An Enhanced Account of Relative Identity: Double-Reference Starting Point and Dual-Track Feature

AbstractThis article gives a holistic re-examination of the semantic content and syntactic structure of the concept of relative identity: it suggests and explains an expanded and enhanced dual-track characterization of relative identity. It is expanded in this sense: its due coverage is not narrowly restricted to the equal-status case of identity statements (the symmetric case for identity simplex) but also includes the category-assimilating case (the asymmetric case for identity complex), both of which are unified by the shared semantic core content of relative identity. It is enhanced in this sense: it is intended to give a more refined characterization of relative identity for the sake of enhancing our understanding of the structure and content of real-life relative-identity statements in people’s basic employment of language in view of the relation between thought, language, and the world.KEYWORDS: Double referencerelative identitysemantic-sensitivitysymmetric case for identity simplex and asymmetric case for identity complex AcknowledgementsThe exploration of the basic ideas explained in this essay has benefited from recent years' engaging discussions in various forms; I am thankful to these colleagues (especially, Yiu-ming Fung, Marshall Willman, and Byeong-uk Yi) for their valuable questions and comments that are directly or indirectly related to the issue under examination. I am grateful to one anonymous referee and the editorial team for their helpful comments and suggestions that have strengthened the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 Historically speaking, in my view, Gongson Long was the first in the history of philosophy who has explicitly and reflectively addressed the case of category-assimilating-identity statements in his ‘White-Horse-Not-Horse’ argumentation and shown what can be labeled ‘double-reference’ semantic-sensitivity. This author’s relevant discussions have been partially inspired by Gongsun Long’s approach. However, the central content of this essay (its central points and their argumentations and explanations) does not rely on how to interpret Gongsun Long’s relevant texts/ideas but is examined independently of them. In this way, this essay does not examine Gongsun Long’s text/thought in this connection; for this author’s recent detailed explanation of Gongsun Long’s relevant text/thought, see Mou Citation2020, chapter 8.2 Frege Citation1879.3 Cf. Griffin Citation1977, chapter 1; Deutsch & Garbacz Citation2018, sections 1 and 2. For related issues, also cf., Lowe Citation1997; Noonan Citation1997; Noonan & Curtis Citation2018.4 Geach Citation1967, 238 (the page number is that of its reprint in his Citation1972). Later in his Citation1969, he takes restricting the interpretation of ‘A’ to count nouns (as sortal general terms) to be a slip of pen and allows both sortal general terms and mass terms.5 Wiggins Citation1967, 1.6 It is arguably the case that the addressed second type of real-life relative identity is also implicitly in the general subject-predicate statements of people’s basic employment of language, which I will explain in another writing rather than here for two considerations. On the one hand, the explanation of this case deserves a separate writing in view of its significance; on the other hand, the central features of the enhanced characterization of relative identity, which are focused on in this writing, can be sufficiently shown by the two explicit types as explanans.7 As those in the relative-identity track would typically agree that such identity statements of the form ‘a is identical with [to] or the same as b’ is ‘incomplete’ (including something implicit) and need to complete what is incomplete (or make explicit what is implicit). However, such sayings concerning what is incomplete or what is implicit can be ambiguous and vague. Following Grice Citation1975 and Bach Citation1994, we can label ‘implicature’ (Grice Citation1975) such implicit meanings in statements/utterances: one says and communicates one things and thereby communicates something else in addition (though the latter is closely related to the former); in contrast, we label ‘impliciture’ such implicit meanings in statements/utterances: ‘part of what is communicated is only implicit in what explicitly expressed, either because the utterance is semantically underdeterminate and completing is required or because what is being communicated is an [pragmatically] expanded version of the proposition expressed’ (Bach Citation1994, 324). In the current logical context, by default, the addressed ‘incompleteness’ is semantic underdetermination, neither conversation implicature nor pragmatic expansion.8 The examination here is ontologically neutral regarding the debate over the nature of universals in treating the problem of universals in metaphysics.9 Such phrases [the definite article ‘the’ + a common noun] as ‘the brown cat’ and ‘the cat’ used in this context does not mean one specific or unique individual object (such as one specific cat) but the collection of all individual objects in the addressed class. It is noted that this usage in English is grammatical: the definite article ‘the’ plus a common noun can be used to express a collection of all individual objects that possess the (general) attribute given by (the descriptive content of) the common noun.10 It might be labeled ‘universal’ or ‘unifying force’,11 In the latter case, a descriptive name is sometimes labeled ‘a definite description’ in its technical sense.12 There is the need for clarifying what I mean by the ‘semantic’ dimension. Given the identities of the semantic and the pragmatic, two presuppositions can be made concerning the legitimacy of the semantic examination of the basic employment of language: (1) we can presuppose pragmatic contributing elements and give a non-pragmatic semantic examination focusing on the semantic dimension of the basic employment of language; (2) in the foregoing non-pragmatic semantic examination, sentences are used to linguistically express manifestations (tokens) of the pre-sentential basic employment of language(type).Several notes are due. First, one implication of presupposition (1) is that, as a matter of fact, the semantic dimension and the pragmatic dimension of the double-reference character of the basic employment of language are not absolutely separated from each other but are distinct and somehow complementary dimensions. Second, when the semantic dimension is focused on in one’s semantic examination, it does not automatically imply that those relevant pragmatic elements (or those elements in the pragmatic dimension of the issue of how reference is possible concerning the basic employment of language) are ignored or dismissed; rather, they can be legitimately presupposed, although they are not focused on in such a semantic examination. Third, to the foregoing extent, we can legitimately talk about what a linguistic expression (instead of its speaker, in Strawson’s fasion – see Strawson Citation1950) can refer to or express. Fourth, it is important to note that the basic employment of language per se and thus the foregoing presuppositions per se amount neither to committing itself to the Context Principle (CP) to the effect that it is only in the context of a sentence that words have any meaning nor to dismissing a non-propositional referential model of (direct) reference: (1) they do not amount to the former to the extent that the referential meaning of the subject expression as addressed in the basic employment of language is established prior to the sentential predicate being given; the sentential-predicate-related predication is a further comment on the subject-expression-related predication that is intrinsically made through the specific-part reference, although the basic employment of language gives a sentential context; (2) they do not amount to the latter to the extent that the semantic-whole reference as one dimension of the double reference made in the basic employment of language is essentially non-propositional rigid reference (either directly or indirectly, sensitive to the nature and status of distinct types of referring terms), though it is intrinsically related to the specific-part reference in the double reference of the basic employment of language.13 A separate writing by this author presents a double-reference-related account of predication, labeled ‘subjective-perspective’ account, which gives a detailed explanation of how the semantic-whole referent in view of the specific-part referent (in perspective focus) is further commented on via the sentential predicate. With consideration of the major purpose here, I will not elaborate the predication part of such preliminary double-aboutness analyses in this writing. Nevertheless, a brief explanation of it will be given in the third pre-theoretic observations on the double-aboutness character below in terms of the double-reference analysis below.14 It is presupposed, instead of being further explained, that ‘Biden’ here designates Joe Biden via various relevant pragmatic contributing elements to the communication link between the use of the name and Joe Biden as the current USA President.15 Or more than one specific attribute part. For the sake of simplicity of discussion, I focus on the one-part case.16 Although the word ‘comment’ might bring about an impression of being theoretically-loaded, one consideration for using the word here is that it seems to be user-friendly in capturing what really happens in the addressed people’s basic employment of language in this connection.17 This linguistic observation shows that we actually render the object richer (or thicker in metaphoric terms) than what the above second linguistic observation shows us (i.e., explicitly addressing only one aspect or certain finite aspects in focus) and thus further strengthens the point of the first linguistic observation.18 In this and subsequent symbolizations via a predicate logic account, primitive vocabulary of its syntax is standard with the exception of definite description symbol ι*; it is an expansion on the standard ι operator that is semantically defined in a modified way: the semantics for the symbol ‘ι*’ is different from but an enhanced expansion of the standard one for ‘ι’ (signifying the uniqueness of the single one object as the referent of a definite description) 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 12 a unique set of objects that meet(s) the description of the noun phrase.19 See footnote 9.