Abstract
This writing focuses on those most reflectively interesting and arguably representative ideas on the issue of reference, as a semantic issue, in classical Chinese philosophy which are relevant to reasoning and semantic interpretation. My strategy is this. First, I explain several basic points as revealed in Gongsun Long’s account. Second, I analyze how, essentially in line with Gongsun Long’s relevant point, the Later Mohists significantly show their semantic sensitivity to the due identities of the referents in reasoning. Third, I look at how, essentially in line with Gongsun Long’s general point on the due-place actuality, Confucius’ account of name rectification together with Xun Zi’s and Wang Chong’s further developments addresses the issue of reference in moral reality. Fourth, I explain how Lao Zi makes interesting and engaging points concerning the relationship between language engagement and the ultimate concern and between the “speakable” and the “unspeakable”. Fifth, I briefly examine a relatively recent debate on the relation of the structure of Chinese nouns to Chinese thought from the referential point of view: I focus on how the mass-noun-semantics part of Hansen’s mass-noun hypothesis are challenged by some competing accounts in view of the referential relation between Chinese nouns and referents. Sixth, I end the examination with a brief discussion of how reference and truth, as two basic semantic notions, are intrinsically related.
Most of the materials in this writing are either shortend versions or excerpts of the relevant parts of Mou 2003, 2007, 2015, 2016, 2018. Thanks to their publishers for permission to re-use the materials here. I am grateful to Yiu-ming Fung for his helpful comments on an early version of this essay. As much of the content of this essay come from some of the previous relevant publications of this author, I would like to express my sincere thanks again to all those colleagues listed in the acknowledgements of these writings for their helpful comments and suggestions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
For example, I will not discuss the issue of naming and reference in the classical text Yi-Jing here, although I render philosophically interesting and signficant the relevant thoughts on the issue in the Yi-Jing text; for a detailed discussion of it by this author, see Mou 2014, 2019, chapter 2. I will not discuss Zhuang Zi’s relevant ideas here, which I examine in Mou 2019, chapter 6.
- 2.
For my discussion of distinct linguistic ways in Chinese and Western languages of delivering pre-theoretic understanding of truth, see this author’s discussion of it in Mou 2019, Section 1.4 in chapter 1.
- 3.
In this writing, unless otherwise indicated, the translations of the cited passages from the relevant Chinese classical texts are mine.
- 4.
By ‘semantic’ I mean the following strict or narrow sense of the term. It is known that the term ‘semantic’ is used in its strict or narrow sense and in its broad (loose) sense. In its strict or narrow sense, ‘semantics’ means the study of the non-(purely)-linguistic, cross-categorical two-pace relations between linguistic expressions and the extra-linguistic objects for which they stand. Such a non-linguistic relation is usually called a ‘semantic relation’; the notion that captures such a semantic relation is called a ‘semantic notion’. The principal semantic relations are referring and being true; the principal semantic notions are thus the notions of reference and truth. However, in its broad sense, ‘semantics’ means the study of (a variety of) meanings of words and sentences, although often especially pointing to their relatively stable ones (such as “objective” referents, “inter-subjective” senses, etc.). If the extra-linguistic objects in question are taken to be the meanings of the linguistic expressions, semantics in the narrow sense of the term can be viewed as an investigation of the “meaning” (the referential meaning of the linguistic expressions). The two senses of ‘semantic’ are thus related. However, especially in logic and the philosophy of logic and thus in this writing, the strict or narrow sense of the term ‘semantic’ is used, unless indicated otherwise. In contrast, pragmatics is the study of situated uses of language which involve particular utterance contexts and the language users’ (particular) intentions (or their situated ‘epistemic’ attitudes), or the study of what speakers do with language in its situated uses (speech acts).
- 5.
In our linguistic practice and logical inference, people use words and concepts to refer to things and that the two-place semantic relation comes into existence through speakers’ referential activities. Nevertheless, Strawson renders the pragmatic dimension of people’s linguistic practice decisive indiscriminately in any theoretical treatment of meaning (Strawson 1950) and thus criticizes Russell’s semantic treatment in his Theory of Descriptions (Russell 1905); Russell responds to Strawson explaining why, in this connection, Strawson misses the point of the theoretical treatment of the semantic relation (Russell 1957).
- 6.
Due to space and the goal of this writing, I will not discuss how Gongsun Long’s thought on reference can engage with two representative approaches in the contemporary philosophy of language, i.e., the Lockean-Fregean approach (Locke 1690; Frege 1892) and the Milian-Kripke’s approaches (Mill1881; Kripke1980), which I explain in Mou 2018.
- 7.
For example, Chung-ying Cheng and Yiu-ming Fung give their distinct elaborations of a representative and influential Platonic-realistic interpretation which was originally suggested by Fung Yu-lan. Fung Yu-lan renders Gongsun Long Platonic-realistic: Gongsun Long’s arguments are intended to argue that ‘white horse’ and ‘horse’ represent two distinct Platonic universals (or universal/abstract qualities) and thus the universal of white-horseness is not (identical to) the universal of horseness (Yu-lan Fung1952–1953). Chung-ying Cheng makes a defense of a Platonic realistic interpretation in terms of his version of Platonic abstract ontology (Cheng 1983). In contrast, Yiu-ming Fung gives a defense of the realistic account in terms of his realistic understanding of universals, which takes it that Gongsun Long’s universals exist in their separate, transcendent and unchanged world but they can emerge, and participate, in the phenomenal world (Fung 2000). Chad Hansen proposes a radical shift of interpretation based on mereology (part-whole logic) and his mass-noun hypothesis: ‘white horse’ is a mass noun and refers to a mass-sum whole of horse-mass and white stuff; the whole of white-part and horse-part is not its horse-part. Hansen’s mereological interpretation is to by-pass class-member relation but resort to whole-part division alone (Hansen 1983). In the metaphysical-interpretation part of my account, I suggest a modest mereological interpretation: the denotational semantics and deep structure of Chinese common nouns are like those of collective nouns (in a semantic-syntatic, instead of grammatical sense), and its implicit ontology is a mereological one of collection-of-individuals with both part-whole structure and member-class structure; the denotation of ‘white horse’ is neither a realistic universal nor a mereological sum of white and horse nor an empty set but a collection of white horses with member-class structure (Mou 2007). As far as their metaphysical interpretations are concerned, Cheng’s and Fung’s accounts respectively demonstrate two distinct versions of realism concerning universals, Hansen’s account presents a strong or radical version of nominalism, while the metaphysical-interpretation part of my account involves a kind of moderate nominalism (conceptualism). Also see Chmielewski1962 for a set-theoretic account.
- 8.
For my detailed discussion of the referential dimension of Gongsun Long’s thesis, see Mou 2007.
- 9.
Though in English the term “are” in the phrase “the way things are” can be understood as the present tense of “be” (a local grammatical feature of many phonetic languages like English to which presentism or more generally speaking A-theories in the philosophy of time, is intended to be sensitive), it can be also treated as a neutral and unrestricted “existential” quantifier from an atemporal perspective (as taken by eternalism or more generally speaking B-theories in the philosophy of time), whose meaning is captured in the “absolute” unrestricted existential quantifier in the first-order logic; and the latter understanding more fits the case of Chinese language which does not have its explicit counterpart “tense” expressions.
- 10.
It is important to note this: the term ‘identity’ and its associated concept of identity both in its ordinary usage (in its dictionary literal sense) and in logic and philosophy implies neither static identity nor fixed identity nor absolute identity; what it delivers is not only totally compatible with changing process and dynamic development of things but also includes and covers the latter; it is not the same as ‘sameness’ (although a traditional formulation of the law of identity via absolute identity (in terms of ‘=’) unfortunately facilitates such an narrow or ad hoc understanding. The case is similar to the term ‘being’: ‘being’ in philosophy, in its general sense, is used to express various kinds of existence, although in the Western tradition it is used to specifically expression one kind of existence, something definite, stable, constant, essential, universal or unchanging, and although some philosophers, say, in the Western tradition argue that such a kind of existence captures the essence of being (in its broad sense).
- 11.
For my previous discussion of this, see Mou 2006.
- 12.
It has been considered that there was something missing with “疑其所正” in the original text. Here I translate it in terms of the meaning paraphrase in view of the context. Cf., Wing-tsit Chan translation of it into “[What is correct is not used to] doubt what is correct.” (Chan1963, 243).
- 13.
It is noted that, for the purpose of philosophical interpretation, I first discuss Gongsun Long’s relevant thought and then Confucius’ relevant thought, although the former historically appeared after the latter.
- 14.
For a further discussion on how to formally and accurately capture the later Mohist point in this connection and give a general condition for the validity of the parallel inference via a modern logical treatment, see Mou 2016.
- 15.
In the literature on the issue of the status and nature of the parallel inference, it is controversial whether the parallel inference is a type of deductive reasoning or a kind of analogical reasoning. Those scholars such as Graham1967, Liu2004, and Fung 2012 explicitly render it deductive: though Graham does not explain why he thinks so, while Liu and Fung give essentially the same reason by formally presenting the parallel inference in terms of the standard first-order predicate logic resources. In contrast, some other scholars such as Hansen 1983 and Fraser 2013 render it analogical. On this issue, I agree to the former’s position, while disagreeing to the latter; however, my reason for rendering the parallel inference deductive is substantially different from that as presented in Liu 2004 and Fung 2012. Without elaborating this here, the interested reader can see Mou 2016 for the details in this connection.
- 16.
One note is due here about the English translation of those phrases like ‘乘馬’ (and ‘乘車’ below) in such a context of parallel inference. I hold a collective-name hypothesis concerning the semantic-syntactic structure of a common noun (for its earlier version concerning common nouns in Chinese, see the brief introduction to it in Section 5; for its expanded version concerning common nouns in general not limited to Chinese, see another forthcoming article of this author); with consideration that one standard grammantical means in English to express a collection designation is via “the definite article plus the [addressed] common noun” (for instance, grammantically adequate, one can say “the wolf is not really a dangerous animal”, with this usage of the definite article to talk about any individual member of the collection of wolfs), I thus use the English phrase ‘the horse’ to designate a collection of horses consistently both in a single subject-predicate statement [like ‘the white horse is (identical to) the horse (with regard to the shared common aspect of being horse)] and in a parallel inference here (like the inference from the premise statement ‘the white horse’ is the horse’ to the conclusion statement ‘riding the white horse is riding the horse’). Different from a kind designation or a universal designation, part of the sophisticated semantic point of a collection designation is this: individualization of a collection of individual objects consists totally in (any) individual members of the collection, instead of a collection entity that is separate from its individual members; in this way, ‘riding the horse’ means riding any one individual horse in the collection of horses (instead of some members being ridden while some others not) and more accurately captures the involved collection designation. Although, grammatically and partially semantically, one can use ‘riding a horse’ here, I think that some sophisticated semantic point of what is expressed via ‘riding the horse’ would be lost.
- 17.
In this fundamental connection, the line of the later Mohists in diagnosing the parallel inference and Gongsun Long’s rationale in treating the “White-Horse-Not-Horse” thesis as presented before are essentially the same: any identity expression without being sensitive to which aspect is in reference focus would be semantically incomplete. This idea, logically speaking, is also labeled ‘relative identify’, which is often attributed to Geach 1967 in which Geach criticizes the standard notion of absolute identity in the standard first-order predicate logic (also see Deutsch 2007). For the reason explained here, the basic idea of relative identity as a kind of semantic sensitivity is quite pre-theoretic; in my view, its first explicit presentation can be traced back to one fundamental point of Gongsun Long’s “White-Horse-Not-Horse” thesis to the effect that, relative to what is sought, one can say that the white horse is identical to the horse or that the white horse is not identical to the horse. As for an explicit logical presentation of the Gongsun-Long-style concept of relative identity (in predicate logic resources), see the relevant discussion in Mou 2016.
- 18.
It is important to note that the saying “common attribute” here does not necessarily commit itself to a platonic realism regarding universals but is open to distinct ontological interpretations.
- 19.
There is one substantial implication of such understanding of identity (as labeled ‘relative identity’ in contemporary logic discourse): as one might object, it is thus possible that all different things in the world, in some sense, can be regarded as the same [or similar] from a relevant perspective. I would render such possibilities (or even some related “seemingly-bizarre” but really open-minded ways of classification) very positive and constructive; this would give a thoroughly open-minded approach to look at identities/similarities among things in the world and at how to classify them: this would be sensitive to distinct eligible perspectives that point to certain aspects which are commonly or jointly possessed by things and thus meet certain reflective needs, though some of these classifications seem trivial or can be against people’s current ready-made or habitual ways of classification.
- 20.
However, with some enhanced predicate logic resources, the deep semantic-syntactic structure of the parallel inference can be captured and presented in a formal way, although both ancient logical resources during the later Mohist times and the so-far-available logical resources (including those currently available expanded predicate logic accounts) have yet to be refined enough to take on, or are unable to formally apprehend, this. For a detailed discussion on this, see Mou 2016; for an expanded predicate logic account with enhanced identity sign that can be used to formulate the Later Mohist way in this connection, see “Appendix”.
- 21.
Xun-Zi, chapter Zheng-Ming.
- 22.
For this author’s detailed examination of the issue, see Mou2018b, section 5.2.
- 23.
For my detailed discussion of Wang Chong’s approach related to thise, see Mou 2015.
- 24.
One might question whether xu (虛) is the negation of shi (實) (thus they are contradictory) or they are merely contrary, given that the former is stronger than the latter in the sense that in a pair of contradictory sentences, one is true and the other is false, while in a pair of contrary sentences they could not both be true but could both be false. Although the text does not explicitly tell whether Wang Chong treated the relationship between shi and xu as contradictory or contrary, the weaker “contrary” relationship is assumed here.
- 25.
With consideration that it is agreed that Wang treated shi as univocal, and to save space, I will not make a wide range of citations from the Lun-Heng here to show the textual evidence for this. The interesting reader can examine such chapters in the Lun-Heng as Qi-Guai (奇怪), Shu-Xu (書虛), Tan-Tian (談天), Zi-Ran (自然), Shi-Zhi (實知), Zhi-Shi (知實), Zheng-Shuo (正說) besides the chapters Wen-Kong (問孔) and Dui-Zuo (對作).
- 26.
Lun-Heng, Chapter Dui-Zuo. (《论衡校注》, 569 and 571).
- 27.
For a different interesting interpretation of Wang Chong’s approach via his conception of shi, see McLeod2011.
- 28.
- 29.
- 30.
It is known that there has been a controversy over the identity of Lao Zi. Nevertheless, throughout this essay, Lao Zi is taken as a proxy figure who speaks for the ideas delivered by the text of the Dao-De-Jing; the appearance of the name ‘Lao Zi’ thus stays neutral to the controversy.
- 31.
In my pin-yin transliterations in this section, unless in the case of proper names, the transliteration of a Chinese character with the first letter being capital is used to indicate that the character in the relevant context of the Chinese original is used as a noun. In contrast, the transliteration of a Chinese character without the first letter being capital is used to either indicate the non-noun-status of the character in the context or suspend claiming its syntactic status. A prominent example in this aspect is the transliteration ‘Dao’ in contrast to ‘dao’; and, by the same token, ‘Ming’ in contrast to ‘ming’.
- 32.
Lau1963, 5.
- 33.
Chan1963, 139.
- 34.
In Creel1983, Herrlee Creel reviews 29 English translations of the opening passage. Among them, as Creel sees it, the standard pattern is used in 14 translations, if some rearrangement and some use of synonyms are tolerated. As I see it, all those 29 translations examined in Creel’s article seem to share the same core structure regarding the opening statement to the effect that the Dao (as a noun) that can or may be dao (as a verb) is not the chang-Dao.
- 35.
Cf., e.g., Chapters 14, 21, 25 of the Dao-De-Jing.
- 36.
For the notion of rigid designation, see Kripke1980. It is noted that the notion per se presupposes neither Kripke-style essentialism nor any other ontological commitment beyond the minimal one—the existence of what is rigidly designated; to this extent the notion of rigid designation is metaphysically neutral.
- 37.
Cf., Chapter 1 of the Dao-De-Jing.
- 38.
Cf., Chapters 25 and 34 of the Dao-De-Jing.
- 39.
For example, Wing-tsit Chan commented: “Lao Tzu…rejected names in favor of the nameless….To Lao Tzu, Tao is nameless”, suggesting that, to Lao Zi, what is named is simply not the genuine Dao. Cf., Chan1963, 139.
- 40.
The term ‘ming’ as a verb in ancient Chinese can be used to (rigidly or descriptively) name a non-linguistic object or descriptively paraphrase a linguistic object (say, a remark). One example of the latter case is ‘mo-ming-qi-miao’ meaning that, referring to something (often to some linguistic remark; e.g., “A remark mo-ming-qi-miao”), one cannot descriptively paraphrase or explain its subtlety; another is ‘bu-ke-ming-zhuang’x meaning that something can hardly be descriptively paraphrased or explained.
- 41.
- 42.
It is noted that what is focused on in the collective-noun hypothesis is the semantic-syntactic structure of Chinese common nouns, instead of some “grammatical” feature of collective nouns in a certain natural language (say, English); in this way, not merely these nouns ‘team’, ‘jury’, ‘committee’ in English and their counterparts in other natural languages, but also ‘people’, ‘cattle’ and ‘police’ in English and their counterparts in other natural languages, are all collectivenames with regard to their shared semantic-syntactic structure, whether or not they would “grammatically” count as collective nouns in a natural language (if there is such a ready-made grammatical category in that natural language).
- 43.
Actually, I now hold a stronger expanded collective-name hypothesis concerning the semantic-syntactic structure of common nouns in natural languages (not restricted to the case of common nouns in the Chinese language). For my detailed discussion of this, see Mou 2018, Section A1.2 of Appendix 1.
- 44.
It is noted that, in the literature, different things are talked about in the name ‘truth’. To avoid mere verbal disagreement, I explicitly specify that what is addressed here is the semantic notion of truth as conceived and delivered by people’s pre-theoretic “way-things-capturing” understanding of truth, instead of something else.
- 45.
This “collective-generic” operator can be viewed as a further development from Krifka, M. et al. 1995 in which a “generic” operator is suggested.
- 46.
When saying that it is new, I mean that the logical notation to be given below, i.e., “the identity symbol with ‘perspective-attribute-in-focus’ parameter []=”, is new in view of a standard predicate logic account, instead of the basic idea of relative identity or its other logical expressions being new. The basic idea of relative identity is not odd but quite pre-theoretically intuitive in view of its close relation to our pre-theoretic understanding of the “double-reference” phenomenon of the basic language employment, which is addressed and explained in discussing Gongsun Long’s account, though he did not use the Chinese counterpart of the very phrase ‘relative identity’, and though in the logic literature it is often attributed to Geach1967 in which Geach criticizes the standard notion of absolute identity in the standard first-order predicate logic and suggests his “modern” version of relative identity which I think presupposes absolute identity. It is noted that, in Mou 2016, the relative identity sign is given in the form of “=[],” in contrast to “[]=” given here for some substantial consideration.
- 47.
The presentations of those added materials that are labeled “not new” are quite standard; their basic presentation lines and fashions can be found in many textbooks or more advanced source books for classical and non-classical predicate logic, such as Gamut1991, Priest2008, and Sider2010, though newly introduced resources into the system unavoidably bear on some aspects of the presentations of those previous materials.
- 48.
See its semantic interpretation (2.2)<1.3> below, which distinguishes itself from the standard semantic interpretation of the “definite-description” symbol “ι.”
- 49.
See its semantic interpretation (2.3)<2.3> below, which distinguishes itself from those of the “identity” symbol “=" and of the Geach-style "relative identity” symbol (it places the “relative-identity” parameter beneath equation symbol in the middle, indicating its symmetric character, cf., Wiggins2001, 24-28). It is noted that Geach (1967) presents another logical notation to express relative identity (basically: x and y are the same F but x and y are different Gs, where F and G are predicates). Generally speaking, I contend that this logical notation in treating relative identity is not merely less natural and expressive (for example, it would be hard to present Gongsun Long’s “white-horse-not-horse” case) but also somehow presupposes absolute identity; the suggested identity notation with the parameter as a primitive, together with its semantic interpretation (2.3)<2.3> below, treats the traditional identity sign expressing absolute identity as one special case, and it treats as not symmetric the type of relative identity that is intrinsically related to the category-belonging predication. The issue of symmetricity involved in the conception of relative identity is beyond the coverage of this book, which I will examine in another writing.
- 50.
In Krifka, M. et al. 1995, a generic operator is suggested concerning only the feature (4) of common nouns mentioned above or the case <2.3.2> below, having yet to take care of the feature (5) of common nouns mentioned above or the case <2.3.3> below.
- 51.
Such identities of individual objects with its associated attributes as a whole capture our pre-theoretic understanding of individual objects as “thick” objects, which constitute the semantic-whole referents of the names of such thick objects if they do have names.
- 52.
Two notes are due. First, it is not necessary for any sortal collection to include all these types of sortal-collection-associated subsets. Second, these three subsets are not exhaustive (because some “accidental” attributes possessed by some of these objects in Oi do not fall into any of these three subsets), though they are exclusive.
- 53.
Indeed, a purely-mathematically-oriented logician would render this characterization of the domain of quantification too much metaphysically-loaded. It is noted that the primary purpose of presenting this enhanced and expanded predicate logic account is to capture the Gongsun-Long-stylerelative identity and the collective-name hypothesis regarding the semantic-syntactic structure of common nouns in natural languages in a more accurate and effective way, instead of merely formal consideration.
- 54.
Notice that the semantics for the symbol “ι*” is different from the standard one for “ι” (signifying the uniqueness of the single one object as the referent of a “definite” description) but an enhanced expansion of the latter so as to have it (in the predicate logic) more adequately capture how “definite” descriptions (descriptive noun phrases with unique referents) are used in our linguistic practice (in natural languages): a definite description as a noun phrase denotes either <1> an unique object or <2> a unique set of objects that meet(s) the description of the noun phrase; formally speaking, as indicated in the clause (2.2)<1.3>, the semantics for ‘ι*’ is presented as follows: if α is an ι* term: the case <1> is presented this way: if φ is a formula and α is an individual variable, then v(ι*αφ) is a unique object in the domain D, while the case <2> is presented this way: if φ is a formula and α is a sortal variable, then v(ι*αφ) is a (unique) subset (sort) of D, which is named, and whose membership is specified, by ι*αφ.
References
Ames, Roger and David Hall. 1987. Thinking Through Confucius. Albany: SUNY Press.
Confucius (Kong Zi) 孔子. Analects (Lun-Yü) 《論語》 [the Chinese original text].
Chan, Wing-tsit 陳榮捷. 1963. A Source Book in Chinese Philosophy. Princeton: Princeton University Press.
Cheng, Chung-ying 成中英. 1983. “Kung-sun Lung: White Horse and Other Issues.” Philosophy East and West 33.1: 341–354.
Cheng, Chung-ying. 1987. “Logic and Language in Chinese Philosophy.” Journal of Chinese Philosophy 14: 285–307.
Chmielewski, Janusz. 1962. “Notes on Early Chinese Logic (I).” Rocznik Orientalistyczny 26(1) (1962): 7–21.
Creel, Herrlee. 1983. “On the Opening Words of the Lao-Tzu.” In Journal of Chinese Philosophy 10: 229-329.
Deutsch, H. 2007. “Relative Identity.” Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/identity-relative/.
Fraser, C. 2007. “Language and Ontology in Early Chinese Thought.” Philosophy East and West 57.4: 420–456.
Fraser, C. 2013. “Mohist Canons.” Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/mohist-canons/.
Frege, Gottlob. 1892. “On Sense and Reference” (English translation of “Über Sinn and Bedeutung”). In P. Geach and M. Black, eds., 1960. Translations from the Philosophical Writings of Gottlob Frege (2nd edition): 56–78. Oxford: Blackwell. Reprint in Martinich, A. P. and Sosa, David, eds., 2013: The Philosophy of Language (sixth edition). New York and Oxford: Oxford University Press: 35-47.
Fung, Yiu-ming 馮耀明. 2000. Gong-Sun-Long-Zi 公孫籠子 Taipei: Tung-tai Book Company.
Fung, Yiu-ming. 2009. “The School of Names.” In Bo Mou ed., History of Chinese Philosophy (164–188). London/New York: Routledge.
Fung, Yiu-ming. 2012. “A Logical Perspective on the Parallelism in Later Moism.” In Journal of Chinese Philosophy 39: 333-350.
Fung, Yu-lan. 1952–1953. A History of Chinese Philosophy, 2 vols. tr. Derk Bodde. Princeton: Princeton University Press.
Gamut, L.T.F. 1991. Logic, Language, and Meaning (2 vols). Chicago/London: The University of Chicago Press.
Geach, P. T. 1967. “Identity.” In Review of Metaphysics 21: 2–12.
Gongsun, Long 公孫龍. Gong-Sun-Long-Zi 《公孫龍子》 [the Chinese original text].
Graham, A.C. 1967. “History of Logic.” In P. Edwards, ed., The Encyclopedia of Philosophy, Volume IV. New York: Macmillian.
Hansen, Chad. 1983. Language and Logic in Ancient China. Ann Arbor: University of Michigan Press.
Hansen, Chad. 1992. A Daoist Theory of Chinese Thought. New York: Oxford University Press.
Harbsmeier, Christoph. 1991. “The Mass Noun Hypothesis and the Part-Whole Analysis of the White Horse Dialogue.” In Henry Rosemont, Jr., ed., Chinese Texts and Philosophical Contexts (49–66). La Salle: Open Court.
Krifka, M. et al. 1995. Genericity: An Introduction. In G. Carlson, and F.J. Pelletier, eds. (1995). The Generic Book (1–124). Chicago: The University of Chicago Press.
Kripke, Saul. 1980. Naming and Necessity. Oxford: Basil Blackwell.
Lao Zi 老子Dao-De-Jing 《道德經》 [the Chinese original text]. The English translations of this text addressed in Section 4 include those in Chan 1963 and Lau 1963.
Lau, D.C. (trans.). 1963. Lao Tzu: Tao Te Ching. Penguin Books.
Locke, John. 1690. An Essay Concerning Human Understanding, Book III, Chs. i, ii and iii. Reprint in Martinich, A. P. and Sosa, David, eds., 2013: The Philosophy of Language (sixth edition). New York and Oxford: Oxford University Press: 656-660.
Liu, Peiyu 劉培育. 2004. “Chinese Studies of Names and Argumentation” (中國名辯學). In Part I of Zhang, J. 張家龍 ed., An Intellectual History of Logic 逻辑学思想史 (1–158). Changsha: Hunan Education Press.
McLeod, Alexus. 2011. “Pluralism about Truth in Early Chinese Philosophy: A Reflection on Wang Chong’s Approach.” In Comparative Philosophy 2.1: 38–60. http://www.comparativephilosophy.org.
Mill, John Stuart. 1881. “Of Names.” In his System of Logic, Book 1, Ch.2, Section 5. Reprint in Martinich, A. P. and Sosa, David, eds., 2013: The Philosophy of Language (sixth edition). New York and Oxford: Oxford University Press: 29-34.
Mo-Zi 《墨子》 (the Chinese original text). [The original text on which the relevant part of this essay is based: Wu, Y. 吳毓江, ed., 2006. The Mo-Zi Text with Annotations 墨子校注. Beijing: Zhong-Hua-Shu-Ju 中華書局.]
Mou, Bo 牟博. 1999. “The Structure of Chinese Language and Ontological Insights: A Collective-Noun Hypothesis.” Philosophy East and West 49.1: 45–62.
Mou, Bo. 2000. “Ultimate Concerns and Language Engagement: A Re-Examination of the Opening Message of the Daodejing,” Journal of Chinese Philosophy 27.4: 429–439.
Mou, Bo. 2003. “Eternal Dao, Constant Names, and Language Engagement.” (A substantial expansion and revision of Mou 2000). In Comparative Approaches to Chinese Philosophy (245–262). Aldershot: Ashgate Publishing Ltd.
Mou, Bo. 2006. “Chinese Philosophy: Language and Logic.” In Donald M. Borchert ed., Encyclopedia of Philosophy (second edition) (202–215). Chicago: Thomson-Gale/Macmillan Reference USA.
Mou, Bo. 2007. “A Double-Reference Account: Gongsun Long’s ‘White-Horse-Not-Horse’ Thesis.” The Journal of Chinese Philosophy 34.4: 493–513.
Mou, Bo. 2009. Substantive Perspectivism: An Essay on Philosophical Concern with Truth (“Synthese Library: Studies in Epistemology, Logic, Methodology, and Philosophy of Science” monograph series, vol. 344). Dordrecht: Springer.
Mou, Bo. 2014. “On the Double-Reference Character of ‘Hexagram’ Names in the Yijing: Engaging Fregean & Kripkean Approaches to the Issue of How Reference is Possible.” Frontiers of Philosophy in China 9.4: 523–537.
Mou, Bo. 2015. “Rooted and Rootless Pluralist Approaches to Truth: Two Distinct Interpretations of Wang Chong’s Account.” Comparative Philosophy, 6.1: 149–168. http://www.comparativephilosophy.org.
Mou, Bo. 2016. “How the Validity of the Parallel Inference is Possible: From the Ancient Mohist Diagnose to a Modern Logical Treatment of Its Semantic-Syntactic Structure.” History and Philosophy of Logic: 301–324.
Mou, Bo. 2018. “A Double-Reference Account of Names in Early China.” In Bo Mou, ed., Philosophy of Language, Chinese Language, Chinese Philosophy: Constructive Engagement (69–169). Leiden: Brill Academic Publishers.
Mou, Bo. 2019. Semantic-Truth Approaches in Chinese Philosophy: A Unifying Pluralist Account. Lanham: Lexington Books.
Priest, Graham. 2008. An Introduction to Non-Classical Logic. Cambridge: Cambridge University Press.
Roetz, Heiner. 1993, “Validity in Zhou Thought, On Chad Hansen and the Pragmatic Turn in Sinology,” In H. Lenk and G. Paul, eds., Epistemological Issues in Classical Chinese Philosophy (69–113). Albany: State University of New York Press.
Russell, Betrand. 1905. “On Denoting.” Mind 14: 479–493. Reprint in Martinich and Sosa, eds., 2013: 105-113’ to ‘Martinich, A. P. and Sosa, David, eds., 2013: The Philosophy of Language (sixth edition). New York and Oxford: Oxford University Press: 105-113.
Russell, Bertrand. 1957. “Mr. Strawson on Referring.” Mind 66: 385–389. Reprint in Martinich, A. P. and Sosa, David, eds., 2013: The Philosophy of Language (sixth edition). New York and Oxford: Oxford University Press 136–139.
Sider, Theodore. 2010. Logic for Philosophy. Oxford: Oxford University Press.
Strawson, P.F. 1950. “On Referring.” Mind 59: 320–344. Reprint in Martinich, A. P. and Sosa, David, eds., 2013: The Philosophy of Language (sixth edition). New York and Oxford: Oxford University Press: 121–135.
Wang Chong王充. Lun-Heng 《論衡》 (the Chinese original text) [The original text on which the relevant part of this essay is based: Zhang Zongxiang 張宗祥, ed., 2013. Annotated Lun-Heng論衡校注. Shanghai: Shanghai Gu-Ji Publishing House上海古籍出版社.]
Wiggins, David. 2001. Sameness and Substance Renewed. Cambridge: Cambridge University Press.
Xun, Zi 荀子. Xun-Zi 《荀子》.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix: An Expanded Predicate Logic Account with Enhanced Identity Sign and Collective-Generic Operator
This appendix writing is from Mou 2018, which is a substantial revision of an earlier version of the suggested expanded predicate logic account as given in Mou 2016 (including the addition of the coverage of collective-generic operator).
Appendix: An Expanded Predicate Logic Account with Enhanced Identity Sign and Collective-Generic Operator
For the sake of formally and more accurately capturing, presenting and illustrating some of the addressed points that have been made in this essay (among others, the relative identity and semantic sensitivity as addressed in Gongsun Long’s and the Later Mohist accounts, the due relationship between the two basic semantic notion (reference and truth) as addressed in the last section and as resorted to in the semantic interpretation of a logical system, and the collective-name hypothesis regarding the semantic-syntactic structure of common nouns in natural languages), I propose the syntax and semantics of an enhanced expanded and strengthened account of “relative-identity-sensitive” and “collection-sensitive” predicate logic (“RI-C PC” for short) with an enhanced identity sign (called “identity with attribute-in-focus parameter”), many-sorted variable, and “collection-generic operator” symbol.
In this expanded predicate logic account, there are the following additions on the basis of the standard predicate logic account, some of which are new or partially new while the others not: (1) adding the “collective-generic operator” symbol, which is partially new;Footnote 45 (2) adding the sign ‘[]=’ for “aspect-in-focus parameter” identities, which is new;Footnote 46 (3) adding the sign ι∗ for complex noun phrases (definite descriptions), which is a further expansion on the standard ι operator – semantically defined in a modified way; (4) adding the sign λ for complex predicates, which is not new; (5) turning one-sorted logic into many-sorted logic in the way to be defined, which is not new either; (6) this expanded logical system includes both predicate variables and predicate constants (added in our primitive vocabulary) that symbolize attributes; their semantics is partially standard one while being enhanced with modified domain and interpretation, which is partially new.Footnote 47
-
(1) Syntax of RI-C PC
-
(1.1) Primitive vocabulary
-
<1> individual variables x, y… with or without numerical or letter subscripts
-
<2> individual constants (names) a, b…, with or without numerical or letter subscripts
-
<3> sortal variables s, p…, with or without numerical or letter subscripts
-
<4> for each n > 0, n-place function symbols f, g…, with or without numerical or letter subscripts
-
<5> “definite description” symbol ι*Footnote 48
-
<6> for each n > 0, n-place predicate variables X, Y…, with or without numerical or letter subscripts
-
<7> for each n > 0, n-place predicates (predicate constants) A, B…, with or without numerical or letter subscripts
-
<8> “identity” symbol with “perspective-attribute-in-focus” parameter []=Footnote 49
-
<9> “complex predicate” symbol λ
-
<10> “collective-generic operator” symbol CGFootnote 50
-
<11> connectives: →, 〜
-
<12> (universal) quantifier: ∀
-
<13> collective-generic quantifier: CG ∀
-
<14> parentheses: (,)
-
-
(1.2) Definition of terms:
-
<1> Any individual variable, sortal variable or individual constant is a term
-
<2> If f is an n-place function symbol and α1… αn are terms, then f (α1… αn) is a term
-
<3> If φ is a formula and α is an (individual or sortal) variable, then ι*αφ is a term
-
<4> Only strings that can be shown to be terms by the preceding clauses are terms
-
-
(1.3) Definition of formulas:
-
<1> If Π is an n-place predicate and α1… αn are terms, then Π α1… αn is an (atomic) formula
-
<2> If π is an n-place predicate variable and α1… αn are terms, then π α1… αn is a formula
-
<3> If α, β and γ are terms, then α[γ]=β is a formula
-
<4> If φ is a formula, α is a variable and β is a term, then λαφ(β) is a formula
-
<5> If φ is a formula, α is a term, then CGφ(α) is a formula
-
<6> If φ and ψ are wffs, and α is any variable, then 〜φ, (φ → ψ), and ∀αφ are formulas
-
<7> Only strings that can be shown to be formulas using <1>, <2>, <3>, <4>, <5> and <6> are formulas
-
-
(1.4) Definition of derivative logical symbols:
-
<1> Definition of ∧: “φ∧ψ” is short for “〜(φ →〜ψ)”
-
<2> Definition of ∨: “φ∨ψ” is short for “〜φ →ψ”
-
<3> Definition of ↔: “φ↔ψ” is short for “(φ→ψ)” ∧“(ψ → φ)”
-
<4> Definition of ∃: “∃αφ” is short for “〜∀α〜φ”
-
<5> Definition of ≠: “α[γ] ≠ β” is short for “〜(α[γ]=β)”
-
-
(1.5) Definition of free and bound variables:
-
An occurrence of a variable x in a formula φ is bound in φ if and only if that occurrence is in the context of the form ∃αφ or ∀αφ within φ. If it is not bound, it is free. A formula with no free variables is a closed formula or sentence; otherwise it is an open formula
-
-
(2) Semantics of RI-C PC
-
Definition of value-assigning interpretation, model, for RI-C PC: A RI-C PC model is an ordered pair〈D, v〉such that:
-
(2.1)Dis a non-empty set (“the domain of quantification”);Dis divided into two types of primary subsets as sorts:
-
<1> individual-object subsetsO of individual objects, d1, d2, …, which are divided into various secondary subsets (sorts or sortal collections), O1, O2, … whose “nominal” identities (or whose memberships) are given by the distinct term ι*αφ (where φ is a formula and α is a sortal variable)
-
<2> subset A of all specific grounded parts (specific aspects, particular attributes,…) that are grounded in, and depend on, individual objects (though the defining identities of some of them, such as relational attributes, are grounded in more than one individual objects), which can be further divided into three kinds of subsets whose members can be overlapped:
-
<2.1> universal-attribute subsets, A1,A2,…, which are various subsets of particular attributes whose memberships constitute (or are given respectively by) various universal attributes
-
<2.2> individual-object-association subsets, Ad1, Ad2, …, which are different subsets of specific grounded parts (specific aspects: such as collection-nominal-identity-determining attributes, collectively-holding attributes, generically-holding attributes, …) whose memberships are given by their respective associations with different individual objects, d1, d2, …; each of individual objects d1, d2, …, as a whole can be thus labeled d1-Ad1, d2-Ad2, …Footnote 51
-
<2.3> sortal-collection-associated subsets of attributes concerning sortal collections which might be further divided into three types (for a sortal collection of individual object Oi, it includes one, or more than one, of the following three types of sortal-collection-associated subsets of attributes):Footnote 52
-
<2.3.1> the subset Oi-collection-identity-attributes of collection-identity-determining attributes, which can be abstractly presented by the related universal attributes (such as the “horseness” attribute), and which are possessed by any individual objects of Oi(for example, the “horseness” attribute or the “white-color” attribute is possessed by any individual object in the white horse as a sortal collection of individual white horses);
-
<2.3.2> the subset Oi-collection-generic-attributes of collection-generic attributes, which are not necessarily possessed by each individual member of Oi,(for example, the attribute of having four legs is not necessarily possessed by each of the individual members of the collection of horses but generically (typically or normally) possessed by the members of the collections);
-
<2.3.3> the subset Oi-collection-created-attributes of collection-created attributes, which are possessed not by any individual member of Oi, but only by Oi, as a whole (for example, the attribute of winning a team game cannot be possessed by any individual member of a team of the team members but by the team as a whole).Footnote 53
-
-
-
-
(2.2)vis an (interpretation) function such that:
-
<1>vfor terms
-
<1.1> if α is a (non-predicate) constant, then v (α) ∈D:
-
<1.1.1> if α is an individual object-identifying constant: v (α) is an individual object in D [which is designated by α]
-
<1.1.2> if α is a particular-attribute-identifying constant: v (α) is a particular attribute aij, which is a member of a “grounded” subset (sort) Ai in A (notes: <i> the subset or the membership of the subset is identified by a “nominal” universal attribute Ai that is symbolized by a predicate Pi, <ii> the member of the subset is possessed by an individual object in D, which is a member of a subset (sort) of D, whose membership is specified and named by a “nominalized” predicate Pi, i.e., the term ι*xPi)
-
<1.1.3> if α is a universal-attribute-identifying constant: v (a) is a universal attribute which (as the membership) gives the identity of a universal-attribute subset Ai in A
-
-
<1.2> if α is an individual or sortal variable:
-
<1.2.1> if α is an individual variable: v (α) is an individual object in D
-
<1.2.2> if α is a sortal variable: v (α) is either <i> an individual object in a subset of O, whose membership is specified and named by a “nominal” universal attribute, i.e., the term ι*αφ,Footnote 54 or <ii> an (universal) attribute among various universal-attribute subsets, A1,A2,…, of A (A as a sort in D), or <iii> a particular attribute among various members of a universal-attribute subset, Ai, of A (Ai as a sort in A), or <iv> a particular attribute among various members of an individual-object-association subset, Adi, of A (Adi as a sort in A)
-
-
<1.3> if α is an ι* term:
-
<1.3.1> if φ is a formula and α is an individual variable, then v(ι*αφ) is a unique object in D <1.3.2> if φ is a formula and α is a sortal variable, then v(ι*αφ) is a (unique) subset (sort) of D, which is named, and whose membership is specified, by ι*αφ
-
-
<1.4> if α is an n-place function term of the form f (α1… αn), where α1… αn are terms, and v(α1),… v(αn) are well defined, then v(α) = v(f)[v(α1)… v(αn)], which is an n-place (total) function on D
-
-
<2>vfor formulas
-
<2.1> if Pi is an n-place predicate (predicate constant) and αi1… αin are terms, then <i> vo(Pi) concerning individual objects in D, vo(Piαi1… αin) = 1 iff〈v(αi1)… v(αin) 〉∈ vo(Pi), an n-place relation over D, i.e., a subset of n-tuples, individual objects, from D, and <ii> va(Pi) concerning attributes that are shared by individual objects in D, va(Pi), is the subset (the universal attribute Ai that identifies the membership of the subset) of particular attributes Ai1, Ai2 … which are possessed respectively by these individual objects. [In the following, by default, v (Pi) means vo(Pi) unless indicated otherwise.]
-
<2.2> if p is a predicate variable
-
<2.2.1> if p is an n-place predicate variable and α1… αn are terms, then v(p α1… αn) = 1 iff〈v(α1)… v(αn) 〉∈vo(p)
-
<2.2.2> if p is an n-place predicate variable and α1… αn are terms, then <i> va(CG p) is concerned with the subset of collection-generic attributes in the subset Oi-collection-generic-attributes or the subset of collection-created attributes in the subset Oi-collection-created-attributes, and <ii> vo(CGp) is this: vo(CG p α1… αn) = 1 iff v(αi1)… v(αin)〉∈ vo(CGp), an n-place relation over sortal collections, i.e., a subset of n-tuples, sortal collections in D;
-
<2.2.3> if p is a predicate variable and φ is a formula, then vo(∀pφ) = 1 iff for every set of n-tuples from D, vo(φ) = 1.
-
<2.2.4> if α is a sortal variable and CGφ is a formula, then vo(CG∀(α CGφ)) = 1 iff for every subset of n-tuples, sortal collections in D, vo(CGφ) = 1.
-
<2.2.4.1> if p is an n-place predicate variable and α1… αn are terms, then v(p α1… αn) = 1 iff〈v(α1)… v(αn) 〉∈vo(p);
-
<2.2.4.2> if p is an n-place predicate variable and α1… αn are terms, then <i> va(CG p) is concerned with the subset of collection-generic attributes in the subset Oi-collection-generic-attributes or the subset of collection-created attributes in the subset Oi-collection-created-attributes, and <ii> vo(CGp) is this: vo(CG p α1… αn) = 1 iff v(αi1)… v(αin)〉∈ vo(CGp), an n-place relation over sortal collections, i.e., a subset of n-tuples, sortal collections in D;
-
<2.2.4.3> if p is a predicate variable and φ is a formula, then vo(∀pφ) = 1 iff for every set of n-tuples from D, vo(φ) = 1.
-
<2.2.4.4> if α is a sortal variable and CGφ is a formula, then vo(CG∀(α CGφ)) = 1 iff for every subset of n-tuples, sortal collections in D, vo(CGφ) = 1.
-
-
-
<2.3> for any terms α, β and for a term γ which is either a universal-attribute-identifying constant or a sortal variable ranging over the universal-attribute subsets in A, v(α[γ]=β) = 1 iff v(α) and v(β) share v(γ) [v(α[γ]≠ β) = 1 iff v(〜(α[γ]=β))= 1]; that is, the formula α[γ]=β is true iff what the term α denotes is identical to what the term β denotes regarding the shared attribute which the term γ denotes. Especially, when what the term α denotes is identical to what the term β denotes regarding ALL (universal) attributes in A, the term α and β refer to the same object, which case is symbolically labeled ‘α = β’, as ∀γ α[γ]=β [that would restrict the domain of the second-order quantifier to a particular collection of “universal-attribute subsets, A1,A2,…, which are various subsets of particular attributes whose memberships constitute (or are given respectively by) various universal attributes” (see (2) (2.1) <2.1> above)]. In this way, the traditional identity sign together with its semantic interpretation is one special case of the identity sign with the “aspect-in-focus-parameter”.
-
<2.4> for any formula φ, (individual or sortal) variable α and term β, v(λαφ(β)) = 1 iff v(β)∈v(φ)
-
<2.5> for any formula φ, α is a term, then v(CGφ(α)) = 1 iff v(α)∈v(CGφ).
-
<2.6> for any formulas φ, ψ, and any variable α [‘1’ is to be treated as being true while ‘0’ as being false]:
-
v(φ→ψ) = 1 iff either v(φ) = 0 [being false] or v(ψ) = 1
-
v(〜φ) = 1 iff v(φ) = 0
-
v(∀αφ) = 1 iff for every v(α)∈D, v(φ) = 1
-
-
-
-
It is noted that, in view of the purpose here, the inference rules of this expanded account of predicate logic are not given; to this extent, the foregoing formal system has yet to be complete. As indicated before, the purpose to present the foregoing expanded predicate logic account is to capture, present and illustrate some of the addressed points made in this essay in a more accurate and effective way: the relative identity and semantic sensitivity as addressed in Gongsun Long’s and the Later Mohist accounts, the due relationship between the two basic semantic conceptions (reference and truth) as addressed in the last section and as resorted to in the semantic interpretation of a logical system, and the collective-name hypothesis regarding the semantic-syntactic structure of common nouns in natural languages. In so doing, the current standard predicate logic is thus refined and enhanced in some relevant connections. It is rendered especially relevant to the logic-concerned subject of a volume like this one.
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Mou, B. (2020). Naming, Reference and Truth. In: Fung, Ym. (eds) Dao Companion to Chinese Philosophy of Logic. Dao Companions to Chinese Philosophy, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-030-29033-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-29033-7_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-29031-3
Online ISBN: 978-3-030-29033-7
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)