Text and Translation

Abstract

The chapter presents text, translation and commentary for the 68 sections of the Mohist Canon on which our analysis in the preceding chapter is based. The topics of the sections range from epistemological foundations via the consideration of logical, set-related and spatio-temporal conditions of knowing to themes in optics and mechanics.

3.1 Epistemological Foundations, A 1–A 6

The Mohist Canon starts out with six sections identifying fundamental notions of argument and knowledge, in this way defining terms that will figure either directly or indirectly in subsequent parts of the text.

A 1 introduces the concept of ‘basis’, which can be understood as a condition for something to come about.

A 2 introduces the concept of ‘element’ as a part of a composite whole, which has already been used in the Explanation of A 1, and which reoccurs in later sections (A 61 and A 67 in our selection).

A 3–A 6 describe different kinds of knowing and thinking: ‘knowing’ as an innate capacity (A 3), ‘thinking’ as starting from this innate knowledge (A 4), ‘knowing’ as having experienced something, again based on innate knowledge (A 5), and ‘wisdom’ as having applied one’s knowledge in discussing a thing and therefore seeing it more clearly (A 6). These concepts of knowing are not used in the later scientific sections, but they show the Mohists reflecting about different sources of knowledge. In particular, they distinguish a given capacity for knowing, which is also the basis of thinking, experience as a source of knowledge and (rational) discourse as a means of further developing and refining one’s knowledge. Acquiring knowledge through the senses is differentiated from having experiential knowledge itself, as illustrated in B 46 (which is not included in our selection) with respect to knowledge gained through the senses.¹ The Mohist also recognizes the fact that, until you can give a name to what you do not know, you do not know that you do not know it.² Both B 46 and B 48 are propositions, not definitions, and are thus set apart from the opening definitions. Section A 80 deals with how one may come to know something and how to act on that, distinctions that are conceived of as introducing ambiguity into the meaning of the term. This likely accounts for its placement at the end of the definitions, among those sections that explain other ambiguous terms (see Chap. 4).

A 1

C::

故, 所得而後成也。

E::

故:小故, 有之不必然, 無之必不然。 體也^a。 若有端。大故, 有之必然^b。若見^c 之成見也。

C::

gù ‘basis’ is what must be the case before something will come about.

E: :

gù ‘basis’: Minor basis: having it does not entail the inevitability of (a certain thing) becoming so. Lacking it does entail the inevitability of (the same thing) not becoming so. It is an element, like having an ‘end-point’. Major basis: having it entails the inevitability of (a certain thing) becoming so, like the fact of something becoming visible entailing someone seeing it.

• (a) R: 體也; Graham supplies the phrase 最前之 as a modifier to tǐ 體 and understands it as “the unit which precedes all others” (1978, 263). The emendation seems unnecessary; the term tǐ 體 alone, meaning ‘element, part, unit, component’ (see A 2) makes sense here, identifying the ‘minor basis’ as one part of an argument, in the same way that an end-point is an elemental part (of a measuring rod, per A 2).

• (b) R: 有之必無然; emendation Liang Qichao 1923, 67. Graham emends to 有之必然, 無之必不然 “having this, it will necessarily be so: lacking this, necessarily it will not be so” so as to show explicitly the contrast between something inevitably becoming so when the major basis is present and inevitably not becoming so when it is absent (1978, 263). The less radically emended text of Liang Qichao, which we follow here, leaves the second part of Graham’s contrast unexpressed.

• (c) R: 見 is understood here as xiàn ‘to appear’ (modern 現).

The Mohist Canon begins with a set of six basic, epistemic terms, each presented in an individual section. The first of these introduces the concept of a basis as a condition for something to come about. In particular it distinguishes between a ‘minor’ and a ‘major’ basis.

Graham’s extensive emendations seem motivated by a wish to show that this section, Canon and Explanation together, establishes for the Mohists the clear distinction between a ‘necessary condition’ and a ‘necessary and sufficient condition’ (Graham 1978, 264). But in fact the passage, absent Graham’s conjectural emendations, does not explicitly show this, and we can only surmise that such a distinction may have been understood from the definitions and explanations of the ‘minor basis’ and ‘major basis’ given here. The second phrase of Graham’s emendation of R: 有之必無然 is 無之必不然, identical to the phrase that has already been stated as the consequence of lacking the ‘minor basis’. It seems unlikely, and perhaps also unnecessary, that the same observation would be made about the ‘major basis’, since it is already implied. The distinction between the ‘minor’ and ‘major’ bases’, as we see it, is simply that the former may or may not bring about something, whereas the latter will inevitably bring it about.

The argument can be formally expressed as follows: let B stand for the ‘basis’ and R for the ‘result that may be brought about’. The Canon defines a basis by the implication

$$ \mathrm{R}\Rightarrow \mathrm{B}. $$

In the Explanation, then, two kinds of basis are distinguished. A ‘minor basis’ is defined by the additional information that B does not necessarily imply R, i.e.,

$$ \mathrm{B}\nRightarrow \mathrm{R}. $$

It is further stated that

$$ \mathrm{not}\ \mathrm{B}\Rightarrow \mathrm{not}\ \mathrm{R}, $$

which implies R ⇒ B, a mere restatement of the general definition of basis.

The ‘major basis’ is defined by

$$ \mathrm{B}\Rightarrow \mathrm{R}, $$

so that for it

$$ \mathrm{B}\iff \mathrm{R}, $$

i.e., the ‘major basis’ is sufficient and necessary for R to come about. Summing up, the Canon defines the set of all bases by the implication R ⇒ B, while the Explanation distinguishes two subsets, one specified by B ⇏ R (‘minor basis’), the other by B ⇒ R (‘major basis’).

The word gù < *kkak-s 故 means ‘basis, precedent’ i.e., something ‘solid, dependable, fixed’ that can be reliably expected to lead to a certain consequence, hence the more conventional rendering ‘reason, cause’. Cf. hù < *gga-q 怙 ‘rely on, reliable’, gù < *kkak-s 固 ‘solid, firm, fixed’; the sense is ‘durable ~ enduring’, which accounts for gǔ < *kkak-q 古 ‘past, antiquity’ and gù < *kkak-s 故 ‘old, former’ (in addition to ‘basis, precedent’). The same sense can be seen in the Lüshi chunqiu text, from about a century after the Mozi, using much the same terminology: 凡物之然也必有故 ... 水出於山而走於海水非惡山而欲海也高下使之然也 “In general as for things being the way they are, there is inevitably a basis for it. ... When water emerges from a mountain and runs toward the sea, it is not because the water dislikes the mountain and prefers the sea. It is rather the difference in elevation that causes it to be so” (Chen Qiyou 1990, 498). The Shuowen jiezi dictionary of a.d. 100 defines gù 故 as 使為之也 “causing something to take a particular form” (SWGL 1329).³ These examples suggest an understanding of gù 故 closer to ‘basis’ or ‘cause’ than to ‘reason’. For the Mohists gù 故 was not something associated with ‘reckoning’, ‘counting’ or ‘calculating’ (Lat. ratiō), but seems to have been an empirical notion, associated with the solid dependability of a precedent and the predictability of a consequence. To the extent that these first six sections of the Canons together with their Explanations constitute a set of criteria for constructing defensible arguments in philosophical debates, the term gù 故 designates a ‘solid basis’ from which to argue some point.

The verb rán 然 ‘to be like this; to be such, so’ is typically used in the Mojing text, as it often is in other Classical Chinese texts, to refer in the abstract to any situation that may pertain, or to whatever the case in question may be, without designating any particular situation or circumstance explicitly; thus, 不必然 “...does not entail the inevitability of...becoming so” means that for whatever it is that is at issue, a ‘minor basis’ will not necessarily bring it about, and so mutatis mutandis for the other phrases with rán 然.

The word bì 必 (see A 51), normally functions adverbially, meaning ‘necessarily, inevitably’. The lines here could be translated less formally as “[something] will not inevitably become so” and “[something] will inevitably not become so.” But the significance of the inevitability arises from the inalienable relation between something becoming visible and someone seeing it. This is not presented as a casual occurrence here, but as a logically inevitable pairing, like the ‘elder brother~younger brother’ relation given as an example in A 51.

For the entry for tǐ 體 ‘element’ see A 2; for duān 端 ‘end-point’ see A 61.

A 2

C::

體, 分於兼也。

E::

體:若二之一, 尺之端也。

C::

tǐ ‘element’ is a part of a composite whole.

E: :

tǐ ‘element’: like one of two; the end-points on a measuring rod.

As an illustration of one element of a composite whole the Explanation specifies simply “one part of two,” and gives as an example a duān 端 ‘end-point’, the end-points of a measuring rod as two elements of the rod. For the definition of duān 端 ‘end-point’ see A 61.

The word jiān 兼 ‘composite whole’ refers specifically to two or more separate things brought or held together in combination; the Shuowen definition is bìng 並 ‘to be coupled together’ (SWGL 3142). The crucial sense here is precisely the “compositeness” of the whole. A tǐ 體 ‘element’ is not just an accidental or random part of a whole, like a piece of broken chalk, but is a ‘separable component’ of an analyzable whole. The word tǐ < *hrrij-q 體 ‘element’ is cognate with the word lǐ < *rrij-q 豊 ‘ritual vessel’ and by extension with homophonous lǐ < *rrij-q 禮 ‘ritual, ceremony’. The semantic implication is that just as a lǐ < *rrij-q 豊 ‘ritual vessel’ is a meaningful physical component with a precise, well-defined position and function in a lǐ < *rrij-q 禮 ‘ritual or ceremonial performance’ (cf. zhì < *lit ‘the proper order or sequence of ritual vessels in a ceremonial performance’), so a tǐ < *hrrij-q 體 ‘element’ is a meaningful component in any composite whole, whether concrete or abstract, of a quotidian, non-ceremonial nature.

For the term 尺 chí ‘measuring rod’ see the commentary to A 42.

A 3

C::

知, 材也。

E::

知:材^a知也者^b, 所以知也而必知。若明。

C::

zhī ‘knowing’ is an innate capacity.

E: :

zhī ‘knowing’: the ‘innate knowing’ means that, given the wherewithal for knowing something, one then will inevitably know it; it is like vision.

• (a) The character 材 is generally regarded as intrusive here and not original, since it is inconsistent in format with other Explanations, and is therefore usually edited out. All the same, given the clear effort to distinguish ‘knowing’ as an innate capacity in A 3 here from ‘knowing’ as a consequence of experience in A 5 and ‘knowing’ as perceptivity in A 6, it is not at all unreasonable to take the text as it stands and read this as ‘innate (capacity type of) knowing’, i.e., ‘innate knowing’ specifically in contrast to the others.

• (b) The sequence 也者 occurs in A 3, A 4, A 5, and A 6, and by Graham’s count in seven additional passages (Graham 1978, 266). This seems to be a particularly explicit way of setting off a topic and in that respect suggests that the repeated topic word in the Explanation is intended to be understood precisely in the sense defined in the accompanying Canon.

This is the first of four sections that in the aggregate present a paradigm of different kinds of ‘knowing’ and ‘thinking’ as the Mohist understands it, starting with a notion of ‘innate knowledge’.

The word cái < *ddzǝ ‘innate capacity’ written 材 as here is fundamentally the same word as the homophonous words cái < *ddzǝ 才 ‘talent’ and cái < *ddzǝ 財 ‘inherent material worth’. All three refer to a kind of innate or ingrafted quality; the difference is only in the contextual application of the word. Written 材 it generally refers to ‘timber’ or ‘natural resources’, as 財 it refers to inherent material worth, and as 才 it is simply the basic sense of ‘innate talent’. The word, in all three graphic forms and semantic nuances, is related to the verb zhí < *dǝk 植 ‘to plant, implant’, in the concrete phytogenic sense of an implanted quality the result of grafting, cf. homophonous 殖 ‘to set up, plant’ and zhì < *tǝks 置 ‘to set up’. The etymonic sense of the word is most clearly seen in its close relative zāi < *ttzǝ 栽 ‘to implant, as a cutting grafted onto a parent stalk’. The early inscription forms of the character 才 may well be an iconographic representation of the binding of a cutting to a stalk onto which it is being grafted; the Shang inscription form is and the bronze form is .

For the Mohists, then, what we think of as zhī 知 ‘knowing’ is first a natural ability, not an acquired competence of any kind (but cf. A 5). This is what the Explanation means when it says “it is like ‘vision’,” that is, if you have the capacity to see something, then you will inevitably see it; the ability to see is not acquired or learned, but is innate. This innate knowledge is the pre-condition for ‘thinking’ (A 4), ‘acquired knowledge’ (A 5), and for ‘wisdom’ (A 6). For further remarks on cái < *ddzǝ 才 and its lexical affines see the discussion at B 16.

A 4

C::

慮, 求也。

E::

慮:慮也者, 以其知有求也, 而不必得之。若睨。

C::

lǜ ‘thinking’ is seeking.

E: :

lǜ ‘thinking’: ‘thinking’ means that, taking one’s (innate) knowing as a starting point, there is something sought, but one does not inevitably get it. It is like looking around for something.

This section identifies ‘thinking’ as a process taking innate knowing as its starting point and aiming at something, but not necessarily reaching it.

The zhī 知 ‘knowing’ of 以其知 “taking one’s knowing” in the Explanation must refer to the innate capacity of A 3. The same phrase 以其知 “taking one’s knowing” occurs also in the Explanations of A 5 and A 6, a parallelism that cannot be accidental. It therefore seems that the ‘innate knowing’ of A 3 is intended as a pre-condition in these subsequent cases. In the opening passage of the Daxue 大學 (“The Grand Doctrine,” often translated as “The Great Learning”) we find the phrase 慮而後能得 “think about it, and then you will be able to grasp it” as the final element in a progressive sorites concerned with Ruist goal of “coming to rest at the ultimate good” (zhǐ yú zhì shàn 止於至善). The word lǜ 慮 ‘thinking’ is thus ‘musing on’, ‘contemplating’, ‘cogitating’ (Johnston 2010, 377), ‘pondering’; for the Mohists an atelic process, not necessarily entailing reaching a conclusion, but, as clearly expressed in the Daxue line, intended to lead to some kind of a result.

A 5

C::

知, 接也。

E::

知:知也者, 以其知過^a物而能貌之。若見。

C::

zhī ‘knowing’ is coming into contact with [i.e., acquired-knowing].

E: :

zhī ‘knowing’: ‘(acquired-)knowing’ means that, taking one’s (innate) knowing as a starting point, having passed by something one then is able to describe it; it is like perceiving something.

• (a) Sun Yirang suggested that the character 過 guò ‘to pass by’ should be emended to 遇 yù ‘to encounter’ on the grounds that 遇 yù is semantically closer to the 接 jiē ‘come into contact with’ of C than 過 guò is and that this makes better sense overall: “... to encounter something and then ...” (see Liang Qichao 1923, 73). He explains the 過 guò as an error for an original 遇 yù arising from graphic confusion, because the two characters are similar in appearance. There are two reasons to doubt Sun Yirang’s proposed emendation: (i) there is no textual evidence for a variant with 遇 yù; the emendation is therefore entirely conjectural, and (ii) the reading with 遇 yù is by SunYirang’s own argument easier to understand than the reading with 過 guò; but the general rule is, all other things being equal, lectio difficilior potior ‘the more difficult reading is to be preferred’. The rationale is that it is likelier for something that is difficult to understand to become changed, either editorially or inadvertently, to something easier to understand than vice versa. For these two reasons we do not follow Sun Yirang’s emendation. Moreover, the meaning of 過 guò ‘to pass by’ includes a sense of ‘to experience’; Graham draws particular attention to that by pointing out that the text stresses that “the test of knowing a thing is that after experiencing and leaving it behind ... one is still able to describe it” (Graham 1978, 267).

This section seems deliberately intended to draw a contrast with A 3, ‘knowing’ as an innate capacity and anticipates a distinction with A 6, ‘knowledge’ as ‘seeing clearly’. Here we have ‘knowing’ as the result of having come into contact with something, i.e., experiential knowledge. As discussed in the commentary to A 4 above, the zhī 知 ‘knowing’ of 以其知 “taking one’s knowing” in E refers to the innate capacity of A 3.

Graham points out that the Lüshi chunqiu has a section titled zhī jiē 知接, which he translates as “In touch by knowing”, and which deals, he says, with “people who are acquainted with the facts but do not chieh (i.e., jiē) ‘connect, catch on’” (Graham 1978, 268). But the Lüshi chunqiu passage, and indeed even its chapter title zhī jiē 知接 “Knowing through direct contact,” seems not to mean exactly what Graham has proposed, but appears actually to be more explicitly consistent with the Mohist passage here. The opening passage of this section says:

人之目以照見之也, 以瞑則與不見同。其所以為照所以為瞑異。

As for a person’s eyes, they are the same whether he sees something thanks to its being illuminated or if he doesn’t see it because of its being darkened. It is the way in which the thing is either illuminated or darkened that is different.

After a short anecdote we then have this:

智亦然。其所以接智所以接不智同。其所能接所不能接異。

The capacity for knowledge is also this way. Whether one knows something through direct contact or does not know something through direct contact, the capacity to know is the same. It is whether one is able to be in contact or not with something that is different. (Chen Qiyou 1990, 968)

The sense seems to be that, just as everyone has eyes and therefore the potential to see, and that external conditions govern whether they actually see something or not, so everyone has the capacity for knowing from contact, i.e., from experience, and it is only whether one has come into contact with something or not, i.e., has had a particular experience or not, that governs whether a person has the knowledge in question.

A 6

C::

, 明也。

E::

也者, 以其知論物而其知之也著。若明。

C::

zhì ‘wisdom’ is seeing clearly.

E: :

zhì ‘wisdom’: ‘wisdom’ means that, given one’s (either innate or acquired) knowledge, in discussing a thing, one’s knowing about it is then brought into focus; like seeing clearly.

• (a) : the character in R is not otherwise known as a part of the received orthography, but all the same it seems clearly to stand for the word zhì ‘wisdom’, usually written 智.

A 6 identifies ‘wisdom’ as the abstract nominal form of verbal ‘knowing’. The Explanation suggests that ‘wisdom’ is the result of thoughtful discussion, consideration or judgement of something on the basis of one’s knowing. Whether written or with the more familiar character 智, the word is a deverbal noun zhì < *tre-s ‘knowledge’ or ‘wisdom’, in *-s from the verb zhī 知 < *tre ‘to know’. While the character is otherwise unknown in the received writing system, still it conforms completely to the conventions of that system by using the semantic determinative 心 ‘heart-mind’ as the component typically suggestive of cognitive or emotional meanings, added to the etymonic phonophoric graph 知.

This nominal form of the verb zhī 知 ‘to know’ completes the Mohist’s initial identification of kinds of ‘knowing’:

• zhī 知 ‘knowing’ as an innate capacity (A 3)

• zhī 知 ‘knowing’ from experience (A 5)

• zhì ‘knowledge’ or ‘wisdom’ as seeing clearly (A 6).

The nominal form zhì ‘knowledge, wisdom’ in the paradigm is distinguished graphically by the addition of the “heart-mind” classifier, but the two kinds of verbal knowing are not graphically distinguished one from the other. This suggests that notwithstanding the distinction that is drawn here between innate knowing and experiential knowing, these are in some sense seen as different kinds of the same mental phenomenon of ‘knowing’. Accordingly, we can understand the 以其知 “taking one’s knowledge” phrase in E here as referring equally to either innate or acquired knowledge, unlike the same phrase in A 4 and A 5, where this understanding does not obtain. In A 4 experiential knowledge has not yet been introduced, and in A 5 it is precisely experiential knowledge that is being identified.

These three words for ‘knowing, knowledge’ together with lǜ 慮 ‘thinking’ (A 4) constitute a kind of rudimentary set of descriptive terms for ‘cognition’. Taken together with the first two items, gù 故 ‘basis’ (A 1) and tǐ 體 ‘element’ (A 2), they make up what seems to be a set of meta-discursive terminological starting points for the canons and explanations.

3.2 Definition of Force, A 21

The following section is part of the sequence that Graham (1978, 229) designates “Conduct and government”. We include it here because it deals with the concepts of force and weight, both of which figure in the sections on mechanics. ‘Mechanics’ as seen in sections B 25a–B 29, involves specifically the vertical tendency of weights, exactly as described in the Explanation line of A 21.

A 21

C::

力, 形^a之所以奮也。

E::

力:重之謂也^b。下舉^c重, 奮^d也。

C::

lì ‘force’ is that whereby the body exerts itself.

E: :

lì ‘force’: ‘Weight’ is a reference to it. Lifting a weight from below is exerting oneself.

• (a) R: 刑, the graphic interchange between 刑 and 形 is common. In the received writing system the character 刑 is conventionally used to write the word xíng < *geng ‘punishment’ and the character 形 for the homophonous word xíng < *geng ‘(corporal/physical) form’. This suggests that the appearance of classifier 018, 刀 ‘knife’, in the former is to be associated directly with some kind of maiming or disfiguring, i.e., ‘deforming’, as corporal punishment, but in fact the graph 刑 is used write the word xíng < *geng with the sense of ‘form’ as something cut or carved on the basis of a model and this is the likely reason for the appearance of the 刀 classifier. Sensu stricto this emendation is not necessary.

• (b) R: null; supplied by Graham on the model of passage number eight in his reconstructed fragmentary “Names and Objects” text, (Graham 1978, 147, 279).

• (c) R: 與, emendation (Graham 1978, 279; see also the discussion at Graham 1978, 80).

• (d) R: 舊, emended on the basis of the text of C (Graham 1978, 279).

The term lì 力 ‘force’ occurs in section B 26 in a mechanical context, but is here introduced as the physical counterpart to yǒng 勇 ‘courage’ defined in A 20 (勇, 志之所以敢也 “courage is that whereby the will emboldens itself.”). While the Canon defines lì in connection with bodily strength, the Explanation includes the term zhòng 重 ‘weight’, a term used technically in the mechanics sections, that is, the section dealing with the vertical tendency of weights, as an example of force.

3.3 Spatial and Temporal Contingency and Inevitability, A 40–51

These 12 sections contain the definitions of ‘enduring’, ‘spatial extent’, ‘reaching a limit’, ‘to be exhaustive’, ‘beginning’, ‘transforming’, ‘lessening’, ‘circling around’, ‘rotating’, ‘moving’, ‘remaining fixed’, and ‘being inevitable’.

A 40 and A 41 present parallel definitions of ‘duration’, as temporal extent, and ‘spatial extent’, terms that reoccur frequently in subsequent passages.

A 42 and A 43 present definitions of two kinds of limit, spatial (‘reaching a limit’) and set-theoretical (‘to be exhaustive’), respectively.

The following seven sections deal with change and motion. A 44 defines ‘beginning’ as a change from ‘not yet’ to ‘already’, and thus being without duration. A 45 describes ‘transforming’ as a change from ‘this’ to ‘that’, thus entailing a substitution or replacement. A 46 describes ‘lessening’ as a change from ‘more’ to ‘less’, i.e., the subtraction of elements from a composite whole. Sections A 47–49 deal with changes in place or position, describing three different types of motion: ‘circling around’, ‘rotating’, and ‘moving’, respectively. A 50 under the term ‘remaining fixed’ illustrates that ‘absence of motion’ cannot occur in the absence of temporal duration, while ‘not being fixed’ is compatible with both having duration and not having duration.

A 51 defines ‘being inevitable’ as either entailing the existence of a counterpart, or the necessity of something either being a certain way or not being this way, thereby turning this sequence of sections into one about contingency and inevitability.

A 40

C::

久, 彌異時也。

E::

久:今^a 古合^b旦^c暮^d。

C::

jiǔ ‘enduring’ is spanning different times.

E: :

jiǔ ‘enduring’: ‘present’ and ‘past’ match ‘dawn’ and ‘dusk’.

• (a) R: 今久; the order of the head character of E and the first character of the explanation text has become reversed; see Graham 1978, 95–6.

• (b) R: 今, emendation Liu Chang, (Graham 1978, 293).

• (c) R: 且, emendation Graham 1978, 81.

• (d) R: 莫, emendation Graham 1978, 293, although not strictly necessary. The character 莫 is attested writing the word mù ‘dusk, evening’ in transmitted texts.

The passage refers to the extension, or ‘span’, of time of a specific duration, i.e., the extent of time between two moments, here illustrated by the example of ‘past’ and ‘present’ as an abstract representation of the duration of time correlated with ‘dawn’ and ‘dusk’ as a concrete representation. Note that if the correlation is to be understood in a precisely parallel fashion, the word mù 暮 must be understood as referring to the evening previous to the ‘morning’ in question.

For mí 彌 ‘span, spread’ generally see, e.g., Sima Xiangru 司馬相如, Shang lin fu 上林賦 “Rhapsody on the Imperial Hunting Park,” describing the extent of palaces and lodges that can be seen mí shān kuà gǔ 彌山跨谷 “spreading throughout the mountains, straddling the valleys.” (Wen xuan 8.7b. See also Knechtges and Xiao 1987, 88–89.)

A 41

C::

宇^a, 彌異所也。

E::

宇:東西蒙^b南北。

C::

yǔ ‘spatial extent’ is spanning different places.

E: :

yǔ ‘spatial extent’: east and west entails north and south.

• (a) R: 守, emendation Graham 1978, 293.

• (b) R: 家, emendation Liu Chang, (Graham 1978, 293). The sense of 蒙 méng, usually ‘to cover or enshroud’, here has the meaning of ‘include, comprehend, entail’.

What we translate as ‘spatial extent’ is in its more traditional context usually understood as ‘celestial canopy’, a word that generally carries cosmological overtones. Its concrete meaning is ‘eaves’ of a building, or more particularly, the space defined by the eaves. The word 宇 yǔ < *gwaq in both meanings, ‘celestial canopy’ and ‘eaves’, is easily seen to be related to the less common word 于 yú < *gwa ‘space between the corners of the mouth of a bell’. This 于 yú < *gwa is a technical term, explained in the “Kao gong ji” 考工記 section of the Zhou li with the phrase 銑間謂之于 “the space between the corners of the mouth of a bell we call yú 于” (40.8b), that is, the space defined by the “arched” portion of the mouth of a yong-type bell as seen in the illustration here (Fig. 3.1):

Fig. 3.1

Yong-bell (Hubei Sheng 1996, 15; courtesy of the Hubei Provincial Museum)

The parallel of A 41 here with the preceding section, A 40, jiǔ 久 ‘enduring’, i.e., ‘temporal extent’, suggests the general sense of ‘spatial extent’, in particular because the same verb mí 彌 ‘to span, spread (over, out, through)’ is used in both passages. This is consistent with the meaning of yǔ 宇 as ‘eaves’ and with its lexical affine yú 于 as ‘the space between the corners of the mouth of a bell’, both constituting concrete senses of spatial extent, and also with yǔ 宇 as ‘celestial canopy’, a somewhat less concrete use of the word.

The two sections, A 40 and A 41, seen in tandem suggest that the word mí 彌 ‘to span, spread’ is applicable both to space and to time. Spatially, the sense of ‘east and west’ “entailing” ‘north and south’ is, as Graham notes (1978, 294), that the two directional spans are not separated from each other as independent manifestations of space, but are rather two different aspects or perspectives of a single comprehensive spatial extent.

A 42

C::

窮, 或^a 又^b 前不容尺也。

E::

窮:或不容尺, 有窮。莫^c 不容尺, 無窮也。

C::

qióng ‘having a limit’ means that somewhere advancing further will not accommodate any (additional) measure.

E: :

qióng ‘having a limit’: if somewhere it does not accommodate any (additional) measure, then you have a case of ‘having a limit’. If nowhere it does not accommodate any (additional) measure, then you have a case of ‘not having a limit’.

• (a) The word huò < *ggwək 或 occurs several times in these passages, translated variously as ‘in any case’, ‘somewhere’ (A 49, B 13), ‘(in) one (case)’ (A 67), and ‘something’ (B 27), according to context. All of these translations are alternative reflections of the basic meaning of the word huò as a verb phrase adjunct indicating distributional scope of the verb phrase over some, but not all members of an explicit or implicit set, i.e., {set X} 或 VP means that the verb phrase applies to some, but not all of the members of set X. The word mò < *mmak 莫 is the counterpart distributional adjunct indicating the null set, thus ‘in no case’, ‘nothing’ (A 43), ‘nowhere’ (A 65). Both huò < *ggwək 或 and mò < *mmak 莫 belong to a small set of words likely morphologically related by having in all cases a suffix -k as the ‘distributional’ morpheme.

• (b) R: 有; emendation Graham 1978, 294, 有 stands frequently in manuscripts and early texts for yòu ‘again’, typically written 又 in the received writing system.

• (c) For 莫 see note a above.

The archaeological evidence for the chí 尺 ‘measuring rod’ shows clearly that it came to be a fixed, standard length of about 23–24 cm, typically subdivided into 10 equal units. All the same, the word chí 尺 is used frequently throughout these chapters of the Mozi as a concrete way to refer to any short linear measure without necessarily specifying a fixed length. Thus, when the present passage refers to “not accommodating any (additional) measuring rod,” the meaning must be understood as “not accommodating any further linear measure of any length.”

A 43

C::

盡, 莫不然也。

E::

盡:俱^a止動^b。

C::

jìn ‘to be exhaustive’ means that nothing is not so.

E: :

jìn ‘to be exhaustive’: all are either fixed or moving.

• (a) R: 但, emendation Graham 1978, 81.

• (b) Graham emends the text by shifting 動 to the opening line of the Explanation of A 44. We maintain the text as transmitted.

In A 42 the qióng 窮 refers to ‘exhausting’ space by reaching a limit. Here the ‘exhaustiveness’ refers to identifying all of the options available for any given condition, for example, the two options, being fixed in place or moving, exhaust the possibilities for anything in regard to motion; there is no third option. This is a condition that could have been described by the mǎ fēi mǎ 馬非馬 ‘horse/non-horse’ rubric, the Mohist’s label for a tertium non datur situation, but that connection is not made here in any explicit way. Rather the fact that this section follows immediately on qióng 窮 implies that the Mohist recognized the pertinence of jìn ‘to be exhaustive’ beyond spatio-temporal contexts.

When the verb rán 然 ‘to be like this, to be so’, does not refer to any explicit state or phenomenon already expressed in the immediate context, it has a generic meaning ‘to be like whatever might be at issue’; see also A 1.

For zhǐ 止 ‘remaining fixed’ see A 50 and for dòng 動 ‘moving’ see A 49.

A 44

C::

始, 當時也。

E::

始:時, 或有久, 或無久。始當無久。

C::

shǐ ‘beginning’ pertains to time.

E: :

shǐ ‘beginning’: time in some cases has duration and in some cases does not have duration. The ‘beginning’ corresponds to [the case of] not having duration.

Identifying shǐ ‘beginning’ as having no duration, thus a “dimensionless” temporal point matches conceptually the identification of duān 端 ‘end-point’ as the spatial element having no magnitude. See A 61.

A 45

C::

化, 徵易也。

E::

化:若為鶉。

C::

huà ‘transforming’ is when the set of identifying features switches from one to another.

E: :

huà ‘transforming’: like a frog becoming a quail.

• (a) R: , a hapax graphomenon. The R character is likely a corruption of an original wā (var. & 蛙), identified in the Shuowen jiezi as 蝦蟆 hámá a kind of ‘frog’ (SWGL 6067). The emendation is confirmed by a story in the Liezi that says 蛙為鶉 “a frog becomes a quail” (Yang Bojun 1965, 7). The same transformation is recorded in the Huainanzi as 蝦蟆為鶉 (He Ning 1998, 763) “a frog becomes a quail,” using the bisyllabic word 蝦蟆 hámá ‘frog’ instead of 蛙 wā and the single verb 為 wéi ‘become’ instead of 化為 huà wéi.

This section describes transformation as a change of the characteristics of something. The salient point here, as Graham mentions (1978, 214), is the use of the verb yì 易 ‘to switch, change’. Specifically, this is a “substitution” or “replacement”, i.e., the kind of change that entails replacing A with B. The word yì < *lek 易 in its most concrete sense seems to have referred to agricultural crop rotation, and is likely cognate with yì < *lak 譯 ‘to translate’ < ‘replace language A with language B’ (Behr 2004, 173–208; esp. 180). Cf. also 鬄 dì < *llek ‘hair-piece’, i.e., “replacement” hair.

Graham notes that the association of 徵 zhēng ‘identifying feature’ with the verb 化 huà ‘to transform, shift’ is found also in the Lüshi chunqiu: 徵雖易, 表雖難, 聖人則不可以飄矣 “Although the identifying features may be changed, although the outward appearance may be difficult (to discern), if one is a sage, then he could not (by those things) be caused to waver” (Chen Qiyou 1990, 1413) and in the Huainanzi: 故聖人見化以觀其徵 “Assuredly, a sage will see a transformation and thus observe its identifying features” (He Ning 1998, 946; Graham 1978, 295). The “Zhèng míng” 正名 section of the Xunzi is more precise than the Lüshi chunqiu about the nature of 化 huà ‘to transform’, describing it as 狀變而實無別而為異者謂之化。有化而無別謂之一實。 “Being seen as different when the appearance is altered but the entity is without distinction, we call huà ‘being transformed’. When there is a transformation but no distinction we refer to that as a ‘single entity’.” (Wang Xianqian 1972, 16.11; cf. Knoblock 1994, 131: “Where the appearance undergoes metamorphosis, but there is no distinction in the reality, yet they are deemed different, it is called ‘transformation’. Where there is transformation but no distinction, it is called one object.”) The complete passage of the Huainanzi line cited in the textual note above is 夫蝦蟆為鶉。生非其類。唯聖人知其化。“As for any case of a frog becoming a quail, as living creatures they are not in the same class, so only a sage recognizes this as a transformation.” The implication is that the frog and the quail are the same basic entity, and only appear different as a result of a transformation in their distinguishing marks, their ‘identifying features’ (徵 zhēng), i.e., their appearance. (See Liang Qichao 1923, 101.)

A 46

C::

損, 偏去也。

E::

損: 偏也者, 兼之體^a也。其體或去或^b存, 謂其存者損。

C::

sǔn ‘lessening’ is partially removing.

E::

sǔn ‘lessening’: to be ‘partial’ is to be an element of a composite whole. When some of its elements are removed and some are retained, we refer to what is retained as ‘lessened’.

• (a) R: 禮; emendation Graham 1978, 296.

• (b) R: null; emendation Graham 1978, 296. In a conventional narrative style we would expect the huò 或 to be repeated before the second verb, here cún 存, hence Graham’s emendation. The text is, even without the second huò 或, still understandable as ‘some ... are removed or maintained’.

The present section identifies the process of ‘lessening’ in material terms, specifically referring to the tǐ 體 ‘element’ introduced in A 2. There is evidence for a complementary section on yì 益 ‘increase’ immediately following this one that has been entirely lost, except for the head word yì ‘increase’. See Graham 1978, 296.

A 47

C::

儇^a, 秪^b也^c。

E::

儇:句^d皃^e也。

C::

xuán ‘circling around’ is coiling and curving.

E: :

xuán ‘circling around’: a curving appearance.

• (a) R: 大益儇; Graham (1978) deletes the two-character phrase 大益, suspecting that it is a remnant from a lost entry for 益 yì ‘increase’, the counterpart to the preceding A 46 entry for 損 sǔn ‘lessen, decrease’, and not actually a part of A 47. The character 儇 stands for the word xuán, usually written 旋 or 還 in the received writing system.

• (b) The first of the two characters of R here, , is a hapax graphomenon, with an apparent phonophoric 具 jù < *gro-s. Only 秪, the second of the two, is attested in the transmitted writing system, but it is not entirely clear what word this character stands for in this entry. Understood as zhī < *tij ‘grain beginning to ripen’, the word with which it is conventionally associated, it seems not to make any sense here. Sun Yirang suggests that it is a variant for 柢 dǐ < *ttij ‘base of a plant stalk’ (i.e., the phytomorphic specialization of the basic word 底/氐 dǐ ‘base’), but this also is difficult to fit to the present context. Graham 1978, 296–97 identifies the two characters 秪 together as likely constituting a binome, perhaps inadvertently metathesized, equivalent to 枝拘 zhī gōu < *ke-kko, found in Huai-nan zi 19 (He Ning 1998, 1368) where it seems to mean ‘(branches) coiling and curving’ (see below), but the two modern Chinese readings zhī 秪 (*tij) and zhī 枝 (*ke) are misleading in this regard; their respective OC values as usually understood do not allow for such a graphic interchange.

• (c) R: null; emendation Graham 1978, 296–97. This is the only canon entry from A 1 to A 75 with no final yě 也. On this basis Graham adds it.

• (d) R: 昫; emendation Graham 1978, 297, cf. also 枸 gōu ‘curved or bent piece of wood’.

• (e) R: 民; emendation based on the graphic similarity of the guwen form of 民, viz. , to , one of the common, if non-standard, graphic variants of the character 貌 mào ‘visible characteristics’ (Graham 1978, 195).

This is the first of three sections describing different kinds of motion (‘circling around’, ‘rotating’ and ‘moving’). A 50 then describes rest (‘remaining fixed’). Yang Shuda suggests that the binome 枝拘 zhī gōu in Huainanzi ought to be read as zhǐ jǔ < *ke-q - ko-q, a phonetically acceptable variant of 枝拘 zhī gōu < *ke-kko, meaning ‘coiled and curved’ or ‘coiling and curving’, a sense that fits the present context exactly (Yang Shuda 1985, 193).

A 48

C::

運^a, 易也。

E::

運:區穴若斯^b貌常。

C::

yùn ‘rotating’ is switching from one to another.

E::

yùn ‘rotating’: An outline, when like the appearance of a parapet, is recurrent.

• (a) R: 庫, emendation Wu Yujiang (Graham 1978, 297); see also A 80 in the “Lexical Appendix” infra.

• (b) Graham 1978, 297 observes that 斯 sī ‘this’ is not a part of the pronominal system of the Mozi and so the character 斯 is not likely standing for that word here. He understands it as the verb sī ‘cut’ (Kangxi zidian 斯析也 ‘split’), though this meaning is difficult to understand here. In the opening sections of Mozi 52, “Bei cheng men” 備城門 (“Preparing the city walls and gates [for defense]”) the word xī, written either 撕 or , occurs in the meaning ‘parapet’. Johnston 2010, 737, 739 understands the word correctly as ‘parapet’ in the two chapter 52 occurrences, but fails to make the ‘parapet’ connection with the character 斯 here.

The sense of the word yì 易 in the Canon includes the meaning of cyclical switching, i.e., the replacement of one item by another in a defined sequence. It also includes the meaning of switching orientation in space, which we find in the optics Sect. B 23: 景一小而易, 一大而正 “the image is sometimes small and switched, and sometimes large and upright.” The switching involved in the B 23 section must be an inversion in that it is the complement of zhèng 正 ‘upright’. The sense of cyclical switching is commonly seen for the word yùn 運 denoting the cycle of seasons, e.g., in the Dadai Liji 大戴禮記 we find the phrase 觀四時之運 “Observe the rotation of the four seasons” (Wang Pinzhen 1989, 62). Just as for the word yì 易, the meaning of the word yùn 運 also entails spatial orientation, as is seen in optics section B 19: 景運內 “the shadow is rotated on the inside.” Switching in orientation can be seen as a variant sense of rotation about an axis, a sense clearly inherent in yùn 運 as it is found used in, e.g., Mozi 35 & 37, yùn jūn 運鈞 ‘rotating potter’s wheel’.

We understand qūxué 區穴 ‘outline’ as derived from an underlying verb-object construction ‘to delineate the empty/hollow space’. The same term occurs also in A 63. The outline in question here is described as having the appearance of a crenelated parapet. The recurrent switching between crenels and merlons of the parapet fits as a concrete example of the rotational switching from one thing or state to the next.

A 49

C::

動, 或徙^a也。

E::

動: 偏 際^b 徙^c 者, 戶樞, 兔^d 蝨^e。

C::

dòng ‘moving’, implies a shifting about somewhere.

E: :

dòng ‘moving’: something that shifts asymmetrically about a contact point, the pivot of a door, the louse on a rabbit.

• (a) R: 從, emendation Graham 1978, 298.

• (b) R: 祭, emendation Liang Qichao 1923, 103.

• (c) R: 從, emendation Graham 1978, 298.

• (d) R: 免, emendation Graham 1978, 298.

• (e) R: 瑟, emendation Graham 1978, 298.

The precise meaning of the Canon seems straightforward and unambiguous; the Explanation is by contrast somewhat puzzling in view of the two apparent examples of ‘shifting about’ that it offers. By specifying piān jì 偏 際 ‘from an oblique, i.e., asymmetrical, contact point’ the Explanation seems to limit the ‘moving about’ to irregular movement rather than extended, purposeful motions. The “louse on a rabbit” image occurs again in section A 88, dealing with basic pairs of seeming opposites, tóng yì 同異 ‘same and different’, and the fact that sometimes ‘sameness’ and ‘difference’ are absolutes and sometimes they are not absolute, but dependent on a given perspective. The “louse on a rabbit” image is used to represent the non-absolute relation between ‘coming’ and ‘going’, jiù qù 就去. The louse can be moving haphazardly in one direction on the rabbit, while the rabbit itself can be moving in another direction at the same time.

The ‘louse’ figures in B 6, this time as a part of an example intended to illustrate the non-comparability of things, and by extension the difference between ‘name’ and ‘thing’: C: 異類不, 說在量 “things of different categories are not comparable; the explanation lies with ‘gauging’.” E: … 木與夜孰長 … 蝨與瑟孰瑟 “… a tree in comparison with the night, which is longer? … a louse in comparison with a zither, which is more ‘zither-like’?” The latter-mentioned of these two incomparable pairs is a play on words, i.e., it is based on the near homophony of the two words shī < *srit (from an earlier *srik) ‘louse’ (蝨) and sè < *smrit ‘zither’ (瑟), and, according to Graham, on the further lexical fact that there is a third word sè < *smrit ‘glistening’ written with the same character as sè < *smrit ‘zither’, viz., 瑟. The sense then could be understood as “… a louse in comparison with a zither, which is more ‘zither-glistening’?” or simply “… which is more glistening?”

The two words shī < *srit 蝨 ‘louse’ and sè < *smrit 瑟 ‘zither’ seem to have been already at the time of this text phonetically close, *srik already having become *srit. By Han times they have become completely homophonous. We find the following passage in the Huai-nan zi, a text from the second century b.c.e.: 頭蝨與空木之瑟, 名同實異也。“the ‘head-louse’ sè and the ‘hollow-wood zither’ sè, the name is the same, but the thing is different” (He Ning 1998, 1208). This passage clearly bears on the prevalent “language-philosophy” concern of the time with the difference between ‘names’ and ‘things’. The B 6 Mozi passage may have the same sense, ‘name’ and ‘thing’ presented as an example of “incomparability”.⁴

For 或徙 see B 13.

A 50

C::

止, 以久也。

E::

止: 無久之不止, 當牛非馬。若矢^a過楹。有久之不止, 當馬非馬。若人過梁。

C::

zhǐ ‘remaining fixed’ means thereby enduring.

E: :

zhǐ ‘remaining fixed’: The not-remaining-fixed that lacks duration corresponds to ‘ox/non-horse’; like an arrow passing a pillar. The not-remaining fixed that has duration corresponds to ‘horse/non-horse’; like a person passing across a bridge.

• (a) R: 夫, emendation Graham 1978, 298.

‘Remaining fixed’ means ‘fixed in place’ and is inherently a durative phenomenon; there is no other possibility. But for the relation between ‘remaining fixed’ and ‘not remaining fixed’ there are two possibilities: (i) the ‘remaining fixed’ is durative and the ‘not remaining fixed’ is punctual or (ii) both are durative. The former is of the “ox/non-horse” type; the ‘not remaining fixed’ is exemplified by an arrow passing a pillar, a momentary, punctual event. The latter is of the “horse/non-horse” type, where the ‘not remaining fixed’ is exemplified by a person crossing a bridge, clearly a durative event.

We can describe the relation as follows:

• (a) being fixed (+F) entails by definition duration (+D): {+F, +D} is the only +F possibility;

• (b) not being fixed (−F) can be punctual (i.e., non-durative, −D) or durative (+D), so there are two possibilities: {−F, −D} and {−F, +D};

• (c) the relation between {−F, −D} and {+F, +D} is “x, not y”, because changing one feature of the first does not tell you anything definite about the second;

• (d) the relation between {−F, +D} and {+F, +D} is “x, not x” (tertium non datur); because “x” and “not-x” cannot apply simultaneously to something.

In the terms familiar from other parts of the Mohist dialectical sections, and from the texts of the so-called “Logicians” or “Sophists”, the relation between {+F, +D} and {−F, −D} is “ox/non-horse” meaning that while being an ox necessarily entails not being a horse, the converse is not the case; that is, not being an ox does not necessarily entail being a horse. By contrast, the relation between {+F, +D} and {−F, +D} is “ox/non-ox”, a simple “either/or”, “yes or no” choice, with no third possibility. As the following diagram shows, just as the set of ‘horses’ is a subset of the set of things that are ‘non-oxen’, but not all ‘non-oxen’ are ‘horses’, so the set of +F ‘remaining fixed’ phenomena is a subset of the set of +D ‘durative’ phenomena, but not all +D phenomena are +F.

The diagram in Fig. 3.2,⁵ reflecting the Mohist text’s use of animal names to illustrate the points at issue, is restricted to the +D possibilities. We could use the same diagram to represent the non-durative case marking that portion outside the outer circle as −D, but we would have to change the animal labels, e.g., labeling everything outside the outer circle with ‘non-horse’ and everything within as ‘horse’, which would be inconsistent with the animal name labeling given in the diagram here. This is because the Mohists are using the animal names on a case-by-case basis, and not systematically for all possibilities.

Fig. 3.2

Set diagram for ‘durative’ and ‘fixed’

The text’s image of “an arrow passing a pillar” is intended to represent the conjunction of ‘not being fixed’ and at the same time ‘not being durative’, since clearly a flying arrow is moving and therefore not fixed, and just as clearly its passing a stationary point, here the ‘pillar’, is perceived as momentary and therefore not durative, thus {−F, −D}. Similarly, the image of a person crossing a bridge is just as obviously ‘not fixed’, and also clearly ‘durative’, thus {−F, +D}. These two images, together with the original Canon statement, which amounts to {+F, +D}, represent all empirically possible combinations of +/− F and +/− D. The fourth combination, viz., {+F, −D}, is a contradiction in terms and, given the premise of the Canon here, is not an actual possibility; that is, from the Mohist perspective as reflected here there is no possibility of a non-durative ‘being fixed’.

A 51

C::

必, 不已也。

E::

必:謂 孰^b者也。若弟兄。一然者, 一不然者, 必^c不必也。是非必也。

C::

bì ‘being inevitable’ means being unable to get rid of.

E: :

bì ‘being inevitable’: refers to counterparts bringing about each other, like younger and elder brothers. One thing being so and one not so may entail inevitability or may not entail inevitability; but either being this or not being this is a case of inevitability.

• (a) R: 臺; emendation Graham 1978, 299.

• (b) 孰 = 熟 shú ‘bring to maturity, develop(ed) fully’.

• (c) Graham 1978, 299 proposes an emendation to 止 because the character 止 is frequently confused graphically with 心, a character that in the received orthography clearly suggests 必 and on the grounds that the text is in his view “surely unintelligible” as it stands. We are not persuaded that an emendation is called for and we understand the text of R as registered in the translation above.

The sense in which yǐ 已 ‘to end, stop’ is understood here as ‘to get rid of’ is a fundamental part of the meaning of the word, as can be clearly seen from A 76 (in the lexical appendix) where yǐ 已 is given two senses, one chéng 成 ‘to complete’ and the other wàng 亡 ‘to get rid of’ (sc. as of an affliction or illness). Thus, bì ‘being inevitable’ is ‘being unable to be gotten rid of’ > ‘unavoidable, inevitable, necessary’.

The sense of the Canon and the Explanation taken in tandem here is to identify two kinds of ‘inevitability’. First, the Canon itself simply defines ‘inevitability’ broadly as something ‘not stoppable’, i.e., that will come about absent any external intervention that might interrupt it. This includes the sense of 必 bì that we find in, e.g., the line 景亦小而必正 “the image too is small and inevitably upright” from B 23 describing one aspect of an image of an object seen reflected in a concave mirror. The ‘inevitability’ here is a statement of what will be the case as a consequence of the arrangement of light source, mirror and object, that is of the empirical situation itself.

The second kind of ‘inevitability’, exemplified in the Explanation, is what we might call ‘logical inevitability’, a sub-type of the broad definition given in the Canon. The existence of an older brother inevitably entails the existence of a younger brother (the terms used in the Explanation are, more sinico, exclusively male), and similarly for all such ‘counterpart’ () pairs. In the same way, there is not necessarily an inevitability in one thing being so or not being so, but there is a logical inevitability in something being either this or not being this, i.e., when there are only two choices, “yes” or “no”, it is inevitable that if something is one it is not the other. This is another statement of the “ox/non-ox” (tertium non datur) relation. In this sense this aspect of inevitability recapitulates the “either/or” sense of part d given in the discussion of A 50. This may account for this section following directly A 50.

The word bì < *pit 必 ‘to be inevitable’ is likely a phonetic “fusion” (sometimes called an allegro form) form of the negative prefix p- plus the word shī < *hlit 失 ‘to make a mistake’, thus it is, etymologically, ‘unmistakeable’.

Compare Lexical Appendix, A 76.

3.4 Corporeal Extension (“Geometry”), A 52–A 69

The 18 sections contain the definitions of ‘level’, ‘being of the same length’, ‘center’, ‘having magnitude’, ‘the sun at the center’, ‘to be straight’, ‘circle’, ‘square’, ‘doubling’, ‘end-point’, ‘having an interstice’, ‘interstice’, ‘king-post’, ‘being filled out’, ‘hard-and-white’, ‘overlapping’, ‘side-by-side comparing’, and ‘contiguous’. Graham 1978, 230 designates these as dealing with “Geometry” and puts them parallel to the sections on mechanics, optics and economics. Designating these sections as dealing with geometry is clearly inspired by the close similarity of some of the sections with parts of the Greek tradition of mathematics. In particular the definition of an ‘end-point’ (A 61) and of a ‘circle’ (A 58) look strikingly similar to the corresponding definitions of point and circle in Euclid’s Elements. Other sections deal with geometrical attributes such as ‘to be straight’ (A 57) or procedures such as ‘doubling’ (e.g., of a line, A 60).

These similarities should not prevent us from recognizing the fundamentally different character of the Mohist doctrine as compared to Euclidean geometry. While the latter deals with the properties of figures that can be constructed with straight-edge and compass and, crucially, leaves out the material dimension of the world, focusing on pure extension, the core and goal of these Mohist sections appears, precisely to the contrary, to focus on the corporeal, or material, aspect of extension. Matter thereby does not enter the stage as some kind of substance as a counter-concept to space, but apparently through the attributes of bodies, such as being hard or being white. These attributes fill out the spatial extension (magnitude) of bodies (A 65), or fill out each other (A 66), thus constituting materiality, the central concept that these sections add to the spatio-temporal extensions introduced in the previous sequence of sections.

The first nine sections (A 52–60) all define spatial attributes that can be determined through measurement by means of an instrument, or can even be constructed using an instrument. The instrument may be a measuring rod, or a more elaborate instrument such as a leveling device (seen in A 52 by implication, but not explicitly mentioned); gnomons or sundials (seen in A 56 by implication, but not explicitly mentioned), compasses (A 58), or the carpenter’s square (A 59) may be involved. In A 53, defining the feature ‘of the same length’, the measuring rod is, of all places, not mentioned. A 53 in fact may be taken as describing the basic practice and principle underlying the use of a measuring rod. (‘Of the same length’ is later made use of in A 54 and A 57.) ‘Doubling’ (A 60), by contrast, is explicitly exemplified through construction by putting two measuring rods together.

The end-point, defined in A 61, is a theoretical artifact, albeit a fundamental one, and may be seen as a consequence of the systematic reflection on various configurations of measuring rods. It seems to be introduced here in anticipation of the different arrangements of physical objects discussed in A 67–69. The ‘end-point’ is in part the spatial counter-part to the temporal concept of ‘beginning’ introduced in A 44. The ‘beginning’ is a purely temporal concept, denoting a point in time. The end-point, by contrast, does not denote a point in space, but a point as an element of a physical object. This can be seen from the fact that the phrase 無久 wú jiǔ ‘lacking duration’ occurs in the definition of ‘beginning’, while the term ‘end-point’ is defined as the absence of physical magnitude (無厚) rather than the absence of spatial extension (e.g., 無宇).

The relation between spatial and corporeal extensions is further differentiated in the following three sections, starting with contrasting definitions of ‘having an interstice’ and ‘interstice’ (A 62, A 63). In particular, a case of a measurement that does not result in a valid application of the concept of interstice is pointed out in the Explanation of A 63. A 64 then addresses the question of the (non-)materiality of the interstice itself. The point is made that ‘emptiness’ pertains to the interstice and not the thing having an interstice. ‘Emptiness’ is thus given through contrast with the materiality of the thing having the interstice, which makes it a relative rather than an absolute notion.

A 65 then contains an explicit discussion of material filling out that goes together with having magnitude. As will become clear in A 66, the materiality of filling out consists in attributes being present and presumes a physical object.

A 66 introduces the concept of hard-and-white. This further explores the relation of attributes to their spatial distribution, now considering more than one attribute. This brings about the question of the compatibility or the mutual exclusion of two attributes. The concept of hard-and-white establishes a connection between spatial and logical aspects: the condition of the attributes filling out each other is a spatial one, the condition of the attributes not contradicting each other is a logical one.

A 67–A 69 then discuss the different spatial arrangements of ‘overlapping’, ‘side-by-side comparing’, and ‘being contiguous’. ‘Overlapping’ figures in both of the following Canons, and all three Explanations employ the concept of ‘end-point’. It is stated that the overlapping occurring in the case of a hard-and-white situation must be exhaustive, the point being probably that the two attributes must fill out each other (A 67).

A 52

C::

平, 同高也。

E::

[null]

C::

píng ‘level’ means of the same height.

E: :

[null]

This is the first of three sections involving equal measured lengths.

A 53

C::

同長, 以正相盡也。

E::

同:楗^a與框^b之同長也正^c。

C::

tóng cháng ‘of the same length’ means that by being laid straight (next to each other) each exhausts the other.

E: :

tóng ‘(of) the same (length)’: As for a door barrier-post and its door frame being of the same length, they are laid straight.

• (a) R: 捷, emendation Graham 1978, 304.

• (b) R: 狂, emendation Graham 1978, 304.

• (c) R: 心, emendation Graham 1978, 304.

The equal length of two things is defined as the end-points of each matching those of the other when laid side-by-side. We can only imagine what was the structure of the door frame and how the barrier-post operated as a device for preventing the door from being opened, but it is clear that the sense of the example in the Explanation is that when laid straight with each other these two parts of the door will be of the same length.

Here jìn 盡 ‘exhaust’ has a spatial reference; for jìn 盡 referring to attributes more generally see A 43.

A 54

C::

中, 同長也。

E::

中:自是往, 相若也。

C::

zhōng ‘center’ implies being of the same length.

E: :

zhōng ‘center’: extensions starting from this match one another.

Using the meaning of the term tóng cháng 同長 ‘to be of the same length’ as just explained in A 53, the Canon here defines what can be understood as a center-point. The simplest example of a center-point is that of a linear span, the extensions in opposite directions from which will be of equal length. For a circle zhōng 中 is the center and the equal length extensions are the radiuses (see A 58). In a limited way the definition is also applicable to any symmetrical non-circular two-dimensional figures, defining the center point of a square, of a rectangle (sc. the diagonal cross-lines) or of an equilateral triangle. Such an understanding of a center-point could, clearly, apply to three-dimensional figures, but there is no indication that the Mohist was including that in these analyses.

A 55

C::

厚, 有所大也。

E::

厚:惟端^a無所大。

C::

hòu ‘having magnitude’ means that there is something in relation to which it (i.e., the thing that has magnitude) is bigger.

E: :

hòu ‘having magnitude’: Only an end-point has nothing in relation to which it is bigger.

• (a) R: null; restoration of 端 by Graham 1978, 305.

In everyday language the word hòu 厚 means ‘to be thick’ (one dimensionally). In this passage it has been turned into an abstract term which is then used as a technical element within a conceptual framework, as can be seen from its usage in A 61 (端), A 65 (盈), and A 69 (次).

For the definition of duān 端 ‘end-point’ see A 61.

A 56

C::

日中, 正南也。

E::

[null]

C::

rì zhōng ‘the sun at the center’ is being due south.

E: :

[null]

In this case the ‘center’ refers to the mid-point on the sun’s trajectory between rising and setting, which would have been determined with a device such as a gnomon or sundial.

A 57

C::

直, 參也。

E::

[null]

C::

zhí ‘to be straight’ is to be in alignment.

E: :

[null]

The Canon defines ‘straightness’ as being in ‘alignment’. The Shuowen defines zhí 直 as 正見也 ‘to see evenly, directly, straight on’ (SWGL 5714).

As Graham points out (1978, 307, 369–70), cān 參 is the standard term in Chinese astronomy for aligning two gnomons with an observed heavenly body. Given the astronomical context of A 56, the reference here to an astronomical practice seems likely.

Beyond this, cān 參 refers to the three stars of the constellation Orion that in their linear arrangement are sometimes identified as Orion’s ‘belt’.

The word cān < *ttshrum 參 itself is cognate with the word sān < *ssrum 三 ‘three’; cf. cān < *ttshrum 驂 ‘team of three horses’. The implication seems to be that in the simplest sense ‘alignment’ is understood as having a third point in a line with two others. In everyday Euclidean terms any two points, of course, define a line; a third point may or may not lie on the same line, i.e., be in ‘alignment’. ‘Alignment’, in other words, allows for an opposite, viz., unaligned.

A 58

C::

圜, 一中同長也。

E::

圜:規寫也。

C::

yuán ‘circle’ implies being of the same length from a single center.

E: :

yuán ‘circle’: When drawing with a compass, it is the plainest form.

• (a) Apart from its occurrence here, the graph in R is unattested standing as an independent character. It is known in the received writing system only as a graphic component, typically functioning as a semantic classifier (classifier number 066 of the Kangxi scheme), written , in many compound characters. Structurally the character consists of the ‘hand’ component 又 with 卜 bǔ as the phonophoric. Given the propensity of the Mozi text to include uncommon forms of characters, it is not unlikely that this is a graphic variant of the received character 扑 standing for the word pǔ ‘uncut, unadorned, rough, plain’, which has basically the same two graphic constituents but arranged horizontally rather than vertically. Such positional variation of graphic constituents is not uncommon in the pre-Han script. The character then we take as standing for the word pǔ (normally written 扑) meaning ‘uncut, rough, plain’. See also Graham 1978, 307–08.

Based on the prior identifications of zhōng ‘center’ (A 54) and tóng cháng ‘to be of the same length’ (A 53) this section identifies a ‘circle’ and goes hand-in-hand with A 59 following.

The gūi 規 ‘compass’ and jǔ 矩 ‘carpenter’s square’ (see A 59) are two of the most frequently invoked examples intended to represent adherence to objective rules or guidelines. In chapter four of the Mozi, “Fa yi” 法儀 (“Rules and Proprieties”) we find this observation:

天下從事者, 不可以無法儀。無法儀而其事能成者無有也。雖至士之為將相者, 皆有法, 雖至百工從事者, 亦皆有法。百工為方以矩, 為圓以規, 直以繩, 正以縣。

Anyone who pursues affairs in the sub-celestial realm cannot do without rules and performance guidelines. There is no instance where, without rules and performance guidelines, one’s affairs were able to be accomplished. Even the highest officers who serve as leaders and ministers in all cases have rules. And even those various craftsmen who pursue their trades also in all cases have rules. The craftsmen will use a carpenter’s square to make a square, a compass to make a circle, a snap-line to make something straight, and a plumb-line to make something vertical.

The difference between the indirect admonition of the “Fa yi” chapter and sections A 58 and A 59 of the Mohist Canon is that the former is intended to influence social behavior while the latter are meant to provide precise definitions within a terminological system.

A.C. Graham suggests that the sense of pǔ  ~ 扑 here is closer to ‘rough’ in the sense of “a rough outline” than it is to ‘plain’ as we have translated it (Graham 1989, 81). This interpretation he gets from the fact that in the “Tian xia” 天下 chapter of the Zhuangzi there occurs a list of apparently intentionally self-contradictory or ironic statements of the “dogs can become sheep,” “the eye does not see” kind ascribed to the so-called Sophists, and in this list we find these two statements: 矩不方, 規不可以為圓 “the carpenter’s square does not make a ‘square’; the compass cannot make a ‘circle’” (Guo Qingfan 1975, 1106). Graham, often following the Chinese commentarial tradition, finds rationales or explanations for most of these statements that fit or rebut the point that the Sophist was allegedly trying to make by invoking such statements in the first place. In the case of the guī 規 ‘compass’ he suggests that the explanation lies with the fact that a perfect circle is an ideal form, and is in principle unachievable in practice, and so mutatis mutandis for the jǔ 矩 ‘carpenter’s square’. And so he understands the word pǔ as meaning “a rough approximation (to the ideal).” This interpretation hints at the Greek sense of a geometrically perfect or ideal form, an understanding for which there is no evidence in the Mohist Canon, and which therefore seems to us an unjustified, if unconscious, appeal to a Greek conceptual perspective that has no pertinence to the Mohist world.

A 59

C::

方, 匡^a隅四雜^b也。

E::

方:矩見也。

C::

fāng ‘square’ implies that the frame corners number four and are closed up.

E: :

fāng ‘square’: When drawing with a carpenter’s square, it is the plainest form.

• (a) R: 柱, emendation Graham 1978, 308.

• (b) R: 讙, emendation Sun Yirang, (Graham 1978, 308).

• (c) See the note re in A 58.

Complementing the immediately preceding section describing a ‘circle’, this section similarly identifies a ‘square’. The Canon would seem to allow for any kind of quadrangle; only the Explanation by virtue of invoking the carpenter’s square excludes all such that do not consist of only right angles. In normal parlance both the word fāng 方 and the word kuāng 匡 ‘square-frame basket’ are typically used for squares, though technically they can refer also to rectangles.

A 60

C::

倍, 為二也。

E::

倍:二, 尺與尺俱^a去一端, 是無同也。

C::

bèi ‘doubling’ is making two.

E: :

bèi ‘doubling’: ‘two’ means a measuring rod together with another measuring rod both extending (linearly) away from a single end-point, in this case (i.e., the case of doubling), they will have no shared portion.

• (a) R: 但, emendation Graham 1978, 81, 309.

The general notion of ‘doubling’ is illustrated very concretely in linear terms by explaining that two identical measuring rods laid end-point to end-point (in a straight line) such that there are no coincident points will give a doubled length.

A 61

C::

端, 體之無厚^a而最前者也。

E::

[null]

C::

duān ‘end-point’ is the element that, having no magnitude, comes foremost.

E: :

[null]

• (a) R: 序, emendation Graham 1978, 310.

Note that although the Chinese term duān 端 is here used with the meaning of a starting point, generally it is used in the Mohist Canon just as English ‘end-point’, to refer equally to the “starting point” as well as the “termination point” of a line or rod. A rod has two “ends”, a front end and a back end. At the same time the word is often used abstractly. In the Lunyu (Analects of Confucius) Confucius uses it to mean both ‘starting point’ and ‘end-point’: 有鄙夫問於我, 空空如, 我叩其兩端而竭焉。 “If some rustic chap were to ask me about something, no matter how vacuous, I would exhaust myself over it, knocking my head against it top to bottom” (Lun yu 9.8).

About a century later the word has taken on a moralistic or ethical dimension and figures in some of the best-known passages of the Mencius as the “starting point” for what is innately good within a person, e.g.,: 惻隱之心, 仁之端也; 羞惡之心, 義之端也; 辭讓之心, 禮之端也; 是非之心, 智之端也。人之有是四端也, 猶其有四體也。有是四端而自謂不能者, 自賊者也。 “A feeling of sensitivity and sympathy is the starting point for humaneness; a feeling of diffidence and distaste is the starting point for propriety; a feeling of deference and yielding is the starting point for ceremony; a feeling for right and wrong is the starting point for wisdom. People have these four starting points just as they have four limbs. One who, having these four starting points, says of himself ‘I am unable [to meet these desiderata]’ does himself an injurious disservice” (Mencius 2A.6).

For the entry for hòu 厚 ‘magnitude’ see A 55. For the entry for tǐ 體 ‘element’ see A 2.

A 62

C::

有間, 不及^a中也。

E::

有間^b:謂夾之者也。

C::

yǒu jiān ‘having an interstice’ is (the sides) not reaching to the center.

E: :

yǒu jiān ‘having an interstice’: refers to what flanks it (i.e., what flanks the interstice).

• (a) R: null; emendation Graham, restoring the two-character phrase 不及 on the basis of a perceived parallelism with A 63 (1978, 311).

• (b) R: 聞; emendation Graham 1978, 310.

Beginning here with A 62 the text presents a series of eight terms dealing with spatial arrangements, from ‘having interstices’ to ‘being contiguous’. This section refers not simply to an ‘interstice’ (that is what we find in A 63), but to the object(s) in relation to which the interstice occurs. This may seem to be in some respects a subtle distinction, but it appears to be for the Mohist important.

A 63

C::

間, 不及旁也。

E::

間^a:謂所^b夾者也。尺前於區穴而後於端, 不夾於端與區穴^c。及及非齊之及也。

C::

jiān ‘interstice’ is not reaching to the sides.

E: :

jiān ‘interstice’: refers to what is flanked. Measurements starting from an outline and ending at an end-point should not be considered as flanked by the end-point and the outline. Those two reachings are not equivalent reachings.

• (a) R: 聞. emendation Graham 1978, 310.

• (b) R: null; 所 added by Graham 1978, 311.

• (c) R: 內, emendation Graham 1978, 310.

To be able to speak of an ‘interstice’ you need two flanking objects that are comparable in their capacity to be identified as boundaries of the interstice. Measuring from an outline with a measuring rod and considering the opposite end of the measuring rod as a flanking point does not define an interstice because on one side the measuring rod reaches the outline but on the other it “reaches” only to its own end-point. The two “flanking” parts are not comparable, and so the two reachings are not equivalent reachings.

As mentioned above (A 48) we understand qūxué 區穴 as a verb-object construction ‘to delineate the empty/hollow space’; and presumably the “empty space” can be filled with something and still remain amenable to an ‘outline’.

A 64

C::

櫨^a, 間虛也。

E::

櫨^b:虛也者兩木之間, 謂其無木者也。

C::

lú. ‘king-post’ the interstices are empty.

E: :

lú ‘king-post’: What is empty is the interstice between two pieces of wood. It refers to the fact of having no wood.

• (a) R: 纑; emendation Sun Yirang (Liang Qichao 1923, 51). The character in R, written with 糸, read lú < *rra, is defined in the Shuowen jiezi as bù lǚ 布縷 ‘hempen thread’ (SWGL 5906), a definition that may owe as much to the apparent near homophony of lú < *rra 纑 with lǚ < *ra-q 縷 (or of bù lǚ 布縷 with bó lú 薄櫨 [see below]) as with any precise meaning. Graham avers that he finds no meaning of lú 纑 that makes any sense here (1978, 311). The word lú 櫨, by contrast, means a kind of ‘rectangular piece of wood mounted on top of a pillar, as used, e.g., in the construction of a roof beam’ and would seem to fit the context here. It is entered in the Shuowen (SWGL 2499, as emended by Ding Fubao, based on a citation in Hui Lin’s Yiqie jing yin yi) identified with the binome bó lú 薄櫨. Ian Johnston identifies 櫨 lú as a ‘king-post’ (Johnston 2010, 428), i.e., “a structural member running vertically between the apex and base of a triangular roof truss.”⁶

• (b) R: 纑; see note a supra.

The Mohist has recourse to the everyday object of a king-post to illustrate the relation between an interstice and the material frame that forms it (Fig. 3.3).

Fig. 3.3

King-post (Wikimedia Commons)

This reference to the structure of a king-post takes the understanding of ‘interstice’ one step beyond the descriptions of A 62 and A 63 in that it explicitly recognizes the interstice as ‘empty’ (xū 虛) relative to the material frame. We might have expected the head character of a section such as this to have been xū 虛 ‘empty’, but that notion generally would include much that does not pertain to interstices. By the same token, the word ‘empty’ is here used only relative to the material flanking the interstice, not in any absolute sense. The choice of ‘king-post’ to illustrate this sense of ‘empty’ here may have been triggered by the immediately preceding sections on interstices (A 63) and things that have interstices (A 62). The king-post section completes the picture by identifying what is missing when something has an interstice.

A 65

C::

盈, 莫不有也。

E::

盈:無盈無厚。於尺無所往而不得^a二。

C::

yíng ‘being filled out’ is nowhere not having something.

E: :

yíng ‘being filled out’: Where there is no filling out there is no magnitude. On the measuring rod there is no place to which it extends such that you do not get both (i.e., filling out and magnitude).

• (a) R: 得得; the repetition of the character 得 is a mistake; emendation Graham 1978, 313.

The pair of concepts, ‘magnitude’ and ‘filling out’, consistently differentiate the spatial and the material aspects of physical bodies, yet the passage suggests that neither can occur in the absence of the other, that is, spatial extension of a physical object cannot occur without a material filling out, nor vice versa. (Note that in this case the term chí 尺 ‘measuring rod’ must refer to the physical object and not to an abstract measure.) The canon here commenting on yíng 盈 ‘being filled out’ seems intended to complement the immediately preceding canon dealing with the empty interstices characteristic of the structure of a lú 櫨 ‘king-post’. The ‘interstice’ (jiān 間) is a spatial extension described as lacking a given material, i.e., is the part that has no wood and therefore is said to be xū 虛 ‘empty’. ‘Magnitude’ (hòu 厚), by contrast, is a spatial extension that is always accompanied by some material ‘filling out’ (yíng 盈).

For the entry for hòu 厚 ‘magnitude’ see A 55.

A 66

C::

堅白, 不相外也。

E::

堅白:異處不相盈。相非是相外也。

C::

jiān bái ‘hard-and-white’ is neither excluding the other.

E: :

jiān bái ‘hard-and-white’: (Attributes in general) when occurring in different locations, do not fill out each other. When attributes are at odds with each other, this means they exclude each other.

This term jiān bái 堅白 ‘hard-and-white’ is central to many aspects of the Mohist’s logical discourse. It is defined here, at first unexpectedly, among the terms referring to spatial arrangements, because when understood literally, it refers to features that “fill out each other”, that is, that are co-occurring or coincident. This is precisely the sense of A 65 immediately preceding. The term wài 外 ‘excluding’ is to be understood concretely as spatial exclusion, but it equally implies logical exclusion. The explanation states that attributes cannot be called jiān bái ‘co-occurring, yet independent’ if they are located on objects in different places, or if they are incompatible with each other. In other words, the sense of jiān bái is delimited in two respects; it requires (a) spatial coincidence and (b) logical compatibility. It follows that for any two attributes to be in a jiān bái ‘hard-and-white’ relation they must be independent of each other.

A 67

C::

攖, 相得也。

E::

攖:尺與尺俱不盡, 端與^a端俱盡, 尺與端^b或盡或不盡。堅白之攖相盡,體攖不相盡^c。

C::

yīng ‘overlapping’ means each entailing the other.

E: :

yīng ‘overlapping’: When a measuring rod is put together with another measuring rod neither is exhausted. When an end-point is put together with another end-point both are exhausted. When a measuring rod is put together with an end-point one is exhausted and one is not. When attributes of the jiān bái ‘hard-and-white’ type overlap they exhaust each other. When elements (by contrast) overlap they do not exhaust each other.

• (a) R: 無; emendation Sun (Graham 1978, 314).

• (b) R: null; emendation Sun (Graham 1978, 314).

• (c) R: 盡端; the received text has the character 端 after 盡, which seems to be intrusive.

The first example of the Explanation depicts ‘overlapping’ in the most straightforward way, one thing partially coinciding with another. The ‘overlapping’ of attributes of a jiān bái type by contrast must by definition be exhaustive because they “fill out” a single object, just as the overlapping of two end-points will be exhaustive. Similarly, the two elements (tǐ 體) referred to in the last phrase of the Explanation must be elements of a single object, and their overlapping corresponds to the overlapping of the two measuring rods of the first line, except now we see that an ‘element’ is understood in an abstract sense, just as ‘hard-and-white’ is the abstract counterpart to the end-point. A 2 exemplified a tǐ ‘element’ as an ‘end-point’, yet the overlapping of two end-points cannot be the same thing as the overlapping of two elements, since both elements must belong to a single object, and it is impossible that two end-points of a single object could ever overlap.

A 68

C::

仳^a, 有以相攖, 有不相攖也。

E::

仳:兩有端而後^b可。

C::

bǐ ‘side-by-side comparing’ means there is a part where you make (two things) overlap one with the other and there is a part where they do not overlap.

E: :

bǐ ‘side-by-side comparing’: Only given that the two have an end-point (in common) is this possible.

• (a) R: 似; emendation Graham 1978, 315.

• (b) R: 后; sensu stricto the emendation is not necessary, since the two characters 后 and 後 in early texts are commonly used interchangeably for the word hòu ‘after’.

It is possible to lay two measuring sticks side by side such that they partially overlap and partially do not, but such a side-by-side comparison is not possible with shapes such as circles and ellipses, which do not have end-points. The explanation of the Canon here makes it clear that bǐ ‘side-by-side comparing’ must be of linear shaped objects, and for a meaningful comparison they should have one end-point in common.

A 69

C::

次, 無間而不相^a攖也。

E::

次:端^b無厚而後^c可。

C::

cì ‘contiguous’ is having no interstice but yet not overlapping one with the other.

E: :

cì ‘contiguous’: Only because the end-point has no magnitude is this possible.

• (a) R: 攖; emendation Graham 1978, 315.

• (b) R: null, emendation Graham 1978, 315.

• (c) R: 厚, emendation Graham 1978, 315.

Whereas A 68 deals with the side-by-side comparison of a linear shaped object, A 69 here is concerned with the same linear shape now arranged tip to tip.

3.5 Model and Duplicate, A 70, A 71

The following two sections define the related concepts of model (A 70) and duplicate (A 71). They have here been included owing to the central role of the idea of a model in Mohist thought (Fraser 2015, 2017), and because the circle and the compass appear as examples.

A 70

C::

法, 所若而然也。

E::

法:意規員三也, 俱可以為法。

C::

fǎ ‘model’ is that to which something has been made alike and is thus so.

E: :

fǎ ‘model’: thoughts, compass, circle, these three things can all serve as models.

The apparent claim that yì 意 ‘thoughts’ can serve as a model seems at first somewhat odd. Similarly, the compass mentioned as item two in the Explanation is also not actually a model per se, but is a device used to insure that something conforms to a given model. We must understand the phrase wéi fǎ 為法 as including a sense of “serving as a means or tool to test something against a model, or against a standard.” This is most clearly the case with tools such as the carpenter’s square and compass, or a plumb-line. These are not ‘models’ of anything; they are tools that will show whether something conforms to a given model or not. In the same way ‘thoughts’ are the means for testing behaviors or attitudes for their conformity (or not) to established models of ethical principles or beliefs. In the Mozi text these principles and beliefs are most clearly set out in the so-called “core” chapters (8–37, see the Introduction supra.) This capacity to match something, physical or abstract, against a preferred or desired ideal was the crucial feature of fǎ ‘model’. See Fraser 2015, 2017.

Chapter four of the Mozi text is titled fǎ yí 法儀 ‘models and exemplars’ and sets out propositions about the nature and importance of models. After mentioning the tools that a craftsman uses to insure his work adheres to the desired model, viz., the carpenter’s square, the compass, plumb-lines, etc., and after dismissing parents, teachers and sovereigns as unworkable prospective role models because the majority of all of these classes of people are not humane (rén 仁), the text concludes with the observation that 莫若法天 “nothing is as good as taking heaven as a model.” Heaven serves as an acceptable model, indeed the model for ethical considerations par excellence, precisely because its “operations are broad and free of self-interest” (天之行廣而無私). Heaven is not a remote, religious entity to be worshiped or revered abstractly, but is rather the premier example of an undiscriminating—but still judgmental—agency, rewarding the good with benefits and the bad with misfortune, regardless of social status or rank. The point is not simply to esteem heaven for this, but to take it as a model, a basis to on which to gauge one’s own behavior, and act with comparable equanimity toward people similarly, regardless of social status or rank.⁷

For notes on yí 儀 see the discussion under B 53, below.

A 71

C::

佴^a , 所然也。

E::

佴: 然也者, 皃^b 若法也。

C::

èr ‘duplicate’ is that which has been made to be like this.

E: :

èr ‘duplicate’: The word rán ‘to be like this’ means the appearance is like the model.

• (a) R: 佴 here Graham emends to yīn 因 (1978, 316), which he translates as ‘criterion’, chiefly on the basis of his understanding of this passage in a Mohist dialectical context overall. See Graham 1978, 214–16. He translates the Canon line as “The yin (criterion) is that wherein it is so.”

• (b) R: 民, emendation Graham 1978, 316; see also Graham 1978, 194–96 and infra A 47. In several other sections the same word is written in the conventional way, as 貌.

The character/word 佴 èr is uncommon, but not unattested. The Shuowen glosses it as cì yě 佽也 ‘to serve as a second; to assist’, emended by the Southern Tang Shuowen exegete Xu Kai 徐鍇 (920–74) in his Shuowen jiezi xizhuan 說文解字繫傳 to cì yě 次也 ‘sequel, second’ (SWGL 3537), and the Erya (shi yan 釋言 section) glosses it as èr 貳 ‘two, second, duplicate’. The sense of cì 佽 ‘to serve as a second’ is nothing more than a somewhat specialized sense of the basic word cì 次 ‘sequel, second’. Understood in this way the Canon line makes sense as written, and we have translated it accordingly, preferring not to follow Graham’s emendation on the grounds that when a text can be understood as written, absent other textual evidence to the contrary, emendation is not called for. In a 1964 article Graham himself did not emend the line and translated it as “The duplicate is what is made so” (Graham 1964, 18).

To be sure, a meaning ‘criterion’ as Graham would have it can be seen as a quasi-technical sense of yīn 因 ‘to rely on something’ > ‘to serve as grounds for’ and follows nicely from A 70 fǎ ‘model’. Graham prefers to see the Canon as defining yīn ‘criterion’, ‘criteria’ being the set of identifiable individual features on the basis of which something can be said to conform to a model. Three sections in the jing and jing shuo chapters mention yīn 因 explicitly, A 97, B 3 and B 15; in the last two it occurs as the object of the formulaic shuo zai 說在 phrase, thus 說在因 “the explanation lies with yīn ‘the basis’.” In both of these sections the context implies choices of one of a pair things, and yīn is the ‘basis’ upon which the choice is made. While this could be understood as ‘criteria’, it seems not to refer to a set of features as much as simply something on the basis of which to choose between alternatives. A 45 uses the word 徵 zhēng as the set of ‘identifying features’ of some X that, when changed, turns X into Y. Because it involves a set of features, this seems to come closer to the sense of ‘criteria’ than does the word yīn.

See also the discussion of yīn 因 in B 15.

3.6 Spatial and Temporal Contingency and Inevitability—Reprise, B 13–B 16

As Graham (1978, 30, 230) has observed, these four sections can be characterized as being parallel to (A 40–51). They present propositions on spatial extent, duration, and motion. In contrast to the definitions (A 40–51), the discussion is now augmented with the concept of hard-and-white which was introduced only in A 66.

B 13 establishes a relation between motion and spatial extent.

In B 14 the concept of hard-and-white, which so far has been solely applied to attributes of spatially extended objects, is now used in connection with space and time themselves. It is argued that the relation between spatial extent and duration is not of the hard-and-white type, since they are neither mutually pervasive nor independent. They are not mutually pervasive, because spatial extent exists separately at different periods of time, and they are not independent, because they are linked by motion. B 15 then states that the hard-and-white relation does in fact apply to lacking duration (a point in time) and spatial extent. These are considered to be independent from each other but also to fill out each other.

B 16 discusses the non-arbitrary contingent relation between events and time; uncharacteristically invoking an ostensibly historical event to illustrate the point.

B 13

C::

宇或徙^a, 說在長。

E::

宇:長^b 徙而又^c 處宇。

C::

‘Spatial extent’ [allows for] a shifting about somewhere. The explanation lies with ‘expanding’.

E: :

yǔ ‘spatial extent’: expanding is shifting about and thus occupying further spatial extent.

• (a) R: 從, emendation Graham 1978, 82.

• (b) R: 長宇, head character in second position.

• (c) R: 有, emendation Graham 1978, 367.

This and all following sections are distinguished from the preceding ones in that they state a proposition rather than delineating the meaning of a term. Because these are not definitions, the head character appears purely as a formality introducing the Explanation.

The sense of ‘expansion’ intended here by the word zhǎng 長 ‘growing’ is seen most clearly in the closely related modern Chinese expression péng zhàng 膨脹 ‘to expand, inflate’, used in connection with both an inflating economy and an expanding universe; zhǎng < *trang-q 長 ‘growing’ is likely a close cognate of zhàng < *trang-s 脹 ‘expanding’, both < **b-trang-q/s, as the binome péng zhàng < *bbrang - trang-s 膨脹 would suggest; cf. also zhàng < *trang-s 帳 ‘curtain’ < “billowing”, zhāng < *trang 張 ‘to stretch, expand’ (as e.g., a bow-string or a string on a musical instrument), also read zhàng < *trang-s meaning ‘to swell’.

Space is here associated with a capacity for movement in one direction or another. The immediately following section B 14, gives a characterization of the nature of the ‘extent of space’—‘duration of time’ relation in an explicit, technically phrased statement. This in turn may account for the proposition of yǔ 宇 ‘spatial extent’ here in concrete terms as ‘shifting about somewhere’.

B 14

C::

宇久^a 不堅白, 說 在 <?>。

E::

宇:南北在旦^b, 又^c 在暮^d。宇徙久。

C::

(The relation between) ‘spatial extent’ and ‘temporal duration’ is not of the hard-and-white type. The explanation lies with ...

E: :

yǔ ‘spatial extent’: South and north exist in relation to the dawn and also exist in relation to dusk. Within spatial extent, shifting about (entails) temporal duration.

• (a) R: The two parts of the first line of C are not contiguous in R at this point and have been (re-)joined by Graham (1978, 368) basing himself on the earlier work of Luan Tiaofu (1957, 14). The same instance of a defective text accounts for the missing word of the 說在 phrase.

• (b) R: 且, emendation Graham 1978, 81.

• (c) R: 有, emendation Graham 1978, 81.

• (d) R: 莫, emendation Graham 1978, 368.

The hard-and-white relation type is defined as that relation in which one attribute occurs coincidentally with, but independently of the other. Graham specifies jiān bái ‘hard-and-white’ as the technical term for “the separation of distinct, but mutually pervasive properties” (Graham 1978, 171). But spatial extent exists in connection with the dawn, and again separately in relation to the dusk. Furthermore, spatial extent is defined as that which allows for a shifting about (B 13), and because shifting about entails temporal duration, spatial extent therefore has a dependent relation to temporal duration. So ‘spatial extent’ and ‘temporal duration’ are not independent attributes, but are inherently linked. Thus they are not of the ‘hard-and-white’ type.

B 15

C::

無久與宇堅白, 說在因。

E::

無:堅得白必相盈也。

C::

(The relation between) ‘being without duration’ and ‘spatial extent’ is of the hard-and-white type. The explanation lies with the criterion.

E: :

wú ‘being without’: When the hard entails the white, each inevitably fills out the other.

The Explanation states that the ‘hard-and-white’ relation requires as a matter of definition that each attribute fills out the other, i.e., is co-incident with, but independent of, the other, and phrases this requirement as a matter of ‘inevitability’. (See A 51, bì 必 ‘inevitability’.) Here ‘inevitability’ is thus a consequence of the definition of ‘hard-and-white’ and therefore an instance of its logical use. (See A 66, jiān bái 堅白 ‘hard-and-white’.)

The relation between the absence of temporal duration, i.e., being temporally punctual, and spatial extent is said to be of this type, that is to say that there is no dependent relation between spatial extent and a moment in time. Section B 14 has just made clear that the relation between yǔ 宇 ‘spatial extent’ and jiǔ 久 ‘temporal duration’ is not of the ‘hard-and-white’ type. We now have in a sense the complement to that, the relation between a ‘point in time’ (wú jiǔ ‘being without duration’) and yǔ ‘spatial extent’, which is said to be of the ‘hard-and-white’ type. This implies that a single point in time was conceived of as filling out the whole of space, and in this respect the basic condition of being mutually pervasive is met, yet neither of the two is contingent on the other; there is no dependent relation between spatial extent and a moment in time. B 14, by contrast, explicitly states that there is a dependent relation between temporal duration and spatial extent, to wit, that mediated by a shifting about. Here, in B 15, ‘mutual pervasiveness’ is the necessary precondition for the pertinence of the hard-and-white relation, and in this way the former is a basis for the latter.

The word yīn < *ʔin 因 ‘the basis on which something is determined or decided’, i.e., ‘criterion’, is the introvert “-n extension” of the word yī < *ʔǝj 依 ‘to rest on, depend on’. The difference between the -i- vowel in yīn < *ʔin 因 and the -ǝ- in yī < *ʔǝj 依 may be the result of a vocalic raising and fronting accompanying the suffix -n, i.e., perhaps a shift **ʔǝn > *ʔin. There can in any case be little doubt that the two words are cognate; cf. yīn < *ʔin 茵 ~ 絪 ‘mat’, ‘a physical object on which to rest something’. The -ǝ- shows up in the yīn 因 xié shēng series in ēn < *ʔʔǝn 恩 ‘kindness’, where the geminate (or pharyngealized) initial consonant characteristic of type A syllables blocked any vocalic fronting.

B 16

C::

在諸其所然, 未然者^a。說在於是。

E::

在:堯善治, 自今在諸古也。自古在之今, 則堯不能治也。

C::

Locating something in relation to where (in time) it is properly so, or where (in time) it has not yet become so. The explanation lies with being in relation to this (appropriate or inappropriate time).

E::

zài ‘locating’: “Yao was good at keeping order.” This is, from a present perspective, locating it in the past. If one, looking from a past perspective, locates it in the present, then it means Yao will not be able to keep order.

• (a) R: 未者然; emendation Liang Qichao 1923, 361.

The point seems to be that there is a non-arbitrary relation between events and time. Events are spatial occurrences and by the same token they occur over time. Therefore they are characterized as having both a ‘spatial extent’ (yǔ 宇) and ‘temporal duration’ (jiǔ 久), and this pairing is, according to B 14 not of the hard-and-white type, i.e., does not entail independent attributes. This means that the two features ‘spatial extent’ and ‘temporal duration’ as they pertain to events (such as Yao keeping order) are dependent in some way each on the other; events are temporally contingent and therefore are not independent of the time in which they occur; thus the example regarding Yao. Located in the proper time he is good at keeping order (an event that is historically recognized, even if legendary from a modern perspective); located in an inappropriate time, he is unable. See also B 53.

Note that the use of the verb zài 在 ‘to be located somewhere’ or causatively, ‘to place something somewhere’, has both here and in B 14 a specification of time as the grammatical direct objects. Typically zài 在 locates things in space. The Mohist use of zài 在 this way must be intended to underscore the dependent connection between space and time that B 16 sets out.

Etymologically, zài < *ddzǝ-q 在 ‘to be located somewhere’ is closely related to the word cái < *ddzǝ 材 ‘innate capacity’ and to what we suggested above is fundamentally the same word, cái < *ddzǝ 才 ‘talent’, both referring to a kind of innate or ingrafted quality. The underlying sense for all of these is ‘implanted’, thus for zài 在, ‘set, located’. The character 在 is in its original structure simply the basic graph 才 augmented by the “earth” semantic determinative, 土 (Kangxi number 032), thus indicating clearly the spatial sense of the ‘locating’ (and concretely, in origin, probably also the phytological sense, i.e., ‘planting’ or ‘trans-planting’; cf. shì < *dzǝ-q 剚 ‘to dibble’, the Old Chinese type B counterpart to zài < *ddzǝ 在). See also the discussion at A 3.

For brief etymological speculations about the words gǔ 古 ‘past’ and jīn 今 ‘present’ see Boltz 1992.

3.7 Shadows and Mirror Images (“Optics”), B 17–B 24

The eight sections usually described as dealing with optics (see, e.g., Graham and Sivin 1973) deal in fact only with the properties of shadows (B 17–21) and mirror images (B 22–24). The character 景 is used commonly in Warring States period texts to write both the word yǐng meaning ‘shadow’ (typically written 影 in the transmitted writing system) and the word jǐng ‘light, luminescence; luminescent image, mirror image’. Which word is intended in any instance of the character must be inferred from context. The written language of the Mohist text does not differentiate the two words, suggesting that they are seen as closely related to each other and that they represent complementary aspects of light, viz., an image cast as a shadow and an image reflected in a mirror. It is not an ‘optics’ in the Greek sense of a theory of vision, but a study of shadows and a catoptrics (study of mirrors).

B 17 appears to make the point that the motion of a shadow is only apparent. The shadow does not move; what does in fact move is either the light source or the object casting a shadow (or both). The apparent motion of the shadow is created through the effect of light reaching places that were in shadow before and no longer reaching places that were illuminated before.

B 18 deals with a configuration of three lights in a row that results in a division of the surrounding space into a portion without shadow, a portion with a single shadow, and a portion with a double shadow. Since the first and the second are illuminated by two or three light sources, the paradoxically-sounding statement holds that the areas of double shadow are exactly those that are illuminated by a single light source each.

B 19 describes the inversion of the silhouette of a shadow projected through a pinhole onto a screen. The text implies a propagation of light rays along straight lines. Interestingly, that implication is seen only in those sections where image inversion is involved, as here and in B 23. In other sections where straight-line light propagation might be invoked, as in B 24, we do not find it explicitly mentioned. Therefore we have no clear evidence that the Mohists generalized the concept of light propagation along straight lines, which would have been a necessary condition for the development of a geometrical optics.

B 20 deals with the paradoxical situation that a person’s shadow is cast in the direction of the sun, rather than away from it, a situation that occurs when the sunlight is reflected or scattered off of an upright plane surface.

B 21 states that the shape and the size of a shadow depend not only on shape and size of the object casting the shadow but also on its position and place, as, e.g., an object’s distance from the screen or light source in a shadow theater.

B 22 describes the image one sees observing a plane mirror from above, pointing out the unexpected properties of size and shape as the image source moves.

B 23 describes the different variations of an image in a concave mirror (enlarged and upright or reduced and upside down), and explains them in terms of three elements: the thing mirrored, the image, and the occupied area on the surface of the mirror. The reversal of the image is explained by means of a geometrical treatment in which light is assumed to travel along straight lines in tandem with a concept of focal point (‘center’).

B 24 describes the variation of an image in a convex mirror (large or small but always upright) and explains it, as in B 23, in terms of three elements: the thing mirrored, the image, and the occupied area on the surface of the mirror.

B 17

C::

景不徙^a。說在改為。

E::

景:光至景亡。若在盡古息。

C::

A shadow does not shift about. The explanation lies with being re-cast.

E::

yǐng ‘shadow’: When light reaches a place, the shadow disappears; as if its existence has been exhausted and its past extinguished.

• (a) R: 從, emendation Graham 1978, 82.

This is the first of a series of sections dealing with optics. The sense is that what might appear at first to constitute the shifting of a shadow, is to be understood instead as the disappearance of the old shadow and its re-emergence anew in a different position. When the shadow seems to move it is actually being extinguished, perhaps only partially, by the arrival of light, and re-cast in a different place. It is either the object casting the shadow or the light source that moves, not the shadow itself as if it were an actual object. Just as the former shadow is gone, the past is extinguished (not shifted); both are replaced by the new.

This is one of the comparatively few Mozi “jing” or “jing shuo” passages that is found cited in later, transmitted texts. The Liezi, “Zhongni” 仲尼 section, includes it in a kind of seriatim listing of “imponderables,” that is, short counter-intuitive statements that seem to propose paradoxes or impossibilities, presumably intended to provoke unconventional thinking. One of these statements says 有影不移 “There are shadows that do not move.” Each such statement is then given what purports to be an explanation. For this one we find a passage that is essentially the same as the B 17 Canon here, though using the verb yí 移 ‘move’ rather than xǐ 徙 ‘shift about’: 影不移者說在改也 “As for the fact that the shadow does not move, the explanation lies with it [instead] changing” (Yang Bojun 1965, 88). The received text of the Liezi is a late third century compilation, and is thus half a millennium or more later than the Mozi text. Its reference to the “shadow not moving” is therefore clearly derived from the Mozi line. Apart from the chronological improbability of the “Mo jing” line somehow being derived from the Liezi line, the difference between 說在改也 in Liezi and 說在改為 in Mozi also suggests that the Liezi line is taken from a Mozi original because the latter, with 為 as a somewhat uncommon sentence final word, is clearly the lectio difficilior relative to the former. An editorial change from 改為 ‘re-made, re-cast’ to 改也 ‘changed’ is easier to imagine than the reverse.

The “Tian xia” 天下 chapter of the Zhuangzi has a line that seems likely to reflect the same underlying sense, though not worded in a way that suggests the Mozi line directly: 飛鳥之景未嘗動也 “The shadow of a flying bird has never moved.” This occurs in the same kind of list as in the Liezi of counter-intuitive statements characteristic of that “philosophical” group usually called the Sophists, intended presumably to stimulate discussion and debate. Other examples of the same kind of statement are “a wheel does not touch the ground,” “fire is not hot,” “fast though the barbed arrow flies, there is a time when it is neither moving nor at rest.” (Translations of the “non-shadow” lines from Graham 1981, 284.) As Graham (1978, 274) points out, the late third century commentator Sima Biao 司馬彪 in his note to this line says

鳥之蔽光猶魚之蔽水。魚動蔽水而水不動。鳥動影生, 影生光亡。亡非往, 生非來。墨子曰影不徙也。⁸

A bird’s interrupting the light is similar to a fish’s interrupting the water. As a fish moves it interrupts the water, but the water does not move. A bird moves; a shadow arises. A shadow arising [means] the light disappears. Disappearing is not moving away; arising is not coming forth. Mozi said “A shadow does not shift about.”

Sima Biao’s point seems to be that since a shadow is an interference or absence of light, it is not actually anything in its own right, and an absence of something is not something that can move forward. So, mutatis mutandis for a shadow arising. We cannot know with certainty if the Mohist was thinking of it this way, but it seems consistent with the sense of this Mojing section.

B 18

C::

景二, 說在重。

E::

景:二光夾一光, 一光者景也。

C::

The shadows are two in number. The explanation lies with doubling.

E: :

yǐng ‘shadow’: Two lights flanking one light; what is singly lighted is a shadow.

What is referred to as ‘singly lighted’ in the Explanation means an area illuminated by only one of the light sources. In Fig. 3.4 below these are the areas marked by the number 2. When three light sources are arranged linearly as A–B–C in the figure, B flanked by A and C, A will cause a shadow of B towards C; C will cause a shadow of B towards A. And B will cause shadows of both A and C, each directed outward from A, resp. C. These two symmetrical shadows caused by B will each fall within the scope of the shadows of B caused by A, resp. C, but will be perceptible by virtue of being darker than the surrounding shadow. The schematic diagram shown in Fig. 3.4 illustrates the patterns of shadows that can be observed when three candles are put in a row, as A, B, and C (see the photograph in Fig. 3.5).

Fig. 3.4

Arrangements of light sources A–B–C and corresponding single (1) and double (2) shadows

Fig. 3.5

Three candles in a row

The “two in number” phrase refers to the fact that on each side of the central light source B there is a dual-shadow pattern; a darker shadow completely encompassed by a lighter shadow (numbers 2 and 1 in the figure). The “doubling” refers to the darker part being the result of shadows of two different objects caused by two different light sources. The area of these double shadows is illuminated by a single light, A, resp. C. Therefore the areas that are singly lighted are precisely those that consist in double shadows.⁹

B 19

C::

景倒^a在午有端與景長。說在端。

E::

景:光之入^b煦若射。下者之入^c也高, 高者之入^d也下。足蔽下光, 故成景於上^e, 首蔽上光, 故成景於下。在遠近有端與於光, 故景運^f內也。

C::

The shadow becomes upside down at a crossing, where there is a point in conjunction with which the shadow elongates. The explanation lies with the point.

E: :

yǐng ‘shadow’: When light enters, it emanates like arrows shot from a bow. The entry of the low part is upward, the entry of the high part is downward. The foot blocks the light from below; on this basis it forms a shadow above. The head blocks the light from above; on this basis it forms a shadow below. Located at some distance there is the point conjoined with what is in the light. On this basis the shadow is rotated on the inside.

• (a) R: 到, emendation Graham 1978, 375.

• (b) R: 人, emendation Graham 1978, 82.

• (c) R: 人, emendation Graham 1978, 82.

• (d) R: 人, emendation Graham 1978, 82.

• (e) R: 止, emendation Graham 1978, 376.

• (f) R: 庫, emendation Graham 1978, 376; see A 48 where 運 is defined as yì 易 ‘to switch’, a definition that fits its usage in this passage perfectly.

This section seems to describe the inversion of an image as it appears silhouetted on a surface from light passing through a pinhole in another surface. The Explanation makes it clear that the Mohist conceived of this image as a shadow. The entering of the light into and its emanation from the pinhole is compared to the shooting of arrows from a bow. The verb xù 煦 usually means simply ‘warm, congenial’, but occurs in passages specifically associated with the warmth of a sunrise, a warmth that accompanies the impression of sunlight emanating from a rising sun. The Shuowen jiezi includes the gloss chì 赤 ‘red’ for this word, a gloss that suggested to Sun Yirang (1986, 390) the word xiá 霞 ‘the reddening sky of a sunrise, aurora’, an image that is not inconsistent with the general meaning ‘emanate’. The character 煦 of the received text sometimes alternates with the related character 喣 standing for the phonetically similar word xǔ ‘to exhale, blow out (from)’, a meaning that is not unrelated to the sense of ‘emanate’ suggested here. Using this word and this understanding then the Mohist passage describes the inversion of the image of what is in the light (於光) passing through a pinhole (端, the base point) and the consequent inversion of the top and bottom parts of the silhouette.

The duān ‘base point’ in the Canon line is the point of the ‘crossing’ (午) that was perceived as the starting point from which the cone of the inverted shadow image grows. The ‘base point’ in the Explanation line is now described as the end-point of the cone of the shadow image on the side where the light enters the pinhole. The two cones together describe the geometry of the situation that is defined by the “arrow-like” behavior of light proceeding along straight lines, passing through a pinhole (Fig. 3.6).

Fig. 3.6

Reconstruction of arrangement in section B 19

This is sometimes thought to describe the image produced by a camera obscura, but the text only refers to blocking the light and therefore allowing only for a shadow image. Graham and Sivin 1973, 120–25 discuss this section at length, in the end not agreeing with each other on the correct interpretation. Graham 1978, 375–78 is largely unchanged from his earlier analysis, thinking that it describes reflection in a concave mirror. For his part Sivin prefers to understand this as describing a kind of camera obscura. We have in our understanding differed from both, but ended up closer to Sivin’s explanation than to Graham’s.

B 20

C::

景迎日。說在慱^a。

E::

景:日之光反燭人則景在日與人之間。

C::

The shadow turns toward the sun. The explanation lies with completing the cycle.

E: :

yǐng ‘shadow’: If the light of the sun reverses and illuminates a person, then the shadow lies between the sun and the person.

• (a) 慱: tuán ‘to complete a cycle’; this character rarely occurs in transmitted literature. It is said to occur in one (non-standard) version of the Tai xuan jing 太玄經 (compiled by Yang Xiong 揚雄, late first century b.c.e.), in the line 月闕其慱賤始退 “as the moon becomes defective (i.e., begins to wane), its completed cycle becomes attenuated and begins to retreat.” The received Tai xuan jing text of this line has 摶 tuán which is understood as 團 tuán ‘round’, in this context simply “full”, but the subtler sense of 慱 tuán is ‘a completed cycle’ (Liu Shaojun 1998, 6).

The ‘completed cycle’ sense characterizes the light-shadow phenomenon that the Mohist is describing here in that the light emanates from the sun, reverses by being reflected off of something, illuminates a person which then casts a shadow back towards the sun, in a sense thus completing the cycle. This sense is inherent in the Canon’s use of the word yīng 迎 ‘to turn toward, to meet from an opposing direction’. The first part of the cycle consists in the behavior of the light, the second part in that of the shadow, yet for the Mohist these seem to be two aspects of a single phenomenon. The character 景 can be used to write the word yǐng ‘shadow’ (in the received script typically written 影) and also the word jǐng ‘light, image’. The two words yǐng < *qrangʔ and jǐng < *krangʔ (perhaps from an earlier *C.qrangʔ, see Baxter and Sagart 2014, 28) ‘(sun-)light, brightness’ are likely related to each other as variants of a single lexical base. In the sections describing the optical features of mirrors, beginning with B 22, the character 景 clearly refers to the reflected image, not a shadow, thus probably writing the word jǐng, not yǐng.

B 21

C::

景之大小。說在杝^a正遠近。

E::

景: 木杝景短大, 木正景長小。大小於木則景大於木。非獨小也, 遠近也^b。

C::

The shadow’s being large or small, the explanation lies with tilt and distance.

E: :

yǐng ‘shadow’: If the post is tilting, then the shadow is short and broad; when the post is straight upright, then the shadow is long and thin. As for its size in relation to the post, the shadow is bigger than the post. This is not solely due to its smallness, but also due to its distance.

• (a) R: 地, emendation Graham 1978, 379.

• (b) R: has no 也; to understand the meaning as ‘due to ...’ the final 也 is necessary.

The Canon raises the subject of a shadow’s size, and the Explanation first observes that the length and size of a post’s shadow will vary according to whether the post is upright or tilted (toward the light source). This does not address the question of the size of the shadow relative to the post itself. The shadow will generally be bigger than the post, irrespective of the post’s tilt, and this is said not to be due to actual size alone, but distance as well. A possible arrangement in which these features of a shadow could be observed is one similar to a shadow theater where a single or confined light source casts an object’s shadow on a vertical surface.

B 22

C::

臨鑑而立, 景倒^a, 多而若少。說在寡區。

E::

臨:正鑒^b景寡, 貌態^c 白黑遠近杝正異於光。鑒景當, 俱就去。參^d當, 俱^e 向^f 背^g。鑒者之澤^h 於鑒無所不鑒, 景之澤無數而必過正。故同處。其體俱然, 鑒分。

C::

Looking down from above into a mirror and then standing up, the image is upside down. It becomes more, but seems as if fewer. The explanation lies with reducing the area.

E: :

lín ‘looking down’: In a flat mirror the image is reduced; in appearance, brightness, distance and tilt it may be different from what is in the light. When the image in the mirror (and the object mirrored) are vis-à-vis each other, both approach and recede in tandem. When they are kept in alignment this way they turn either face-to-face or back-to-back in tandem. The parts of the object mirrored shining toward the mirror are nowhere not mirrored. The image’s lustrousness is unlimited and will inevitably have passed beyond the plane (of the mirror); on that basis it will be confined to the same area (on the mirror surface). All of its elements will behave like this, mirroring the parts.

• (a) R: 到, emendation Graham 1978, 379.

• (b) the word jiàn ‘mirror’ is written 鑑 in C and consistently 鑒 in E. This is a case of free allography, there is no difference in the word written.

• (c) R: 能.

• (d) R: , emendation Graham 1978, 379–80.

• (e) R: 俱俱.

• (f) R: 用, emendation Graham 1978, 380.

• (g) R: 北.

• (h) R: 臭, for an obsolete character , standing for zé ‘lustrous, glossy’ (modern orthography 澤), emendation Li Yü-shu (Graham 1978, 380), 2x.

This is the first of three types of mirror, flat, concave and convex, that the text discusses and is the only one that includes any reference to the internal features of an image. Other sections deal only with silhouette-images or shadows. Here the character 景 clearly writes the word jǐng and refers to the image reflected in a mirror, whereas in preceding sections the same character was writing the word yǐng ‘shadow’. See the note in B 20.

The section discusses visual effects that can only be observed when internal features of the image are taken into account. The Canon has to be understood as describing a movement and the consequent change in the mirrored image. As a person stands up from looking down into a mirror what he sees will change from a partial image “looking back up at him” to a fully standing image that will appear upside down. The image will have become smaller in mirror area yet contain a larger part of his person, hence the comment that 多而若少 “it becomes more, but seems as if fewer,” so also for the comment that 說在寡區 “the explanation lies with reducing the area.” The Explanation first identifies those respects in which a mirror image might vary from the features of the actual object and then notes how the movement of the object is reflected symmetrically in the movement of the mirrored image. By contrast, then, the Explanation goes on to state that only those parts of the actual object that “shine toward the mirror” are mirrored. In other words, the mirror image only includes what faces the mirror; nothing from the back of the object will appear in the mirrored image, unless of course turned toward the mirror. The image will appear to be located not on the surface of the mirror but “beyond” it, because a mirror image is naturally seen as three dimensional. Even though the mirrored object may be large, depending on its position relative to the mirror the place of the image on the surface of the mirror may be small. And because this is true for every part of any object mirrored, the mirroring is understood as a perfect part-to-part isomorphism, even when the image area is reduced from that of the object.

B 23

C::

鑑洼^a, 景^b一小而易, 一大而正。說在中之外內。

E::

鑒^c:中之內。鑒者近中則所鑒大, 景亦大。遠中則所鑒小, 景亦小, 而必正。起於中緣正而長其直也。中之外。鑒者近中則所鑒大, 景亦大。遠中則所鑒小, 景亦小, 而必易。合於<中... > ^d而長其直也。

C::

The mirror is concave; the image is sometimes small and switched, and sometimes large and upright. The explanation lies with being inside or outside the center.

E: :

jiàn ‘to be mirrored’: As for being within the center, when the thing mirrored is near to the center, then what it is mirrored on is large, and the image also is large. When it is distant from the center, then what it is mirrored on is small, and the image also is small and (in both cases) inevitably upright. This is due to (the light) arising from the center, skirting the upright object and then extending along its direct path. As for being outside the center, when the thing mirrored is near to the center, then what it is mirrored on is large, and the image too is large; when it is distant from the center, then what it is mirrored on is small, and the image too is small and (in both cases) inevitably switched. This is due to (the light) converging at < the center … > and then extending along its direct path.

• (a) R: 位, emendation Graham 1978, 381; the character interchanges with 窪, 哇 and 窊, all writing the same word wā ‘concave’.

• (b) R: 量, emendation Graham 1978, 382.

• (c) Here and in B 24 following the text systematically registers an orthographic distinction between the noun jiàn ‘mirror’ and the homophonous verb jiàn ‘to be mirrored’, the former written 鑑 and the latter written 鑒, two characters that are conventionally taken as standing in free variation for jiàn ‘mirror’. Thus in this case the head character of E is not simply a token reference to C, but reflects the fact that it is the verb ‘to be mirrored’ that figures centrally in the E text.

• (d) R: null. Graham suggests that parallelism with 起於中緣正而長其直也 in the preceding line implies a lost three-character phrase, beginning with 中.

The Mohist recognizes three components to a reflection on a concave mirror, (i) the thing mirrored (鑒者), (ii) the image itself (景), and (iii) the area on the surface of the mirror that the image occupies (所鑒). Recognizing a distinction between the image itself and the surface that the image occupies is because there is a three-dimensional perception that makes the image appear to be behind the plane of the mirror. What the text refers to as the ‘center’ (中) is from a modern perspective the focal point only in regard to how size and orientation of the image change depending on the position of the mirrored object relative to that point. It is seen by the Mohists as the point of confluence of the straight lines that define the contours of the silhouette-image, but that understanding is not correct from the viewpoint of geometrical optics, although qualitatively it produces the right results. The fact that the Mohists call this point the ‘center’ may indicate that they conceived of it as the geometrical center of the curvature of the mirror.

The Explanation includes the observation that when an object stands between the ‘center’ and the mirror, the light that is responsible for the image seems to ‘arise from’ (起於) the ‘center’ and then proceeds in a straight line to produce an upright image. The crucial corresponding phrase in the text that would explain the behavior of the light when an object stands outside of the area defined by the ‘center’ and the mirror is regrettably defective, but the first words suggest that the understanding might have been that the light ‘converges’ or ‘comes together’ (合於) at the ‘center’ and then proceeds in a straight line to produce an inverted image. This Explanation only considers the silhouette-image. It cannot explain the internal features of a mirrored image, because it always considers light as coming from behind the object mirrored.

For yì 易 see A 48.

B 24

C::

鑑團, 景一^a小一^b大^c而必正。^d

E::

鑑:鑒^e 者近則所鑒大, 景亦大。其^f 遠, 所鑒小, 景亦小, 而必正。景過正故招^g。

C::

The mirror is convex; the image is sometimes small and sometimes large, but inevitably upright.

E: :

jiàn ‘mirror’: When the thing mirrored is near, then what it is mirrored on is large, and the image too is large. As for its being at a distance, what it is mirrored on is small, and the image too is small and (in both cases the image is) inevitably upright. The image extends beyond the (vertical tangent) plane (of the mirror) and on that basis is drawn out (on the sides).

• (a) R: The two parts of C are not contiguous in R at this point and have been (re-)joined by Graham (1978, 384) basing himself on the earlier work of Luan Tiaofu (1957, 87).

• (b) R: null, the two characters 小一 are added speculatively by Graham 1978, 384.

• (c) R: 天, emendation Graham 1978, 384, as part of a restoration of the whole line.

• (d) R: 說在得. Graham suspects the three-character sentence 說在得 is misplaced here and belongs to a later, now defective, canon. See infra 25b. This leaves B 24 as a rare case of a Canon without a shuō zài phrase among the B numbers.

• (e) see textual note c in B 23, immediately preceding.

• (f) R: 亦, emendation Graham 1978, 384.

• (g) 招 zhāo ‘beckon, call’, here in the particular sense of being “called,” i.e., drawn out or stretched in an increasingly attenuated form toward the edge of the mirror.

As in the preceding section, the Mohist recognizes three components to a reflection, now on a convex mirror, (i) the thing mirrored (鑒者), (ii) the image itself (景), and (iii) the area on the surface of the convex mirror that the image occupies (所鑒). The passage correctly describes the variation in size of the latter two qualitatively according to the distance of the thing mirrored from the mirror itself. Specifically in the case of a convex mirror, the image gives the appearance of shrinking at the edges as the surface recedes.

While in section B 23 a complete account was given of why the image varies in size and orientation, including the notion of a ‘center point’ (中), no such explanation is provided in this section.

3.8 Vertical Tendency of Weights (“Mechanics”), B 25a–B 29

These six sections, usually described as “Mechanics” (Graham 1978, 385), all deal expressly with the vertical descent of weights (重 zhòng) and anomalies arising from either deviation from the vertical direction (e.g., B 27) or disparity of the effect of equal weights (e.g., B 25a and 25b). To be sure, these are mechanical behaviors, but as described here the clear emphasis is on the behavior of weights when manipulated in various ways, so we use the more specific phrase ‘vertical tendency of weights’ rather than ‘mechanics’.

B 25a deals with the different effect of weights placed either on a horizontally hung rope or on a horizontal beam. While the rope bends already under its own weight, the beam does not bend even if you place a weight on it. The difference is explained by referring to the ‘rigidity’ (極 jí), which we may also call ‘pole-quality’, prevailing in the case of the cross-bar but not in the case of the rope. The different effect of a weight in the two situations is thus explained by means of the additional term ‘rigidity’.

B 25b deals with the different effect of weights placed on different sides of a beam whose fulcrum is not in the middle of the beam. Placing equal weights on the two sides, the longer side (measured from the fulcrum) will descend. This is explained by referring to the ‘effectiveness’ (權 quán) this side of the beam has gained over the other by having become the longer side. The different effect of a weight in the two situations is thus explained by means of the additional term ‘effectiveness’.

B 26 deals with the different behavior of the two sides of a pulley, or a curtain pole, over which a curtain is pulled, depending on the length of the cloth on the two sides. To pull the curtain up from the shorter side, a force has to be exerted. If the curtain remains fixed in place although no force is exerted, this is due to the construction having been arrested in some way. When the curtain is equally long on both sides of the pulley or pole, it may remain fixed. But when the curtain is longer on the pulling side, it will come down by itself. The different behaviors are again explained by the pair of terms encountered in B 25b: weight (zhòng 重) and effectiveness (quán 權). This time we do not have equal weights on two sides of different effectiveness, but two sides whose weight and effectiveness are changing in tandem; the side that is getting longer constantly gains both weight and effectiveness, while the other side loses both. When weight and effectiveness are equal on both sides there is equilibrium. But if the weight and effectiveness get used up, the curtain falls down. The different behavior of the two sides of a pulley is thus explained by the same pair of terms, weight and effectiveness, that was employed in explaining the unexpected behavior of the arrangement involving a lever (B 25b).

B 27 contains the general statement that weights descend vertically if nothing interferes with them. The device referred to in this section, whose description remains obscure and which is sometimes speculatively thought to be a kind of wheeled ladder, may have presented a prominent instance exactly of such an interference. Moreover, this interference with vertical descent appears to have been instrumental for the functioning of the device, the movement of the ladder. This establishes a strong connection with the next section, which makes a general statement about the necessity of the deviation from the vertical whenever horizontal forces are in play.

B 28 deals with the case of leaning and makes the general claim that, whenever horizontal forces are involved (pressing against, pushing, dragging or being bent under something), the agent cannot be exactly upright, just as a ladder leaning against a wall cannot be exactly upright. In fact, speaking from a modern perspective, in leaning, a person’s or an object’s weight, which is a vertical force, is used to produce a horizontal force component. Given the emphasis on the vertical descent of weights in the previous section, this section apparently reflects an intuitive understanding of the use of leaning in producing a stable arrangement when horizontal forces are involved. The section thus fits very well into this sequence of sections on deviations from vertical descent.

B 29 comes back to the discussion of the vertical, now considering the relation between being fixed in place and moving downwards. The point is made that piling things one above the other actually fixes the position of the object on top; it cannot descend due to the ‘pillar-quality’ (zhù 柱) of the arrangement. Construction techniques often involve this when stones or bricks are arranged to build walls. Fixing something with a string from above does not have this pillar-quality: the string may be drawn out thus turning the ‘pulling (holding) from above’ into a ‘letting gradually down’. The section thus emphasizes the close connection between the vertical descent of weights and the stability of a plinth. The difference in behavior (being fixed in place or descending) is due to the difference between piling up and suspending. Considering the material aspect of this difference, the section is reminiscent of the first section in this sequence, explaining the different behavior of weights on rigid objects as compared to that on cords. But the explanation is not given in terms of rigidity (jí 極) but rather in terms of pillar-quality, thus emphasizing the difference in arrangement over that in material.

B 25a

C::

負^a而不撓, 說在勝。

E::

負:衡木加^b重焉而不撓, 極勝重也。右校交繩, 無加焉而撓, 極不勝重也。

C::

Bearing but not being deformed, the explanation lies with prevailing.

E: :

fù ‘bearing’: A cross-bar when you add a weight to it is not deformed. This is due to the rigidity prevailing over the weight. A plaited cord twisted to the right, [even] when nothing is added to it, becomes deformed. This is due to the rigidity not prevailing over the [cord’s own] weight.

• (a) R: 貞, emendation Graham 1978, 387.

• (b) R: 如, emendation Graham 1978, 387.

The Canon addresses the phenomenon of something not bending under a load. The Explanation goes on to contrast a wooden beam with a plaited cord, each set out horizontally, in that the former does not bend though burdened with a weight, while the latter does bend even in the absence of any weight added. The difference lies in the varying degrees of rigidity (jí 極) of the two objects. This shows that for the Mohist the term zhòng 重 refers not only to heavy objects but also to the more abstract quality of weight, here the weight of the rope itself.

The word jí 極 ‘ridge-pole’ here means ‘rigidity’ indicating the quality pertinent to this explanation.¹⁰ Eng. rigid, from Latin rigeō ‘to be stiff, rigid’, is cognate with both Eng. reach and Ger. reichen, showing the same semantic link between ‘rigidity’ and ‘reach’ as seen in jí 極 ‘ridge-pole’ itself, which also means ‘reach’ as a noun in the sense of ‘furthest reach, extremity’.

In this interpretation the phrase 交繩 is taken to refer to a plaited or braided (modern jiǎo 絞) rope, and the phrase 右校 is understood as the act of braiding such a rope, so there is a puzzling redundancy overall: “a rightward braided plaited rope.” This may refer to a kind of ‘double braided rope’, i.e., a rope that is braided out of strands that are already plaited, in order to enhance its strength. It is not clear what the significance of the adverbial 右 ‘right(ward)’ is; the same phenomenon would be observed when the rope is twisted leftward. All the same, the point presumably is that in the everyday act of horizontally stringing up a plaited rope, even when taut, the rope will deform downwards of its own accord, that is, from its own weight.

B 25b

C::

衡^a […]。說在得^b。

E::

衡:加重於其一旁必垂^c, 權重相若也。相衡則本短標長。兩加焉重相若則標^d 必下, 標得權也。

C::

The beam […] The explanation lies with gaining.

E: :

héng ‘beam’: If you add a weight to one of its sides [that side] will inevitably drop down. This is due to the effectiveness and the weight matching each other. If they are made level with each other, then the base is short and the tip is long. Add equal weights to both sides, then the tip will inevitably go down. This is due to the tip having gained effectiveness.

• (a) R: original text defective, restored by Graham 1978, 387.

• (b) R: restored here from B 24, Graham 1978, 387.

• (c) R: 捶,

• (d) R: 摽.

The passage may be understood as based on a practical situation in which a beam is balanced either by being suspended or supported at one point, i.e., a fulcrum. If a weight is attached to one side of the beam then this side will drop down. Here, the term zhòng 重 ‘weight’ is complemented by another term, quán 權 ‘effectiveness’. We understand this term as designating an abstract measure of the effect of the weight. In the case at hand, the weight and its effectiveness match each other, i.e., the effect of the weight is as expected, the side where the weight is placed goes down. So far, this is in accord with our expectations and would not have required the introduction of any additional technical term. The beam with the weight attached to one of its sides is then brought back into a horizontal position by moving the fulcrum. The result is that one side of the beam, when measured from the fulcrum, is shorter than the other. The Mohist calls the side having the weight attached to it the běn 本 ‘base’, which is now short, and the other side the biāo 標 ‘tip’, which is now long. Adding equal weights to both sides of the beam, the tip declines. This appears inconsistent with the assumption that equal causes have equal effects and therefore is not what one would intuitively expect. One would expect the tip to go down only if the weight laid on that side was greater than that laid on the side of the base. It thus seems that the weight on the tip-side is somehow more effective than that on the base-side. This is expressed by the statement that the tip has gained in quán 權 ‘effectiveness’. Most probably, the lost Canon referred to this phenomenon which forced the Mohist to introduce the technical term ‘effectiveness’.

The central question addressed by this section is as follows: how can it be that one and the same heavy body has, under certain circumstances, a different effect from what one would expect it to have? It is answered by introducing a pair of abstract terms, weight and effectiveness, that differentiate the concept of weight in order to account for its different behavior under certain circumstances.

This section is sometimes interpreted as referring to an unequal-arms balance, such as a steelyard or a bismar. But not only is there no evidence that such balances existed this early in China, neither does that kind of balance conform to the description given here, with weights added to both sides.¹¹ Instead, the Mohist would have likely been familiar with the kind of situation described from the use of a shoulder-pole, where the shifting of the fulcrum is an automatic reaction to adding a load to one side.

B 26

C::

挈^a與收^b反^c。說在薄。

E::

挈:有力也^d 引, 無力也不止^e。所挈之止於施^f 也, 繩掣^g挈之也。若以錐刺之。挈:長重者下, 短輕者上。上者愈得, 下^h者愈亡。繩直, 權重相若, 則止ⁱ矣。收:上者愈喪, 下者愈得。上者權重盡, 則遂^j。

C::

Pulling something up in conjunction with letting something gradually down are the reverse of each other. The explanation lies with [the behavior of] curtains.

E::

qiè ‘pulling something up’: when one exerts force, it is drawn up and taut; in the absence of force, it does not remain fixed. When that which is pulled is fixed mid-way it is due to the cord being pulled askew, sticking it [in place] as if with an awl.

Pulling something up: The long and heavy is below, the short and light is above. The more the one above gains, the more the one below loses. When the cord hangs straight and the effectiveness and the weight match each other, then it would remain fixed.

Letting something down gradually: The more the one above loses, the more the one below gains. If the effectiveness and the weight of the one above are exhausted, it drops.

• (a) R: 契, emendation based on E.

• (b) R: 枝, emendation Graham 1978, 390).

• (c) R: 板 [băn ‘wood block’] understood as 反 făn ‘to reverse, turn back, alternate’.

• (d) R: Graham emends 也 to 之 here, but not in the parallel next line, on the grounds that nowhere else in these chapters do we find the “subjectless” initial clause marked by 也 (1978, 390). The text is understandable as written with 也 in both places, and therefore the emendation is not required.

• (e) R: 心, emendation Graham 1978, 82.

• (f) R: 施 [shī < *hlaj ‘spread out’] for yí < *laj ‘shift, move, reach to’ (移 in the received script), nominally ‘reach’ as an extent or span or trajectory; the locus classicus for this reading and meaning of the character 施 is Xunzi, “Ru xiao”: 若夫充虛之相施易也 “It’s like the shifting and alternating of full and empty,” where Yang Liang says 施讀若移 “施 is to be read like 移.” Graham suggests an emendation to 迤 yǐ ‘slanting, turning’, but this seems to be unduly influenced by the next phrase.

• (g) R: 制 for 掣 chè ‘to drag sideways, to skew’.

• (h) R: 下下, erroneous doubling of the 下; emendation Graham 1978, 391.

• (i) R: 心, emendation Graham 1978, 82.

• (j) R: 遂 [suì < *s-lut-s ‘advance’] for zhuì < *lrut-s ‘fall, drop down’ (隊/墜 in the received script).

The two phases of motion, that of the pulling up and that of the letting something down in a controlled descent, are portrayed as complementing each other, hence the use of the verb 反 făn ‘to reverse, turn back, alternate’ in the Canon. When pulling something up a force must be maintained in order to keep it from falling back down. To fix the object being pulled over the pulley mid-way on the far side, the cord is pulled askew and anchored by some device (the passage specifies an awl). When pulling a curtain over a rod, for example, if the two sides of the curtain hang at equal lengths and the pull-cord can be released and hangs vertically, then the curtain will remain fixed by itself.

As in the preceding section, the word quán 權 ‘effectiveness’ is used in tandem with zhòng 重 ‘weight’. The phrase 權重相若 (“the effectiveness and the weight match each other”) here, as in B 25b, refers to a situation where the lengths on both sides of the mechanism are equal to each other and therefore the weight by itself determines the effectiveness. Letting something down gradually is the complementary process to pulling something up. When there is no longer either effectiveness or weight of the upper part on the near side, the thing simply falls down on the far side.

B 27

C::

挈 […] 車梯 […]。^a

E::

挈:兩輪高, 兩輪為輲^b, 車梯也。重其前, 弦其前載^c, 弦其而縣重於其前, 是梯^e 挈, 且挈則行。凡重, 上弗挈, 下弗收, 旁弗劫, 則下直。扡^f, 或害之也。者不得直也。今也廢尺於平地, 重不下, 無 也。若夫繩之引也, 是猶自舟中引橫也。

C::

Pulling something up […] a cart-ladder […].

E: :

qiè ‘pulling something up’: One pair of wheels is tall, another pair serves as trundle wheels; this is a cart-ladder. Weigh down its front part, string up its front load-bearing part, string up its gu-part, then suspend a weight from its front part. This kind of ladder is pulled up, and at the same time that it is pulled up, it goes forward. Weights, in principle, when you are not pulling them from above, and not letting them down gradually, and not exerting any force on them from the side, then they will come straight down. If they shift sideways, it is because something has interfered with them. The thing that makes the ladder move smoothly is unable to come straight down. If you erect a measuring stick on level ground, the weight will not descend because it does not have any sideways tilt. If on the other hand you tie a cord to it and pull the gu-part, this is similar to pulling the cross-bar from within a boat.

• (a) R: null; the canon is lost. Restored to this extent by Graham 1978, 392–93. Some scholars consider that there is no missing Canon text at all and that the Explanation text is actually a part of the Explanation of B 26, the preceding section. That analysis largely disregards the occurrence of the word 挈 in E preceding the sentence 兩輪高 “one pair of wheels is tall.” The 挈 in E looks like an entry character and suggests, as Graham points out, a corresponding Canon. Even taking it as a portion of the Explanation of B 26 does not help overcome the defective and obscure nature of the passage.

• (b) R: 輲 for the more common character 輇, standing for the word quán ‘a spokeless wheel’, i.e., a solid wheel.

• (c) R: erroneously repeats the four-character phrase 弦其前載.

• (d) The character is rare; it occurs in the Shui hu di 睡虎地 manuscripts (third cen. b.c.e.) as the name of a part of a carriage, but is as vague there as it is here (Shuihudi 1990, pt. 2, 49). Sun Yirang identifies it as the same word as is written 胡 in Zheng Xuan’s commentary to a Zhou li passage, where it seems to mean the ‘front part of a carriage’. Sun Yirang [1893] 1986, 336.

• (e) R: ; emendation Sun Yirang (Graham 1978, 393).

• (f) Understood as yǐ ‘sideways’.

• (g) : this is a well-attested gu wen variant for liú 流 ‘to flow’.

• (h) : Graham understands this character as explicitly writing the verb xià ‘to descend’ as opposed to the word xià ‘below’, written with the conventional character 下 (Graham 1978, 393).

• (i) : writing páng ‘beside’.

The text is sufficiently vague and what it purports to describe sufficiently obscure that we do not see any purpose in speculating idly about the structure of the device in question. That part of our translation given in italics is very tentative and incomplete, owing to the obscure and likely corrupt nature of the original text.

Beginning in the middle of the Explanation we find a description of the behavior of weights in general, preceding an observation about how, by contrast, the device in question works: the general statement says that in the absence of any external perturbation, the weight ‘will come straight down’; the description of the device says that it ‘is unable to come straight down.’ This would suggest that the intention of this part of the description is to contrast explicitly the operation of the device, whatever it is, with the normally expected behavior of a weight.

B 28

C::

倚者不可正。說在梯^a。

E::

倚:倍, 拒, , 倚焉則不正。

C::

What is leaning cannot be made upright. The explanation lies with a ladder.

E: :

yǐ ‘leaning’: if one is pressing back against something, or pushing forward on something, or dragging something, or bent under something; in all of these cases one is leaning relative to it, and thus not upright.

• (a) R: 剃 [tì ‘to shave off fur or hair’].

• (b) R: 堅 [jiān ‘hard’] for qiān ‘to drag’; variation between the presence and absence of a semantic classifier is exceedingly common.

• (c) : non-standard allograph for qū 屈 ‘to bend or bow down’; the classifiers 身 and 尸are both in origin semantically associated with ‘corporal or somatic form, body’ and thus the graphic alternation is historically not surprising.

By referring to the example of a leaning ladder, the section claims that whenever horizontal forces are involved (in actions such as of pushing and dragging) the agent cannot be upright. The summing-up formula (說在 X) of the canon in this case gives no more than an illustrative example.

B 29

C::

堆^a之必住^b, 說在廢^c材^d。

E::

堆^e: 石絫^g 石, 耳夾 者, 廢ⁱ 也。方石去地尺, 關石於其下, 縣絲於其上, 使適至方石。不下, 柱也。繆^j 絲去石, 挈也。絲繼^k, 引也。未變而名易,收也。

C::

A pile’s inevitably being fixed in place. The explanation lies with setting a plinth in place.

E: :

duī ‘pile’: Setting out stones side-by-side or in piles, or laterally flanking rooms, these are instances of setting out in place. A square stone is separated from the ground by the distance of a chi; fill in the space beneath it with stones, suspend a string above it, let it just reach the square stone. The stone does not come down due to the pillar-quality [of the stones underneath it] keeping it fixed in place. Wrap the string around it, remove the [other] stones; the square stone is now being pulled (and held) from above. If the string is extended, it is now being drawn [i.e., let] down. [The arrangement] still has not changed, but the feature at issue [what holds the stone] is switched; the square stone is now being gradually let down.

• (a) R: 推; emendation Chang Ch’un-yi (Graham 1978, 395).

• (b) R: ; a rare graphic variant for 往, which is in turn often found as an error for 住; emendation Sun Yirang (Graham 1978, 395).

• (c) For 撥 bō ‘to set out in place’.

• (d) The character 材 here stands for the basic word cái ‘material resources (used for some purpose)’, but in the particular sense of ‘plinth’; cf. the term shí cái 石材 in the Shangshu dazhuan 尚書大傳 line 大夫有石材 “For the Grand master there is a stone plinth”, where the phrase 石材 is glossed by Zheng Xuan as 柱下礩也 “the stone base underneath a pillar” (Shangshu dazhuan 1937, 103).

• (e) R: 誰; emendation Chang Ch’un-yi (Graham 1978, 395).

• (f) For 並 bìng ‘side-by-side’.

• (g) guwen for 累 lěi ‘to pile up’.

• (h) For 寢 qǐn ‘side rooms’.

• (i) R: 法; emendation Graham (1978, 396) and then understood as c above.

• (j) R: 膠 for 繆 jiū ‘to wrap around’.

• (k) R: 絕; The pre-Han Guodian 郭店 and Wangshan 望山 bamboo strip manuscripts include at least half a dozen occurrences of a graph that, in a standard kaishu transcription, looks like . Perhaps the best-known instance of this graph is found in the opening line of the Guodian text that matches chapter 19 of the received Laozi. The character there corresponding to the Guodian is 絕 standing for the word jué ‘to cut off, terminate’. Because of this correspondence and because the Laozi passage is so well known, the graph is usually understood as an early form of the character 絕 and understood as jué ‘cut off’. But the palaeographic data, including evidence from the Shuowen jiezi, suggest instead equally compellingly that the Guodian could just as well be an early graph for the character 繼 standing for the word jì ‘to continue, extend’, a sense directly opposite to 絕 jué ‘cut off’ (See Boltz 1999, 598–99; Boltz 2013, 21–23). Scholars are about equally divided as to which is the preferred conclusion. We suspect that the same uncertainty obtains here and that in spite of what we find in the transmitted, received text the word of the original passage could have been jì ‘to continue, extend’, written as a non-standard form of 繼. The word jué 絕 occurs in B 52 with a meaning ‘snap’ (Graham’s term) or ‘breaking’ of a hair. This occurrence may have influenced the passage here, leading to the corruption of 繼 jì ‘to continue, extend’ to 絕 jué ‘to cut off, terminate’.

The section illustrates the effect of ‘piling’ rocks to form a plinth, a procedure known as ‘pillaring’, and the supporting capacity of such a structure. In particular, pulling something from above and letting something down gradually are the same in not providing any “pillar support.”

The relation between 挈 qiè ‘pulling something up’ and 收 shōu ‘letting something down’ as explained here is consistent with that set out in B 26 above, where these two actions are described as complementary to each other. Here their behaviors are shown to be no more than different ways of looking at the same thing. The sense of 挈 qiè can be seen to include ‘holding from above’ as well as ‘pulling from above’.

Without emendation (k) as given above, the penultimate sentence of the Explanation says 絲絕, 引也 “if the string breaks, it is due to having been pulled.” To be sure, this by itself makes sense and the whole Explanation could be so understood. But it means that the square stone falls freely, crashing into the ground, and yet the Explanation refers to this process as 收 shōu, which we saw in B 26 is best understood as ‘letting something down gradually (as for example by a connected cord)’, and says that (the arrangement) 未變 “still has not changed”. The snapping of the string would seem to constitute a “change” in the structural arrangement of the device governing the behavior of the large stone. And the use of the modal negative 未 ‘still not’ (emphasis on the ‘still’) seems to suggest further the unchanged nature of the structure in question.

What has changed is the míng 名. Graham translates the last part of the Explanation 未變而名易 “Without any alteration except the substitution of the name...” and goes on to remark that many scholars and translators ill-advisedly emend the míng 名 to something else, often to shí 石 ‘stone’, thereby losing precisely the Mohist’s point (Graham 1978, 396). He is certainly correct to speak against any emendation of the word míng 名. But his understanding of it as ‘name’ coupled with his translation of yì 易 as ‘substitution’ slightly misses the salient point. The word ming here means ‘the point/question/feature at issue’ and the word yì 易 here means specifically ‘switch (something with its complement, opposite or counterpart)’. The two word phrase thus refers to the ‘central feature at issue’ (míng 名, viz., what holds the large stone) ‘switching’. That is, switching from suspension by a cord from above to being let down gradually by the same cord and coming to rest, its movement governed by what receives it and then supports it from below. The relation between cord and stone remains intact; the point where the controlling force is exerted is what switches.

3.9 Mechanical and Temporal Bases for Judgment, B 52–B 53

In view of these two sections we can see that the Mohists recognize that judgments can be contingent on either mechanical (B 52) or temporal (B 53) circumstances or conditions.

B 52

C::

均之絕否^a, 說在所均。

E::

均: 髮均縣。輕而髮絕, 不均也。均^b其絕也, 莫絕。

C::

Whether things in equal conditions break or not. The explanation lies with what conditions are made equal.

E: :

jūn ‘being equal or even’: Hairs are suspended evenly. If, (when attaching the hair to even) a light weight, a hair breaks, it is because (the attaching) was uneven. When (the attaching) is even, as for their breaking, none will break.

• (a) R:不, sensu stricto the emendation is not necessary, since the character 不 can stand by itself for the negative fǒu ‘or not’.

• (b) There is a matching passage in the Liezi that adds a 也 at this point, clearly indicating that the word 均 jūn ‘making equal’ is to be understood as a topic (Yang Bojun 1965, 107).

The Explanation does not actually specify attaching anything, but the occurrence of the verb xuán 縣 ‘to suspend’ and the following word qīng 輕 ‘light weight’ seem to demand this understanding. In spite of the hairs being even, i.e., hanging down with the same length, if a weight is attached unevenly, i.e., such that not all of the hairs bear an equal share of the weight, those bearing the greatest weight may break. Therefore, evenness of the length of hairs does not prevent the hair from breaking, it is evenness of the attaching that is crucial.

The word jūn < *kwin ‘to be even, equal’, here written 均, is etymologically the same word as jūn ‘potter’s wheel’, conventionally written 鈞. In view of the use and purpose of a potter’s wheel, the meaning ‘even, equal’ can easily be seen to be an abstraction of that word. The word jūn ‘potter’s wheel’ itself, irrespective of how it is written, is a lexical affine of yùn < *win-s ‘rotate’ (運), explained by the mechanism whereby a potter’s wheel functions.

B 53

C::

堯之儀^a也, 生於今而處於古而異時。說在所義二。

E::

堯: […]^b 霍^c。或以名視人, 或以實視人。舉友富商也, 是以名視人也。指是臛也, 是以實視人也。堯之義也, 是聲也生^d 於今, 所義之實處於古。若殆於城門與於臧也。

C::

Yao’s serving as a paragon, lives in the present, but is located in the past; thus differentiating the times. The explanation lies with that whereby someone may be deemed a paragon numbering two.

E: :

yáo ‘Yao’: […] braised meat. In one case one takes the name as the means to show something to others, in the other case one takes the object as the means to show something to others. If you present a friend as a ‘rich merchant’, this is taking the name as the means for showing him to others. If you point out that this is a piece of braised meat, this is taking the object as the means for showing it to others. As for “Yao’s serving as a paragon,” the sound of this phrase lives in the present, the object that is deemed ‘a paragon’ is located in the past. It is like ‘possibly at the city gate’ or ‘with truant Zang himself’.

• (a) R: 義, see Graham 1978, 421.

• (b) R: Graham suggests missing words or a missing phrase, given the subsequent lines of E (Graham 1978, 422). The missing part may have mentioned the 友 ‘friend’ or perhaps the 富商 ‘rich merchant’, balancing the seemingly isolated mention of the 霍 ‘braised meat’.

• (c) Writing the word huò ‘braise’, for 臛, which occurs with the conventional classifier later in the Explanation.

• (d) R: null; restored from C (Graham 1978, 422).

The last sentence of the Explanation seems intended to be an example of the contrast between subjective and objective belief. The word dài 殆 in the first of the two possibilities mentioned indicates a reticent subjective judgment on the part of the speaker. The absence of any corresponding word in the second of the two possibilities suggests this is to be taken as an objective judgment. This complementarity matches the míng 名 and shí 實 of the main part of the Explanation. The word zãng 臧 is conventionally used as a generic name for any kind of a person, especially people of little distinction and low repute. The Xiaoqu 小取 chapter (Mozi chapter 45) has a line that says: 臧人也, 愛臧愛人也。 “Zang means person, to care fondly for Zang means to care fondly for someone” (see also Graham 1978, 226–27, 257, 422–23).

The word yí, translated here as ‘paragon’ and written in the received text of this line as 義, is elsewhere in the Mozi written with the expected character 儀, i.e., with classifier 009, 人. The sense is primarily ‘what is suitable or what matches appropriately (some particular reference point or circumstance)’, and thus by extension a ‘standard’ or ‘model’. In referring to an individual the sense is someone who is an “ideal model” of some desirable type, thus a ‘paragon’ or ‘exemplar’. In the majority of its occurrences in classical Chinese literature generally the word yí means ‘proper, suitable or exemplary ceremonial behavior or performance’. In the Mozi it is paired pleonastically with fǎ 法 ‘model, pattern’, as fǎ yí 法儀 ‘models and exemplars’, the title of chapter four of the Mozi text. See also the discussion under A 70 supra.

References to historical (or legendary) figures in these passages are uncommon. The focus of this passage and B 16, which also mentions Yao, is the distinction between past (古) and present (今), and it seems that the only way the Mohist can refer concretely to this is by using the name of what was for them a historical figure associated with the past.

3.10 Spatial and Temporal Paradoxes, and Spatiotemporal and Modular Correspondences, B 60–B 65

The six sections B 60–65 are part of the sequence B 32–82, which Graham (1978, 230) groups together and designates “Problems in disputation.” We include them in our selection of scientific sections because of their close relation with spatial and temporal contingency and inevitability (B 60, 61, 63 and 64), with vertical tendency of weights (B 62) and with model and duplicate (B 65).

B 60 and 61 both describe paradoxes relating to space and time, ‘approaching but not reaching’ (B 60) and ‘absent but not dismissible’ (B 61). In B 62 a ball is explicitly said to be vertically oriented, and its vertical orientation is distinguished from all other possibilities. This privileging of the vertical likely has its origin in the behavior of weights and thus establishes a relation to the sections on mechanics. In B 63 the paradox raised in the Canon again has the sense of a riddle. How can one advance in space without coming closer to any given place? This is resolved in the Explanation by describing the motion of spreading out.

B 64 specifically points out the connection, but also the distinction, between linear extent and duration in travel. Interestingly, the spatial counterpart of ‘duration’, ‘spatial extent’, is here replaced by ‘linear extent’. The section reiterates, now for linear extent, the dependent relation between time and space in regard to movement that was first formulated in B 14. B 65 shows that the dependent relation between object and category is determined alone by whatever criteria are chosen.

B 60

C::

非半弗 則不動。 說在端。

E::

非: 半進, 前取也。前則中無為半, 猶端也。前後取, 則端中也。必半, 毋與非半, 不可也。

C::

If you do not hoe except for half, then you do not make any headway. The explanation lies with the starting point.

E: :

fēi ‘except for’: When hoeing, to advance half-way is taking it from what is in front. With respect to what is in front, the mid-point does not constitute a half-way point, rather it is like a (new) starting point. Taking what is in front and what is behind, then the starting point is the mid-point. In hoeing you inevitably do half, so you do not get anything other than a half remaining. And that remaining half cannot be hoed.

• (a) the character in R is a non-standard allograph for zhuó 斲 ~ 斫 ‘hoe’.

The Explanation here illustrates a mathematical, logical sense of bì 必 ‘inevitability’ (A 51). “In hoeing you inevitably do half” means that no matter how much or how little you hoe, you will inevitability do half of it before you do all of it. Once you have done half, there is still half remaining. And what was the half-way point when you started out becomes a new starting point when you begin to hoe the second half. Clearly, this will be the case no matter how many first halves you hoe, repeatedly. So there will always be a new starting point that was the half-way point of the immediately preceding part that was hoed, and thus there will always be a part that cannot be hoed. The ‘inevitability’ in this is relational; the fact that you inevitably first hoe a half, means that there is a half remaining. And the relation between this “hoed half” and the “remaining half” is comparable to the relational ‘inevitability’ in the “younger sibling” ~ “older sibling” pair seen in A 51. As a logical consequence the one presupposes the other.

The argument set out here is reminiscent of Zeno’s paradox “Achilles and the tortoise” or “the race-course” discussed by Aristotle (Physics VI, 2; Aristotle 1995, 103–117). There it is alleged that motion is impossible because before a moving body starting out from an origin O can reach an end-point E it must first reach a half-way point, which will be the distance from O to E divided by two, thus, OE/2. But since the half-way point OE/2 is its own end-point, a moving body must reach the half-way point relative to OE/2 before it can reach OE/2. That half-way point will be half of OE/2, or OE/4. And since OE/4 is also an end-point, the moving body must reach its half-way point, viz., OE/8 before it reaches OE/4. It is easy to see where this is leading. Since any movement, no matter how small, takes some amount of time, and since there are an infinite number of progressively smaller (each by half) half-way distances between any starting point O and any ultimate end-point E, the implication is that it would require an infinite amount of time to move from O to E. Therefore, motion is impossible in any finite period of time. Aristotle’s refutation of this argument is to observe that it presumes that distance is continuous and is infinitely divisible (hence all of the half-way points), but fails to treat time in the same way. Aristotle’s pointed observation is that time also is infinitely divisible, just as distance is, but by the same token just as time can be finite in extension, so can distance. The two are precisely comparable in this respect, infinitely divisible but finite in extension. So, while he does not say so explicitly, Aristotle seems to understand ‘space’ as comparable to ‘time’ in these respects, both of them entailing extension. (See Shields 2007, 215–20.)

The same understanding, expressed in elementary mathematical terms, underlies the explanation that, if the distance from O to E is defined as ‘one’ (whatever the unit), the sum of all of the increments I, each half as long as its preceding increment, necessary to reach E is equal to ‘one’; thus the first increment is I₁ = 0.5; I₂ = I₁ plus half of I₁, thus 0.5 + 0.25 = 0.75; I₃ = I₁ plus half of I₁ plus half of half of I₁, which is 0.5 + 0.25 + 0.125 = 0.875; I₄ = 0.5 + 0.25 + 0.125 + 0.0625 = 0.9375, and so forth. The limit of I_n as n approaches infinity is 1.0. (David Berlinski in his popular “tour of the calculus” explains Zeno’s paradox in just this way; see Berlinski 1995, 122–25.)

The Mohist section appears at first to refer primarily to a paradox similar to the Greek one. In hoeing there is always a moment when you have hoed half the field. When you then continue to hoe the remainder, you always reach a half-way point and you always have a half left. Therefore you can never hoe the whole field. But in fact there is a subtle point expressed here, to wit, that the relation between a hoed half and the remaining half is logically, not just empirically, inevitable.

Zhuangzi 33 includes a similar paradoxical observation: 一尺之捶, 日取其半, 萬世不竭。“Given a stick of one chi in length, if you remove half of it daily even in a myriad generations it will not be exhausted.” In neither the Zhuangzi nor the Mohist text is the paradoxical character of the statements made explicit. The Zhuangzi passage occurs as part of an enumeration of similar paradoxes identified as useful in repartees with the logicians. This shows that it was understood as a paradox.

While the Mohist generally shows no recognition of a dimensionless point other than the two end-points of a measuring stick or of a line, in this section a mid-point is recognized and identified with a new starting point.

B 61

C::

可無也, 有之而不可去。 說在嘗然。

E::

可: 無也。已給則當^a 給, 不可無也。久有窮, 無窮。

C::

It can be lacked, but having had it, then it cannot be disposed of. The explanation lies with having experienced it being so.

E: :

kě ‘can’: Lacking, when something has already been provided then you have encountered its having been provided, and that cannot be lacking. As for duration, (in one respect) there is a limit and (in one respect) there is no limit.

• (a) Based on the wording of the Canon, Graham (1978, 433) emends this dāng 當 < *ttang ‘to encounter, confront’ < ‘apposite’ to cháng 嘗 < *dang ‘once’, but the emendation is not necessary, and the text can be translated and readily understood as it stands. The word dāng 當 here is effectively the full verbal form of the adverbial cháng 嘗 ‘once, to have experienced’; the two words may well be related to each other.

In one respect there being a limit and in one respect there being no limit refers to the fact that the thing having been provided may no longer be present, but the experience of it having been provided endures. The distinction between the temporally finite nature of the event and the enduring nature of the experience matches the distinction seen in B 53 between Yao as an example of proper behavior (the object) in the past and the enduring reputation of Yao (the name) as an example of proper behavior in the present.

B 62

C::

正而不可擔^a, 說在摶。

E::

正:丸^b無所處而不中縣, 摶也。

C::

Being upright, but not permitting of being put crosswise; the explanation lies with being round.

E: :

zhèng ‘being upright’: A ball is in no position not in line with its vertical axis; due to it being round.

• (a) Graham accepts Sun Yirang’s emendation to 搖 yáo ‘shake, agitate’ and translates “cannot be made to waver.” While this makes good sense, to be sure, the graph 擔 in R, standing for the word dān ‘to carry on a cross-bar across one’s shoulders’, can be understood as ‘to put something crosswise, i.e., out of vertical alignment’. Apart from the conservative guideline for accepting the received version of a text whenever feasible, this reading allows the sentence to be understood as it stands in a way perhaps even preferable to the emended version in that it recognizes the use of vocabulary from everyday experience to express a seemingly technical phenomenon.

• (b) R: 九 emendation (Graham 1978, 435).

The formulation of the Canon suggests something of a deliberate riddle. How can something, standing upright, not be able to be put crosswise? This is resolved in the Explanation by identifying the thing as a ball. The interesting aspect of this section is that it clearly privileges the vertical direction. With a ball one might argue that it has no orientation, or that it has any orientation one wishes to attribute to it. Here it is explicitly said to be vertically oriented, and its vertical axis is distinguished from all other possibilities. This is likely to be connected to the vertical tendency of weights, which is dealt with in sections B 25a–29.

B 63

C::

宇進無近, 說在敷。

E::

宇:區^a不可偏^b 舉, 宇^c 也。進行者先敷近, 後敷遠。

C::

Advancing in spatial extent, yet without drawing near to any place, the explanation lies with ‘becoming spread out’.

E: :

yú ‘spatial extent’: When a demarcation cannot be established in any direction, this means spatial extent. (As concerns) people who go forward, first the spread is near, later the spread is far.

• (a) R: 傴, emendation Sun Yirang (Graham 1978, 435).

• (b) Perhaps to be understood as 遍 / 徧 biàn ‘in all directions, universally’.

• (c) R: 字 (Graham 1978, loc. cit.).

The motion at issue is undirected, with no limit or goal. In the case of such motion, advancing entails a starting point, but does not imply coming near to any specified or defined thing. The Canon itself can be understood as describing diffusion; but the 進行者 (“people who go forward”) of the Explanation suggests intentionality and therefore seems to imply an animate subject. The association of motion with time is clearly included in the Explanation, though not directly mentioned. Cf. in this regard B 64.

B 64

C::

行脩^a以久, 說在先後。

E::

行^b:行者必先近而後遠。遠近^c, 脩也。先後, 久也。民行脩, 必以久也。

C::

Traveling a long distance takes a long time. The explanation lies with ‘earlier and later’.

E: :

xíng ‘traveling’: travelers will inevitably be near earlier and then become distant later. ‘Distant or near’ has to do with linear extent; ‘earlier or later’ has to do with temporal duration. When people travel a long distance they inevitably take a long time.

• (a) R: 循, emendation Graham 1978, 435.

• (b) R: 行者, with 者 intrusively following the “head” character, probably under influence of the immediately following phrase 行者 ‘travelers’.

• (c) R: 遠脩近, emendation Graham 1978, 436.

Here again we see the Mohist drawing attention to the dependent relation between space and time in regard to movement, but in this case space is referred to linearly with the term xiū 脩 ‘linear extent’ whereas in earlier passages the term used was regularly yǔ 宇 ‘spatial extent’. This may be due to the emphasis on linear extent in traveling as contrasted with the two-dimensional nature of ‘spatial extent’ in B 63, explained as fū 敷 ‘becoming spread out’.

See in this connection B 14; see A 40 for the entry for jiǔ 久 ‘enduring, temporal duration’. There is no entry for the comparable term xiū 脩.

B 65

C::

一法者之相與也盡, 若方之相召^a 也。說在方。

E::

一:方貌盡俱有法而異, 或木或石, 不害其方之相召^b 也。盡貌, 猶方也^c,物俱然。

C::

The correspondence among objects based on the same model is exhaustive, like squares evoking one another. The explanation lies with being square.

E: :

yī ‘one’: When the aspects of the appearance of the square are exhaustively (accounted for) and all (of the objects in question) adhere to the model, then their being different—some wood, some stone—is not detrimental to their evoking one another as squares. Exhausting the aspects of their appearance, like squares, the objects are all so.

• (a) Sun Yirang, followed by Graham (1978, 437), emends zhào 召 ‘to evoke, call forth’ in the received text to hé 合 ‘to match’ presumably because the phrase xiāng hé 相合 ‘to match one another’ is a common phrase and seems to fit the sense readily, whereas xiāng zhào 相召 seems at first sight to make little sense. But in fact 相召 is attested more than a dozen times in early transmitted texts with a meaning ‘call forth/evoke one another’, or ‘one calls forth/evokes the other’, e.g., 物故以類相召也 “objects assuredly evoke each other according to their category” (Lü shi chunqiu), 飲食相召 “eating and drinking call forth each other” (Zhuangzi). One of the cardinal rules of thumb in regard to emending texts is that the less understandable or less common reading (lectio difficilior) is likelier to be the original than is the easier reading (lectio facilior), the reasoning being that it is likelier that a difficult reading will be emended or altered in a way that makes it understandable than the reverse. In this instance clearly the sense of the phrase 相召 is less obvious than that of 相合, making it the lectio difficilior. A second guideline is simply that if the text makes sense as written, there must be very persuasive evidence to justify an emendation. For these reasons we read the text here as it stands in its received form.

• (b) R: 台. Graham (1978, 437), following Sun Yirang, emends this also to hé 合. Clearly 台 tái does not make any sense in this line, but our emendation to 召, consistent with the received text of the Canon, is a less radical proposal than the dual emendations to 合 suggested by Sun Yirang and endorsed by Graham.

• (c) the three-character phrase 猶方也 “like squares” is identified by Graham as a likely a gloss on the original text that has been inadvertently elevated to the level of primary text.

Using the concept of ‘set of identifying features’ (zhēng 徵) as used in A 45, we may rephrase the Canon as saying that adhering to a model means fulfilling the set of identifying features that characterize the model. The Explanation then clearly states that differences outside the set do not violate the adherence to a model.

3.11 Sets of Indeterminate or Unknown Extent, B 73–B 75

The three sections here argue that the fundamental concept of a composite whole, or set, is applicable even if certain information about the components is unknown or unknowable. In B 73 the unknowable arises from the infinite nature of the composite whole. In B 74 it is the number of elements that is unknown, but there is no implication that this number may be infinite. In B 75, by contrast, it is the place of the elements that is unknown.

B 73

C::

無窮不害兼。 說在盈否。

E::

無:「南者有窮則可盡。無窮則不可盡。有窮無窮未可智則可盡不可盡^a未可智, 人之盈之否未可智, ^b 人之可盡不可盡亦未可智而必人之可盡愛也誖。」人若不盈無^c 窮則人有窮也。盡有窮無難。盈無窮則無窮盡也。盡無^d窮無難。

C::

Being without limits is not detrimental to being a composite whole. The explanation lies with being filled out or not.

E: :

wú ‘being without’: [claim:] If the south has a limit, then it can be exhausted. If it does not have a limit, then it cannot be exhausted. If whether having a limit or not cannot yet be known, then whether it can be exhausted or not cannot yet be known, and thus people’s filling it out or not cannot yet be known. Whether people can be exhausted or not also cannot yet be known, and so inevitably (it follows that) people’s being able to be exhaustively cared for is fallacious.—[rebuttal:] If people do not fill out the limitless then they have a limit. And exhausting what has a limit presents no difficulty. If they fill out the limitless then the limitless is exhausted. And (therefore) exhausting what has no limit presents no difficulty.

• (a) R: 不可盡不可盡, accidental repetition of the three-character phrase; emendation Graham 1978, 448.

• (b) R: 而必, introduced erroneously from the same phrase later in the passage; emendation Graham 1978, 448.

• (c) R: 先, graphic confusion with 无, allographic for 無; the same error in the reverse occurs in the C text of B 57; emendation Graham 1978, 448.

• (d) R: 有, apparently a misreading of 其, itself (in its early form 亓), the result of a confusion with 无, allographic for 無; emendation Graham 1978, 448.

What we have termed the “claim” in the Explanation often uses the phrase 未可智 “cannot yet be known” or “still cannot be known”; using the aspectual negative wèi 未, indicating incomplete action and allowing for the possibility that it could become known at a later time. To have written 不可智 would have meant something is ‘unknowable’, but such an absolute claim does not fit the present argument, because it is unnecessarily strong and might be wrong. The phrase “cannot yet be known” will never be absolutely wrong; the circumstances may change such that the thing in question becomes knowable. All applications of the phrase 未可智 “cannot yet be known” follow from the first, which refers to the limitedness or unlimitedness of something, in particular the south. If in the future a limit is experienced, the south will be known to be limited. As long as no limit is encountered the answer remains still not knowable. Graham accommodates this aspectual sense of the wèi 未 by translating 未可智 as “unknowable a priori” (Graham 1978, 448–49). The knowing 智 involved here must refer to the ‘acquired-knowing’ defined in A 5, rather than the ‘innate knowing’ defined in A 3.

This is one of three sections that have the structure of an explicit claim and a rebuttal. (The other two are B 38 and B 82, see Graham 1978, 449.) The reference in the Explanation is clearly to jiān ài 兼愛 ‘comprehensively caring fondly’, one of the best-known Mohist doctrines. By using terms that have been defined in earlier parts of the Canon, e.g., ‘knowing’ 智 zhī, ‘filling out’ 盈 yíng, ‘exhausting’ 盡 jìn, and ‘reaching a limit’ 窮 qióng, and by examining and resolving the alternative cases, the argument laid out in the Explanation comes close to what can be considered an ideal formal proof of a proposition.

B 74

C::

不知其數而知其盡也。說在明者。

E::

不: 二, 智其數。「惡智愛民之盡之^a也」, 或者遺乎其問也。盡問人則盡愛其所問。

C::

Not knowing their number, but knowing that they are exhaustively (accounted for). The explanation lies with one who is clear about (the scope of his reference).

E: :

bù ‘not’: Being two, we know their number. (So, in asking) “How do we know someone’s caring fondly for the people (accounts for) them exhaustively,” some have been left out from this question. If one is exhaustive in asking about people, then being exhaustive in caring fondly for those about whom one has asked (follows).

• (a) R: 文, emendation Graham 1978, 449; this is a frequently seen graphic corruption in the Mozi text.

The section appears to presume a discussion about jiān ài 兼愛 ‘comprehensively caring fondly’, only asking about the possibility of showing care to the set of all people. If the question “how do we know someone’s caring fondly for the people accounts for them exhaustively” refers only to a restricted set of people, that set will by definition exclude others and the question becomes irrelevant in the discussion of ‘comprehensively caring fondly’. If, by contrast, the question refers to all people exhaustively, then the set of all people to be taken care of has been defined by the reference in the question.

Graham (1978, 450) excepts Sun Yirang’s emendation of the phrase 明者 of the Canon to 問者 ‘the one who asked’. The received text reading 明者 ‘one who is clear about (it)’ seems understandable as given, referring to being clear about the difference between asking about a limited set and about an all-inclusive set.

B 75

C::

不知其所處不害愛之, 說在喪子者。

E::

不:若^a 智其數而智愛之盡之^b 也, 無難。

C::

Not knowing where they are located is not detrimental to caring for them fondly. The explanation lies with one who has lost a son.

E: :

bù ‘not’: It is like “when knowing their number, then knowing that the caring fondly exhaustively (accounts for) them presents no difficulty.”

• (a) R: 若不, head character in second position; see Graham 1978, 95–6.

• (b) R: 文, emendation Graham 1978, 449; this is a frequently seen graphic corruption in the Mozi text.

The Explanation does not live up to the level of argumentation reached in B 73 nor even B 74’s argument that not knowing the number does not stand in the way to complete exhaustion.