenon of sentence parallelism to show that it hides some partially formalizable elements of the theory of argumentation such as arguments by generalization,and that it contains some implicit but perfectly valid arguments.Section 7 presents a detailed analysis of examples of reasoning by analogy in the Mencius and suggests some formal ways of evaluating their strength.

The pre-Qin period is a very rich period for the development of logic in China.The Chinese society of the time undergoes a serious crisis.The feudal system is fading away,the Zhou(周)dynasty is losing its influence and a number of different states are fighting continuous wars in search for supremacy.It is precisely at that moment that some thinkers arise to solve the political and moral challenges of the changing society and one is struck by the similarity between that period and the situation of Greece at approximately the same moment.China and the Western world have known for a long time some of these thinkers,who have had a fundamental influence on the future of China:Confucius(Kongzi 孔子)and Mencius(Mengzi 孟子),considered as the founders of the Confucian school;Laozi(老子)and Zhuangzi(庄子),the supposed initiators of the Daoist movement.But it took more time for China and especially for the Western world to recognize the importance of other thinkers such as the confucianist Xunzi(荀子),or Shang Yang(商鞅),Shen Dao(慎到)and Han Feizi(韩非子),initiators of Legism and Mozi(墨子),founder of Mohism.

Moreover,it is only very recently that philosophers,and in particular logicians,have understood the interest of the pre-Qin (先秦) period from the point of view of logic:the so-called School of Names and the Mohist Canons are the foremost examples of those contributions to the development of logic in China.

The aim of this article is to sketch how some notions arising from notions or techniques mainly due to contemporary logic and some elements of the theory of argumentation may allow us to reach a better understanding of the logical contributions of the great thinkers of China’s past.

The first section will remind the reader of a few recent important moments marking the exchanges between Western logic and Chinese logic.

The second section discusses the notion of logic which is used here and contrasts it with other methods of studying the subject.An important distinction will be made between what thinkers have written about logical subjects and how they used logic in their writings.These are indeed two aspects which are often tied together,but which are in principle independent:the Later Mohists constitute an eminent example of thinkers who discussed logical notions using logical methods; strictly speaking,Gongsun Long(公孙龙)’sBaimalun(白马论)does not directly discuss logical notions in the same way as the Mohists,but proposes challenges using very clever arguments of a logical type;except for a few mentions of questions of language,Confucius’Analects(Lunyu论语)do not discuss logical notions,but this does not mean that theAnalectsare devoid of argumentative techniques which are worth being studied;poetry would be a typical example of writings that do not in general1This qualification is necessary.Indeed,Gregor Paul rightly insists on the fact that ethical,pragmatical,empirical but also logical arguments are included in the Shujing,the“Classic of Documents”,and even in the Shijing,the “Classic of Poetry”.This is argued in detail in Chapter V of his forthcoming book[35].discuss logical themes and that do not in general use logical or argumentative methods.

The third section will be devoted to the example of the Mohists and the basic laws of logic.

The fourth section will discuss the theme of definitions in pre-Qin logic.

The fifth section will emphasize some contributions of Mohist Logic,which are important from the point of view of contemporary logic and analyze the example of theirmou(侔)type of reasoning.

The sixth section will turn to logic in its argumentative use and present the example of parallel sentences,especially in Confucius’Analects.

The seventh section presents the case of analogical reasoning and studies some analogies used in theMencius.

The last section presents some conclusions of this study.

Let me apologize for referring the reader to many of my previous publications,but the present article is intended as a summary of different uses of contemporary logic.I feel sometimes obliged to shorten the presentation but think it useful to refer the reader to texts containing complements and more detailed information.

1 Logic between East and West

If one wants to avoid many misunderstandings,it is necessary to sketch what we mean here by“logic”,especially in its relation with the exchanges between“Western logic”and“Chinese logic”.The historical allusions given below are designed to give some precisions on the notion of logic used in this article and are in no way intended to be a history of the exchanges between Chinese logic and Western Logic,for which the reader can consult the very complete[16],which contains references in English,but also many references in Chinese.

Logic in its more traditional sense arose from the work of Aristotle and was technically explored during the Middle Ages.It remained dominant in the Western world for many centuries[39].It was still the dominant model when Hu Shih wrote his pioneering thesis[14],emphasizing among others the work of the Later Mohists,Hui Shi (惠施) and Gongsun Long.Hu Shih had a rather inclusive conception of logic,to the point of including many epistemological considerations as well as discussions on theYijing,Confucius’Analects,LaoziandZhuangzi.But his conception of logic was also restricted,insofar as his technical tools of analysis were essentially confined to the notions of Aristotelian logic,more particularly to the theory of syllogisms.The advances of logical studies were at that moment mainly due to the work of mathematicians and were not yet well known by Western philosophers,let alone by Chinese philosophers.

Another significant step is given by Fung Yu-lan’s work ([6]),whose translation[8]brought to the knowledge of the Western world the large domain of Chinese philosophical thinking.Fung’s work is very impressive by its breadth,but from the philosophical and logical point of view,it remains very dependent from a neo-realist conception of philosophy:existence of universals,distinction between abstract concepts and their realization.

I consider that another important step is given by the foundation in 1973 of theJournal of Chinese Philosophy.This academic Journal,founded by Cheng Chung-Ying,has published in English numerous articles devoted to Chinese philosophy,with a considerable number of them studying the logical aspects of Chinese philosophy.The articles show a clear consciousness of the advances of logic in the Western world.

To finish with this brief presentation,I want to mention Christoph Harbsmeier’s work ([13]),which is a part of Needham’s encyclopedia([34]).This is a very documented study of language and logic in Ancient China and it abundantly uses the concepts of contemporary logic,while carefully respecting the Chinese context of that logical thought.

That too brief sketch should make it clear that we can in no way restrict Western logic to the theory of syllogisms,a position which was provocatively denounced by Russell in his[37]:“In most universities,the beginner in logic is still taught the doctrine of the syllogism,which is useless and complicated.If you wish to become a logician,there is one piece of advice which I cannot urge too strongly,and that is:Do NOT[capitals in the original text]learn the traditional formal logic.” In this respect,it is important to mention the names of Henryk Greniewski and Olgierd Wojtasiewicz,who in a short paper published in 1956,appear to have been the first to apply logical instruments going beyond the theory of syllogisms to Gongsun Long’sBaimalun([11]).They were soon followed by Janusz Chmielewski,who in 1962 also used the theory of classes to explain part of theBaimalunand later published a number of studies devoted to early Chinese logic([2,3]).Since then,many other scholars have applied contemporary logical techniques to analyze pre-Qin logic;they are too numerous to be mentioned here,but the reader will find many of them mentioned in the bibliography of[13].Our first task will now be to arrive at a notion of logic which encompasses enough to bring together Western and Chinese logic into a common space.

2 What is Logic? Questions of Method

There are many conceptions of logic,but I would like to start from an approximative definition which is neither too general nor too restricted:logic is the study of reasoning which is embedded in arguments and it tries to identify which arguments are acceptable.

There should not be too much disagreement about the notion of argument,the important point being that it gives rise to a sequence of propositions,from which one distinguishes the premises and the conclusion.It should not bea priorirequired that the argument be fully explicit:the vast majority of our arguments are indeed based on many implicit premises which are given by the context of their enunciation.One should also not require that the argument be formalized:the huge majority of arguments of real life or given in books,be they written by philosophers or scientists,is given in plain language.But,if we want to understand the structure of an argument,exhibiting its structure is important and formalization is in that respect a very useful tool.Although arguments are almost always used to express not yet recognized consequences of what we know,or to convince somebody,we should also not require that an argument gives us something really new:“it is cold and it is raining; hence it is cold” is a perfectly correct argument,but it can barely be said to bring “new knowledge”.

If we understand“acceptable”in a very strict sense,we will soon reach the very common contemporaneous conception of formalized logic.According to that strict sense,an argument will be acceptable if it is correct or valid,that is,if the truth of the premises necessarily entails the truth of the conclusion.“Necessarily”means that an argument should not be declared valid on the sole truth of its conclusion,something which could be given by a happy concourse of circumstances.It should be declared valid if all arguments of the same form,when they have true premises,also have a true conclusion.A valid reasoning has thus a compelling force for every reasonable person.With such a definition,one is immediately led to a formalized conception of logic.In a very restricted sense,if we consider that genuine arguments are constituted by propositions which are either true or false,one is almost inevitably driven to accept only the so-called classical logic.But a more open conception,aided by purely formal studies,will admit the study of other types of logic such as intuitionistic logic,admitting propositions which are neither true nor false,or many-valued logic,admitting propositions having other truth values than true or false,or even paraconsistent logics,admitting propositions which are both true and false.

However,we may understand“argument”and“acceptable”in a broader sense,which covers also part of what is called“argumentation”2In this section,I am using rather freely terms such as “argument”,“acceptable”,“convincing”,“informal logic”,“rhetoric”and so on.The notions to which they correspond are dealt with in argumentation theory and it is well beyond the scope of this article to discuss them,even summarily.I can but refer the reader to the very complete Handbook of Argumentation Theory([5])..In that case,“acceptable”often takes the meaning of“convincing”.Take for example the well known argument by analogy; it has no compelling force,but it may be very convincing.The comparison of the state and of its structure with the structure of the family is extremely frequent among pre-Qin thinkers and gives much light on their conceptions.This broader conception of arguments is thus extremely interesting,but it is unfortunate that they have misled many Western thinkers to very fuzzy conceptions of argumentation,relying on a vague notion of“informal logic”.Fortunately,there are now more and more studies trying to explain the functioning of different types of argumentation by rigorous and quasi formal methods:non monotonic logic,default logic([40]),logic of belief revision,learning theory([12]),theories of analogical reasoning([1])and so on.

It seems well that there is a progressive transition from compelling types of reasoning to argumentation and less traditional logics.I agree with the idea that formalization is a precious instrument of analysis and that it could be applied also to some parts of the theory of argumentation(see similar assertions in[1]).Thus arguments by analogy have a certain formal structure which contains some premises and a conclusion which can be represented as this:

ais similar toa′;

a′has propertyP;

hence,ahas propertyP.

The following example gives a highly simplified illustration of that kind of argument:

the ruler is analogous to the father of the family;

the father of the family must be obeyed;

hence,the ruler must be obeyed.It is well known that analogical arguments are not valid but this does not mean that a logical analysis is unable to bring information on their structure and value,as will hopefully be shown in section 7.

I will therefore propose here a rather large conception of logic,which covers what is traditionally included in logic,but also some parts of the theory of argumentation.However,I think that it is better to exclude arguments appealing more to the feelings than to reason,or designed to influence the audience by stylistic devices such as rhymes,alliterations,hyperboles,litotes,which have no direct impact on the truth value of the sentences involved in the argument and which should best remain under the heading of rhetorical devices.I want also to take here the precaution of warning readers that the wordluoji(逻辑) has been imported in Chinese from Western languages and originally carries with it a very restricted conception of logic,especially in the studies of logic in the pre-Qin period.One often considers that“Western logic”is Aristotelian logic,or that it is exclusively a formalized and mathematized version of classical logic;it is then opposed to Chinese logic,which has indeed little to do with these two conceptions.It should be emphasized that mathematical logic has now become a reservoir of useful distinctions and technical instruments which has the same kind of neutrality as mathematics:as has already been alluded to,one studies systems which do not obey such fundamental principles as the excluded middle or even noncontradiction.Nothing can forbid us to use these instruments to study paradoxical formulations such as those proffered by Gongsun Long in hisBaimalun.Moreover,that a word comes from outside and carries with it the traces of its origins does not mean that the concepts it covers are foreign to the importing culture.I am not thinking here of formulas or very elaborate theorems of mathematical logic but of basic concepts of logic.The relation name-object,the distinction between individual names,predicates and general names,the relation between quantifiers,the principles of non contradiction and of excluded middle,paradoxes,the idea of an organized system of definitions were all clearly a subject of preoccupation in the work of Later Mohists.And after all,Confucius,Mencius,Zhuangzi and many other thinkers did not have to learn arguments by induction or arguments by analogy to use them in a competent manner in their writings.

This being said,it is equally important to remind one that logic is not an omnipotent instrument.If I want to understand the logical structure of an ancient text,be it Chinese or Western,I will have to rely on a good philological analysis of the text,on historical and sociological studies describing the context of its production.This is absolutely necessary to restrain the potential interpretations and it will very often remain true that the use of logical instruments often suggests different possible interpretations,without being able to decide which one is better.It is also obvious that in general,as the saying goes,“one finds only what one is looking for”.In other words,everyone has a certain preconception of the text he is trying to explain and he will choose his instruments in function of that preconception.However,this is common to all approaches of a text and should not exclude an approach using the contemporary techniques of logic.

It remains to be said that in this study of pre-Qin logic,one should also distinguish two different aspects.People like the Later Mohists or members of the so-called School of Names discussed and studied questions of language,they made them an explicit subject matter and used sometimes quasi formal methods of presenting them.Other people did not explicitly study those questions,but they used a number of perfectly reasonable arguments which are often put under the heading of argumentation,but which obey certain formal schemes;these arguments should also be studied and they are part of the broad conception of logic which I want to promote here.If we agree on such an enlarged conception of logic,we can find a common space where we can discuss the logic in pre-Qin texts as well as Aristotelian logic or Indian logic or many other types of logic.

In what follows,I want to give a few examples showing how the pre-Qin period discovered or used concepts which are genuinely logical in the broad sense which I described above.This will be done by using some basic tools of contemporary logic,but using a formal presentation only when I think that it is useful to clarify the discussion.

3 Later Mohists and the Basic Laws of Logic

Later Mohists are often credited with the discovery of the law of non-contradiction and of the law of excluded middle,to which we refer here as the basic laws of logic(thus omitting a discussion of the law of identity).The clearest assertion of these laws is given in Canons A74 and B35 which I recall here3In this article,the Chinese text,the references and the translations of the Mohist Canons,of the Daqu and of the Xiaoqu are those of[10]..

Canon A74.

经上：辩，争(彼)*仮也。辩胜，当也。

经说上：(辩)。或谓之“牛”，或谓之“非牛”，是争(彼)*仮也。是不俱当，不俱当，必或不当。(不若当“犬”)。

Canon.Bian(disputation) is contending over claims which are the converse of each other.Winning in disputation is fitting the fact.

Explanation.One calling it an“ox”and the other“non-ox”is“contending over claims which are the converse of each other”.Such being the case they do not both fit the fact; and if they do not both fit,necessarily one of them does not fit.(Not like fitting“dog”).

Canon B35.

经下：谓辩无胜必不当，说在辩。

经说下：(谓)。所谓，非同也则异也。同则或谓之狗，其或谓之犬也，异则或谓之牛，(牛)*其或谓之马也，俱无胜，是不辩也。“辩”也者，或谓之是，或谓之非，当者胜也。

Canon.To say that there is no winner in disputation necessarily does not fit the fact[dang当].Explained by:disputation.

Explanation.The things that something is called are either the same or different.In a case where they are the same,one man calling it a“whelp”and the other man a“dog”,or where they are different one calling it an“ox”and the other a“horse”,and neither winning,is failure to engage in disputation.In“disputation”,one says it is this and the other that it is not,and the one who fits the facts[dangzhe当者]is the winner.

It seems quite clear that the assertion“Such being the case they do not both fit the fact”expresses a law of non-contradiction and“to say that there is no winner in disputation necessarily does not fit the fact” expresses some law of excluded middle.This is fundamentally true,but after a second thought,we should be more critical of such assertions and explain more clearly in what way these canons express the basic laws of logic.First,what is the exact status of these laws of logic? Secondly,the Canon mainly deals with disputation;what is the relation between disputation and the basic laws of logic?

Concerning the first point,it is important to say that the so-called basic laws of logic appear in various guises and that they fully make sense only when they are considered in relation with the other laws of logic.Let us explain the point with the law of excluded middle.In a first sense,the law of excluded middle is a scheme which is represented by a formula such that(p ∨¬p),which is considered informally as a basic principle of thought,or is considered formally as a proposition which is provable in any reasonable formal system.However,as soon as you introduce some notion of meaning or truth in the study of your formal systems,you are led to consider semantic versions of that law:

(1) for every propositionp,(p ∨¬p)is true;

(2) for every propositionp,pis true or¬pis true;

(3) for every propositionp,pis true orpis not true;

(4) for every propositionp,pis true orpis false.

It is important to distinguish here our object language and our metalanguage.Indeedp,¬p,(p ∨¬p),¬(p ∧¬p),q,(p ∧q),(p →q),(p ↔q)are in the object language,but when we say thatpis true,e.g.“this is an ox” is true,we relatepwith the facts,and we are in our metalanguage.Accordingly,one should distinguish the symbols “¬”,“∧”,“∨”,“→”,“↔” and the corresponding “not”,“and”,“or”,“implies” and “iff” (shorthand for “if and only if”); to avoid confusions,we do not introduce special symbols for our metalanguage,but sometimes use parentheses to clarify the scope of the connectives.

This being recalled,observe that the four formulations of the law of excluded middle given above are not immediately equivalent! They depend on your semantics.Formulation(1)presupposes that you have a notion of truth.Formulation(2)is not the same as(1),because in(1)the symbol“∨”is in the object language(the language you discuss)and in(2)the“or”is in your metalanguage(the language you are using to discuss the object language).Formulation(2)is equivalent to formulation(1)if you have an interpretation of “∨”which satisfies:(p ∨q)is true if and only ifpis true orqis true(or both).Formulation(3)is not the same as(2),because in(1)the symbol“¬”is in your object language while the“not”is in your metalanguage.Formulation(3)is equivalent to(2)if you have an interpretation of“¬”which satisfies:¬pis true if and only ifpis not true.And finally,(4)is equivalent to(3)if you accept in your metalanguage that “not true” is equivalent to “false”.Formulations (3) and (4) are commonly accepted as semantic versions of the law of excluded middle.

Similar considerations apply to the law of non-contradiction and give semantic versions such as:

(1’) for every propositionp,¬(p ∧¬p)is true;

(2’) for every propositionp,it is not the case that(p ∧¬p)is true;

(3’) for every propositionp,it is not the case that(pis true and¬pis true);

(4’) for every propositionp,it is not the case that(pis true andpis not true);

(5’) for every propositionp,it is not the case that(pis true andpis false).

These are not idle distinctions,because some logicians have given good arguments to introduce special semantics and to reject,at least in some contexts,the law of excluded middle(intuitionism)or the law of non-contradiction(paraconsistent logics).We do not discuss this here,but we already note that the Mohists were quite far from our modern notion of formal system,so that we can certainly not credit them with a formal conception of the basic laws of logic.Their use of“当”suggests that they had in mind a certain notion of truth as a correspondence between propositions and facts;this is a semantic notion and their formulation is certainly akin to(3),(4),(4′)and(5′).

But moving to our second point,we can say that this is not yet enough if we want to understand their formulation in canons which explicitly discuss“disputation”,bian(辩).We should be able to give a better connection between their formulation and our modern formulations of the law of excluded middle.I think that a bit of rigor can help us to situate their contribution with a maximum of precision.

The clue seems indeed to be their concept of disputation,which is clearly explained in B35.The explanation of the canon shows that their notion of disputation relies on a staging of two persons,one person,saya,asserting propositionp,the other person,sayb,asserting propositionq.Let us represent this situation by the metaformula Disc(a,b;p,q),a discussion in whichaassertspandbassertsq.As the explanation makes it clear,this is not yet disputation.It is a disputation if one of the two persons,sayb,asserts the negation of the assertion made bya,a situation which we may represent by the metaformula Disp(a,b;p)and which the Mohists define like this,a formulation to which we will refer as(DISP)in the sequel:

(DISP)Disp(a,b;p)if and only if(Disc(a,b;p,q)andqis the negation ofp).

Thus,as the examples show,ifpandqare equivalent(here represented bytong(同)),like “this is a dog” and “this is a whelp”,qis certainly not the negation ofpand there is no disputation.Or if propositionspandqare incompatible but not contradictory(here represented byyi(异))like“this is an ox”and“this is a horse”,qis not equivalent to the negation ofp,henceqis certainly not the negation ofpand there is no disputation either.The typical disputation should be a discussion in whichaasserts “this is an ox” andbasserts “this is not an ox” (see explanation of Canon A74)4We base ourselves on the examples to give the strict analysis(1);a more liberal notion would be to allow Disp(a,b;p)for q equivalent to the negation of p,but this is irrelevant for the main point of this section..

Now,both canons bring in two other notions:to win and to fit the facts.We could represent “xwins” by a metaformula such as Win(x).For “to fit the facts”,we need a notion of truth,which we could express by True(“p”).It is customary to represent that kind of situation with a predicate True which applies to terms designating propositions,so that we need a way of designating propositionp,something which will be done here by simply using the familar quotation marks,in agreement with their use in ordinary texts,as in the example:

proposition：this is an ox;

designation of the proposition：“this is an ox”.

Now,we are ready to represent the Mohist assertion of Canon A74 that“winning in disputation is fitting the fact”,to which we will refer as(WIN)in the sequel:

(WIN)Disp(a,b;p)implies((Win(a)iff True(“p”))and(Win(b)iff True(“notp”)).

Let us now consider the Mohist formulation“To say that there is no winner in disputation necessarily does not fit the fact”of Canon B35.It may be represented byA.Disp(a,b;p)implies not(not Win(a)and not Win(b)).

Consider also the assertion Canon A74“Such being the case they do not both fit the fact”,which may be represented by

B.Disp(a,b;p)implies not(True(“p”)and True(“notp”)).In the presence of(WIN)and on the basis of a classical metatheory,we see that we have inAandBwhat we could qualify as a dialogical version of the excluded middle and of the non-contradiction law:

A1Disp(a,b;p)implies(Win(a)or Win(b))

B1Disp(a,b;p)implies not(Win(a)and Win(b)).In the presence of(WIN),we could also present the MohistAandBas

A2Disp(a,b;p)implies(True(“p”)or True(“notp”))

B2Disp(a,b;p)implies not(True(“p”)and True(“notp”)).

Interestingly enough,this second formulation looks more like a semantic version of the two basic principles,becauseaandbdo not appear in the consequent of the implication.Could it be that the Mohists basically had a semantic version of these principles? The answer lies in a context analysis of their use of disputation.It is clear that disputation here is not a trivial matter of analyzing the behavior of real disputers or of deciding whether this is really an ox or a horse or a dog.The Mohists had certainly in mind practical or moral purposes,but they were also very sensitive to questions of logic,and from that point of view,disputation is here just a theoretical setting which allows them to discuss the truth of sentences in general.That setting may be convoked for any sentence you want to consider.In other words,they would consider that any sentencepmay be the subject of disputation,a principle which could be qualified of“disputation as a tribunal of truth”and which we abbreviate as(DTT):

(DTT)For all sentencesp,there exist disputersaandbsuch that Disp(a,b;p).

This being admitted,universal quantification ofA2inaandbwill give for allafor allb(Disp(a,b;p)implies(True(“p”)or True(“notp”)).

But becauseaandbdo not appear in the consequent of the implication,this is classically equivalent to

(existsaexistsb(Disp(a,b;p))implies(True(“p”)or True(“notp”)).

But(DTT)tells us that the antecedent of this implication is true,so thatA2entails

A3(True(“p”)or True(“notp”)).

Similar considerations forB2will give

B3not(True(“p”)and True(“notp”)).

A3is exactly the semantical version(3)of the law of excluded middle quoted above.SimilarlyB3is the semantical version(4′)of the law of non-contradiction.

There remains a question.What is missing to obtain the formalized version of these principles? A first element of answer is that,although the Mohist had some clear ideas and usages preparing formalization,they were quite normally still far from formal versions of logic.A complementary element of answer is that if you want to connect the semantic versions of the basic principles of the basic laws of logic with their formal expressions(p∨¬p)and¬(p∧¬p),you need a theory of truth satisfying principles such as:

True(“p”)iffp(Tarski’s convention T)([42]);

True(“(p ∧q)”)iff True(“p”)and True(“q”);

True(“(p ∨q)”)iff True(“p”)or True(“q”);

True(‘‘¬p′′)iff not True(“p”).

If such is the case,then you can prove thatA3andB3are equivalent to(p ∨¬p)and¬(p∧¬p)respectively.But this element of answer leads us to the much discussed theories of truth which are indeed very far from the Mohists’theory and practice([7]).

To summarize this discussion,we can say that a rigorous analysis of the Mohists’assertions shows us that they had dialogical versions of the basic laws of logic(versionsA1andB1,versionsA2andB2).The theoretically minded context of their use ofbianvalidates(DTT)and shows us that they had in fact a semantic version of these laws(versionsA3andB3).On the other hand,we have no reasons to think that they had a formal version of them.It is worth noting that dialogical versions of logic were revived by Lorenzen’s dialogues([21]).Game theory may also be considered as a powerful extension of these dialogues5See[36]for a general presentation and[19]for an application to the Mohist argumentation..

4 Definitions in Pre-Qin Logic

There does not seem to be much theoretical reflection on the status of definitions in pre-Qin logic.However,one could consider that Xunzi in his chapters 18Zhenglun(正论)and especially 22Zhengming(正名)establishes the preliminary elements of a theory of definition.An important clue is given by his technical usage ofming(命),meaning“naming”,“name”,“term”andqi(期),meaning“alignment”,“fixed period”,but also“procuring agreement”,which some authors([15,33])do not hesitate to translate by“defining”or“definition”.

Thus,18.366故凡言议期命是非，以圣王为师。links together 言,议,期,命which Knoblock translates:“Thus,as a general rule discussions[yan言]and deliberations[yi议]on definitions[qi期]and terms[ming命]of right and wrong,take the sage kings as your teachers[…].”

In the opening section 22.17后王之成名：刑名从商，爵名从周，文名从礼，散名之加于万物者，则从诸夏之成俗曲期，远方异俗之乡，则因之而为通。of chapter 22,Xunzi repeats that names were instituted by the Sage Kings,which applied the various names to all things,following the established custom and that this allowed people from different villages to communicate.Thus,procuring agreement is essential in the use of names and this is in accord with the practical use of definitions;when people do not understand each other or disagree on a notionX,they will often ask“what do you mean byX?”,“what is your definition ofX?”.When he speaks of“agreement”,Xunzi has certainly in mind the practical aim of guaranteeing a stable and ordered society,but“procuring agreement” has also the logical function of fixing the reference of terms,so that we are bordering here a theory of definition.In this connection,sections 22.88名无固宜，约之以命，约定俗成谓之宜，异于约则谓之不宜。名无固实，约之以命实，约定俗成，谓之实名。名有固善，径易而不拂，谓之善名。and 22.119实不喻，然后命，命不喻，然后期，期不喻，然后说，说不喻，然后辨。故期命辨说也者，用之大文也，而王业之始也。名闻而实喻，名之用也。累而成文，名之丽也。用丽俱得，谓之知名。名也者，所以期累实也。辞也者，兼异实之名以论一意也。辨说也者，不异实名以喻动静之道也。期命也者，辨说之用也。辨说也者，心之象道也。心也者，道之工宰也。道也者，治之经理也。心合于道，说合于心，辞合于说。正名而期，质请而喻，辨异而不过，推类而不悖。听则合文，辨则尽故。以正道而辨奸，犹引绳以持曲直。are especially important and we can recognize in them pure logical elements which must underlie a theory of definition,among which:

-names have no predetermined reference;

-the delimitation of their reference is given by(qi期)[procuring agreement/fixing/defining];

-the agreement/definition fixes what counts as same (tong同) and what counts as different(yi异)and so classifies things into categories(lei类);

-once the agreement is reached,people should keep to the fixed meaning;

-although the agreement/definition is somewhat arbitrary,there are good names,namely those who are straightforward,simple and nonambiguous;

-names can be combined to form compound terms having complex designations.

However,Xunzi is not fundamentally interested in logic and his embryonic theory of definition is essentially turned to the goal of reaching a harmonious society.Instead of looking for a theory of definitions in pre-Qin authors,we will have to turn to their practice to examine how they are using definitions.

Xunzi himself made an extensive use of definitions,very often signalled by the expressionssuowei(所謂),kewei(可谓),weizhi(谓之)orzhiwei(之谓)which have been studied in great detail by Cua in his[4],chapter 3,pages 88-137,and it seems clear that definitions and distinctions constitute an essential element of his methodology.However,my opinion is that there are better practitioners10I would not like to minimize Xunzi’s system of definitions or partial characterizations of notions,which is very rich from a philosophical point of view.However,from the formal point of view of the organization,it is rather complex and quite entangled.Thus,taking the well-known example of 22.2(“散名之在人者：生之所以然者谓之性；……