Analogies and Analogical Reasonings in the Mencius

Thierry Lucas

Abstract.The article starts from the idea that analogy is a relation of similarity between structures and applies it to analyze examples taken from the Mencius,exhibiting the hidden complexity of analogies and the non trivial use of analogical reasonings.The article also introduces the idea that moral reasonings and recommendations of pre-Qin thinkers very often deal with behaviors which may be qualified as“right”or“wrong”and lead to positive or negative recommendations.It is also shown that a liberal notion of analogy covers reasonings by appeal to the past,to the sacred texts as well as arguments of reciprocity and some aspects of metaphors.This formal presentation of analogies suggests their universal range and significance and lends support to the opinion that while there is a historical specificity of Chinese thinking and of Chinese logic,its characterization should nevertheless be found elsewhere than in the use of analogies.

1 Introduction

The use of analogies is perhaps the keystone of the different conceptions of“Chinese Logic”.One trend of thought maintains that analogical reasoning is what makes“Chinese logic”so unique and so different from“Western Logic”:many Chinese authors and quite a number of Western authors promote that opinion and they see in it a justification of the existence of a genuine Chinese logic.On the other hand,many Western authors and a number of Chinese authors maintain that analogical reasoning is a general feature of human reasoning,that it has been extensively used in China,but that it is also very frequent in the best writings of the best Western philosophers.On that account,we should probably speak of“Logic in China”rather than“Chinese Logic”.

There are good arguments,coming among others from cognitive sciences,to question the use of analogies as a distinct characteristic of Chinese thought(see for example[17]and[8])or arguing more generally against the“special logic thesis in Chinese philosophy”([18]).But we want to argue here from the point of view of logic and show that there is in analogical reasoning more logic than meets the eye.

There is in this quarrel a question of definition.If one takes a very strict definition of logic,say“the study of valid reasonings”or even more strictly“the medieval study of aristotelian syllogisms”,it is obvious that the distinction Chinese Logic vs Western Logic is fully justified.But if one takes a liberal definition of logic,say“the study of reasoning”,the distinction Chinese vs Western Logic is only a matter of convenience,which remains useful but has no fundamental justification1The same could be said of“Indian Logic”..It is true that one often distinguishes logic and argumentation;logic concentrates on the study of valid reasonings while argumentation concentrates on the study of plausible reasonings;logic will naturally be formal while argumentation will have to take into account the content of the assertions.The present author thinks that that distinction is not clear enough to be usefully maintained.A first justification of that opinion is that inside formal logic,the notion of validity depends on the standard of rigor which you adopt:e.g.intuitionists do not accept the law of excluded middle and reject it as not valid,while classical logicians consider it as fundamental;on the other hand,the adepts of paraconsistent logic will gladly accept some contradictions,something which is unthinkable for classical logicians.A second argument is that the distinction formal logic vs informal argumentation is not as strong as could be thought at first sight:the study of defeasible reasonings,of non monotonic logics,of artificial intelligence,of computer modelling all include formal aspects and formal techniques which constitute a transition from the purely mathematical aspects of classical logic to the most qualitative evaluation of everyday reasonings2See[6]for a fuller presentation of the problem..

Since it is so important for the study of pre-Qin Chinese authors,analogical reasoning is a type of argumentation which is worth being studied in detail and we believe that a concrete case by case approach of the phenomenon may help to advance the study of the subject.In this article,we concentrate on analogies in theMenciusand present a general scheme which covers most if not all analogies and reasoning by analogy which are found in the text.This scheme is far from being a full formalization of analogies,but it constitutes a simple formal frame which forces one to exhibit the structure of the reasoning,often including its hidden assumptions and its unexpressed conclusions;it may also be used to compare the logical style of different authors,for example,we occasionally compare here Confucius’AnalectsandMencius’ text in that respect.We hope that this partially formal analysis will convince the reader that,whereas the notion of“Chinese Logic”is dubious,there is much interesting logic in pre-Qin Chinese authors.This is true in particular of Mencius,who,after having been considered as argumentatively very poor (see the often quoted [20,p.194]and [7,p.188 sq]),was on the contrary praised in articles such as[10,16]and more recently[2,9,15]and many others.For a general presentation of Mencius,see[3]or[19].

Translations are generally taken from the universally accessible [12],but we have also used[1,5,11,4]and their comments.

2 Analogical Structures

Analogies are often—but not always—used when one wants to explain an unknown structure by comparing it to a supposedly well known structure.A first basic example is often expressed by the motto“ais tobwhata′is tob′”.A famous canonical example of this is the analogy used by Confucius(Lunyu12.19)and quoted almost literally by Mencius:

Example 1

“The relation between superiors and inferiors is like that between the wind and the grass.The grass must bend,when the wind blows across it.”(Mencius3.A.2)

In this case,and accepting some simplifications,the supposedly unknown structure is given by two individuals(in the logical sense of the term)and a relation:

The familiar structure is given by

The relationRis explained by comparing it to the relationR′and all readers will understand that the relationRis thatbmust obeya:bis toaasb′is toa′;we put into square brackets the description which follows implicitly from the analogy.A scientific analogy which has a similar structure and had a tremendous success is the famous analogy of the structure of the atom with the structure of the solar system,with atoms turning around a nucleus like planets orbiting the sun.But many analogies go beyond the simple scheme of the motto.A famous didactical analogy is that of electricity with water in a pipe,relating potential with height,intensity with quantity of water,resistance with friction,etc.In Chinese pre-Qin literature we find also seemingly simple but in fact quite elaborate analogies.Here are two examples taken fromMencius,which we analyze with more details below:

Example 2

“Mencius said,‘a bad year cannot prove the cause of death to him whose stores of grain are large;an age of corruption cannot confound him whose equipment of virtue is complete.’”(Mencius7.B.10)

Example 3

“Mencius said,‘Bo Yi among the sages was the pure one;Yi Yin was the one most inclined to take office;Hui of Liu Xia was the accommodating one;and Confucius was the timeous one.

In Confucius we have what is called a complete concert.A complete concert is when the large bell proclaims the commencement of the music,and the ringing stone proclaims its close.The metal sound commences the blended harmony of all the instruments,and the winding up with the stone terminates that blended harmony.The commencing that harmony is the work of wisdom.The terminating it is the work of sageness.’”

(Mencius5.B.1)

This sets the problem of clarifying the notion of structure.Logicians often use the notion of first order structures.A first order structure is a set with distinguished elements,functions and predicates on the set,for example the set of natural numbers,the distinguished elements 0 and 1,the binary functions of addition and multiplication,the predicate“being a prime number”,the binary relation“less than or equal”.A more informal but slightly simplified similar example is given by the set of men,the distinguished elements Caesar and Qin Shi Huang Di,the predicates“is an emperor”and“lives in India”and the binary relation“lives longer than”.But we need not limit our definition to first order structures.A liberal definition will admit predicates of predicates such as“having all properties satisfied by emperors”,or modifiers of predicates such as the one given by adverbs which transform predicates into new predicates(“prematurely”transforms the predicate“die”into the predicate“die prematurely”),etc.The following definition of structure will be enough for our purpose:a set equipped with all kinds of elements,functions,predicates,predicates of functions,predicates of predicates,modifiers of predicates and so on.The important point is that each ingredient of the structure be associated with a clearly defined syntactic category,because analogies have to relate ingredients of the same category:elements with elements,n-ary predicates withn-ary predicates,n-ary functions withn-ary functions,modifiers of unary predicates with modifiers of unary predicates,etc.It will be enough for our purpose to see structuresSas setsEequipped with ingredientsa1,a2,...,an;notation:S=〈E,a1,...,an〉.

This leads us to the following presentation:an analogysim(for“is similar to”)or similarity relation from structureS=〈E,a1,...,an〉to structureis given by a binary relation fromEtoE′and more generally from the ingredients ofSto the ingredients ofS′of the same syntactic category(n-ary predicates ton-ary predicates,n-ary functions ton-ary functions,etc.),satisfying

We will require that the identity relation on the domain of a structureSbe an analogy fromStoSand that the inverse relation of an analogy fromStoS′be an analogy fromS′toS.Since our analyses,when dealing with two structures,will only consider one fixed analogy from one structure to the other structure,there is no harm in writing thatsimis a binary relation between structures which is reflexive (S sim S)and symmetric (ifS sim S′,thenS′ sim S).Symmetry is a natural assumption,but practically speaking,one of the structures,sayS,is often supposed to be explained,while the other structure,S′,is a familiar well known structure.When symmetry is dropped,we may have more general definitions,but we will not use them here.In the opposite direction,when dealing with clear-cut ingredients,we could also require that the composition of analogies be an analogy,makingsima transitive relation,but when dealing with fuzzy ingredients such as shades of color,this would lead us to soritestype pardoxes:this shade of green is similar to that shade of green-blue which in turn is similar to that shade of blue,leading us to the possibly unacceptable conclusion that this shade of green is similar to that shade of blue.To finish this short discussion of the formal features of analogies,we add that a precise definition will require that the relation be compatible with the syntactic nature of the ingredients;for example,if the elementais similar toa′andfis a unary function similar tof′,we will assume thatfais similar tof′a′;or ifais similar toa′,bis similar tob′andRis a binary relation similar toR′,we will assume thatRabif and only ifR′a′b′.We leave the technical details out of consideration here.

Usual analogies may be sometimes difficult to present in that way,especially when they use quantifier words such as“some”,“all”,“many”,“a few”,“a”,but we will boldly leave aside these difficulties and rely on the natural idea of term-to-term correspondence which is embodied in the definition.In our examples,the domains will remain undefined:it suffices that they contain the distinguished elements and be closed under the distinguished functions.Note also that given a concrete analogy,there is more than one way to analyze it,exactly as when you formalize a proposition,exposing more or less structure according to the necessities of the case.The point is that we think that these notions are already precise and rich enough to clarify the structure of explicative analogies,analogies which do not involve reasoning but clarify structureSby declaring it similar toS′.Such is the example of Confucius’analogy:

Example 1(revisited)

The analogy is given by the declarations of analogy

and the explicative power of the analogy lies in these declarations.

Examples of that elementary type are frequent inMencius:“The people turn to a benevolent rule as water flows downwards,and as wild beasts fly to the wilderness.”(Mencius4.A.9);“the people would flock to the ruler as water flows downwards with a rush”(Mencius1.A.6).

But when analyzed in detail,examples of that type often show more complexity,involving quite precise term to term comparisons.Here is an example which involves the detailed comparison of many ingredients:

Example 4

“A bad year cannot prove the cause of death to him whose stores of gain are large;an age of corruption cannot confound him whose equipment of virtue is complete.”(Mencius7.B.10)

Example 5

Another example is given in 5.B.1 comparing the complete harmony of Confucius,his wisdom,his sageness,with a complete concert,with its bell and ringing stone:

In theLunyu,there are many such analogies,sometimes very complex as inLunyu19.23(see[14]),but they are generally restricted to their descriptive,explicative use.Reasoning on analogies is at best implicit,in that one must fill the missing ingredients to complete the description of the relation of similarity.From the point of view of logic,what distinguishes Mencius from Confucius is the explicit use of analogies in reasoning,to which we now turn.

3 Analogical Reasoning

Let us begin with a rather simple but very nice example of the use of analogical reasoning.This is the opportunity to repeat that we do not confine the analogies to the explanation of abstract structures by supposedly more familiar structures(contrast this with e.g.[17]).The analogy in the following example is given by a relation between equally understandable structures,having exactly the same level of abstraction.

Example 6

“Chen Zhen asked Mencius,saying,‘Formerly,when you were in Qi,the king sent you a present of 2,400 taels of fine silver,and you refused to accept it.When you were in Song,1,680 taels were sent to you,which you accepted;and when you were in Xue,1,200 taels were sent,which you likewise accepted.If your declining to accept the gift in the first case was right,your accepting it in the latter cases was wrong.If your accepting it in the latter cases was right,your declining to do so in the first case was wrong.You must accept,Master,one of these alternatives.’”

(Mencius2.B.3)

Logically speaking,this is a simple but remarkable use of an assimilation of cases,followed by a kind of dilemma,which is well worth being explained in detail.Although the analogy is not used here to explain an obscure structure by a supposedly well known structure,there is no doubt that we have an analogy of three structures in the sense defined above,and even one in which transitivity of the relation may be safely assumed.Here is a presentation of them.

Note first that in factais the same asa′anda′′,andGis the same asG′andG′′,so that the assimilation of cases bears onb,b′,b′′,and onQ,Q′,Q′′:the amounts of money are not differentiated and similarly the situation are considered analogous.We keep however the notation to exhibit the full declaration of analogy:

Now comes the reasoning by analogy.Since situations given by structuresS,S′andS′′are similar,what happens in one of them should also happen in the other two.Let us now introduce the behaviorsBeh(S),Beh(S′),Beh(S′′)associated with these situations:

(1)inS:when Mencius was in Qi,hedid notaccept a gift of 2400 taels,something which we can represent by the formulaBeh(S)=notAab;

(2)inS′:when Mencius was in Song,he did accept a gift of 1680 taels,which may be represented asBeh(S′)=Aa′b′;

(3)in situationS′′:Beh(S′′)=Aa′′b′′(as inS’).

In the present case,since behaviors are described by clear-cut predicates“to accept”and“to refuse”,we may admit that such behaviors may be qualified as Right,may be negated and for all structuresS*(S*stands forS,S′andS′′)involved here obey

(*)Right Beh(S*)andRight not Beh(S*)are incompatible;

(**)one of the sentencesRight Beh(S*)andRight not Beh(S*)must be true.3We do not want to convey the idea that in general,behaviors may be negated,may all be qualified as right or wrong and above all obey non-contradiction and excluded middle laws such as(*)and(**).Besides right and wrong behaviors,we should admit neutral ones and we should perhaps even allow behaviors which at the same time are right and wrong: Mencius’ 4.A.17 sets the question of a man rescuing his drowning sister-in-law by holding her hand,a clear example of a conflict of norms by standards of the time.This issue is too complex to be discussed here,but is certainly an interesting theme of research not only in general,but also in the specific case of Mencius.

In the case ofS,eitherAabisRightor notAabisRight,i.e.either it is right for Mencius to accept the gift of 2400 taels or it is right to refuse it;similar considerations apply toS′andS′′.To simplify the analysis,we keepS′′out of consideration and we observe that the reasoning may be reconstructed essentially on the basis of the well known rule of analogy,essentially a transfer of a property Φ concerningS′toSaccording to the following schema:

FromS sim S′,Φ(S′),deduce Φ(S)(Rule of analogy)

This rule translates the idea that in analogical situationsSandS′,what holds ofS′should also hold of S;we will say that property Φ transfers fromS′toS.It is well known that such a rule is not valid in general(see next section),but it gives the essence of reasonings by analogy.It is worth remarking that some logic texts dealing with the rule of analogy restrict the transfer of properties to the so-called relevant properties.There are two major drawbacks to that approach;the first one is that it is already concerned with the reliability of the reasoning,a question which should be separated from the pure form of the reasoning;the second one is that the notion of relevance is desperately unclear,unless you give such restrictions as to make the rule of analogy automatically valid.We prefer to keep the rule as it stands,considering the question of relevance as a not purely formal element to be used to criticize the application of the rule(see(Ref 1)and example 9 here below).

The reasoning ofMencius2.B.3 may then be reconstructed as follows:

(i)IfRight Beh(S),this means

Right not Aab,

Right not Aa′b′by transfer ofRight not AabfromStoS′,i.e.

not Right Aa′b′by(*),i.e.

not Right Beh(S′).

(ii)IfRight Beh(S′),we derive symmetrically

Right Aa′b′,

Right Aabby transfer ofRight Aa′b′fromS′toS,i.e.

not Right not Aabby(*),i.e.

not Right Beh(S).

Note in fact that(ii)repeats(i)up to a contraposition.Even more simply,we can say that(i)and(ii)are different presentations of the incompatibility ofRight Beh(S)andRight Beh(S′).

We still have to explain the dilemmatic structure by showing that (1)and (2)constitue an alternative.This is done using(**):

Right not AaborRight Aab.

By transfer ofRight AabfromStoS′,we have

Right not AaborRight Aa′b′,i.e.

(iii)Right Beh(S)orRight Beh(S′).

This reconstruction aims at following the text as closely as possible,but the clear import of the argument is that there is a“contradiction in behaviors”.To see this,we claim that in similar situations the behaviors should be similar and similarly appreciated:

(iv)FromRight Beh(S),we should deriveRight Beh(S′)by transfer fromStoS′.

(iv′)FromRight Beh(S′),we should deriveRight Beh(S)by transfer fromS′toS.

Now,from(i)and(iv),we derive thatRight Beh(S)leads to a contradiction(not Right Beh(S′)andRight Beh(S′));this provesnot Right Beh(S).Symmetrically,from (ii)and (iv′),we provenot Right Beh(S′).In this way,we obtainnot Right Beh(S)andnot Right Beh(S′),contradicting (iii).In words:one of the behaviors should be right,but no one is!

Note that our presentation of the scheme of analogical reasoning is accurate enough to prove that it obeys some elementary logic.We mention the following ones,which are typical and routine consequences of the definition:

(1)If Φ transfers fromS′toS,then not Φ transfers fromStoS′;

(2)If Φ and Ψ transfer fromS′toS,then the conjunction Φ and Ψ transfers fromS′toS;

(3)If Φ and Ψ transfer fromS′toS,then the inclusive disjunction Φ or Ψ transfers fromS′toS;

(4)If Φ is a logical tautology,then it transfers fromS′toS;

(5)If Φ is a logical contradiction,then it transfers fromS′toS;

(6)If Φ and Ψ are logically equivalent and if Φ transfers fromS′toS,then Ψ transfers fromS′toS.

Similar considerations apply to quantifiers but need more elaborate formulations.4To avoid possible misunderstandings,we do not claim here that if Φ and Ψ represent right behaviors Right Beh1and Right Beh2in S′,then their conjunction represents a right behavior Right (Beh1and Beh2)in S′;in such a case,the rule simply states that if the proposition((Right Beh1)and(Right Beh2))holds in S′,then it also holds in S.In(Beh1and Beh2),we have a conjunction of behaviors,whatever that means,while in((Right Beh1)and(Right Beh2)we have a usual conjunction of propositions.

Now,what are the possible critiques that can be made to a reasoning by analogy?We discuss this in the next section.

4 Critiques of Analogical Reasonings

Our presentation of the rule of analogy makes it clear that there are three ways of criticizing such a reasoning:

(Ref 1)(Refutation ofS sim S′)We can refuse to accept the premisses in a first way:we refuse the assimilation of structures by claiming that at least one ingredient of structureSis not similar to the corresponding ingredient of structureS′;

(Ref 2)(Refutation of Φ(S′))We can refuse to accept the premisses in a second way:while accepting the similarity of structures,we claim that property Φ(S′)does not hold;

(Ref 3)(Refutation of transfer of Φ)We accept the premisses,i.e.S sim S′and property Φ (S’),but we claim that Φ is not the kind of property which it is reasonable to transfer fromS′toS.

As a first actualized illustration of these techniques,let us imagine three critiques of the planetary model of the atom:(Ref 1)we refuse the planetary model and claim that atoms are similar to indivisible points;(Ref 2)we accept the planetary model but insist on the fact that the orbits of the electrons are not ellipses,but perfect circles;(Ref 3)we accept the planetary model with elliptic orbits but(rightly—if we accept quantum theory)claim that Newton’s law does not transfer as such.

Here are examples of the three techniques taken from theMencius.

Example 7Application of(Ref 1).Refutation ofS sim S′.

In the well known dialogue withGaozi6.A.2,we find a good example of a refutation of similarity of structures.Gaozi compares here human tendency towards good or bad to water going east or west indifferently;to this,Mencius opposes the analogy of water naturally going down and going up only when forced.

The analogical reasoning of Gaozi is given by the rule of analogy applied to structuresSandS′and to the following Φ:

Φ(S′)=T′a′b′orT′a′c′indifferently(water goes east or west indifferently)

which by transfer fromS′toSgives:

Φ(S)=TaborTacindifferently

The analogical reasoning of Mencius is based on the similarity of structuresSandS′′and to the following Φ:

Φ(S′′)=T′′a′′b′′naturally andT′′a′′c′′against nature (water goes naturally down and not naturally up)

which by transfer fromS′′toSgives:

Φ(S)=Tabnaturally andTacagainst nature.

Note also that in dialogues,it is in general a good tactic to keep unchanged as many ingredients of the first similarity as possible:in the present case,a′anda′′are identical;T′andT′′are identical;the change is inb′,b′′and inc′,c′′.

Example 8Application of(Ref 2).Refutation of Φ(S′).

In the opening dialogue 6.A.1,Gaozi compares the fashioning of human nature by benevolence and righteousness with the manufacturing of a cup from a willow tree and Mencius replies by criticizing the truth of the property to transfer:manufacturing a cup from the willow violates the nature of the willow.

The analogical reasoning of Gaozi is given by the rule of analogy applied to structuresSandS′and to the following Φ:

Φ(S′)=fashioningb′out ofa′agrees with the nature ofa′,which by transfer fromS′toSgives:

Φ(S)=fashioningb′out ofa′agrees with the nature ofa′,The structure proposed by Mozi is the same asS′,but property Φ′(S′)is criticized and in fact negated:fashioning a cup out of willow does violence to the nature of the willow and Mozi proposes the transition of property Ψ,which is in fact the negation of Φ:

Ψ(S′)=fashioningb′out ofa′violates the nature ofa′.hence

Ψ(S)=fashioningbout ofaout of a violates the nature ofa,

Example 9Application of(Ref 3).Refutation of transfer of Φ.

In our example 6,Mencius could refuse to assimilate the amounts of moneyb,b′,b′′,or refuse to assimilateQ,Q′andQ′′.His answer in fact shows that he agrees with the similarity of structures:his answer does not mention the different amounts of money;it does not question the fact that there is a similarity in his staying in the different countries;what he refuses is the transition the formulaRight not Aab;he maintains that one hasRight not AabandRight Aa′b′;it is also interesting to note that his justification uses the notion of purpose:A′a′b′is justified by the fact that the the giftb′was morally good(a present to cover his travel expenses),whilebwas morally wrong(a bribe).

5 Critiques of Complex Reasonings Using Analogies

Let us now look at more complex reasonings using analogies.A good example is given once again in the dialogues with Gaozi,in 6.A.4,from which we extract the following:

Example 10

“[Gaozi:]‘There is a man older than I,and I give honour to his age.It is not that there is first in me a principle of such reverence to age.It is just as when there is a white man,and I consider him white;according as he is so externally to me.On this account,I pronounce of righteousness that it is external.’

Mencius said,‘There is no difference between our pronouncing a white horse to be white and our pronouncing a white man to be white.But is there no difference between the regard with which we acknowledge the age of an old horse and that with which we acknowledge the age of an old man? And what is it which is called righteousness? The fact of a man’s being old? Or the fact of our giving honour to his age’.”

(Mencius6.A.4)

Gaozi wants to prove that benevolence is internal and righteousness is external and he justifies his claim by calling an analogy between structureSandS′

The analogical reasoning of Gaozi is based on the similarity ofSandS′and on the following property Φ:

Φ(S′)=T′a′b′O′is external.

which by transfer gives

Φ(S)=TabOis external.

The assertionT′a′b′O′seems to be preceded by a reasoning essentially amounting to:

O′is external,

hence

T′a′b′O′is external.

The reasoning is also implicitly completed by a natural generalization:

TabOis a typical example ofYi義,

hence

Yiis external.

The first objection of Mencius is to criticize the similarity.His move is to start from the given analogy but to show its absurdity by bringing in two other structures and two analogies essentially obtained by substituting“horse”to“man”in Gaozi’s analogies.

Mencius accepts the analogyS sim S′proposed by Gaozi but adds the analogiesS′sim S′′′(replacing“man”by“horse”inS′)andS′′′sim S′′and(replacing“man”by“horse”in Gaozi’s analogyS sim S′);these similarities give the assertions that

TabO sim T′a′b′O′:to treat a man as old is similar to treat a man as white(Gaozi)

T′a′b′O′sim T′′′a′′′b′′′O′′′:to treat a man as white is similar to treat a horse as white(Mencius)

Ta′′′b′′′O′′′ sim Ta′′b′′O′′:to treat a horse as white is similar to treat a horse as old(Mencius on the model of Gaozi’s similarityS sim S′)

From these,Mencius derives by transitivity:

TabO sim Ta′′b′′O′′:to treat a man as old is similar to treat a horse as old(Mencius)

This consequence is considered absurd by Mencius and should also be accepted as such by Gaozi.

Going from this example to general considerations,we may say that there is in this reasoning a powerful argumentative instrument but also a weakness.The powerful instrument is given by a rule of substitution applied to the similarityS sim S′to obtain the similarityS′′ sim S′′′,making the apparently innocent replacement ofb(which is the same asb′)byb′′(which is the same asb′′′).This has a natural justification:if your reasoning has a sufficiently universal value,it should apply to similar reasonings obtained by substitution;such is indeed the case in most systems of logic.The weakness is that it applies a rule of transitivity to the relation of similarity;but a critical eye will soon refuse to apply such a rule here,maintaining the idea that one should distinguish three similarity relations,the similarity proposed by Gaozi and the two similarities proposed by Mencius.A more precise notation of the analogies should make it clear that in his reasoning Mencius uses three different similarity relations:S sim1S′(proposed by Gaozi),S′ sim2S′′′(proposed by Mencius)andS′′′ sim3S′′(proposed by Mencius by substitution in Gaozi’s),and applies a transitivity which amounts to the hidden assumption that the composition ofsim1,sim2andsim3gives again a similarity relation fromStoS′′.

The second critique of Mencius is to object to Φ(S′);he does not accept thatOis typicalYibut accepts thatTabOis typicalYi;he says in fact that it isOthat is external but thatTabOis internal;it is our treatment of a man as old that isYi,not the pure fact that he is old;our treatment is internal,the pure fact is external.

Note that other reasonings in the dialogue with Gaozi may be analyzed along similar lines.

6 Analogies and A Fortiori Arguments,Analogies and Reciprocity Arguments

In general a fortiori arguments elaborate on an analogy.Let us look at the proverbial“climbing a tree to seek a fish”(緣木求魚)example (Mencius1.A.7),which compares the desire of the King Hui of Liang to enlarge his territory by war to the desire of finding a fish in climbing a tree:

Example 11At the basis of this there is a descriptive analogy clarifyingSbyS′:

The analogy is of course accompanied by an implicit reasoning based on the common knowledge that there are no fish in trees so that climbing on a tree to capture a fish is a useless action,which may be represented byUseless W′a′b′.By the the rule of analogy,this is a property Φ which may be transferred toSand gives the result thatUseless Wab:it is useless to make war to enlarge one’s territories.

This reasoning is immediately followed by a fortiori argument,claiming that the situation described bySis worse than the situation described byS′,the argument being thatS′has bad consequences whileShas none.The final conclusion will be given by an implicit use of the rule of analogy:

not Right Wa′b′;

hence

not Right Wab;

This is typical of a general situation.A fortiori argument supposes the analogy of two structuresSandS′.There is an additional information that (the situation described)inSis worse than(the situation described in)S′and the application of a rule of the following type:

S worse than S′,not Right(S′);hencenot Right(S).

Symmetrically,we have a positive a fortiori,based on the information that

S better than S′,Right(S′);henceRight(S).

The additional informationsSworse thanS′andSbetter thanS′are very often given by looking at the consequences generated by the behaviors present inSand inS′.In a first theoretical approach,both relations would be supposed to be irreflexive and inverse of one another.

Other examples of a fortiori may be found at the beginning of 2.B.9(combined with a dilemma)and in 6.A.14.

Let us also mention that reciprocity arguments such as the one given in the socalled golden rules are formally speaking analogy arguments;their structure could be described as a similarity of simple structures such as the following:

The transfer bears on a behavior relating the first element of the structure to the second element of the structure,e.g.:Ra′b′is“a′behaves nicely with regard tob′”.This property gives rise to the judgmentRight R′a′b′which by transfer toSwill giveRight Rab,from which one will naturally deriveRecommended Rab.In words:my behavior with respect to you should be nice as yours is to me.

Clear examples of this kind of reciprocity are given in 1.B.4 (“When a ruler rejoices in the joy of his people,they also rejoice in his joy;when he grieves at the sorrow of his people,they also grieve at his sorrow.”),in 1.B.12(in years of calamities,many people were not defended by the superiors of the state and died;nonetheless,no people put the superiors to death;similarly,in a battle,King Hui’s officers were not defended by the people;by analogy,those people should not be put to death)and in 4.B.28(“He who loves others is constantly loved by them.He who respects others is constantly respected by them.”)

7 Proverbs,Examples from the Past,Reciprocity

Pre-Qin authors like to refer to the examples of the Sage-Kings or heroes of the past(Yu,Yao,Shun,Tang,King Wen,Zhou gong,etc.)opposing them to the Wicked Kings (Jie,Zhou).They like to quote ancient texts and give them interpretations which are usually very far from the original interpretation.These techniques have a certain argumentative force for people of the time,but it is important to realize that this force takes effect via analogies.Here is a very basic example,structurally the same as our example 1:

Example 12

“Mencius said,‘The compass and square produce perfect circles and squares.By the sages,the human relations are perfectly exhibited.He who as a sovereign would perfectly discharge the duties of a sovereign,and he who as a minister would perfectly discharge the duties of a minister,have only to imitate—the one Yao,and the other Shun.He who does not serve his sovereign as Shun served Yao,does not respect his sovereign;and he who does not rule his people as Yao ruled his,injures his people.’”(Mencius4.A.2)

We first have an analogy between structuresSandS′,comparing the way Sages exhibit the human relation to the way compasses and rules trace perfect circles and perfect squares.We leave to the reader the analysis of these simple analogies.We then continue with Yao and Shun as the perfect examples of ruler and minister;the implicit analogy being given by:

WithS′is associated the behaviorR′a′b′,and it is the characteristic of the use of exemplary persons that this behavior is automatically considered asRight.We thus have the assertion

Right Beh(S′),i.e.Right R′a′b′.

Hence by the similarityS sim S′and transfer fromS′toS,

Right Rab.

This is naturally followed by an implicit recommendation:

Recommended Rab.(R1)

In general,the appeal to examples of the past or to sacred texts(structureS′)to explain structureShas exactly the same form:

Right Beh(S′),

Hence by the similarityS sim S′and transfer fromS′toS

Right Beh(S).

Hence

Recommended(S)

Symmetrically,we have a negative rule associated with unexemplary persons:

not Right Beh(S′).

Hence by the similarityS sim S′and transfer fromS′toS

not Right Beh(S).

This is naturally followed by an implicit negative recommendation:

Avoid Beh(S).(R2)

Here is now an example of the frequent use of proverbial expressions or selections of highly respected books of the past,which were often attributed to Confucius,in particular theShijing:

Example 13In 3.A.4,Zixia,Zizhang and Ziyou observing the resemblance of Youruo with Confucius,want to abandon Zengzi,the legitimate heir of Confucius to turn to the heretical Youruo.Zigong deters them with two apparently proverbial expressions and a quote from theShijing:

“This may not be done.

What has been washed in the waters of the Jiang and Han,

and bleached in the autumn sun

how glistening is it! Nothing can be added to it.

I have heard of birds leaving dark valleys to remove to lofty trees,

but I have not heard of their descending from lofty trees to enter into dark valleys.

In the Praise-songs of Lu it is said,

‘He smote the barbarians of the west and the north,

He punished Jing and Shu.’

Thus Zhou Gong would be sure to smite them,

and you become their disciple again;

it appears that your change is not good.”(Mencius3.A.4)

The comparison of the Master with what has been washed in pure waters and bleached in the sun is a very elementary explicative analogy involving the almost simplest type of structures:

The second analogy is given by the following structures:

and it is argued as described in(R2):

not Right A′a′b′c′;

hence by analogy

not Right Aabc.

followed by the negative recommendation:

Avoid Aabc.

The third analogy is given by structuresSandS′′:

and it is also argued as described in(R2):

not Right A′′a′′b′′c′′;

hence by analogy

not Right Aabc.

followed by the negative recommendation:

Avoid Aabc.

8 Metaphors

In the traditional view,metaphors presuppose analogies and they are more implicit than analogies;analogies would be introduced by words of comparison,while metaphors would not:compare the metaphorical“Richard is a lion”with the analogical“Richard is as a lion”.This approach has its literary virtues:the metaphor cannot be literally understood(Richard is not a lion!)but comes with a semantic shock identifying humans and wild animals,two generally foreign semantic domains,while the analogy may be literally understood;note however that to understand this analogy,one has to know the cultural element that lions are considered to be courageous.

Our opinion is that there is a smooth transition from the most explicit analogies to the most implicit metaphors.We do not want to enter here into a discussion of the difference,but we present the idea that metaphors are generally given by concrete notions which tend to constitute an inexhaustible reservoir of analogies.Such is the case of the Dao,which is omnipresent in Chinese thought:it ranges from the strictest material sense of“road”to the notion of“way of”(attaining something),behavior,doctrine,virtue,etc,but remains a source of many analogies.The metaphorical uses of Dao are for Confucius’Lunyuan important source of inspiration:difficulties to reach virtue are analogous to difficulties on the road;who is tired may always take a rest but should not renounce going on;there are dangerous detours;it is a tiring task;the road may be long and the burden heavy;etc.(see[13]).For Mencius who has already a much more transparent use of reasoning,the metaphorical use of Dao does not have the same weight as for Confucius,but this does not mean that there are no important sources of analogies inMencius;Dao remains one of them,Sprouts—extremities端are often mentioned but with a limited number of occurrences in the bookGaozi.On the other hand,Water 水and Wood 木are certainly worth being mentioned.Let us look at the case of Water by systematically examining all its occurrences:

(1)In 1.A.6,people flow to the good ruler as water flows downward with a rush(see above).

(2)[In 1.B.5,water has a literal meaning,but comes in a quotation of theShijing,which is as usual interpreted in an analogical sense.]

(3)In 1.B.10,1.B.11,3.B.6,bad government is assimilated to water and fire (水火）;deeper water and fiercer fire will bring in a revolution.

(4)In 3.A.4,3.B.9,in the time of Yao,the world was not yet ordered;this disorder is associated with inundations by vast waters(洪水);Yu domesticated the waters and order was installed.

(5)In 4.A.8,the use of the water of the Cang Lang,pure or muddy,is very metaphorically(and not too clearly)associated with the use of reason to convince a ruler.

(6)In 4.A.9,people turn to a good rule as water flows downward.

(7)In 4.B.18,water coming from a source is inexhaustible,coming fom the sky in the seventh and eigth month it does not last;similarly,it is better for true sages to have lasting true merits than ephemerous fame.

(8)In 4.B.26,Yu domesticated the waters following their natural courses;similarly,intelligence should follow its spontaneous course to become great wisdom(see[5]).

(9)In 6.A.2(Gaozi),water going East or West indifferently or naturally going down is compared with the natural tendencies to good or bad(see discussion above).

(10)In 6.A.5 (Gaozi),drinking fresh water or a hot liquid depends on the season;the dialogue between Jizi and Gong Du associate it with respect depending on external circumstances(“what is outside”).

(11)In 6.A.18 (Gaozi),‘Benevolence subdues its opposite just as water subdues fire’;but a simple cup of water will not extinguish a big fire and will be lost;similarly,a small amount of benevolence will not be enough to subdue its opposite and will be lost.

(12)[In 6.B.11 (Gaozi),Yu domesticates the waters according to their nature and avoids inundations,which is a waste of water;Bai Gui inundates the neighbouring states and does not respect the nature of water;this is contrary to benevolence,he should follow the example of Yu.There is perhaps here a literal meaning,but the comparison with Yu sets it in a context of analogies(see above,analogies underlying the use of examples of the past).]

(13)In 7.A.23,water and fire are a necessity for life,they should be abundant and people will gladly share them with everybody;similarly in the good government of the kingdom by the sage,resources should be abundant and people will automatically become virtuous.

(14)In 7.1.24,The doctrine of the Sage is like the vast waters of the sea which one contemplates;the doctrine of others are like smaller waters,which one forgets when looking at the sea;the student who wants to learn the doctrine of the Sage should do it progressively as water filling the hollows in its course.

(15)In 7.B.14,overflow of water is again associated with disaster.

9 Conclusion

We started from the idea that analogy is a relation of similarity between structures.A careful examination of examples taken fromMenciusshows the formal interest of an analysis of analogies and of analogical reasonings.It is useful to exhibit the hidden complexity of some elaborate analogies,the non trivial use of analogical reasonings,especially in combination with some purely logical reasonings such as dilemmas or argumentative reasonings such as generalization;it also has the virtue of forcing one to exhibit some hidden premisses or unexpressed conclusions.Since moral reasonings and recommendations are so important for the analysis of pre-Qin thinkers,we have also introduced the idea that those reasonings very often deal with behaviors which may be qualified as“right”or“wrong”and lead to positive or negative recommendations.We have also shown that with a liberal notion of analogy,we cover reasonings by appeal to the past,to the sacred texts as well as arguments of reciprocity.

We have tried to keep our analysis as formal and as simple as possible.This does not mean that considerations of content are unimportant,but we think that a preliminary step is to get an accurate understanding of the formal structure of arguments:before appreciating the convincing character of the dialogues with Gaozi,it is important to understand their articulation.We should also repeat that formal analyses need simplifications and that deeper formal analyses are not only possible,but highly desirable.We think also that a formal presentation of the analogical arguments exhibits their universal range and significance:there is a historical specificity of Chinese thinking and of Chinese logic,but its characterization should be found elsewhere than in the use of analogies.