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definition

def·i·ni·tion / ˌdefəˈnishən/ • n. 1. a statement of the exact meaning of a word, esp. in a dictionary. ∎  an exact statement or description of the nature, scope, or meaning of something: our definition of poetry. ∎  the action or process of defining something. 2. the degree of distinctness in outline of an object, image, or sound. ∎  the capacity of an instrument or device for making images distinct in outline: [in comb.] high-definition television. PHRASES: by definition by its very nature; intrinsically. DERIVATIVES: def·i·ni·tion·al / -shənl/ adj. def·i·ni·tion·al·ly / -shənl-ē/ adv.

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definition

definition The fineness of spatial sampling of a digital image and hence a measure of image sharpness and contrast. It is expressed in pixels.

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Definition

DEFINITION

The problems of definition are constantly recurring in philosophical discussion, although there is a widespread tendency to assume that they have been solved. Practically every book on logic has a section on definition in which rules are set down and exercises prescribed for applying the rules, as if the problems were all settled. And yet, paradoxically, no problems of knowledge are less settled than those of definition, and no subject is more in need of a fresh approach. Definition plays a crucial role in every field of inquiry, yet there are few if any philosophical questions about definition (what sort of thing it is, what standards it should satisfy, what kind of knowledge, if any, it conveys) on which logicians and philosophers agree. In view of the importance of the topic and the scope of the disagreement concerning it, an extensive reexamination is justified. In carrying out this conceptual reexamination, this article will summarize the main views of definition that have been advanced, indicate why none of these views does full justice to its subject, and then attempt to show how the partial insights of each might be combined in a new approach.

All the views of definition that have been proposed can be subsumed under three general types of positions, with, needless to say, many different varieties within each type. These three general positions will be called "essentialist," "prescriptive," and "linguistic" types, abbreviated as "E-type," "P-type," and "L-type," respectively. This classification is not intended as a precise historical summary, but merely as a useful schema for stating some of the problems and disputes. Thus, some outstanding philosophers may very clearly belong to one of these types. Others who, for the purposes of this article, are placed in a certain class hold positions varying considerably from the presentation to be given. It must therefore be borne in mind that not all the criticisms that will be made apply to all philosophers included in the class being criticized. Writers whose accounts of definition fall largely under the E-type include Plato, Aristotle, Immanuel Kant, and Edmund Husserl. Those who support P-type views include Blaise Pascal, Thomas Hobbes, Bertrand Russell, W. V. Quine, Nelson Goodman, Rudolf Carnap, C. G. Hempel, and most contemporary logicians. Supporters of L-type views include John Stuart Mill (in part), G. E. Moore (in part), Richard Robinson, and most members of the school of linguistic analysis.

According to essentialist views, definitions convey more exact and certain information than is conveyed by descriptive statements. Such information is acquired by an infallible mode of cognition variously called "intellectual vision," "intuition," "reflection," or "conceptual analysis." Prescriptive views agree with essentialism that definitions are incorrigible, but account for their infallibility by denying that they communicate information and by explaining them as symbolic conventions. Although linguistic views agree with essentialism that definitions communicate information, they also agree with prescriptivism in that they reject claims that definitions communicate information that is indubitable. The linguistic position is that definitions are empirical (and therefore corrigible) reports of linguistic behavior.

Essentialism

An essentialist account was first proposed by Socrates and Plato. Socrates is renowned for having brought attention to the importance of definitions. His favorite type of question, "What does (virtue, justice, etc.) mean?," became the characteristic starting point of philosophical inquiry. But Socrates did not make clear what kind of answer he was looking for. In Plato's Euthyphro Socrates is reported to have said that the kind of answer he expected to his question "What is piety?" was one giving an explanation of "the general idea which makes all pious things to be pious" and "a standard to which I may look and by which I may measure actions." He did not explain, however, what he meant by "idea" and "standard" nor how one produces an "idea" or a "standard" when one is defining a term. Richard Robinson, in his book Plato's Earlier Dialectic (p. 62), has suggested that the question "What is X? " is more ambiguous than Socrates realized and that it may be answered in all sorts of ways, depending on the context in which it is asked.

plato

Plato's attempts in his later dialogues to explain the meaning of the Socratic question "What is X? " constitute the celebrated Theory of Forms, the trademark of Platonic metaphysics and epistemology. In a passage of central importance (Republic VI), Plato distinguished two kinds of objects of knowledge (sensible things and forms) and two modes of knowledge (sense perception and intellectual vision). Sensible things are objects of opinion, while abstract forms are objects of philosophical knowledge. Physical objects, shadows, and images are imperfect and ephemeral copies of forms; our perceptual knowledge of them is an inaccurate approximation to our knowledge of their abstract archetypes. Definitions describe forms, and since forms are perfect and unchanging, definitions, when arrived at by the proper procedure, are precise and rigorously certain truths. Empirical statements describe objects of perception and are therefore only more or less reliable approximations to truth.

Models and copies

Plato's analogy between definitions and empirical descriptionsan analogy upon which all E-type theories of definition restis supplemented by a second analogy between the relation of a model to a copy and the relation of a definition to an individual predication. This analogy was suggested by Socrates when he asked for "a standard to which I may look and by which I may measure actions." Plato describes the process of coming to know as if it were like the procedure of a craftsman producing a piece of sculpture or a house. The sculpture is a "copy" of the subject who models for it; the house is in one sense a "copy" of the architect's blueprint, in a somewhat different sense a "copy" of a small-scale model, and in still a third sense a "copy" of the idea in the mind of the builder. Plato's frequent references to the arts and crafts in his exploration of conceptual problems indicate that the analogy of the model-copy relation plays a central role in his theory of knowledge.

Thus, Platonic essentialism provides two sets of answers (both of which rest on metaphors) to the questions "What kind of statements are definitions?" "What purpose do they serve?" and "How are they to be judged as good or bad?" It suggests primarily that definitions are descriptions of objects that are somehow analogous to tables, chairs, and other familiar things; that these definitions serve the purpose of providing descriptive information about their objects; and that they are confirmed by a mode of cognition somehow analogous to sense perception, yet independent of the sensory organs. Secondarily, Platonic essentialism specifies the relation between the objects of definitions and those of empirical descriptions by characterizing the former as models of which the latter are "copies."

Adequacy of the model metaphor

Metaphors are apt or inapt, illuminating or misleading, according to two criteria: (1) the number and importance of the known points of resemblance between the things compared; and (2) the number and importance of previously unnoted facts suggested by the metaphor. To what extent does Plato's metaphor of the unseen model satisfy these criteria?

The primary term of comparison in Plato's metaphor is the abstract form or universal that a definition allegedly describes. The secondary term is the model for a painting or, alternatively, a tailor's pattern. As the painter looks to his model and the tailor to his pattern, the philosopher can look to the forms for the specifications that identify things as instances of one class rather than another, as well as for exact information about the properties of that class.

What are the known points of resemblance between forms and models, on which this metaphor is grounded? Merely to ask this question is already to see that the metaphor is defective from the start, since there cannot possibly be any literal points of comparison. The Platonic forms, unlike models and patterns, have no observable properties by virtue of which they can be said to "resemble" anything at all. Thus, if the model metaphor has any value, it must lie entirely in what the metaphor suggests, rather than in its literal grounds.

Primarily, the model metaphor suggests that definitions and their corollaries constitute all there is to knowledge. Whenever a question of fact or of judgment is raised in the Platonic dialogues, it is treated as a problem of definition. For example, when, in the Euthyphro, Socrates and Euthyphro argue about the propriety of a son's prosecuting his father for murder, Socrates proceeds as though the issue could be settled by arriving at a clear definition of pietyas though one could then look at the definition, look at the action, and decide whether they coincide. We can identify a portrait or a garment by comparing it with its model or its pattern, but we cannot classify and judge an action in the same way. Description and evaluation are seldom matters of identification by comparison with a pattern. In this respect Plato's essentialism is misleading rather than illuminating.

The metaphor of the unseen model also suggests that definitions provide us with precise and rigorous knowledge in the way that blueprints make possible a high degree of uniformity and precision in productive arts such as architecture. But definitions increase precision only when they change the original meanings of words for technical purposes. Generally speaking, a definition can be no more precise than the concept it defines, at the risk of shifting to a different concept. Our concept of what constitutes an adult is vague; if we try to make it precise by specifying an exact age at which childhood is divided from adulthood, we merely lose sight of what we started out to talk about by replacing the concept of maturity with that of having passed a certain birthday.

The model metaphor is not entirely misleading; it suggests at least one genuine resemblance between the terms it compares. The relation between definitions and empirical descriptions is, in one respect, rather similar to the relation between portraits and their models. We judge a portrait (to some extent) by noting whether the portrait looks like the model; we verify the empirical description "This table is round" by looking at the table to see whether it has the properties definitive of tables and of roundness. But if we are asked, "Is that person a good model?" or "Is that definition a good definition?" we cannot look toward anything of which the model is himself a portrait, and we cannot look at a definitional form of which the particular definition is itself an instance. Definitions are not evaluated in the same way as empirical descriptions, just as models are not judged in the same way as their portraits. Thus the analogy between definitions and empirical descriptions from which Platonic essentialism starts eventually contradicts itself.

aristotle

One can find in Aristotle's works anticipations of every later theory of definition, but he gave high priority to his own brand of essentialism, whereby he explained the nature of "real" as distinguished from "nominal" (that is, prescriptive or linguistic) definition. Like Plato, Aristotle stressed the similarity between definitions and statements of fact, and he assumed that definitions convey precise and certain information. But Aristotle employed a different supporting metaphor to explain the special nature of definitions. The most noteworthy feature of his many discussions of definition is his insistence that a real definition should provide a causal explanation of the thing defined. In the Physics, Aristotle distinguished four types of causesformal, material, final, and efficient. He characterized the first three types as "internal," while efficient causes are (usually) "external" to their effects. Internal causes are not available to public inspection, but must be discovered in abstract intuition. The causal explanation provided by a real definition is in terms of one or more of these three internal types of cause.

Definition and causality

It is not easy to explain just what Aristotle meant by "internal cause." Part of what he seems to have meant is that, unlike "incidental" causes, internal causes are necessary for their effects. But it is by no means clear what sense of necessity is involved in this instance. To explain this necessity as causal would be a case of circular reasoning. On the other hand, to say that the necessity is logical seems only another way of saying that the effect is definable in terms of its cause, which is again circular reasoning. As an example of a causal definition, Aristotle defined a lunar eclipse as the privation of the moon's light because of the interposition of the earth between the moon and the sun (Posterior Analytics 90a). This example confirms the suggestion that for something to be an internal causal is for it to be part of a definition. But the difficulty then arises that definition has been explained by internal causality, internal causality by necessity, and necessity by definition. Thus, Aristotle's eclipse leaves us in the dark about definition.

Classification and explanation

The trouble is that the idea of internal causality is a metaphor. An essential cause is not "internal" to the thing defined as a kernel is inside a nut, but only metaphorically "inside."

This metaphor suggests two important but dubious principles: that scientific knowledge consists entirely of definitions and their corollaries and that systematic classification is identical with theoretical explanation. If to define a term is, at the same time, to provide a causal explanation of what it denotes and if the classification of a thing in terms of its species and differentia is sufficient for deducing the laws of its behavior, then the work of scientific inquiry is completed when a comprehensive system of classification has been constructed. Thus, Aristotle wrote in the Posterior Analytics (90b) that "Scientific knowledge is judgment about things that are universal and necessary, that the conclusions of demonstration and all scientific knowledge follow from the first principles" and that "the first principles of demonstration are definitions" (italics added).

That scientific knowledge is not entirely derivable from a set of definitions and that systematic classification is only one small aspect of scientific procedure need hardly be argued. Aristotelian concepts of causality and explanation have been almost completely expunged from modern science, and causes are conceived of in quite different ways. But it is not the archaic character of Aristotle's use of "cause" and "explanation" that concerns us here. It is largely a matter of terminological convenience whether we continue to use these words in the Aristotelian manner or confine them to the procedures of modern physical science. In regard to the problem of clarifying the functions and criteria of definitions, however, Aristotle's claim that definitions reveal the internal causes of their definienda must be criticized not as a false, but as a misleading, metaphor, for it dissolves the very distinctions which it is intended to explainnamely, the distinction between definitions and empirical statements of fact, that between the method of evaluating definitions and the method of confirming factual hypotheses, and that between the distinctive functions of definition and the general aims of scientific inquiry.

ideas and concepts

A third metaphor that has been employed in the support of E-type views of definition originated in Cartesian dualism. René Descartes himself leaned toward a prescriptive account of definition, which will be considered later. But John Locke, Kant, Husserl, and other philosophers who accepted the Cartesian division between the "inner world" of the mind and the "outer world" of physical events took the essentialist position that philosophical inquiry should provide information about a special set of objects ("ideas" for Locke, David Hume, and Husserl; "concepts" for Kant, Heinrich Rickert, and G. E. Moore) discoverable by an infallible mode of cognition ("reflection" for Locke and Husserl; "analysis" for Hume, Kant, Rickert, and Moore).

According to Locke, the outer world of material objects and their motions is describable by the laws of physics, while the inner world of ideas is describable by the laws of psychology that are discovered by reflection on the contents of the mind. These contents are simple and complex ideas; the task of philosophy is to analyze complex ideas into their simple elements and to describe their mode of combination.

Kant distinguished between "analytical" and "synthetic" definitions, regarding the former as the identification of the simple elements (predicates) out of which concepts are formed by the understanding and the latter as the formation of rules of serial order that provide the synthetic a priori postulates of mathematics and physics.

The philosophers under consideration, like their predecessors, assumed that definitions convey knowledge of objects (ideas, images, essences, concepts, or meanings) whose special nature guarantees precision and certainty and that this remarkable kind of knowledge is acquired through a special mode of cognition (reflection, introspection, intuition, or conceptual analysis). The literal content of the private-world metaphor thus seems to be identical with that of the essentialist metaphors already considered. The differences between the private-world and essentialist metaphors (other than terminological ones) must be sought in the suggestive implications of the metaphor. But there is an important difference between philosophers such as Locke, Hume, and Husserl, who reserve the word definition for conventions of word usage and do not consider their introspective analyses of ideas to be definitions, and those such as Kant, Rickert, and C. I. Lewis, who regard philosophical definitions as products of conceptual analysis.

Both groups employ the Aristotelian distinction between real and nominal definitions, except that members of the first group avoid calling the results of their introspective studies "definitions" because they think of them as descriptions of the workings of the mind analogous to descriptions of a clock that has been taken apart for inspection. They think of the special mode of cognition by means of which they discover how simple ideas are organized into complex ideas as inner vision or grasp, which is analogous to sight and touch. But members of the more abstractly minded group compare the special faculty by which real (or analytic or explicative) definitions are discovered to the experience (familiar to logicians and mathematicians) of recognizing logical relation, rather than comparing it to any type of sense perception. They speak of "understanding the meanings of words," of "logical analysis," of "understanding what is contained in a concept," rather than of seeing or grasping the "contents of the mind." There are, then, two kinds of world imagined by these theorists: a world of privately visible or tangible ideas, sense data, secondary qualities, and so forth and a world of abstract concepts or meanings. Some, like Kant, Husserl, and, most systematically, C. I. Lewis, posit both kinds of worlds.

What then do these two metaphors suggest, and how illuminating are their implications? The metaphor of the private world of sense data that is allegedly described by definitions of complex ideas suggests that such definitions, like reports of hallucinations, dreams, and other private experiences, must be taken at face value (provided that they are sincerely and consistently expressed), since they cannot be checked by public observation. This would account for the unchallengeable character of definitions and their analytic corollaries, in contrast to the corrigibility of empirical statements. But this view deprives definitions of any claim to objective validity and entails that every person has a right to his own definitions, in the same way that everyone has a right to his own dreams.

The metaphor of the world of concepts and meanings also attributes a self-certifying character to definitions but fares better with respect to the commonsense fact that we balk at some definitions and accept othersfor the recognition of logical relations, no matter how intuitive, is a socially shared experience. We immediately and privately understand, see, or grasp that a statement of the form P · Q implies a statement of the form Q, but we can also argue the fact and summon evidence (in the form of postulates of a logical system) to prove it. But this metaphor, which of all those we have considered comes closest to not being a metaphor at all and blends imperceptibly into a prescriptive concept of definition, suggests both too much and too little. It suggests that definitions are logical truths and possess logical certainty. But although some definitions are worse than others, all logical truths are normatively equal. Moreover, the metaphor fails to indicate how definitions can be evaluated other than by their formal consistency (the standard by which we confirm a system of logical truths). Yet a definition of a cow as a three-legged animal would be universally rejected on grounds having nothing to do with inconsistency. The denial of a logical truth can be shown to involve a contradiction, but the denial of a definition leads to contradiction only if one has already accepted the definition. Although consistency is a sufficient condition for a system of logical truths, it is merely a necessary condition for sound definitions; yet no additional conditions are provided by logistic phenomenalism.

Prescriptivism

E-type views claim that definitions are statements and that they make assertions that can be pronounced true or false. Essentialists, however, have difficulty explaining how and why definitions differ from ordinary statements of fact, and hence they fall back on metaphors. P-type theories avoid this trouble by denying that definitions are statements of any kind. The prescriptivist assimilates definitions to imperative sentences rather than to declarative sentences and endows them with the function of syntactic or semantic rules for prescribing linguistic operations.

There are two main varieties of prescriptivism. The nominalist variety explains definitions as semantic rules for assigning names to objects, while the formalist variety regards definitions as syntactic rules for abbreviating strings of symbols. P-type views of definition can be traced back to the Greek Sophists and Skeptics, but this article will concentrate on the modern sources of these views. The rebirth of science in the seventeenth century was accompanied by a sweeping rejection of medieval thought, in particular the medieval concept of definition as the penetration by metaphysical intuition into a realm of changeless forms. The nominalist theories of language employed by Sophist and Cynic contemporaries of Plato to undermine belief in the objectivity of knowledge, and again by the more radical medieval Scholastics to subvert the control of theology over science, became, in the seventeenth century, a cornerstone of the reconstruction of knowledge on a new scientific foundation.

Seventeenth-century writings on definition are not entirely free of the influence of classical essentialism. Seventeenth-century prescriptive theories of definition try to avoid the obscurities of essentialism by repudiating the informative role of definitions, but they cannot provide adequate criteria for distinguishing good definitions from bad without presupposing some sort of informative role for them.

nominalism

For Francis Bacon and Hobbes, definitions possessed a therapeutic function, as a means of clearing up or avoiding ambiguous, vague, and obscure language. Regarding semantic confusion as the main source of intellectual trouble, they proposed to clear the way for a new system of knowledge by subjecting existing concepts to the test of definitional reduction to observable and measurable properties. Definition was thus a surgical knife for cutting away metaphysical encrustations, as described by Bacon in paragraph 59 of the Novum Organum :

But the idols of the market-place are the most troublesome of all: idols which have crept into the understanding through the alliances of word and names, and this it is that has rendered philosophy and the sciences sophistical and inactive. Whence it comes to pass that the high and formal discussions of learned men end oftentimes in disputes about words and names: with which it would be more prudent to begin, and so by means of definitions reduce them to order.

Thomas Hobbes also stressed the clarifying role of definitions, taking geometry as his model. In the Leviathan he wrote:

Seeing then that truth consists in the right ordering of names in our affirmations, a man that seeketh precise truth had need to remember what every name he useth stands for or else he will find himself entangled in ffords as a bird in lime twigs. And therefore in geometry, which is the only science which it hath pleased God hitherto to bestow on mankind, men begin at settling the significations of their words: which settling of significations they call definitions, and place them in the beginning of their reckoning.

Definitions thus clear up ambiguities and "settle significations," rather than communicate information about a realm of essences. They are introduced at the beginning of inquiry, as in geometry, rather than at the culmination of inquiry, as in metaphysics and Aristotelian natural science.

According to Hobbes, all knowledge consists in the "right ordering of names in affirmation." A proposition connects one name to another, and an inference adds or subtracts one proposition from another. The structure of scientific thought thus maps the structure of the physical world. It would seem then that, for Hobbes, all scientific knowledge is derivable from definitions. Yet Hobbes also stressed the role of perception in knowledge. The solution to this paradox lies in Hobbes's conception of naming. All inquiry is deductive except for the assignment of names to things, and it is to the assignment of names that we must look for the empirical sources of knowledge. But it follows that definitions as assignments of names must be as informative for Hobbes as they are for Plato or Aristotle. This conclusion leads to a further paradox, for, according to Hobbes, definitions provide no information at all; they express conventional decisions to use particular signs as names of particular objects.

There is an ambiguity in Hobbes's account of definitions that must hamper any attempt to reduce definitions to assignments of names. In order to make definitions entail all the propositions of scientific knowledge, Hobbes had to include, in the notion of naming, all the cognitive functions that we ordinarily distinguish from naming. He first compared the highly abstract and sophisticated definitions of concepts in mathematics and natural science to simple naming procedures such as baptism. Then, in order to account for the conspicuous differences between the two kinds of procedures, he was compelled to reinject into the notion of naming the very distinctions he set out to eliminate. The reduction of definitions to assignments of names only appears to solve the problem of whether definitions are informative: It first suggests that definitions are as arbitrary as acts of naming and then suggests that naming is, after all, not always arbitrary.

early formalism

Although the language used by the Cartesians of the seventeenth century in discussing definitions was similar to that of Bacon and Hobbes, their emphasis and direction of interest was different. Bacon and Hobbes were primarily concerned with the role of definitions in achieving semantic clarity, the Cartesians were more interested in the role of definitions in deductive inference. They developed a conception of definitions as theoretically dispensable abbreviations whose value lies solely in the notational economy they make possible. Cartesian references to "names" are rather misleading since, unlike Hobbes, the Cartesians did not regard assignment of names as the initial and fundamental process of inquiry from which the rest of knowledge is derived. This role was taken over by axioms and postulates that relate "simple" (i.e., indefinable) terms to each other, definitions then being introduced as rules for substituting brief expressions for logical complexes of simple terms.

Descartes did not give much attention to the subject of definition. In rejecting classical syllogistic logic as the framework of scientific inference, he abandoned the emphasis on terms or classes as the basic units of inference in favor of propositional units. The simplest inference became, for Descartes, the intuitive recognition of the implication of one proposition by another. Consequently, postulates replaced definitions as the foundation of deductive science, and essential definitions ceased to represent the highest goal of knowledge.

Pascal's analysis of the nature and function of definitions made explicit the view of definition implicit in Descartes's theory of knowledge. The main elements of Pascal's discussion are formalistic. However, it is not free of ambiguity with respect to the purely notational role of definitions as against the informative role ascribed to them by essentialists.

Pascal's theory of definition is expounded in a brief essay, De l'esprit géométrique (Oeuvres, 14 vols., Léon Brunschvicg and E. Boutroux, eds., Paris, 19041914). He began by distinguishing two types of definition, définitions de nom, which he claimed to be the only type appropriate in science, and an unnamed type that seems to be what Aristotle called "real," the type favored by essentialists, about which he thereafter says nothing more.

Définitions de nom are said to be "mere impositions of names upon things that have been clearly indicated in perfectly intelligible terms," as, for example, the definition of "even number" as "number that can be divided by two without remainder." Such definitions, Pascal claimed, are conventional labels that need have nothing in common with the things they name. They communicate no information about their nominata, expressing merely the decision of the writer to use them in the prescribed manner. The sole limitation on définitions de nom is that they be internally and mutually consistent.

When he discussed the methodology of definition, Pascal no longer regarded the relation between language and reality as purely conventional. We must make sure "not to define things that are clear and are understood by everyone." Geometry provides the model for definitional procedure. "It does not define such things as space, time, motion, number, equality because these terms so naturally designate the things to which they refer, for those who understand the language, that the intended clarification would be more likely to obscure them than to instruct." One might think that, in saying "space naturally designates" its referent, Pascal meant that the word space is so familiar that everyone understands what it signifies. But why, then, should he interdict any definition of "space"? If definitions are notational conventions, there could be no objection to stipulating a new use of the word. Indeed, the ordinary use of "space" is quite different from its technical use in mathematics. Why, then, is it improper to define either the ordinary or the mathematical use? Surely, Pascal was not thinking of the word space, but of space itself as an irreducible entity that cannot be analyzed into simpler components, and if so, then he was thinking of definition not as a notational convenience, but as an informative mode of analysis.

The Cartesian theory of knowledge by which Pascal was guided conceives of the world as a system of elements combined according to mathematical laws to form complex objects and events. While Descartes stressed the analytical reduction of complex propositions to simple ones (i.e., axioms), Pascal joined definitions to axioms as the basis from which the deductive reconstruction of science should start. But common to all the Cartesians is the assumption that knowledge is a mathematical mapping of the structure of nature. In the light of this epistemological atomism, the conventional character attributed to definitions contrasts sharply with the requirement that they correspond to an antecedent natural ordera requirement that leads back to essentialism.

modern formalism

The formalistic conception of definitions as rules of notational abbreviation was only vaguely anticipated by seventeenth-century philosophers, who failed to separate this purely syntactic procedure from epistemological considerations such as mapping the order of nature. Only in recent times have formalistic discussions of definition been purified of epistemological assumptions, by (among others) Russell, Alfred North Whitehead, W. V. Quine, Rudolf Carnap, C. G. Hempel, and Nelson Goodman. But it remains doubtful whether this purely formalistic view either is or can be consistently maintained.

Russell and Whitehead, in Principia Mathematica (Vol. I, p. 11), define a definition as follows:

A definition is a declaration that a certain newly introduced symbol or combination of symbols is to mean the same as a certain other combination of symbols of which the meaning is already known. It is to be observed that a definition is, strictly speaking, no part of the subject in which it occurs. For a definition is concerned wholly with the symbols, not with what they symbolize. Moreover, it is not true or false, being the expression of a volition, not of a proposition.

This characterization of definition is not consistently syntactical. It defines definition in terms of sameness of meaning, while claiming that a definition "is concerned wholly with the symbols, not with what they symbolize." Later in the same passage, Russell and Whitehead declare:

In spite of the fact that definitions are theoretically superfluous, it is nevertheless true that they often convey more important information than is contained in the propositions in which they are used. This arises from two causes. First, a definition usually implies that the definiens is worthy of careful consideration. Secondly, when what is defined is something already familiar , the definition contains an analysis of a common idea. (p. 12)

The first and last sentence in the passage above express a nonsyntactical attitude toward definitions. Definitions turn out to be highly informative, and we seem to have returned to an essentialist view of the matter. But a further qualification has been attached, namely, "when what is defined is something already familiar." In fact, two types of definition are being considered, one being a rule of notational abbreviation and the other an "analysis of an idea." But if some definitions are "analyses of ideas" and are highly informative, then these are the important kinds of definitions, and the formalist view proclaimed at the outset loses its force.

Similar difficulties attend the efforts of other modern logicians to deal with the problem of definition from a purely formal point of view. Thus, W. V. Quine, after asserting that "a definition is a convention of notational abbreviation," qualified his statement as follows:

Although signs introduced by definition are formally arbitrary, more than such arbitrary notational convention is involved in questions of definability; otherwise any expression might be said to be definable on the basis of any expressions whatever. To be satisfactory a definition not only must fulfill the formal requirement of unambiguous eliminability, but must also conform to the traditional usage in question. ("Truth by Convention," in Readings in Philosophical Analysis, edited by H. Feigl and W. Sellars, New York, 1949, p. 252)

Nelson Goodman took the same position and fell into the same difficulties:

In a constructional system most of the definitions are introduced for explanatory purposes. In a formal system considered apart from its interpretation, any such definitional formula has the formal status of a convention of notational interchangeability once it is adopted; but the terms employed are ordinarily selected according to their usage, and the correctness of the interpreted definition is legitimately testable by examination of that usage. (The Structure of Appearance, p. 3)

In common with many other logicians, Quine and Goodman distinguish between the function of definitions "in a formal system" and their function when the system is interpretedthat is, when definite meanings are assigned to the symbols of the system. But this distinction overlooks the fact that from a purely formal standpoint, there is no such thing as a definition at all. Before it is interpreted, the formula that we interpret as a definition is just a string of marks. From a "purely formal standpoint," not only is there no difference between a definition and a notational abbreviation, but there is no difference between a definition and any other kind of formula. There are only various strings of marks, some permitted by the rules of formation of the system, others excluded by these rules. Consequently, the distinction made by Quine and Goodman between definitions in a formal system and those in an interpreted system is seriously misleading.

Rudolf Carnap and C. G. Hempel have tried to clarify the difference between informative definitions and mere notational abbreviations by distinguishing between "old" and "new" concepts. Definitions of old concepts are called "explications" by Carnap and "rational reconstructions" by Hempel, while both call definitions of new concepts "notational conventions." When we are "explicating" or "reconstructing" a concept, our definitions are subject to evaluation by the criteria of conformity to usage and increase of precision (Rudolf Carnap, The Logical Syntax of Language, p. 23). When definitions are introduced solely for the purpose of abbreviation, only the criterion of consistency applies. One must therefore wonder why Carnap and Hempel should bother to call notational abbreviations "definitions," since they have nothing whatever in common with explications.

Perhaps the answer to this question lies in the logical difficulties lurking within the notion of explication. What does it mean to "reconstruct" or "explicate" a concept, and what precisely is the difference between "old" and "new" concepts? If definitions of old concepts must conform to established usage, are they not true or false statements about language usage, in which case the distinction between definitions and empirical statements disappears? These problems lead naturally into the linguistic theory of definition.

Linguistic Theories

Anticipations of a linguistic view of definition may be found in classical writings (for example, in Aristotle's discussion of "nominal definition") and in the nominalist and formalist positions previously considered. But while early nominalism attempted to reduce all the varied functions of words to that of proper names and thus to reduce meaning to the arbitrary assignment of a name to an object, formalism added linguistic considerations as an inessential afterthought. The first step from nominalism to an L-type view proper was taken by John Stuart Mill, although his formulations are permeated with elements of both nominalism and essentialism. A further step was taken by G. E. Moore, but Moore's discussion also contains a heavy strain of essentialism. The clearest formulation of the linguistic view was provided by Richard Robinson in his book Definition, which has the distinction of being the only book in the English language devoted to this subject.

In his System of Logic, J. S. Mill defined "definition" as follows: "The simplest and most correct notion of a Definition is, a proposition declaratory of the meaning of a word: namely, either the meaning which it bears in common acceptation, or that which the speaker or writer intends to annex to it" (10th ed., p. 86).

Mill then explained that a definition is a "verbal proposition" that "adds no information to that which was already possessed by all who understood the name (defined)"a tautology that Mill mistook for an important observation. But, unlike the thoroughgoing prescriptivist, Mill did not regard definitions as purely conventional stipulations, at least insofar as terms in general use are concerned:

It would, however, be a complete misunderstanding of the proper office of the logician in dealing with terms already in use, if we were to think that because a name has not at present an ascertained connotation, it is competent to anyone to give it such a connotation at his own choice. The meaning of a term actually in use is not an arbitrary quantity to be fixed, but an unknown quantity to be sought. (p. 91)

At this point, Mill conceded that some definitions are not mere "declarations" but convey some kind of information about "unknown quantities to be sought." Mill gave two reasons for this departure from prescriptivism. The first consideration involves him in a tug of war between nominalist and linguistic theories. "Since names and their significations are entirely arbitrary, such (verbal) propositions are not, strictly speaking, susceptible of truth or falsity, but only of conformity or disconformity to usage or convention; and all the proof they are capable of is proof of usage" (p. 92).

In this instance, Mill first denied and then asserted that definitions are informative. If "all the proof they are capable of is proof of usage," then they are capable of proof after all, despite his initial disclaimer of this possibility.

Mill's second reason for ascribing at least a quasi-informative function to some definitions resembles, to some extent, the phenomenalist conception of definition as analysis of complex ideas into simple constituents. Mill wrote:

A name, whether concrete or abstract, admits of definition, provided we are able to analyze, that is, to distinguish into parts, the attribute or set of attributes which constitutes the meaning both of the name and of the corresponding abstract. We thus see that to frame a good definition of a name in use is not a matter of choice but of discussion not merely respecting the usage of language, but respecting the properties of things, and even the origin of these properties. (p. 91)

The source of Mill's shifts of emphasis and inconsistencies lies in the ambiguity of his notion of meaning. At times he identified the meaning of a term with the object it "names," at other times with the customary usage of the word, and at still other times with an abstract object or "idea" capable of being divided into simpler parts. Thus, depending on which conception of meaning he had in mind, he thought of a definition as the stipulation of a name, a report of linguistic usage, or the analysis of a complex idea into its constituent parts.

g. e. moore

The extent to which G. E. Moore's approach to definitions can properly be called "linguistic" is debatable. Moore placed less stress on the linguistic aspect of definition than later philosophers such as Gilbert Ryle, Peter Frederick Strawson, and Robinson, who were influenced by Moore's analytical method. For Moore, as for Socrates, the clarification of language was only a means toward the discovery of deeper philosophical truths. But there can be no doubt that Moore inspired others to concern themselves with language and that his painstaking attention to the nuances of words was the most distinctive feature of his work.

In his Principia Ethica, Moore characterized "analytical" definitions (the kind produced by philosophical analysis) as follows: "Definitions of the kind that I was asking for, definitions which describe the real nature of the object or notion denoted by a word and which do not merely tell us what the word is used to mean, are only possible when the object or notion is complex" (p. 7).

In order to indicate the kind of descriptive information that he expected philosophical definitions to provide, Moore offered an example that is as misleading as it is famous: "When we say 'The definition of horse is "a hoofed quadruped of the genus Equus"' we may mean that a certain object, which we all of us know, is composed in a certain manner: that it has four legs, a head, a heart, a liver, etc., all of them arranged in definite relations to one another" (p. 8).

This passage is curious; it suggests that an analytical definition lists the physical parts of the thing defined. The example, however, gives the species and differentia of the class of horses but does not mention any physical parts. In commenting on this passage in his Reunion in Philosophy (p. 184), Morton White has observed that Moore shifted inadvertently from logical to physical complexity.

In later writings, Moore maintained that concepts are the proper subject matter of definition. "To define a concept," he wrote, "is the same thing as to give an analysis of it" ("Reply to My Critics," in The Philosophy of G. E. Moore, pp. 664665). It is not easy to tell just what Moore meant by "concept analysis." For the analysis of a concept, he offered three criteria that add up to the relation of synonymity of expressions. Thus, despite his explicit effort to find an informative function for definitions that goes beyond the explanation of how words are used, it is not unreasonable to conclude that all that his obscure notion of "analyzing a concept" finally comes to is linguistic clarification. In denying that analytic definitions "merely tell us what the word is used to mean," Moore was rejecting the view that definitions are generalizations about common usage and suggesting that they have a more explanatory function. But he never made clear what that function is.

In the only full-length volume in English devoted to the study of definition, Richard Robinson formulated a purely linguistic account of definitions as reports of word usage. But he thought it necessary to supplement his main view with a "stipulative," or prescriptive, account. The reasons for his vacillation are that reports of usage are empirical generalizations, while definitions are, if acceptable at all, necessary truths, and that stipulations are uninformative, while definitions are highly informative. Thus, neither the linguistic nor the prescriptive interpretation accounts for all features of definitions. But the mere juxtaposition of the two can hardly overcome the defects of each taken separately.

A Pragmatic-Contextual Approach

Linguistic theories of definition brought needed attention to the close relation between definitions and the meanings of words, but they erred in identifying meanings either with objects or concepts allegedly denoted by words or with linguistic usage. A correct theory of definition would unite the partial insights of E-type, P-type, and L-type views without relying on misleading metaphors, denying the obvious informative value of definitions, or reducing definitions to historical reports of linguistic behavior.

Why should essentialists and linguistic philosophers claim that definitions convey knowledge, while prescriptivists deny that they do? In some sense of the word knowledge, anyone would agree that definitions communicate knowledge. The problem is to identify a special sense of "knowledge" that is appropriate to definitions but does not require us to postulate obscure essences or to reduce definitions to historical reports. This special kind of knowledge may be knowledge of how to use words effectively. Use, unlike usage, is functional. As Gilbert Ryle has observed, there are misuses and ineffective uses, but there is no such thing as a misusage or ineffective usage ("Ordinary Language," in Philosophical Review 42 [1953]). Usage is what people happen to do with words and is determined by habits, while use is what should be done with words and is governed by rules. To explain the right use of a word, as distinct from merely reporting its usage, a definition must give the rules that guide us in using it. In this respect definitions are rules, rather than descriptions or reports.

All three traditional theories of definition assume, mistakenly, that if definitions convey knowledge, then the knowledge they convey is of the same type as that conveyed by ordinary statements of fact. Essentialists conclude that the knowledge conveyed by definitions is descriptive knowledge of essences, linguistic philosophers conclude that it is descriptive knowledge of language usage, while prescriptivists maintain that definitions do not convey knowledge of any kind. There has been a strikingly similar three-way dispute over the status of value judgments: nonnaturalists hold that value judgments convey knowledge of an abstract realm of "values"; naturalists maintain that they convey knowledge of observable causal relations; and emotivists assert that they convey no knowledge whatsoever. Arguments about whether definitions and value judgments convey true or false information mistakenly presuppose that all information must be of the descriptive type, thus overlooking the fact that cookbooks, military manuals, Sunday sermons, and do-it-yourself instruction sheets all convey, in various ways, the kind of normative information that Ryle has called "knowledge-how" in The Concept of Mind (Ch. 2). Practical or ethical advice may be regarded as stating rules that inform us how to act effectively, while definitions provide rules that inform us how to speak or write effectively. In either case it may be said that the information conveyed is subject to being evaluated as good or bad, but not to being verified as true or false.

applications of a contextualist view

The three views of definition distinguished above fail to provide adequate criteria for distinguishing good definitions from bad ones. They assume that the criteria of a good definition can be stated independently of the specific context in which the definition is offered and the purpose it is intended to serve. But no brief list of criteria can be given that would enable us to judge at sight whether a definition is adequate. The most we can do on a general level is to classify the kinds of rules of use that definitions provide and the kinds of discursive purposes they serve, and to say generally that definitions are good if and only if they serve the purpose for which they are intended.

Thus, an evaluation of a definition must begin with the identification of the point or purpose of the definition, and this requires knowledge of the discursive situation in which the need for the definition arises. We use words to incite ourselves and others to action, to express and share emotions, to draw attention to things, to memorize, to make inferences, to evoke and enjoy images, to perform ceremonies, to teach, to exercise, and to show off. It is when we are unsure of the most effective use of an expression for one of these purposes that we seek a definition.

linguistic rules

Rules governing the uses of words can be sorted into three main types: (1) referring rules, which aid us in identifying the things or situations to which a word may be applied; (2) syntactical rules, which govern the ways in which a word may be combined with other words to form phrases and sentences; and (3) discursive rules (the most difficult to formulate), which indicate when we may use language metaphorically (as in poetry) and when we must use it literally (as in science), as well as indicating differences of category or logical type (for example, the rule that one cannot predicate human qualities such as intelligence of inanimate things such as machines) and indicating when a word should be used in one sense rather than another (for example, space in mathematics as distinguished from physics). Discursive rules are the genuinely philosophical rules.

Rules for defining

The practical value of any account of the nature of definition is to be found in the clarity of the standards it provides for judging when a definition is good or bad. How does the pragmatic-contextualist account fare in this respect?

A number of rules of thumb for evaluating definitions have become canonical in the literature on the subject despite the fact that they make no clear sense in terms of any of the traditional views. The following rules can be found in practically every textbook on logic. They were first suggested by Aristotle in his Topica and have survived without change by sheer weight of tradition:

  1. A definition should give the essence or nature of the thing defined, rather than its accidental properties.
  2. A definition should give the genus and differentia of the thing defined.
  3. One should not define by synonyms.
  4. A definition should be concise.
  5. One should not define by metaphors.
  6. One should not define by negative terms or by correlative terms (thus, one should not define north as the opposite of south, or parent as a person with one or more children).

Significance of the rules

Rule 1, which makes sense only according to the essentialist theory, is nevertheless accepted by many writers who hold a prescriptive or linguistic view of definition, although these writers usually mean that a definition should indicate the properties that define the meaning of the term in question rather than those that just happen to hold true of the objects to which the term applies. But in such a case, the rule is vacuous; it asserts only that a definition should define rather than describe.

Rule 2 deserves its high status only if one accepts Aristotle's extension of biological classification to metaphysics, but it retains a limited value when it is reinterpreted in linguistic terms. We may understand "genus" to mean what Ryle has called the logical grammar of a term. The term defined need not be the name of any natural species or, for that matter, any object whatsoever. In defining words such as function, we do not identify a class of objects. We define a function as a certain type of relation, thus indicating that whatever can be said about relations in general can also be said about functions in particular. We thus provide a rule of syntax governing the word function, indicating with what other words it may be combined. The differentia of functionnamely, that the relation is many-one between two variablesis a referring rule (criterion of identification) that helps us to identify the situations or formulas to which the term function may be applied. But it is wrong to think that the genus and differentia are necessary for a good definition. What must be stated in a definition varies with the definition's purpose. The genus may already be known and only the differentia needed or vice versa. Moreover, there are types of definition, such as contextual and recursive definition, that cannot be expressed in genus-differentia form. Contextual and recursive definitions provide rules for substituting a simpler expression for each of an infinite number of complex expressions of a given type.

Synonyms

The rule that forbids defining by a synonym makes sense only on the contextualist view of definitions as rules of use, although it has long been cited by supporters of the traditional views. The same books that cite this rule also insist that the definiendum must be logically equivalent to the definiens. But a synonym is just an expression that is logically equivalent to a given expression. The trouble seems to be that the term synonym is employed in a vaguely restricted sense to signify not just any logically equivalent expression, but a very brief one. Thus, we often find the injunction, "Do not define a word by a single other word." But this formulation, while sufficiently clear, is misleading. Is a two-word definition, such as "phonograph disc" for "record," a case of defining by a synonym or not? Just how many words may the definiens contain if it is not to violate this rule?

To make matters worse, the prohibition of synonyms is inconsistent with rule 4, which demands that a definition be concise; indeed, the more concise the definiens, the more it looks like a synonym. However, we can understand a rule only if we know what specific purpose the rule is intended to serve. A contextualist view of definitions provides the following solution to the conflict between conciseness and nonsynonymity:

Single-word definitions are seldom useful because a person who does not know the rules governing the definiendum, is not likely to know the rules governing the definiens. The more words there are in the definiens, the more likely it is that those for whom the definition is offered are familiar with some of the words and thus understand some of their rules of use. Everyone has experienced the frustration of looking up a word in a dictionary and being confounded by some equally unfamiliar synonym.

But why should definitions be concise if the greater the number of words, the greater are our chances of at least partial comprehension? One obvious answer is that brief explanations are easier to remember. A second answer is that a lengthy definiens is more likely to suggest some rules of use that are inessential to the definiendum. But the most important consideration has to do with the kind of discursive context in which the definition is employed. In mathematics and in other formal contexts such as jurisprudence and contractual language, the purpose of most definitional equations is to abbreviate discourse or notation. In such cases it is a virtue rather than a defect for the definiens to be long and complicated, since it is precisely this fact that makes the definiendum worth introducing as an abbreviation. Moreover, the complexity of the definiens is less likely to produce confusion in technical contexts because of the great pains taken to preserve consistency and precision of language. In contrast, the rule of conciseness is more appropriate to informal discourse, in which definitions are intended to translate or otherwise clarify an expression unfamiliar to some of the participants. In informal discourse, the definiens should be brief, while in formal contexts, the longer and more complicated the definiens, the more useful the definition. Clearly, one can make little sense of criteria of good definitions without specifying the context in which and the purpose for which a definition is needed.

Figurative language

Why should a definition avoid figurative language? This traditional injunction is probably a result of the concentration of classical philosophy on formal discursive contexts such as mathematics and natural science, in which figures of speech are usually out of place. But in informal contexts such as conversation, literature, public debate, and even the less technical discussions of scientists, figurative language may well be the most effective way of getting a point across, and it is certainly the only way to define expressions whose meaning is essentially figurative (for example, fathead may be defined as "a fool puffed up with vanity"). No literal definiens can do justice to the nuances of natural discourse, as every translator knows from bitter experience.

Negative and correlative terms

Why not define by the use of negative or correlative terms? This injunction, in contrast to rule 5, holds for informal discourse and becomes senseless when applied to formal discourse. It is perfectly proper in mathematics or logic to define "p " as "the negation of p " or to define "F 1(x )" as "the inverse of the function F (x )." The reason for prohibiting negative and correlative definitions in informal contexts is that a person who is unclear about the rules of use of the definiendum would be just as puzzled about the rules of use of a negative or correlative definiens.

Meaning equations

In light of the preceding discussion, it is advisable to look again at the problem of synonymity. It has already been noted that every meaning equationthat is, every definition of the form "E " means (or means the same as) "x, y, z "provides a definiens that is synonymous with its definiendum. The very point of the definition is to assert this synonymity and thus to transfer the rules of use already known to govern the definiens to the presumably less familiar definiendum. In order to make sense of the traditional injunction against synonymous definitions, we found it necessary to interpret the synonymity in question as a special and restricted subtype of synonymity, measured by the number of words in the definiens. But although it is absurd to require that a meaning equation must not offer synonyms (in the general sense of "synonym"), it is quite sensible to cast doubt on the usefulness of meaning equations. Meaning equations provide a kind of definition misleadingly called "explicit," in contrast to axioms and postulates, which are frequently regarded as "implicit" or "partial" definitions.

It is unfortunate that meaning equations have come to be called "explicit" definitions, because their function, as we have seen, is to transfer rules of use from definiens to definiendum without articulating the rules in question, so that the rules remain implicit. The most explicit kind of definition, the kind that actually states the rules governing the use of an expression, is a very complicated matter. Outside of technical contexts, it is doubtful whether complete definitions of this kind can ever be provided. On the other hand, it is just as doubtful whether a complete articulation of all the rules of use of the definiendum need be given. We seldom, if ever, require more than one or a few rules of reference, logical grammar, or relevant discourse that happen to be obscure to us in a particular context. Thus, meaning equations are frequently neither the most valuable nor the most appropriate kind of definition. In technical discourse, contextual, recursive, and operational definitions play a far more important role than mere notational abbreviations. And in nontechnical contexts, such as teaching a child or a foreigner the use of a word, definitions by illustration, by enumeration of instances or enumeration of subclasses, and by an indefinite number of other devices (depending on the ingenuity and linguistic sensitivity of the parties concerned) are usually more appropriate and effective than meaning equations. The evaluation of specific definitional procedures remains an important task for philosophically minded experts in each field of discourse and inquiry.

See also Aristotle; Art, Definitions of; Bacon, Francis; Brunschvicg, Léon; Carnap, Rudolf; Descartes, René; Essence and Existence; Geometry; Goodman, Nelson; Hempel, Carl Gustav; Hobbes, Thomas; Hume, David; Husserl, Edmund; Intuition; Kant, Immanuel; Language, Philosophy of; Lewis, Clarence Irving; Locke, John; Logical Terms, Glossary of; Medieval Philosophy; Mill, John Stuart; Moore, George Edward; Pascal, Blaise; Plato; Proper Names and Descriptions; Quine, Willard Van Orman; Rickert, Heinrich; Russell, Bertrand Arthur William; Ryle, Gilbert; Semantics; Socrates; Strawson, Peter Frederick; Universals, A Historical Survey; Whitehead, Alfred North.

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Definition

DEFINITION

A mental process, namely, one of clarifying the meaning of a term by analyzing and relating the elements involved in it; or, alternatively, the product of a mental process, viz, an expression explaining the use of the term or its meaning. Definition is the opposite of divi sion, which separates the elements involved in the meaning of a term or in the thing it signifies.

Notion. As a mental process, definition arises not only from simple apprehension, but also from judg ment and reasoning, and, in the latter case, through both deduction and induction. Thus intellectual apprehension of one's experiences with individual human beings can lead one to realize that "animal in whom instinct is replaced by reason" is what is meant by "man." The process here is often one of defining through division, as exemplified in Plato's Sophist (218D221C). Or, one may judge it true to say, "Man is an animal," and so utilize the notion of "animal" as a clarification of "man." Finally, one may argue to the conclusion, "Man is meant to live in society," from the findings of psychological tests, and then employ "social" as a clarification of "man." This method is often used by St. thomas aqui nas in his Summa theologiae, as when he formulates the full definition of a virtue only at the end of its treatment (for example, that of charity, ST 2a2ae, 23). Definitions can thus be said to grow or expand as one's knowledge is increased and is related consciously to what was previously known. As the product of a mental process, definition is distinguished from the term or thing defined, which is often labeled "the definitum," or "the definiendum." In the examples cited above, "man" is the definitum. Furthermore, definition is not a sentence or proposition, but an expression that merely juxtaposes the definitum and the definition; this can be signified by means of a colon"man: social being." For this reason, definitions are not true and false, but good and bad or adequate and inadequate. For it is generally agreed that definition, as the product of a mental process, is related only to the first act of the mind, that is, to simple apprehension.

Kinds. There are two major groups of definitions. The first includes expressions that explain the use of a term; these are called nominal definitions because the definitum is a term usually in the noun form (Lat. nomen ). There are four classes of nominal definition. The first makes use of a synonym or of the corresponding word in another language, as in "man: human being," or "man: hombre. " Such a definition is of value only when the definition is clearly more known than the definitum. The second employs the etymology of a term"man: from the Anglo-Saxon mann, " or "magnolia: from Magnol, its discoverer's name." The third is based on the history of a term's use throughout the ages; thus one may study the usage of "man" in Chaucer, Shakespeare, Restoration drama, etc. The fourth is based on an imposed or stipulated use of a term, as is done when proving theorems in mathematics and symbolic logic.

The second major group of definitions includes all expressions that explain the meaning of the term and of the concept it signifies. Aristotle explains it as a phrase signifying a thing's essence (Topics, A 101b). This kind of definition is often called "real," not because the nominal definition is fictional, but because the definitum of the second group is taken as referring more directly to reality (Lat. res ).

There are many varieties of real definition. First, a thing may be defined in terms of its efficient causes, or its origins, as in "man: one born of rational parents," or "water: a product of oxygen and hydrogen." Second, one may define something in terms of its end or purpose, as in "man: a being whose destiny it is to rule the universe," or "watch: an instrument for telling time." Third, a thing may be defined in terms of its intrinsic principles, as in "body: a composite of primary matter and substantial form," or "man: a composite of organic body and intellectual soul." This is sometimes labeled a physical definition. Fourth, a definition may be given through a thing's properties and accidents, as in "man: a being capable of enjoying a joke," or "water: a substance with a boiling point of 100°C." This is often called a descriptive definition. Finally, a thing may be defined in terms of its genus and difference, as in "man: rational animal." This is called a metaphysical definition.

These definitions are not all of equal value. The ordinary man tends to define in terms of synonyms, purposes and accidents. The mathematician finds use only for stipulated definitions. The philosopher and the scientist employ all forms of real definition, together with the results of etymological and historical studies, often combining these into one definition that completely expresses the essence of the definitum, as in "man: one born of rational parents, composed of organic body and intellectual soul, made to dominate the universe, meant to live in society, etc."

Rules. In order to bring order and accuracy to the work of defining, logicians have developed several rules for formulating definitions. These may be summarized as follows. First, the definition should be coextensive with the definitum. Thus to define man as "two-legged" is bad form, for other things besides man are two-legged. Second, the definitum should never be found in the definition, as in "man: creature composed of organic body and human soul;" here "human" is equivalent to "man." This is perhaps the most common form of bad definition. Third, whenever possible the definition should be in univocal terms, so as to avoid ambiguity. Fourth, whenever possible the definition should be in positive, affirmative terms, since negative terms do not tell what a thing is but only what it is not. Thus, to define man as "a non-feathered creature" is to say little about him. Finally, every definition should contain a genus and a difference, the genus expressing what the definitum has in common with other things or words, and the difference expressing what is peculiar to the definitum. It may be noted that, while all definitions should indicate a genus and a difference, the best definition will specify the proximate genus and the specific difference, for it is this kind of definition that fulfills perfectly the logical rules cited above. But such a perfect definition is rare (the standard example, "man: rational animal," may well be unique), presupposing, as it does, extensive investigation of its subject matter.

Real definitions that comply with all the rules for definition are difficult to obtain in theology since analogical and negative terms are the best available for defining supernatural entities. Nor do existentialist philosophers feel at home with the notion of a real definition that is oriented to essence. Nevertheless, scientists and philosophers recognize in definition a valid mode of attaining science through continued clarification of terms and their meanings.

See Also: quiddity; species; distinction, kinds of.

Bibliography: The Material Logic of John of St. Thomas, tr. y. r. simon et al. (Chicago 1955). f. h. parker and h. b. veatch, Logic as a Human Instrument (New York 1959). j. a. oesterle, Logic: The Art of Defining and Reasoning (2d ed. Englewood Cliffs, N.J. 1963). v. e. smith, The Elements of Logic (Milwaukee 1957); "Definitions," in From an Abundant Spring (New York 1952), The Walter Farrell Memorial v. of The Thomist, 337362. j. a. mourant, Formal Logic (New York 1963). e. d. simmons, The Scientific Art of Logic (Milwaukee 1961).

[e. bondi]

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Definition

Stomach cancer

Definition

Stomach cancer (also known as gastric cancer) is a disease in which the cells forming the inner lining of the stomach become abnormal and start to divide uncontrollably, forming a mass called a tumor.

Description

The stomach is a J-shaped organ that lies in the left and central portion of the abdomen. The stomach produces many digestive juices and acids that mix with the food and aid in the process of digestion. There are five regions of the stomach that doctors refer to when determining the origin of stomach cancer. These are:

  • the cardia, area surrounding the cardiac sphincter which controls movement of food from the esophagus into the stomach
  • the fundus, upper expanded area adjacent to the cardiac region
  • the antrum, lower region of the stomach where it begins to narrow
  • the prepyloric, region just before or nearest the pylorus
  • the pylorus, the terminal region where the stomach joins the small intestine.

Cancer can develop in any of the five sections of the stomach. Symptoms and outcomes of the disease will vary depending on the location of the cancer.

Demographics

In 2007, the American Cancer Society estimated that 21,260 Americans would be diagnosed with stomach cancer and approximately 11,210 deaths would result from the disease. The risk for developing stomach cancer in the United States is about 1 in 100. The risk is higher for men than for women. Two-thirds of stomach cancer cases are diagnosed in people older than age 65, but in families with a hereditary risk for stomach cancer, cases in younger individuals are more frequently seen.

Stomach cancer is one of the leading causes of cancer deaths in several areas of the world, most notably Japan and other Asian countries. In Japan it appears almost ten times as frequently as in the United States. The number of new stomach cancer cases is decreasing in some areas, however, especially in developed countries. In the United States, incidence rates of stomach cancer have declined. The use of refrigerated foods and increased consumption of fresh fruits and vegetables, instead of preserved foods with high salt content, may be a reason for the decline. Another reason for the decrease may be that antibiotics , which are given to treat childhood illnesses, can kill the bacterium Helicobacter pylori, which is a major cause of stomach cancer.

Causes and symptoms

While the exact cause for stomach cancer has not been identified, several potential factors have led to increased numbers of individuals developing the disease and, therefore, significant risk has been associated. Diet , work environment, exposure to the bacterium Helicobacter pylori, and a history of stomach disorders such as ulcers or polyps are some of these believed causes.

Studies have shown that eating foods with high quantities of salt and nitrites increases the risk of stomach cancer. The diet in a specific region can have a great impact on its residents. Making changes to the types of foods consumed has been shown to decrease likelihood of disease, even for individuals from countries with higher risk. For example, Japanese people who move to the United States or Europe and change the types of foods they eat have a far lower chance of developing the disease than do Japanese people who remain in Japan and do not change their dietary habits. Eating recommended amounts of fruit and vegetables may lower a person's chances of developing this cancer.

A high risk for developing stomach cancers has been linked to certain industries as well. The best proven association is between stomach cancer and persons who work in coal mining and those who work processing timber, nickel, and rubber. An unusually large number of these workers have been diagnosed with this form of cancer.

Several studies have identified a bacterium (Helicobacter pylori) that causes stomach ulcers (inflammation in the inner lining of the stomach). Chronic (long-term) infection of the stomach with these bacteria may lead to a particular type of cancer (lymphomas or mucosa-associated lymphoid tissue [MALT]) in the stomach.

Another risk factor is the development of polyps, benign growths in the lining of the stomach. Although polyps are not cancerous, some may have the potential to turn cancerous. People in blood group A are also at elevated risk for this cancer for unknown reasons. Other speculative causes of stomach cancer include previous stomach surgery for ulcers or other conditions, or a form of anemia known as pernicious anemia.

A history of smoking also increases the risk for developing stomach cancer. Smoking doubles the risk for the development of stomach cancer.

Stomach cancer is a slow-growing cancer. It may be years before the tumor grows very large and produces distinct symptoms. In the early stages of the disease, the patient may only have mild discomfort, indigestion, heartburn , a bloated feeling after eating, and mild nausea. In the advanced stages, a patient has loss of appetite and resultant weight loss , stomach pains, vomiting, difficulty in swallowing, and blood in the stool. Stomach cancer often spreads (metastasizes) to adjoining organs such as the esophagus, adjacent lymph nodes, liver, or colon.

Diagnosis

Unfortunately, many patients diagnosed with stomach cancer experience pain for two or three years before informing a doctor of their symptoms. When a doctor suspects stomach cancer from the symptoms described by the patient, a complete medical history is taken to check for any risk factors. A thorough physical examination is conducted to assess all the symptoms. Laboratory tests may be ordered to check for blood in the stool (fecal occult blood test) and anemia (low red blood cell count), which often accompany gastric cancer.

In some countries, such as Japan, it is appropriate for patients to be given routine screening examinations for stomach cancer, as the risk of developing cancer in that society is very high. Such screening might be useful for all high-risk populations. Due to the low prevalence of stomach cancer in the United States, routine screening is usually not recommended unless a family history of the disease exists.

Whether as a screening test or because a doctor suspects a patient may have symptoms of stomach cancer, endoscopy or barium x rays are used in diagnosing stomach cancer. For a barium x ray of the upper gastrointestinal tract, the patient is given a chalky, white solution of barium sulfate to drink. This solution coats the esophagus, the stomach, and the small intestine. Air may be pumped into the stomach after the barium solution in order to get a clearer picture. Multiple x rays are then taken. The barium coating helps to identify any abnormalities in the lining of the stomach.

In another more frequently used test, known as upper gastrointestinal endoscopy, a thin, flexible, lighted tube (endoscope) is passed down the patient's throat and into the stomach. The doctor can view the lining of the esophagus and the stomach through the tube. Sometimes, a small ultrasound probe is attached at the end of the endoscope. This probe sends high frequency sound waves that bounce off the stomach wall. A computer creates an image of the stomach wall by translating the pattern of echoes generated by the reflected sound waves. This procedure is known as an endoscopic ultrasound, or EUS.

Endoscopy has several advantages because the physician is able to see any abnormalities directly. In addition, if any suspicious-looking patches are seen, biopsy forceps can be passed painlessly through the tube to collect some tissue for microscopic examination. This is known as a biopsy. Endoscopic ultrasound (EUS) is beneficial because it can provide valuable information on depth of tumor invasion.

After stomach cancer has been diagnosed and before treatment starts, another type of x-ray scan is taken. Computed tomography (CT) is an imaging procedure that produces a three-dimensional picture of organs or structures inside the body. CT scans are used to obtain additional information in regard to how large the tumor is and what parts of the stomach it borders; whether the cancer has spread to the lymph nodes; and whether it has spread to distant parts of the body (metastasized), such as the liver, lung, or bone. A CT scan of the chest, abdomen, and pelvis is taken. If the tumor has gone through the wall of the stomach and extends to the liver, pancreas, or spleen, the CT will often show it. Although a CT scan is an effective way of evaluating whether cancer has spread to some of the lymph nodes, it is less effective than EUS in evaluating whether the nodes closest to the stomach are free of cancer. However, CT scans, like barium x rays, have the advantage of being less invasive than upper endoscopy.

Laparoscopy is another procedure used to stage some patients with stomach cancer. This involves a medical device similar to an endoscope. A laparoscopy is a minimally invasive surgery technique with one or a few small incisions, which can be performed on an outpatient basis, followed by rapid recovery. Patients who may receive radiation therapy or chemotherapy before surgery may undergo a laparoscopic procedure to determine the precise stage of cancer. The patient with bone pain or with certain laboratory results should be given a bone scan .

Benign gastric neoplasms are tumors of the stomach that cause no major harm. One of the most common is called a submucosal leiomyoma. If a leiomyoma starts to bleed, surgery should be performed to remove it. However, many leiomyomas require no treatment. Diagnosis of stomach cancers should be conducted carefully so that if the tumor does not require treatment the patient is not subjected to a surgical operation.

Other tests that may be performed to diagnosis stomach cancer include magnetic resonance imaging scan (MRI), positron emission tomography (PET) scan, and chest x ray .

Clinical staging

More than 95% of stomach cancers are caused by adenocarcinomas, malignant cancers that originate in glandular tissues. The remaining 5% of stomach cancers include lymphomas and other types of cancers.

It is important that gastric lymphomas be accurately diagnosed because these cancers have a much better prognosis than stomach adenocarcinomas. Approximately half of the people with gastric lymphomas survive five years after diagnosis.

Treatment for gastric lymphoma involves surgery combined with chemotherapy and radiation therapy.

Staging of stomach cancer is based on how deep the growth has penetrated the stomach lining; to what extent (if any) it has invaded surrounding lymph nodes; and to what extent (if any) it has spread to distant parts of the body (metastasized). The more confined the cancer, the better the chance for a cure.

One important factor in the staging of adenocarcinoma of the stomach is whether the tumor has invaded the surrounding tissue and, if it has, how deep it has penetrated. If invasion is limited, prognosis is favorable. Diseased tissue that is more localized improves the outcome of surgical procedures performed to remove the diseased area of the stomach. This is called a resection of the stomach.

Stomach cancer is staged using the Tumor(T), Node(N), Metastasis(M), classification system. After stage 0, where the cancer has not grown beyond the layers of the tissue lining the stomach, the tumor is labeled stage I through IV. Stage 1 indicates less tumor involvement; stage IV indicates the tumor has spread outside of the stomach and has invaded other tissues or organs in the body.

Treatment

Because symptoms of stomach cancer are so mild, treatment often does not commence until the disease is well advanced. The three standard modes of treatment for stomach cancer are surgery, radiation therapy, and chemotherapy. While deciding on the patient's treatment plan, the doctor takes into account many factors. The location of the cancer and its stage are important considerations. In addition, the patient's age, general health status, and personal preferences are also taken into account.

Surgery

In the early stages of stomach cancer, surgery may be used to remove the cancer. Surgical removal of adenocarcinoma is the only treatment capable of eliminating the disease. Laparoscopy is often used before surgery to investigate whether the tumor can be removed surgically. If the cancer is widespread and cannot be removed with surgery, an attempt is made to remove blockage and control symptoms such as pain or bleeding. Depending on the location of the cancer, a portion of the stomach may be removed, a procedure called a partial gastrectomy. In a surgical procedure known as total gastrectomy, the entire stomach may be removed. However, doctors prefer to leave at least part of the stomach if possible. Patients who have been given a partial gastrectomy achieve a better quality of life than those having a total gastrectomy. Even when the entire stomach is removed, the patients quickly adjust to a different eating schedule, which involves eating small quantities of food more frequently. High protein foods are generally recommended.

Partial or total gastrectomy is often accompanied by other surgical procedures. Lymph nodes are frequently removed and nearby organs, or parts of these organs, may be removed if cancer has spread to them. Such organs may include the pancreas, colon, or spleen.

Preliminary studies suggest that patients who have tumors that cannot be removed by surgery at the start of therapy may become candidates for surgery later. Combinations of chemotherapy and radiation therapy are sometimes able to reduce disease for which surgery is not initially appropriate. Preliminary studies were being performed as of 2008 to determine if some of these patients can become candidates for surgical procedures after such therapies are applied.

Chemotherapy

Whether patients undergoing surgery for stomach cancer should receive chemotherapy is controversial. Chemotherapy involves administering anti-cancer drugs either intravenously (through a vein in the arm) or orally (in the form of pills). This method can either be used as the primary mode of treatment or after surgery to destroy any cancerous cells that may have migrated to distant sites. Most cancers of the gastrointestinal tract do not respond well to chemotherapy; however, adenocarcinoma of the stomach and advanced stages of cancer are exceptions.

Although chemotherapy using a single medicine is sometimes used, the best response rates are often achieved with combinations of medicines. Therefore, in addition to studies exploring the effectiveness of new medicines, as of 2008 there were many clinical trials in progress attempting to evaluate how to best combine existing forms of chemotherapy to bring the greatest degree of help to patients.

Radiation therapy

Radiation therapy is often used after surgery to destroy the cancer cells that may not have been completely removed during surgery. To treat stomach cancer, external beam radiation therapy is generally used. In this procedure, high-energy rays from a machine that is outside of the body are concentrated on the area of the tumor. In the advanced stages of stomach cancer, radiation therapy is used to ease the symptoms such as pain and bleeding. However, studies of radiation treatment for stomach cancer have shown that the way it has been used it has been ineffective for many patients.

As of 2008 researchers were actively assessing the role of chemotherapy and radiation therapy used before a surgical procedure is conducted. They were searching for ways to use both chemotherapy and radiation therapy so that they increase the length of survival of patients more effectively than existing methods were able to do.

Nutrition/dietetic concerns

Following gastrectomy or partial gastrectomy it is important for patients to carefully follow doctor's orders about what foods are eaten and when they should be eaten. In particular, patients may be asked to have small, frequent meals.

QUESTIONS TO ASK YOUR DOCTOR

  • Has the cancer spread to the lymph nodes?
  • Has the cancer spread to the lungs, liver, or spleen?
  • (After endoscopy or barium x-rays and CT scan have been completed) Would I benefit from endoscopic ultrasound or laparoscopy?
  • (If surgery is recommended) Do recent studies show that it might be a good idea to also use chemotherapy or radiation therapy?
  • (If gastrectomy or partial gastrectomy was performed) How should I alter my diet and eating patterns?
  • (Following surgery) What foods should I eat? Is there a registered dietitian I can speak with on a regular basis about what I should eat?

Prognosis

In 2007, the American Cancer Society reported approximately 24% of patients with stomach cancer live at least five years following diagnosis. Patients diagnosed with stomach cancer in its early stages had a far better prognosis than those for whom it is in the later stages. In the early stages, the tumor is small, lymph nodes are unaffected, and the cancer has not migrated to the lungs or the liver. Unfortunately, only about 20% of patients with stomach cancer are diagnosed before the cancer had spread to the lymph nodes or formed a distant metastasis .

It is important to remember that statistics on prognosis may be misleading. Therapies are being developed rapidly and five-year survival has not yet been measured with all of these. Also, the largest group of people diagnosed with stomach cancer are between 60 and 70 years of age, suggesting that some of these patients die not from cancer but from other age-related diseases. As a result, some patients with stomach cancer in 2008 may be expected to have longer survival than did patients, for example, in 1998.

Prevention

Avoiding many of the risk factors associated with stomach cancer may prevent its development. Excessive amounts of salted, smoked, and pickled foods should be avoided, as should foods high in nitrates. A diet that includes recommended amounts of fruits and vegetables is believed to lower the risk of several cancers, including stomach cancer. The American Cancer Society recommends eating at least five servings of fruits and vegetables daily and choosing six servings of food from other plant sources, such as grains, pasta, beans, cereals, and whole grain bread. Following a healthy diet and balancing caloric intake with recommended amounts of physical activity may reduce obesity , which may itself be a risk for developing stomach cancer.

KEY TERMS

Adenocarcinoma —Malignant cancers that originate in the tissues of glands or that form glandular structures.

Anemia —A condition in which iron levels in the blood are low.

Barium x ray (upper GI) —An x-ray test of the upper part of the gastrointestinal (GI) tract (including the esophagus, stomach, and a small portion of the small intestine) after the patient is given a white, chalky barium sulfate solution to drink. This substance coats the upper GI and the x rays reveal any abnormality in the lining of the stomach and the upper GI tract.

Biopsy —Removal of a tissue sample for examination under the microscope to check for cancer cells.

Chemotherapy —Treatment of cancer with synthetic drugs that destroy the tumor either by inhibiting the growth of the cancerous cells or by killing the cancer cells.

Endoscopic ultrasound (EUS) —A medical procedure in which sound waves are sent to the stomach wall by an ultrasound probe attached to the end of an endoscope. The pattern of echoes generated by the reflected sound waves are translated by a computer into an image of the stomach wall.

External radiation therapy —Radiation therapy that focuses high-energy rays from a machine on the area of the tumor.

Infiltrate —A tumor that moves into another organ of the body.

Polyp —An abnormal growth that develops on the inside of a hollow organ such as the colon, stomach, or nose.

Radiation therapy —Treatment using high-energy radiation from x-ray machines, cobalt, radium, or other sources.

Total gastrectomy —Surgical removal (excision) of the entire stomach.

Upper endoscopy —A medical procedure in which a thin, lighted, flexible tube (endoscope) is inserted down the patient's throat. Through this tube the doctor can view the lining of the esophagus, stomach, and the upper part of the small intestine.

Abstaining from tobacco and excessive amounts of alcohol reduces the risk for many cancers. In countries where stomach cancer is common, such as Japan, early detection is important for successful treatment.

Treatment for H. pylori infection, especially for those individuals with chronic infections, may reduce the risk for developing stomach cancer.

Caregiver concerns

Many patients experience feelings of depression , anxiety , and fatigue when dealing with the knowledge of and treatments associated with stomach cancer. Side effects such as nausea and vomiting may also be experienced during treatment. Understanding what to expect as a result of the various treatments and learning about alternative methods for reducing these symptoms may improve the effectiveness of treatments and provide a more positive outlook in regard to the one's situation. A doctor or other health professional should be consulted to develop strategies for managing any negative symptoms or feelings.

Resources

other

“Gastric Cancer Treatment.” National Cancer Institute (NCI) February 22, 2008 [cited April 9, 2008]. http://www.cancer.gov/cancertopics/pdq/treatment/gastric/HealthProfessional

“Overview: Stomach Cancer.” American Cancer Society (ACS) 2008 [cited April 9, 2008]. http://www.cancer.org/docroot/CRI/CRI_2_1x.asp?rnav=criov&dt=40

organizations

American Cancer Society, PO Box 22718, Oklahoma City, OK, 73123-1718, (800) ACS-2345, https://www.cancer.org/.

National Cancer Institute, 6116 Executive Blvd., Room 3036A, Bethesda, MD, 20892-8322, (800) 422-6237, http://www.cancer.gov/.

National Coalition for Cancer Survivorship, 1010 Wayne Avenue, 5th Floor, Suite 300, Silver Spring, MD, 20910, (888) 650-9127, http://www.canceradvocacy.org/.

Lata Cherath Ph.D.

Bob Kirsch

Melinda Oberleitner R.N., D.N.S.

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