Towards a General Theory of Classifications (Studies in Universal Logic)

Logic and Language in Early Chinese Philosophy
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Carnap's involvement with the Vienna Circle developed over the next few years. He met Hans Reichenbach at a conference on philosophy held at Erlangen in Reichenbach introduced him to Moritz Schlick, then professor of the theory of inductive science at Vienna. Carnap visited Schlick—and the Vienna Circle—in and the following year moved to Vienna to become assistant professor at the University of Vienna. In , Carnap published The Logical Structure of the World , in which he developed a formal version of empiricism arguing that all scientific terms are definable by means of a phenomenalistic language.

The great merit of the book was the rigor with which Carnap developed his theory. In the same year he published Pseudoproblems in Philosophy asserting the meaninglessness of many philosophical problems. He was closely involved in the First Conference on Epistemology, held in Prague in and organized by the Vienna Circle and the Berlin Circle the latter founded by Reichenbach in The following year, he and Reichenbach founded the journal Erkenntnis.

At the same time, Carnap met Alfred Tarski, who was developing his semantical theory of truth. Carnap was also interested in mathematical logic and wrote a manual of logic, entitled Abriss der Logistik In , Carnap moved to Prague to become professor of natural philosophy at the German University. It was there that he made his important contribution to logic with The Logical Syntax of Language His stay in Prague, however, was cut short by the Nazi rise to power.

He became an American citizen in From to , Carnap was a professor at the University of Chicago with the year spent as a visiting professor at Harvard University. In the s, stimulated by Tarskian model theory, Carnap became interested in semantics. In Meaning and Necessity , Carnap used semantics to explain modalities. Subsequently he began to work on the structure of scientific theories. His main concerns were i to give an account of the distinction between analytic and synthetic statements and ii to give a suitable formulation of the verifiability principle; that is, to find a criterion of significance appropriate to scientific language.

The latter sets out Carnap's definitive view on the analytic-synthetic distinction. Carnap was also interested in formal logic Introduction to Symbolic Logic , and in inductive logic Logical Foundations of Probability , ; The Continuum of Inductive Methods , The Philosophy of Rudolf Carnap , ed. Philosophical Foundations of Physics , ed. Carnap was working on the theory of inductive logic when he died on September 14, , at Santa Monica, California. In Carnap's opinion, a scientific theory is an interpreted axiomatic formal system. It consists of:. The sets of meaning postulates and rules of correspondence may be included in the set of non-logical axioms.

Indeed, meaning postulates and rules of correspondence are not usually explicitly distinguished from non-logical axioms; only one set of axioms is formulated.

An encyclopedia of philosophy articles written by professional philosophers.

Alonso eds , Oficina do Autor, Rio de Janeiro, In the case of modalized categoricals, the modality is prefixed for the one-sided absolute proposition, I omit the identifier X 1 unless required to avoid ambiguity. Such fragments include, e. The setoid B is the bounding setoid of the cwa, and thus we name the new notion a bounded cwa. Chatti, in the Internet Encyclopedia of Philosophy. Triezenberg

One of the main purposes of the philosophy of science is to show the difference between the various kinds of statements. Among the symbols of the language are logical and non-logical terms. The set of logical terms include logical symbols, e. Non-logical terms are divided into observational and theoretical. They are symbols denoting physical entities, properties or relations such as 'blue', 'cold', ' warmer than', 'proton', 'electromagnetic field'.

Formulas are divided into: i logical statements, which do not contain non-logical terms; ii observational statements, which contain observational terms but no theoretical terms; iii purely theoretical statements, which contain theoretical terms but no observational terms and iv rules of correspondence, which contain both observational and theoretical terms. Observational language contains only logical and observational statements; theoretical language contains logical and theoretical statements and rules of correspondence. The distinction between observational and theoretical terms is a central tenet of logical positivism and at the core of Carnap's view on scientific theories.

In his book Philosophical Foundations of Physics , Carnap bases the distinction between observational and theoretical terms on the distinction between two kinds of scientific laws, namely empirical laws and theoretical laws. An empirical law deals with objects or properties that can be observed or measured by means of simple procedures. This kind of law can be directly confirmed by empirical observations. It can explain and forecast facts and be thought of as an inductive generalization of such factual observations. Typically, an empirical law which deals with measurable physical quantities, can be established by means of measuring such quantities in suitable cases and then interpolating a simple curve between the measured values.

A theoretical law, on the other hand, is concerned with objects or properties we cannot observe or measure but only infer from direct observations. A theoretical law cannot be justified by means of direct observation.

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It is not an inductive generalization but a hypothesis reaching beyond experience. While an empirical law can explain and forecast facts, a theoretical law can explain and forecast empirical laws. The method of justifying a theoretical law is indirect: a scientist does not test the law itself but, rather, the empirical laws that are among its consequences. The distinction between empirical and theoretical laws entails the distinction between observational and theoretical properties, and hence between observational and theoretical terms.

The distinction in many situations is clear, for example: the laws that deal with the pressure, volume and temperature of a gas are empirical laws and the corresponding terms are observational; while the laws of quantum mechanics are theoretical. Carnap admits, however, that the distinction is not always clear and the line of demarcation often arbitrary. In some ways the distinction between observational and theoretical terms is similar to that between macro-events, which are characterized by physical quantities that remain constant over a large portion of space and time, and micro-events, where physical quantities change rapidly in space or time.

To the logical empiricist, all statements can be divided into two classes: analytic a priori and synthetic a posteriori. There can be no synthetic a priori statements. A substantial aspect of Carnap's work was his attempt to give precise definition to the distinction between analytic and synthetic statements. In The Logical Syntax of Language , Carnap studied a formal language that could express classical mathematics and scientific theories, for example, classical physics. He was, therefore, aware of the substantial difference between the two concepts of proof and consequence : some statements, despite being a logical consequence of the axioms of mathematics, are not provable by means of these axioms.

These circumstances explain how Carnap, in The Logical Syntax of Language , gave a purely syntactic formulation of the concept of logical consequence. However, he did define a new rule of inference, now called the omega -rule, but formerly called the Carnap rule:. From the infinite series of premises A 1 , A 2 , Carnap defines the notion of logical consequence in the following way: a statement A is a logical consequence of a set S of statements if and only if there is a proof of A based on the set S; it is admissible to use the omega -rule in the proof of A.

In the definition of the notion of provable , however, a statement A is provable by means of a set S of statements if and only if there is a proof of A based on the set S, but the omega -rule is not admissible in the proof of A. Carnap then proceeded to define some kinds of statements: i a statement is L-true if and only if it is a logical consequence of the empty set of statements; ii a statement is L-false if and only if all statements are a logical consequence of it; iii a statement is analytic if and only if it is L-true or L-false; iv a statement is synthetic if and only if is not analytic.

Carnap thus defines analytic statements as logically determined statements: their truth depends on logical rules of inference and is independent of experience. Thus, analytic statements are a priori while synthetic statements are a posteriori, because they are not logically determined. In any other case, the statement is synthetic. In Meaning and Necessity. Carnap first defines the notion of L-true a statement is L-true if its truth depends on semantic rules and then defines the notion of L-false a statements if L-false if its negation is L-true.

A statement is L-determined if it is L-true or L-false; analytic statements are L-determined, while synthetic statements are not L-determined. This is very similar to the definitions Carnap gave in The Logical Syntax of Language but with the change from syntactic to semantic concepts.

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In , Quine published the article "Two Dogmas of Empiricism," in which he disputed the distinction made between analytic and synthetic statements. In response, Carnap partially changed his point of view on this problem. His first response to Quine came in "Meaning postulates" where Carnap suggested that analytic statements are those which can be derived from a set of appropriate sentences that he called meaning postulates. Such sentences define the meaning of non logical terms and thus the set of analytic statements is not equal to the set of logically true statements.

Later, in "Observation language and theoretical language" , he expressed a general method for determining a set of meaning postulates for the language of a scientific theory. Suppose the number of non-logical axioms is finite. Let T be the conjunction of all purely theoretical axioms, and C the conjunction of all correspondence postulates and TC the conjunction of T and C. The theory is equivalent to the single axiom TC. Carnap formulates the following problems: how can we find two statements, say A and R, so that A expresses the analytic portion of the theory that is, all consequences of A are analytic while R expresses the empirical portion that is, all consequences of R are synthetic?

The empirical content of the theory is formulated by means of a Ramsey sentence a discovery of the English philosopher Frank Ramsey. Look at the following example. O n and theoretical terms T The Ramsey sentence R is. Every observational statement which is derivable from TC is also derivable from R and vice versa so that, R expresses exactly the empirical portion of the theory. Carnap proposes the statement R TC as the only meaning postulate; this became known as the Carnap sentence.

Note that every empirical statement that can be derived from the Carnap sentence is logically true, and thus the Carnap sentence lacks empirical consequences. So, a statement is analytic if it is derivable from the Carnap sentence; otherwise the statement is synthetic. The requirements of Carnap's method can be summarized as follows : i non-logical axioms must be explicitly stated, ii the number of non-logical axioms must be finite and iii observational terms must be clearly distinguished from theoretical terms.

Perhaps the most famous tenet of logical empiricism is the verifiability principle , according to which a synthetic statement is meaningful only if it is verifiable. Carnap sought to give a logical formulation of this principle. In The Logical Structure of the World he asserted that a statement is meaningful only if every non-logical term is explicitly definable by means of a very restricted phenomenalistic language.

A few years later, Carnap realized that this thesis was untenable because a phenomenalistic language is insufficient to define physical concepts. Thus he choose an objective language "thing language" as the basic language, one in which every primitive term is a physical term. All other terms biological, psychological, cultural must be defined by means of basic terms. To overcome the problem that an explicit definition is often impossible, Carnap used dispositional concepts, which can be introduced by means of reduction sentences.

But this proved to be inadequate. Popper showed not only that some metaphysical terms can be reduced to the observational language and thus fulfill Carnap's requirements, but also that some genuine physical concepts are forbidden. Carnap acknowledged that criticism and in "The Methodological Character of Theoretical Concepts" sought to develop a further definition.

The main philosophical properties of Carnap's new principle can be outlined under three headings. First, of all, the significance of a term becomes a relative concept: a term is meaningful with respect to a given theory and a given language. The meaning of a concept thus depends on the theory in which that concept is used. This represents a significant modification in empiricism's theory of meaning. Secondly, Carnap explicitly acknowledges that some theoretical terms cannot be reduced to the observational language: they acquire an empirical meaning by means of the links with other reducible theoretical terms.

Third, Carnap realizes that the principle of operationalism is too restrictive. According to Bridgman, every physical concept is defined by the operations a physicist uses to apply it. Bridgman asserted that the curvature of space-time, a concept used by Einstein in his general theory of relativity, is meaningless, because it is not definable by means of operations. Perhaps influenced by Popper's criticism, or by the problematic consequences of a strict operationalism, Carnap changed his earlier point of view and freely admitted a very indirect connection between theoretical terms and the observational language.

Carnap devoted himself to giving an account of the probability as a degree of confirmation. The philosophically most significant consequences of his research arise from his assertion that the probability of a statement, with respect to a given body of evidence, is a logical relation between the statement and the evidence. Given the great abundance of literature explicitly devoted to interpreting and reconstructing early Chinese views on language, it is impractical to attempt any exhaustive treatment here.

Secondly, in what way did their logical investigations influence their views about language? It is generally recognized today that Chinese philosophy in its classical period was much more preoccupied with articulating and supporting philosophical positions through sustained rational discourse than was previously assumed.

Part of the reason for this oversight in decades past was due to the loss or neglect of ancient texts critical to the understanding of early Chinese ideas on language and logic, particularly the writings of the later Mohists, who developed a sophisticated school of philosophical and scientific thought in the third century BCE, but whose writings were rediscovered by philologists only in the late Qing dynasty — In addition to meticulously developing scientific theories about geometry, mechanics, optics, and economics, the later Mohists also articulated detailed philosophical theories in areas we now recognize as logic, epistemology, metaphysics, and the philosophy of language.

Their writings on language and logic are particularly noteworthy, since the later Mohists appeared to treat these disciplines as embodying a subject matter worthy of independent study, and they devoted more attention to issues about language and logic than any other school of thought of the same period. One finds in later Mohist writings, for instance, the only detailed exposition of bian disputation , the style of argumentation or debate likely practiced in all major schools of thought in ancient China Fraser The later Mohists aspired to become more proficient practitioners of bian by taking it more conscionably as an object of study, and carefully articulating, in the context of a general theory, the terms, rules, and methods for its practice.

A second reason for this oversight is in the fact that those writings of classical Chinese philosophers that did largely survive the vicissitudes of history—particularly the major works of Daoists like Zhuangzi and Laozi, but also those writings attributable to Confucius and his philosophical descendants—tend to embody what appear to be unfavorable appraisals of, or at least alternatives to, philosophical methods that rely heavily on suppositions about the power of discursive rationality at establishing true ethical, metaphysical, or scientific principles.

Such methods take for granted the aptitude of the human intellect to logically deduce true, informative statements about particular objects, events, or states of affairs from general propositions, or establish correct generalizations by induction from particular instances, a practice less self-consciously avowed in most philosophical traditions in China that were unlike Mohism stimulated by centuries of well-established sociocultural practices.

Arguably, much of the interest we see in the study of logic in early Western philosophy was stimulated by the supposition of a dichotomy between appearance and reality, which prompted philosophers to wonder whether judgments or theories about what appears to us do or do not correspond to the structure or content of a mind-independent, objective reality. The obvious case is Plato, whose analysis of Forms was inspired by the methods of Euclidean geometry with the intention that it be carried out in a realm of abstraction largely unimpeded by the diffuse and problematic content of sense experience.

Most Chinese philosophers who lived after the unification of China in BCE, which was largely dominated by Confucianism after a brief period of suppression initiated by the First Emperor Qin Shi Huang, do not appear to have had any special distrust of the content of the senses, or were not responding to those who did, and so were not compelled to view the veracity of representation as a problem of significance.

Consequently, scholars have variously characterized Chinese philosophical thought in ways that contrast it with Western preoccupations with discursive rationality. It is common, for example, to view early Chinese philosophers as largely preoccupied with problems centering on the proper governance of society and how citizens ought to conduct themselves within it. As much as in any other major philosophical tradition, the early Chinese philosophers were concerned with questions about what kind of life is worth living and what things, circumstances, or actions are to be regarded as ultimately valuable.

Their philosophical investigations led them to conceptualize ideals of right conduct, appropriate behavior, and social propriety Hall and Ames But the methods they employed to establish these ideals tended to emphasize reasoning by example from the actions or conduct of key moral exemplars rather than deducing particular judgments of practical action from general principles. For this reason they were more preoccupied with identifying proper normative standards by which to judge the similarity or resemblance of a thing or action with that of a chosen standard.

At the heart of these uses there appears to be a basic preoccupation with the philosophical importance of identifying the similarities and differences of things and events, a process largely determined by cognitive skills associated with pattern recognition. Unlike Aristotle, however, whose methods of classifying things depended on assumptions about metaphysically real essences independent of human agency , the early Chinese philosophers put the burden of correct discrimination at least partly on what they deemed to be appropriate normative standards, based on the efficacy with which they were thought to guide action.

That is to say, which similarities and differences they thought were relevant depended on whether they were thought to guide action in a way that is consistent with general moral principles about right conduct. A central purpose of the ethical investigations of the Mohists, for example, was to identify general standards of judgment that would reliably and impartially guide action in a way that produces beneficial consequences, and they appealed to bian as the principal human faculty for determining how these standards would play out in specific cases.

Towards a General Theory of Classifications

Practical reasoning was conceived as an ability to respond appropriately on the basis of inferences drawn by analogy from various preconceived exemplars or models of moral action. According to Book 4 of the Mozi :. Those in the world who perform tasks cannot do without models fa and standards. There is no one who can accomplish their task without models and standards. Even officers serving as generals or ministers, they all have models; even the hundred artisans performing their tasks, they too all have models.

On the other hand, the Mohists do not seem to have found any reason to doubt the assumption that this appeal to normative standards of discrimination standards relevant to the efficacy of moral action is still grounded in the identification of real similarities and differences among objects, patterns of experience or perception that could in principle be identified by any competent individual with dependable cognitive, perceptual, and linguistic capacities.

This way of summarizing the Mohist philosophical enterprise does leave unanswered important questions about the ultimate justification of ethical claims. Early Chinese thought does not provide an explicit distinction between fact and value, so it is a matter of controversy to determine which has epistemic priority in Mohist thought—the normative standards by which the correct uses of language guide behavior, or the evaluations of reason that are determined by our ability to ascertain real similarities and differences in perception and thought.

This problem is perhaps less controversial in the interpretation of Confucian philosophy because the priority of normative standards in the Confucian program of ordering names is attested by clear examples. The Confucian view is that anyone who is a king ought to act like one; otherwise the name is unwarranted. Hence, correct naming is also a prescription for conduct. One can appreciate, this regard, why the Confucians insisted that the correct use of names is a matter for authority to decide, because only an appropriate authority can justify how one ought to act.

Mohist philosophy complicates this view by divorcing the justification of action from the authoritative individuals who would otherwise serve to institute it, and this raises philosophical concern about how the normative standards of language use are to be decided. Central to Mohist ethical thought are the principles of utility an action is right depending on whether its consequences are useful and universal love the usefulness of an action is determined by the impartial beneficence it contributes to public welfare. So the moral description of an action depends partly indeed, largely on whether it contributes to these ends, or whether these ends may be judged appropriately analogous to the consequences of the actions of a moral exemplar.

But the judgment of similarity here may itself depend on preexisting normative standards of correct use independently of considerations of utility.

Safe to say that since the Mohist Canons do not explicitly address the issue of convention in language, or its role in the justification of principles of naming, the Mohists were probably undecided on this point. Not until the philosophy of Xunzi do we find a clear consideration of this issue, but Xunzi avoids the hard questions it exposes by deferring to the more fastidious judgments of an intellectual elite. Yet some argue that a great many of the Daoist objections one finds in the Zhuangzi are motivated more by a general skepticism about the possibility of identifying invariable standards of discrimination in language than about ineradicable defects in the very human capacity for reason.

One can be a skeptic, for instance, about the role of necessity in reference without having anything disparaging to say about our ability to evaluate the consistency of a theory on logical grounds or reject it by the method of reductio ad absurdum. A number of scholars have even claimed that Daoism, in particular, is not the anti-rational philosophy it has been taken to be, but in some ways an attempt at carrying the methods of reason to their ultimate limits, much as Wittgenstein in his Tractatus attempts to tease out the boundary of the sayable through sustained rational reflection.

Zhuangzi, for all his skepticism about the utility of natural language as a medium for the representation of truth and inclinations towards mysticism, might nonetheless have still venerated reason, independently of language, as the principal mode of thought through which one is able to discern right conduct in accordance with the Dao or Way. This view is controversial, but scholars have not been averse to it cf.

Evidence for it is considered in section 4 below. This fact alone demands caution when making general statements about the logical and linguistic views of early Chinese philosophers working outside the Mohist tradition. One can easily discern an increasing sophistication in methods of disputation in traditions that did not exhibit a great interest in thematizing language and logic independently of other philosophical pursuits, and this should not surprise us given the tumultuous period in which these traditions developed and the contentious struggles of their adherents for varying positions of social status and privilege.

Mengzi, for example, seeking to defend key ideas in Confucian thought, goes beyond his forebears in advancing views on the goodness of human nature by appealing to more sharply formulated premises about innate dispositions for feeling and moral judgment against those asserting that human nature is inherently neutral 2A6, and see Shun for an extensive analysis of argumentation in the Mencius text.

By the time Xunzi enters the fray near the end of the Warring States period we find rebuttals to Mencian thought that dig deep into what it is to have a disposition, how dispositions inform the possibilities of human behavior, and how we ought to act in response to them e. Far from simply explaining his views, Xunzi marshals highly intelligible theories of semantics and reference in their defense, and he explicates these theories with punctilious definitions that are marked improvements over earlier formulations.

According to Cua , methods of disputation reach their highest point in the writings of Xunzi, who in no small way benefited from the standards of rigor that had emerged out of the ongoing disputes of his predecessors. These developments notwithstanding, it is still important to recognize that the demise of Mohism following the Warring States period appears to have squelched philosophical interest in the study of language and logic mostly until modern times, when it was revived in the writings of Sun Yirang Graham []: 70—2.

Matters are complicated by the fact that logic as a unique object of study or discipline disentangled from other philosophical pursuits was historically awakened in Chinese philosophical thought only after the introduction of Western philosophical notions and methods in the 16 th and 17 th centuries. For these reasons, considerable caution has to be exercised in any attempt to reconstruct the philosophical views of classical Chinese philosophers about language and logic, to avoid anachronistically imposing notions that were not part of their original philosophical programs Garrett Debates surrounding these issues are very much alive today, with contemporary scholars of Chinese philosophy tending to fall on one or the other side of the general dispute about whether it is appropriate to utilize concepts, terms, distinctions, modes of expression, or methods of analysis that may have been of foreign origin to interpret the works of classical Chinese philosophers see the entry on comparative philosophy: Chinese and Western for further discussion.

It is indisputable that early Chinese philosophers of all major schools of thought were, at various points in their philosophical development, preoccupied to lesser and greater degrees with issues central to the philosophical studies of language and logic. However, whether they pursued these issues in ways that were similar to, or very different from, Western or other foreign orientations is a matter on which no general consensus has been reached. Common notions in the philosophical study of language include, for example, meaning, truth, reference, assertion, speech act, and propositional structure, notions that may or may not translate successfully into the vocabulary employed by early Chinese philosophers, given radical linguistic and cultural differences.

It is not at all clear that early Chinese philosophers had a conception of logic that involved the typical notions of truth, validity, entailment, consistency, and so forth. Normally, an inference is conceived as a rule-bound transition of some kind from one sentence-like structure—a proposition, statement, or sentence—to another, and is considered valid if it preserves truth. However, there is some dispute about whether early Chinese philosophers were preoccupied with truth as a semantic concept, and even whether they considered sentences to be units of linguistic significance.

On the other hand, contemporary developments of logic have opened up new vistas in the study of ancient ideas. Caveats such as these admonish us to be open to alternative accounts of logic when interpreting the views of early Chinese philosophers, and to exercise caution when representing these views in contemporary nomenclature. Needless to say, any solution to this debate will have to remain open not only to research in the history of Chinese philosophy but also to advances in the general studies of language, logic, cognition and human nature.

Given the universality of language and logic as human capacities or objects of use, can we assume that philosophers interested in these topics will invariably identify, uncover, or utilize analogous concepts, presuppositions, or methods, regardless of time, place, culture, or historical context, or that with conceptual advances in their understanding of these topics, their views will invariably converge? Answers to these questions will inform the methodologies involved in contemporary research on classical Chinese thought, by compelling us to interpret the writings of early Chinese philosophers from perspectives motivated by assumptions about either shared or divergent presuppositions, as the case may be.

The Mohists are generally credited with the first systematic study of language in ancient China, but the inspiration for putting language at the center of philosophical thought certainly comes from Confucius ? Against prevailing skepticism and apathy, Confucius insisted that the correct use of language is essential to the order and harmony of society, and that the conditions by which language is correctly used devolve upon determining how names ming designate objects, events, and actions.

However, the correct use of names is not simply a matter of attaching labels to a preexisting domain of things independent of human affairs. That is, it is commonly recognized that Confucius viewed language as having not simply a descriptive function, but a fundamentally performative one as well.

Attributing names to objects is not a matter of describing the world, but of influencing it in a way that causes certain modes of interaction and existence to be realized. This goes hand-in-hand with the realization that acting on behalf of these meanings and values is itself constitutive of the very relational efficacy one seeks to establish.

In understanding this performative aspect of language one can appreciate why Confucius held that the ordering of society must begin with the ordering of names. A famous exchange in the Analects explains:. When names are not used properly, language will not be used effectively; when language is not used effectively, matters will not be taken care of; when matters are not taken care of, the observance of ritual propriety li and the playing of music yue will not flourish; when the observance of ritual propriety and the playing of music do not flourish, the application of laws and punishment will not be on the mark; when the application of laws and punishments is not on the mark, the people will not know what to do with themselves.

Thus, when the exemplary person puts a name to something, it can certainly be spoken, and when spoken it can certainly be acted upon. Analects Ames and Rosemont The moral dilemmas we face are context-dependent and continuously undergoing transformation, so effective moral action must be motivated by an awareness of these contexts and assume different courses where appropriate.

Departing from Confucian orthodoxy, the Mohists endeavored to justify their ethical views independently of established customs on the basis of general principles, the articulation of which demanded a comprehensive theory of naming and reference. The Later Mohist writings in which logic and language are provided the most extensive treatment are the entire four chapters of Book 10 and the first two chapters of Book 11 of the Mo Zi chapters 40—5, collectively referred to as the Mohist Canons.

The text of the Canons leaves a great deal unsaid; there are missing segments and obvious textual errors, and interpretations of a number of critical passages have exhibited widespread disagreement. For convenience, this entry follows the widely recognized numbering system presented in Graham [], which pairs each Canon with its corresponding Exposition and identifies the passages from each pair by numbers prefixed with the letters A and B.

A great deal of scholarship on Mohist logic in the past 50 years has been devoted to explicating Mohist texts with the purpose of identifying basic similarities with Western logical notions or principles e. In spite of textual errors and incompleteness, there is no dearth of material in Mohist texts that is highly suggestive of these similarities.

They employed special terms for modality, using bi necessity , for example, as an adverbial relation between two things, where one can be said to be the necessary complement of another e. And some scholars have suggested that the Mohists took steps toward formalizing their logical views by conscientiously employing variables and other devices that are capable of functioning in the same grammatical role, such as indefinite and demonstrative pronouns e.

These views are plausible, but support for them is hampered by the fact that the texts do not present them in an organized fashion, but mention them variously in passing as other views more central to their theoretical program are developed. Beyond these superficial similarities with the basic logical notions of contemporary formal-theoretical systems, there is a great deal of material in the Mohist Canons that is indisputably concerned with articulating logical principles, but whose interpretation is still highly debatable.

Scholars have extrapolated from Mohists texts versions of principles common to Western systems of symbolic logic, such as basic rules of inference modus ponens , modus tollens, hypothetical syllogism , necessary and sufficient conditions, the laws of non-contradiction and excluded middle, and reductio ad absurdum. It is hard to believe that the Mohists had anything in mind here but a precise notion of logical inconsistency. Observations such as these might encourage the view that the later Mohists were uncovering basic principles of reasoning that we all share, regardless of culture or history.

Still, it is hasty to assume any resemblance here amounts to an equivalence. A categorical proposition has a subject-predicate structure that partly determines whether or not it is true, and this structure contributes to the explanation of the assertoric force of this proposition when asserted. There is no clear evidence that the Mohists were making a point here about truth, if truth is conceived as a semantic property of propositions that have a subject-predicate structure. Indeed, some scholars have rejected the idea that a subject-predicate structure is a necessary condition of sentences of even contemporary Chinese, let alone is classical forbear e.

More fundamentally, A. Graham claims that the proposition was a philosophical discovery only of the later Mohists, with their earlier counterparts primarily interested in teasing out the philosophical implications of individual terms and their combinations in expressions []. But in his view this discovery did not lead to an analysis of subject-predicate structure. Chad Hansen even rejects the view that early Chinese philosophers were concerned with articulating theories of truth, suggesting instead that their primary focus was on the pragmatic, behavior-guiding functions of language, and how these functions contribute to normative views about proper ethical discourse and conduct.

These important questions aside, it is clear that the Mohists had a primary interest in determining the conditions under which two or more objects may be regarded as the same tong or different yi. Correlatively, they looked for conditions in which an object is admissibly characterized as of a certain kind. This prompted the Mohists to recognize names of different types, three in particular: unrestricted da , classifying lei , and private si. With this, the Mohist art of disputation concentrates on pairs of complementary names e.

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Together, the two names in each pair partition all that exists into two mutually exclusive categories. Any given object is in one or the other category of each pair, but not both. It is in these terms that the Mohists recognized what we would identify as the principles of non-contradiction and excluded middle.

Their primary interest is with naming and reference, and only consequentially are they drawn into reflections on meaning. But this explanation depends on a general theory about the relation between reference and meaning, something the Mohists did not explicitly investigate. Their increasing interest in how names combine into meaningful wholes may have put them on the verge of developing such a theory, but their focus remained mostly at the level of particular acts of naming and uses of words.

This makes it an open question whether or to what extent the logical principles underwriting their specific views on reference, and their general theory of language, are adequately characterized in Aristotelian terms or in some other way. Inference is commonly understood as a syntactic operation on the form of a sentence or assertion that preserves the semantic property of truth.

Like most other early Chinese philosophers, the Mohists do not appear to have conceived of valid inference in this way. Even as they gave increasing attention to matters of logical or grammatical form, they remained skeptical that different categories of form can be regarded as an invariable guide to meaning. In particular, they were consistently wary of assuming that the meaning of a sentence or complex is determined by the meanings of its constituent parts and their modes of combination.

For this reason they maintained that valid inference is partly a semantic affair, hinging on our consideration of the idiosyncrasies of meanings in combination. So rather than developing a theory of inference strictly on the basis of appeals to logical or linguistic form, they instead sought to develop a viable classification of what they took to be valid inference patterns based on analogies in the semantics of terms in combination see section 3. This prioritizing of semantics over formal logic had the effect of encouraging a rather different conception of argumentation based mainly on patterns of analogical reasoning, which the Mohists referred to as bian.

Fraser argues that bian is understood in classical Chinese texts with an assortment of meanings of different levels of generality. Broadly speaking, it refers to processes of reasoning and disputation, basic operations of cognition, and the means by which we acquire knowledge. But in its more specific use it involves correlating things based on their similarities and differences, and drawing conclusions from the distinctions thus established. By ascertaining the resemblance relation between other objects and the standard, we apply the name consistently and identify a class.

Thus, to answer the question of whether or not we should predicate of something x the name G , the Mohists would typically identify a model m a particular object for G , and then inquire whether x resembles the model. The Mohist conception of valid inference may depart from many Western accounts in another way as well. Given their prevailing tendency to regard the action guiding significance of language as its principal function, the Mohists were likely compelled to think of the semantic property that is preserved in valid inference not simply in descriptive terms, but in normative ones as well.

In this way, valid inference was construed as having complex justificatory import. For instance, in claiming that an action x is humane ren by its resemblance with the conduct of a sage, one is also providing justification for it as such, because one is asserting in the act of naming that it resembles the model for humane action, and resembling this model is the very condition that justifies calling it such. Recall again that naming something is classifying it, such that for anything else that is like it one is obligated to use the same name. Moreover, asserting that x is humane justifies the claim that it ought to be recognized as such, because the model which it resembles in being a model is the very justification for how the name ought to be used.

Its resemblance carries with it the normative requirement that language users recognize it as such, for that is what would be expected of a language whose principal function is to guide behavior and encourage proper social conduct. Determining whether x is G depends on whether it resembles the model m , but objects can resemble one another in different ways, and imperfectly. A horse is big not because its eyes are big, but because its body is, whereas it is blind because of its eyes, not its body Xiao Qu [ NO 18].

The Mohists generally identify these criteria by appeal to discriminations directly evident in perception or based on ideas parasitic on acts of perception such as the mental image of a square. But bian is more than just a term for the discriminatory acts of perception; it is about the business of naming objects in virtue of appropriate discriminations, and the application of a name cannot be regarded as correct without an appeal to its semantic content.

These expressions are similar grammatically, but the Mohists analyzed their quantificational content differently, something not given merely in the analysis of perception. The result is the determination of criteria that fix the relations between objects and their chosen models cf. For a fascinating essay on issues arising out of attempts at modeling in modern nomenclature Mohist conceptions of reasoning about yi , see Liu, Seligman, and van Benthem For the Mohists, such practical concerns with the relations between names and objects superseded investigations into logical form.

Indeed, they seem to have presupposed as a paradigm of good reasoning a form of inference that is purely deductive. This principle might not have been rendered explicit in their logical investigations, but their assertion that x is G does not follow without its presupposition or something logically equivalent to it, and they did make a distinguished place for quantifiers among their basic logical notions. So assuming that the model for G is m , the Mohists appear to have taken the following or something equivalent to it as a paradigmatic form of reasoning formally justifying the application of names to objects:.

This argument is deductively valid, and it seems highly improbable that the Mohists were not employing something like it in their assertions about the correct methodology for resolving disputes by bian. So it would be highly misleading to say that the Mohists were simply not doing logic of the kind with which we are familiar today.

That they were not formalizing a theory of logical form does not imply that they were not engaged in rigorously defending their views on the basis of principles that involve or presuppose valid deductive reasoning and other basic methods of logic. To be sure, that the Mohists did not articulate this pattern of reason explicitly could support the claim that their use of it was little more than a trivial exercise of our unconscious aptitude for deductive reason, and hence unwarranted as a distinctive feature of their philosophy.

Even if this is true, however, its consistency with the text makes it not unlikely that they were on the verge of discovering it, for they did endeavor to provide analyses of linguistic form, which point in the direction of formalization, and with the apparent intention of testing theories about various patterns of inference see section 3. Going with this idea, it has been suggested that the Mohists did realize a distinction between singular terms and predicates in their classification of names: lei refers to names that classify they may be true or admissible of many things , whereas si refers to names that point out individuals.

It was noted above that for the Mohists our capacity to correlate objects in various ways is exercised when we name particular objects and then apply these names to all objects that are analogous to them. The term you would have been taken to imply existence. That is to say,. Resemblance is normally construed as a relation that is both reflexive and symmetric. Shape is a common example the Mohists use to distinguish horses when color is irrelevant. But then, given symmetry,.

These are undesirable consequences of this view, but they do follow on standard analyses of resemblance. Did the Mohists really intend it this way? More careful exegesis suggests probably not, but scholarship on Mohist thought has tended to gloss over semantic subtleties in failing to recognize that in Classical Chinese the term for resemblance tong is highly polysemous, with different meanings that the Mohists endeavored to distinguish. In A86—7 of the Canons the Mohists articulate four distinct senses of sameness or resemblance tong , along with difference yi , corresponding roughly to the notions of being identical, being the units of a whole or class, constituting the same object, and being of the same kind:.

What is obvious from the explanations they provide of these terms is that, however much their stock illustrations appeal to acts of perception, the Mohists are using their technical term tong much more broadly than mere perceptual likeness. These examples make it evident, moreover, that tong was intended to cover both mereological and member-set relations cf.

Fraser Such relations are obviously not always symmetrical, and while there is no direct evidence that the Mohists were perplexed by the specific problem posed above, it is evident that their own definitions provided them with various means of response. For purposes here, one way to do this is to adopt the generic notion of an admissible substitute, taking care to provide criteria of admissibility that is inclusive enough to capture the points in the analysis above.

Why do some things count as admissible substitution instances but not others? The Mohists do give many illustrations of relevant criteria, making it evident that there are different kinds; shape, color, and function are common examples. We also judge that a horse is blind because its eyes are impaired in their function.

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Furthermore, this aspect may be used appropriately in that the judgments we make may be true or false depending on whether it is singled out in such an attentive act. Mou argues that this dual-reference account provided the Mohists with the flexibility to determine the truth or falsehood of judgements variously by situating each determination in a context that arises out of the many — perhaps infinite — ways in which we can identify things.

At the same time, this account was also intended to provide an objective ground for the determination of the truth of our judgments by requiring that reference and correlatively our knowledge of the identities of objects be determined in each act by a mind-independent whole from which any particular aspect is identified. But given the subtlety with which the Mohists analyzed their key terms, they seem to have been increasingly sensitive to the worry that no exhaustive list is possible.

Moreover, they were aware that simple terms might have complex or polysemous meanings, and that the problems of analysis are compounded as terms are combined into larger expressions. As a result, it became increasingly evident that complex expressions of the same grammatical form can have different conditions of satisfaction.

Loving people requires loving all people without exception, only then is this called loving people. Not loving people does not require loving no people at all; it is rather not loving all people without exception, and by this it is called not loving people. Riding horses does not require riding all horses without exception; it is rather riding some horses, and by this it is called riding horses.

But not riding horses does require riding no horses at all; only by this is it called not riding horses. These are cases in which something applies without exception in one case but not in the other. Xiao Qu ; tr. Graham []. Revelations such as these prompted what is aptly characterized as a linguistic turn in Mohist philosophy, as the Mohists concentrated their attention on language itself and the implications its grammatical forms have on the analysis of meaning.

The Mohist program was beset with two basic kinds of problems. This was the problem of identifying appropriate salience conditions in perception and thought to serve as criteria for naming the similar similarly and the different differently. Second, in the domain of meaning, they faced unexpected questions in their evaluations of the meanings of names in complex expressions, suggesting problems in extending their theory of reference from simple terms to complex expressions on the assumption that the latter are to be treated compositionally.