lexical definition in critical thinking

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2.1: Breakdown of meaning

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What’s a concept? A concept is something we use in thought, like an idea. We combine concepts to form new concepts, we think about the world through concepts, and we form new concepts. For example, when we see a bunch of striped horse-like animals running around we can use the concept zebra to group them together and then learn more things about them. When we see a bunch of different people betting on the price of commodities, we use the concept futures trading to understand these disparate activities under one idea. One way of putting the point is that concepts are the things expressed by words or phrases. The phrase “futures trading” expresses a concept (an abstract meaning, or an idea in our mind). The word “zebra” expresses a different concept. I can form whole thoughts in my mind by putting concepts together to form propositions.

Zebras are striped

Futures trading is risky and morally suspect

Here we have the concepts Zebra , Striped , Futures Trading , Risky , and Morally Suspect . We can recombine these to make new thoughts:

Zebras are morally suspect

If a thing is striped, then it’s risky

Futures trading is striped

These aren’t very good thoughts or propositions, but they’re thoughts or propositions nonetheless.

The communication of concepts (expressed using words or phrases) breaks down in many ways. That is, when we try to communicate our ideas to other people, we often mess up. We leave ambiguity or speak vaguely and therefore don’t effectively communicate what we intend to communicate. Two such breakdowns are especially important to be able to distinguish: Vagueness and Ambiguity.

Vagueness is problematic unspecificity . Meaning the concept or word or phrase admits of borderline cases (has fuzzy boundaries), and/or doesn’t tell us enough to mean much of anything.

If you can’t easily pinpoint where a concept start and stops—if you can’t draw a clean line around all of the things the concept applies to, excluding all of the things the concept doesn’t apply to—then you have a vague concept. It’s not necessarily a problem to have a vague concept, though, unless you need a more sharp or specific concept.

• 1 inch taller than average? 2 inches taller than average? 7?

• “much warmer” isn’t any more specific than “hot”
• Does that mean being available when you call me? Does that mean going out of my way to comfort you? What degree of support are you expecting? The boundaries aren’t clear.
• Does that mean donate some money to mercy corps? Does that mean spare no expense? What degree of support are you offering? There are many borderline cases for which this statement won’t help us predict what support will be offered. I like to call these “weasel statements” because they allow one to weasel out of obligations later by saying “I said we’d do whatever is prudent and it turned out not to be prudent to do much of anything, so I never lied.”
• Wait, what does that mean? How do we measure “goodness” of dancing? It might be better to say that the winner is whoever the judges score the highest. That’s specific and quantitative—it’s easy to measure.

• Look, we all have lots of stuff to do. If you truly have so much stuff to do that it justifies cancelling our plans, then I’d want to know how much you have to do. Do you have to take the dogs for a walk? Or do you have to rewrite an entire term paper in an evening because your hard drive crashed the day before the paper was due? These are very different scenarios.

Ambiguity is problematic in that the ambiguous word or phrase admits of multiple distinct interpretation s . A sentence could be read in different ways based on how we interpret a word or phrase. There is grammatical ambiguity , and also semantic ambiguity .

Definition: Grammatical Ambiguity

Grammatical ambiguity is where the structure of a sentence (like a dangling modifier or a poorly-placed pronoun) make the sentence compatible with more than one reading.

Definition: Semantic or Lexical Ambiguity

Semantic or Lexical Ambiguity is where a word or phrase could mean multiple different things, each of which makes the sentence as a whole have very different interpretations.

• Pronoun ambiguity: to whom does “he” refer? Grammatical Ambiguity
• Who is wearing the dress? The dog? The Person? This is a dangling modifier. So it’s Grammatical ambiguity.
• “Freedom” is ambiguous between positive freedom and negative freedom (freedom from constraint vs. freedom to accomplish one’s goals). Semantic ambiguity.
• What does “appeal” mean here? Appeal as in “attract” or appeal as in “plead with”? Semantic ambiguity.

• This is a little tricky to identify, but it is a dangling modifier because it’s ambiguous between “she critiqued them poorly” and “playing soccer poorly.” The modifier “poorly” doesn’t clearly attach to the critique or the soccer playing because it could attach to either.
• Did he feed a woman cat food? Did he feed a female cat cat food? Did he feed a woman’s cat with food? Grammatical ambiguity.
• We saw a duck that belongs to her? Or we saw her perform the action of ducking? The word “duck” is ambiguous here.

We need to be able to distinguish between these two breakdowns in meaning to fully understand each of them. Sometimes meaning breaks down because someone is trying to express a concept but uses ambiguous wording which leaves us uncertain which concept they’re trying to communicate. Other times, someone is trying to use a concept to make a point, but the concept they choose is vague, which leaves us uncertain how to apply the concept to the concrete cases because the concept is indeterminate—we’re not sure what to do with certain borderline cases.

Lexical Investigations: Critical Thinking

Though the phrase critical thinking wasn’t coined until the early twentieth century, its principles can be traced back to Aristotle. The educator and psychologist John Dewey first used the phrase in its modern sense in his 1910 book How We Think , though there are instances of the words appearing together in texts before this time. Dewey defined critical thinking as “reflective thought,” requiring healthy skepticism, an open mind, and suspended judgment. Critical thinking is active, in contrast to passive acceptance of the ideas of others. Different criteria and tests used to determine whether or not critical thinking is taking place have been put forth by different educators. Robert Ennis’s popular definition from 1989 also states that, “critical thinking is reasonable, reflective thinking that is focused on deciding what to believe or do,” adding an emphasis on the resulting action. Critical thinking has been a reoccurring fad in education for over a hundred years, and in 1997, Michael Scriven, an educator who served as president of both the American Educational Research Association and the American Evaluation Association, declared it an “academic competency,” similar to reading and writing.

Relevant Quotations:

“The essence of critical thinking is suspended judgment; and the essence of this suspense is inquiry to determine the nature of the problem before proceeding to attempts at its solution. This, more than any other thing, transforms mere inference into tested inference, suggested conclusions into proof.”

—John Dewey, How We Think (1910)

“Critical thinking, as the term is generally used these days, roughly means reasonable and reflective thinking focused on deciding what to believe or do. 2 In doing such thinking, one is helped by the employment of a set of critical thinking dispositions and abilities that I shall outline, and that can serve as a set of comprehensive goals for a critical thinking curriculum and its assessment. Pedagogical and psychometric usefulness, not elegance or mutual exclusiveness, is the purpose of this outline. It could be used for an overall critical thinking curriculum outline, or as a comprehensive table of specifications for critical thinking assessment.”

—Robert H. Ennis, “ An Outline of Goals for a Critical Thinking Curriculum and Its Assessment ” (2002)

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III Lexical Definition

• Published: March 1963
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This chapter begins with a discussion of the nature of lexical definition. It then discusses the settlement of two disputes about lexical definition, how everything is lexically definable and whether lexical definitions should be brief or not.

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[M02] Definitions

Module: Meaning analysis

• M01. Literal meaning
• M03. Evaluating definitions
• M04. Examples
• M05. Verbal disputes
• M06. Necessity and sufficiency
• M07. Types of possibility
• M08. Obscurity
• M09. Distortion
• M10. Empty content

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We might divide definitions into four kinds. Let us look at them one by one.

§1. Reportive definition

A reportive definition is sometimes also known as a lexical definition. It reports the existing meaning of a term. This includes the "bachelor" example above, or the definition of "prime number" as referring to any integer divisible only by 1 and itself . A reportive definition should capture the correct usage of the term that is defined.

But how do we know what the correct meaning of a term is? Many people think that a dictionary is an authoritative guide to reportive definitions. This is actually a misconception, for various reasons.

First, many words in the language are difficult, if not impossible to define. This includes for example color words which we learn from examples. A dictionary might explain "red" as the color of ripe tomatoes, but obviously this is not what "red" means. "Red" does not mean blue even if all tomatoes suddenly were to become blue when they ripe. Explaining 'red' as 'a certain shade of colour' is of course not enough to distinguish the colour red from other different colours.

Also, the main aim of a general dictionary is often to give enough indication of the main usage of a word so that a speaker can use the word adequately in everyday life. Because of the limitation of space the definitions might not capture adequately the exact meanings of words. For example, the Pocket Oxford Dictionary of Current English defines "religion" as "belief in a superhuman controlling power." Suppose a scientist discovers that there are evil but superhuman aliens on Mars who created us and control our destiny. The scientist would then believe in the existence of a superhuman controlling power. But if this scientist does not worship or submit to these beings, surely this does not mean she has a religion in the usual sense of the term.

Finally, many technical words, such as "microwave", "hyper-inflation", and "a priori" are used in rather specialized ways. The entries in a general language dictionary might not be accurate enough when it comes to such terms. In such cases you should consult a special dictionary for the particular discipline in question.

As an exercise, evaluate the following entries from The Pocket Oxford Dictionary of Current English as reportive definitions.

• Cat : Small soft-furred four-legged domesticated animal.
• Magazine : Illustrated periodical publication containing articles, stories, etc. hint
• Impress : Affect or influence deeply.
• Cloud : Visible mass of condensed watery vapour floating high above the ground.
• Swim : Propel the body through water with limbs, fins, or tail. hint

What about this entry from the Merriam-Webster Online Dictionary ?

§2. Stipulative definition

A stipulative definition is not used to explain the existing meaning of a term. It is used to assign a new meaning to a term, whether or not the term has already got a meaning. If the stipulative definition is accepted, then the term is used in the new way that is prescribed. For example, suppose a stipulative definition is proposed to define "MBA" to mean married but available . Accepting such a definition, we can then go about describing other people as MBAs.

§3. Precising definition

A precising definition might be regarded as a combination of reportive and stipulative definition. The aim of a precising definition is to make the meaning of a term more precise for some purpose. For example, a bus company might want to give discounts to old people. But simply declaring that old people can get discounts will lead to many disputes since it is not clear how old should one be in order to be an old person. So one might define "old person" to mean any person of age 65 or above . This is of course one among many possible definitions of "old".

Or consider a situation where two people are arguing whether animals such as birds or apes possess language. To resolve this dispute, we need to be more precise as to what is meant by "language". If by "language" we refer to any system of communication, then obviously birds and other animals do make use of languages. On the other hand, "language" might be used in a different sense, requiring a combinatorial syntax and semantics, allowing a user of the language to communicate information about non-existent objects or situations remote in time and space from the location of discourse. Used in such a way, the communication system of some animals might not qualify as a language. This example illustrates the use of precising definitions to resolve disputes that involve some key concepts whose meanings might not be clear enough.

§4. Persuasive definition

A persuasive definition is any definition that attaches an emotive, positive or derogatory meaning to a term where it has none. For example, someone against abortion might offer the definition of "abortion" as the murder of an innocent person during pregnancy. This definition carries a negative connotation, as the term "murder" suggests that abortion is wrongful killing, and it also assumes that the aborted fetus is already a person. Such a definition is surely not appropriate in a fair debate on the moral legitimacy of abortion, even though it might be useful as a rhetorical tool.

Evaluate these reportive definitions.

• A square is a closed region with four straight sides of equal length.
• To tell a lie is to say something that is false.
• A gun is any device that shoots a projectile.

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Definitions

Definitions have interested philosophers since ancient times. Plato’s early dialogues portray Socrates raising questions about definitions (e.g., in the Euthyphro , “What is piety?”)—questions that seem at once profound and elusive. The key step in Anselm’s “Ontological Proof” for the existence of God is the definition of “God,” and the same holds of Descartes’s version of the argument in his Meditation V . More recently, the Frege-Russell definition of number and Tarski’s definition of truth have exercised a formative influence on a wide range of contemporary philosophical debates. In all these cases—and many others can be cited—not only have particular definitions been debated; the nature of, and demands on, definitions have also been debated. Some of these debates can be settled by making requisite distinctions, for definitions are not all of one kind: definitions serve a variety of functions, and their general character varies with function. Some other debates, however, are not so easily settled, as they involve contentious philosophical ideas such as essence, concept, and meaning.

1.1 Real and nominal definitions

1.2 dictionary definitions, 1.3 stipulative definitions, 1.4 descriptive definitions, 1.5 explicative definitions, 1.6 ostensive definitions, 1.7 a remark, 2.1 two criteria, 2.2 foundations of the traditional account, 2.3 conservativeness and eliminability, 2.4 definitions in normal form, 2.5 conditional definitions, 2.6 implicit definitions, 2.7 vicious-circle principle, 2.8 circular definitions, other internet resources, related entries, 1. some varieties of definition.

Ordinary discourse recognizes several different kinds of things as possible objects of definition, and it recognizes several kinds of activity as defining a thing. To give a few examples, we speak of a commission as defining the boundary between two nations; of the Supreme Court as defining, through its rulings, “person” and “citizen”; of a chemist as discovering the definition of gold, and the lexicographer, that of ‘cool’; of a participant in a debate as defining the point at issue; and of a mathematician as laying down the definition of “group.” Different kinds of things are objects of definition here: boundary, legal status, substance, word, thesis, and abstract kind. Moreover, the different definitions do not all have the same goal: the boundary commission may aim to achieve precision; the Supreme Court, fairness; the chemist and the lexicographer, accuracy; the debater, clarity; and the mathematician, fecundity. The standards by which definitions are judged are thus liable to vary from case to case. The different definitions can perhaps be subsumed under the Aristotelian formula that a definition gives the essence of a thing. But this only highlights the fact that “to give the essence of a thing” is not a unitary kind of activity.

In philosophy, too, several different kinds of definitions are often in play, and definitions can serve a variety of different functions (e.g., to enhance precision and clarity). But, in philosophy, definitions have also been called in to serve a highly distinctive role: that of solving epistemological problems. For example, the epistemological status of mathematical truths raises a problem. Immanuel Kant thought that these truths are synthetic a priori , and to account for their status, he offered a theory of space and time—namely, of space and time as forms of, respectively, outer and inner sense. Gottlob Frege and Bertrand Russell sought to undermine Kant’s theory by arguing that arithmetical truths are analytic. More precisely, they attempted to construct a derivation of arithmetical principles from definitions of arithmetical concepts, using only logical laws. For the Frege-Russell project to succeed, the definitions used must have a special character. They must be conceptual or explicative of meaning; they cannot be synthetic. It is this kind of definition that has aroused, over the past century or so, the most interest and the most controversy. And it is this kind of definition that will be our primary concern. Let us begin by marking some preliminary but important distinctions.

John Locke distinguished, in his Essay , “real essence” from “nominal essence.” Nominal essence, according to Locke, is the “ abstract Idea to which the Name is annexed (III.vi.2).” Thus, the nominal essence of the name ‘gold’, Locke said, “is that complex Idea the word Gold stands for, let it be, for instance, a Body yellow, of a certain weight, malleable, fusible, and fixed.” In contrast, the real essence of gold is “the constitution of the insensible parts of that Body, on which those Qualities [mentioned in the nominal essence] and all other Properties of Gold depend (III.vi.2).” A rough way of marking the distinction between real and nominal definitions is to say, following Locke, that the former states real essence, while the latter states nominal essence. The chemist aims at real definition, whereas the lexicographer aims at nominal definition.

This characterization of the distinction is rough because a zoologist’s definition of “tiger” should count as a real definition, even though it may fail to provide “the constitution of the insensible parts” of the tiger. Moreover, an account of the meaning of a word should count as a nominal definition, even though it may not take the Lockean form of setting out “the abstract idea to which the name is annexed.” Perhaps it is helpful to indicate the distinction between real and nominal definitions thus: to discover the real definition of a term \(X\) one needs to investigate the thing or things denoted by \(X\); to discover the nominal definition, one needs to investigate the meaning and use of \(X\). Whether the search for an answer to the Socratic question “What is virtue?” is a search for real definition or one for nominal definition depends upon one’s conception of this particular philosophical activity. When we pursue the Socratic question, are we trying to gain a clearer view of our uses of the word ‘virtue’, or are we trying to give an account of an ideal that is to some extent independent of these uses? Under the former conception, we are aiming at a nominal definition; under the latter, at a real definition.

See Robinson 1950 for a critical discussion of the different activities that have been subsumed under “real definition,” and see Charles 2010 for ancient views on the topic. Fine 1994 defends the conception that a real definition defines an object by specifying what the object is; in other words, a real definition spells out the essence of the object defined. Rosen 2015 offers an explanation of real definition in terms of grounding: the definition provides the ground of the essence of the object. The meaning of ‘essence’ and of ‘ground’ remain under active debate, however.

Nominal definitions—definitions that explain the meaning of a term—are not all of one kind. A dictionary explains the meaning of a term, in one sense of this phrase. Dictionaries aim to provide definitions that contain sufficient information to impart an understanding of the term. It is a fact about us language users that we somehow come to understand and use a potential infinity of sentences containing a term once we are given a certain small amount of information about the term. Exactly how this happens is a large mystery. But it does happen, and dictionaries exploit the fact. Note that dictionary entries are not unique. Different dictionaries can give different bits of information and yet be equally effective in explaining the meanings of terms.

Definitions sought by philosophers are not of the sort found in a dictionary. Frege’s definition of number (1884) and Alfred Tarski’s definition of truth (1983, ch. 8) are not offered as candidates for dictionary entries. When an epistemologist seeks a definition of “knowledge,” she is not seeking a good dictionary entry for the word ‘know’. The philosophical quest for definition can sometimes fruitfully be characterized as a search for an explanation of meaning. But the sense of ‘explanation of meaning’ here is very different from the sense in which a dictionary explains the meaning of a word.

A stipulative definition imparts a meaning to the defined term, and involves no commitment that the assigned meaning agrees with prior uses (if any) of the term. Stipulative definitions are epistemologically special. They yield judgments with epistemological characteristics that are puzzling elsewhere. If one stipulatively defines a “raimex” as, say, a rational, imaginative, experiencing being then the judgment “raimexes are rational” is assured of being necessary, certain, and a priori . Philosophers have found it tempting to explain the puzzling cases of, e.g., a priori judgments, by an appeal to stipulative definitions.

Saul Kripke (1980) has drawn attention to a special kind of stipulative definition. We can stipulatively introduce a new name (e.g., ‘Jack the Ripper’) through a description (e.g., “the man who murdered \(X, Y\), and \(Z\)”). In such a stipulation, Kripke pointed out, the description serves only to fix the reference of the new name; the name is not synonymous with the description. For, the judgment

is contingent, even though the judgment

Jack the Ripper is Jack the Ripper, if a unique man committed the murders

is necessary. A name such as ‘Jack the Ripper’, Kripke argued, is rigid: it picks out the same individual across possible worlds; the description, on the other hand, is non-rigid. Kripke used such reference-fixing stipulations to argue for the existence of contingent a priori truths—(1) being an example. Reference-fixing stipulative definitions can be given not only for names but also for terms in other categories, e.g., common nouns.

See Frege 1914 for a defense of the austere view that, in mathematics at least, only stipulative definitions should be countenanced. [ 1 ]

Descriptive definitions, like stipulative ones, spell out meaning, but they also aim to be adequate to existing usage. When philosophers offer definitions of, e.g., ‘know’ and ‘free’, they are not being stipulative: a lack of fit with existing usage is an objection to them.

It is useful to distinguish three grades of descriptive adequacy of a definition: extensional, intensional, and sense. A definition is extensionally adequate iff there are no actual counterexamples to it; it is intensionally adequate iff there are no possible counterexamples to it; and it is sense adequate (or analytic ) iff it endows the defined term with the right sense. (The last grade of adequacy itself subdivides into different notions, for “sense” can be spelled out in several different ways.) The definition “Water is H 2 O,” for example, is intensionally adequate because the identity of water and H 2 O is necessary (assuming the Kripke-Putnam view about the rigidity of natural-kind terms); the definition is therefore extensionally adequate also. But it is not sense-adequate, for the sense of ‘water’ is not at all the same as that of ‘H 2 O’. The definition ‘George Washington is the first President of the United States’ is adequate only extensionally but not in the other two grades, while ‘man is a laughing animal’ fails to be adequate in all three grades. When definitions are put to an epistemological use, intensional adequacy is generally insufficient. For such definitions cannot underwrite the rationality or the apriority of a problematic subject matter.

See Quine 1951 & 1960 for skepticism about analytic definitions; see also the entry on the analytic/synthetic distinction . Horty 2007 offers some ways of thinking about senses of defined expressions, especially within a Fregean semantic theory.

Sometimes a definition is offered neither descriptively nor stipulatively but as, what Rudolf Carnap (1956, §2) called, an explication . An explication aims to respect some central uses of a term but is stipulative on others. The explication may be offered as an absolute improvement of an existing, imperfect concept. Or, it may be offered as a “good thing to mean” by the term in a specific context for a particular purpose. (The quoted phrase is due to Alan Ross Anderson; see Belnap 1993, 117.)

A simple illustration of explication is provided by the definition of ordered pair in set theory. Here, the pair \(\langle x,y\rangle\) is defined as the set \(\{\{x\}, \{x,y\}\}\). Viewed as an explication, this definition does not purport to capture all aspects of the antecedent uses of ‘ordered pair’ in mathematics (and in ordinary life); instead, it aims to capture the essential uses. The essential fact about our use of ‘ordered pair’ is that it is governed by the principle that pairs are identical iff their respective components are identical:

And it can be verified that the above definition satisfies the principle. The definition does have some consequences that do not accord with the ordinary notion. For example, the definition implies that an object \(x\) is a member of a member of the pair \(\langle x, y\rangle\), and this implication is no part of the ordinary notion. But the mismatch is not an objection to the explication. What is important for explication is not antecedent meaning but function. So long as the latter is preserved, the former can be let go. It is this feature of explication that led W. V. O. Quine (1960, §53) to extol its virtues and to uphold the definition of “ordered pair” as a philosophical paradigm.

The truth-functional conditional provides another illustration of explication. This conditional differs from the ordinary conditional in some essential respects. Nevertheless, the truth-functional conditional can be put forward as an explication of the ordinary conditional for certain purposes in certain contexts . Whether the proposal is adequate depends crucially on the purposes and contexts in question. That the two conditionals differ in important, even essential, respects does not automatically disqualify the proposal.

Ostensive definitions typically depend on context and on experience. Suppose the conversational context renders one dog salient among several that are visible. Then one can introduce the name ‘Freddie’ through the stipulation “let this dog be called ‘Freddie’.” For another example, suppose you are looking at a branch of a bush and you stipulatively introduce the name ‘Charlie’ thus: “let the insect on that branch be called ‘Charlie’.” This definition can pin a referent on ‘Charlie’ even if there are many insects on the branch. If your visual experience presents you with only one of these insects (say, because the others are too small to be visible), then that insect is the denotation of your use of the description ‘the insect on that branch’. We can think of experience as presenting the subject with a restricted portion of the world. This portion can serve as a point of evaluation for the expressions in an ostensive definition. [ 2 ] Consequently, the definition can with the aid of experience pin a referent on the defined term when without this aid it would fail to do so. In the present example, the description ‘the insect on that branch’ fails to be denoting when it is evaluated at the world as a whole, but it is denoting when it is evaluated at that portion of it that is presented in your visual experience. See Gupta 2019 for an account of the contribution of experience to the meaning of an ostensively defined term.

An ostensive definition can bring about an essential enrichment of a language. The ostensive definition of ‘Charlie’ enriches the language with a name of a particular insect, and it could well be that before the enrichment the language lacked resources to denote that particular insect. Unlike other familiar definitions, ostensive definitions can introduce terms that are ineliminable. (So, ostensive definitions can fail to meet the Eliminability criterion explained below; they can fail to meet also the Conservativeness criterion, also explained below.)

The capacity of ostensive definitions to introduce essentially new vocabulary has led some thinkers to view them as the source of all primitive concepts. Thus, Russell maintains in Human Knowledge that

all nominal definitions, if pushed back far enough, must lead ultimately to terms having only ostensive definitions, and in the case of an empirical science the empirical terms must depend upon terms of which the ostensive definition is given in perception. (p. 242)

In “Meaning and Ostensive Definition”, C. H. Whiteley takes it as a premiss that ostensive definitions are “the means whereby men learn the meanings of most, if not all, of those elementary expressions in their language in terms of which other expressions are defined.” (332) It should be noted, however, that nothing in the logic and semantics of ostensive definitions warrants a foundationalist picture of concepts or of language-learning. Such foundationalist pictures were decisively criticized by Ludwig Wittgenstein in his Philosophical Investigations . Wittgenstein’s positive views on ostensive definition remain elusive, however; for an interpretation, see Hacker 1975.

Ostensive definitions are important, but our understanding of them remains at a rudimentary level. They deserve greater attention from logicians and philosophers.

The kinds into which we have sorted definitions are not mutually exclusive, nor exhaustive. A stipulative definition of a term may, as it happens, be extensionally adequate to the antecedent uses of the term. A dictionary may offer ostensive definitions of some words (e.g., of color words). An ostensive definition can also be explicative. For example, one can offer an improvement of a preexisting concept “one foot” thus: “let one foot be the present length of that rod.” In its preexisting use, the concept “one foot” may be quite vague; the ostensively introduced explication may, in contrast, be relatively precise. Moreover, as we shall see below, there are other kinds of definition than those considered so far.

2. The logic of definitions

Many definitions—stipulative, descriptive, and explicative—can be analyzed into three elements: the term that is defined \((X)\), an expression containing the defined term \((\ldots X\ldots)\), and another expression \((- - - - - - -)\) that is equated by the definition with this expression. Such definitions can be represented thus:

(We are setting aside ostensive definitions, which plainly require a richer representation.) When the defined term is clear from the context, the representation may be simplified to

The expression on the left-hand side of ‘\(\eqdf\)’ (i.e., \(\ldots X\ldots)\) is the definiendum of the definition, and the expression on the right-hand side is its definiens —it being assumed that the definiendum and the definiens belong to the same logical category. Note the distinction between defined term and definiendum: the defined term in the present example is \(X\); the definiendum is the unspecified expression on the left-hand side of ‘\(\eqdf\)’, which may or may not be identical to \(X\). (Some authors call the defined term ‘the definiendum’; some others use the expression confusedly, sometimes to refer to the defined term and sometimes to the definiendum proper.) Not all definitions found in the logical and philosophical literature fit under scheme (2). Partial definitions, for example, fall outside the scheme; another example is provided by definitions of logical constants in terms of introduction and elimination rules governing them. Nonetheless, definitions that conform to (2) are the most important, and they will be our primary concern.

Let us focus on stipulative definitions and reflect on their logic. Some of the important lessons here carry over, as we shall see, to descriptive and explicative definitions. For simplicity, let us consider the case where a single definition stipulatively introduces a term. (Multiple definitions bring notational complexity but raise no new conceptual issues.) Suppose, then, that a language \(L\), the ground language, is expanded through the addition of a new term \(X\) to an expanded language \(L^{+}\), where \(X\) is stipulatively defined by a definition \(\mathcal{D}\) of form (2). What logical rules govern \(\mathcal{D}\)? What requirements must the definition fulfill?

Before we address these questions, let us take note of a distinction that is not marked in logic books but which is useful in thinking about definitions. In one kind of definition—call it homogeneous definition—the defined term and the definiendum belong to the same logical category. So, a singular term is defined via a singular term; a general term via a general term; a sentence via a sentence; and so on. Let us say that a homogeneous definition is regular iff its definiendum is identical to the defined term. Here are some examples of regular homogeneous definitions:

Note that ‘The True’, as defined above, belongs to the category of sentence, not that of singular term.

It is sometimes said that definitions are mere recipes for abbreviations. Thus, Alfred North Whitehead and Bertrand Russell say of definitions—in particular, those used in Principia Mathematica —that they are “strictly speaking, typographical conveniences (1925, 11).” This viewpoint has plausibility only for regular homogeneous definitions—though it is not really tenable even here. (Whitehead and Russell’s own observations make it plain that their definitions are more than mere “typographical conveniences.” [ 3 ] ) The idea that definitions are mere abbreviations is not at all plausible for the second kind of definition, to which we now turn.

In the second kind of definition—call it a heterogeneous definition—the defined term and the definiendum belong to different logical categories. So, for example, a general term (e.g., ‘man’) may be defined using a sentential definiendum (e.g., ‘\(x\) is a man’). For another example, a singular term (e.g., ‘1’) may be defined using a predicate (e.g., ‘is identical to 1’). Heterogeneous definitions are far more common than homogeneous ones. In familiar first-order languages, for instance, it is pointless to define, say, a one-place predicate \(G\) by a homogeneous definition. These languages have no resources for forming compound predicates; hence, the definiens of a homogeneous definition of \(G\) is bound to be atomic. In a heterogeneous definition, however, the definiens can easily be complex; for example,

If the language has a device for nominalization of predicates—e.g., a class abstraction operator—we could give a different sort of heterogeneous definition for G :

Observe that a heterogeneous definition such as (4) is not a mere abbreviation. For one thing, we regard the expression \(x\) in it as a genuine variable which admits of substitution and binding. So, the definiendum Gx is not a mere abbreviation for the definiens. Moreover, if such definitions were abbreviations, they would be subject to the requirement that the definiendum must be shorter than the definiens, but no such requirement exists. On the other hand, genuine requirements on definitions would make little sense. The following stipulation is not a legitimate definition:

But if it is viewed as a mere abbreviation, there is nothing illegitimate about it. (Indeed, mathematicians routinely make use of abbreviations of this kind, suppressing variables that are temporarily uninteresting.)

Some stipulative definitions are nothing but mere devices of abbreviation (e.g., the definitions governing the omission of parentheses in formulas; see Church 1956, §11). However, many stipulative definitions are not of this kind; they introduce meaningful items into our discourse. Thus, definition (4) renders \(G\) a meaningful unary predicate: \(G\) expresses, in virtue of (4), a particular concept. In contrast, under stipulation (6), \(G\) is not a meaningful predicate and expresses no concept of any kind. But what is the source of the difference? Why is (4) legitimate, but not (6)? More generally, when is a definition legitimate? What requirements must the definiens fulfill? And, for that matter, the definiendum? Must the definiendum be, for instance, atomic, as in (3) and (4)? If not, what restrictions (if any) are there on the definiendum?

It is a plausible requirement on any answer to these questions that two criteria be respected. [ 4 ] First, a stipulative definition should not enable us to establish essentially new claims—call this the Conservativeness criterion. We should not be able to establish, by means of a mere stipulation, new things about, for example, the moon. It is true that unless this criterion is made precise, it is subject to trivial counterexamples, for the introduction of a definition materially affects some facts. Nonetheless, the criterion can be made precise and defensible, and we shall soon see some ways of doing this.

Second, the definition should fix the use of the defined expression \(X\)—call this the Use criterion. This criterion is plausible, since only the definition—and nothing else—is available to guide us in the use of \(X\). There are complications here, however. What counts as a use of \(X\)? Are occurrences within the scope of ‘say’ and ‘know’ included? What about the occurrence of \(X\) within quotation contexts, and those within words, for instance, ‘ Xenophanes ’? The last question should receive, it is clear, the answer, “No.” But the answers to the previous questions are not so clear. There is another complication: even if we can somehow separate out genuine occurrences of \(X\), it may be that some of these occurrences are rightfully ignored by the definition. For example, a definition of quotient may leave some occurrences of the term undefined (e.g., where there is division by 0). The orthodox view is to rule such definitions as illegitimate, but the orthodoxy deserves to be challenged here. Let us leave the challenge to another occasion, however, and proceed to bypass the complications through idealization. Let us confine ourselves to ground languages that possess a clearly determined logical structure (e.g., a first-order language) and that contain no occurrences of the defined term \(X\). And let us confine ourselves to definitions that place no restrictions on legitimate occurrences of \(X\). The Use criterion now dictates then that the definition should fix the use of all expressions in the expanded language in which \(X\) occurs.

A variant formulation of the Use criterion is this: the definition must fix the meaning of the definiendum. The new formulation is less determinate and more contentious, for it relies on “meaning,” an ambiguous and theoretically contentious notion.

Note that the two criteria govern all stipulative definitions, irrespective of whether they are single or multiple, or of whether they are of form (2) or not.

The traditional account of definitions is founded on three ideas. The first idea is that definitions are generalized identities; the second, that the sentential is primary; and the third, that of reduction. The first idea—that definitions are generalized identities—motivates the traditional account’s inferential rules for definitions. These are, put crudely, that (i) any occurrence of the definiendum can be replaced by an occurrence of the definiens (Generalized Definiendum Elimination); and, conversely, (ii) any occurrence of the definiens can be replaced by an occurrence of the definiendum (Generalized Definiendum Introduction).

The second idea—the primacy of the sentential—has its roots in the thought that the fundamental uses of a term are in assertion and argument: if we understand the use of a defined term in assertion and argument then we fully grasp the term. The sentential is, however, primary in argument and assertion. Hence, to explain the use of a defined term \(X\), the second idea maintains, it is necessary and sufficient to explain the use of sentential items that contain \(X\). (Sentential items are here understood to include sentences and sentence-like things with free variables, e.g., the definiens of (4); henceforth, these items will be called formulas .) The issues the second idea raises are, of course, large and important, but they cannot be addressed in a brief survey. Let us accept the idea simply as a given.

The third idea—reduction—is that the use of a formula \(Z\) containing the defined term is explained by reducing \(Z\) to a formula in the ground language. This idea, when conjoined with the primacy of the sentential, leads to a strong version of the Use criterion, called the Eliminability criterion: the definition must reduce each formula containing the defined term to a formula in the ground language, i.e., one free of the defined term. Eliminability is the distinctive thesis of the traditional account and, as we shall see below, it can be challenged.

Note that the traditional account does not require the reduction of all expressions of the extended language; it requires the reduction only of formulas. The definition of a predicate \(G\), for example, need provide no way of reducing \(G\), taken in isolation, to a predicate of the ground language. The traditional account is thus consistent with the thought that a stipulative definition can add a new conceptual resource to the language, for nothing in the ground language expresses the predicative concept that \(G\) expresses in the expanded language. This is not to deny that no new proposition—at least in the sense of truth-condition—is expressed in the expanded language.

Let us now see how Conservativeness and Eliminability can be made precise. First consider languages that have a precise proof system of the familiar sort. Let the ground language \(L\) be one such. The proof system of \(L\) may be classical, or three-valued, or modal, or relevant, or some other; and it may or may not contain some non-logical axioms. All we assume is that we have available the notions “provable in \(L\)” and “provably equivalent in \(L\),” and also the notions “provable in \(L^{+}\)” and “provably equivalent in \(L^{+}\)” that result when the proof system of \(L\) is supplemented with a definition \(\mathcal{D}\) and the logical rules governing definitions. Now, the Conservativeness criterion can be made precise as follows.

Conservativeness criterion (syntactic formulation) : Any formula of \(L\) that is provable in \(L^{+}\) is provable in \(L\).

That is, any formula of \(L\) that is provable using definition \(\mathcal{D}\) is also provable without using \(\mathcal{D}\): the definition does not enable us to prove anything new in \(L\). The Eliminability criterion can be made precise thus:

Eliminability criterion (syntactic formulation) : For any formula \(A\) of \(L^{+}\), there is a formula of \(L\) that is provably equivalent in \(L^{+}\) to \(A\).

(Folklore credits the Polish logician S. Leśniewski for formulating the criteria of Conservativeness and Eliminability, but this is a mistake; see Dudman 1973, Hodges 2008, Urbaniak and Hämäri 2012 for discussion and further references.) [ 5 ]

Now let us equip \(L\) with a model-theoretic semantics. That is, we associate with \(L\) a class of interpretations, and we make available the notions “valid in \(L\) in the interpretation \(M\)” (a.k.a.: “true in \(L\) in \(M\)”) and “semantically equivalent in \(L\) relative to \(M\).” Let the notions “valid in \(L^{+}\) in \(M^{+}\)” and “semantically equivalent in \(L^{+}\) relative to \(M^{+}\)” result when the semantics of \(L\) is supplemented with that of definition \(\mathcal{D}\). The criteria of Conservativeness and Eliminability can now be made precise thus:

Conservativeness criterion (semantic formulation) : For all formulas \(A\) of \(L\), if \(A\) is valid in \(L^{+}\) in all interpretations \(M^{+}\), then \(A\) is valid in \(L\) in all interpretations \(M\).

Eliminability criterion (semantic formulation) : For any formula \(A\) of \(L^{+}\), there is a formula \(B\) of \(L\) such that, relative to all interpretations \(M^{+}\), \(B\) is semantically equivalent in \(L^{+}\) to \(A\).

The syntactic and semantic formulations of the two criteria are plainly parallel. However, even if we suppose that strong completeness theorems hold for \(L\) and \(L^{+}\), the two formulations need not be equivalent: it depends on our semantics for definition \(\mathcal{D}\). Indeed, several different, non-equivalent formulations of the two criteria are possible within each framework, the syntactic and the semantic.

There is another, more stringent notion of semantic conservativeness that has been prominent in the literature on truth (Halbach 2014, p. 69). Say that an interpretation \(M^{+}\) of \(L^{+}\) is an expansion of an interpretation \(M\) of \(L\) iff \(M\) and \(M^{+}\) assign the same domain(s) to the quantifier(s) in L, and assign the same semantic values to the non-logical constants in \(L\). Then we have:

Conservativeness criterion (strong semantic formulation) : Every interpretation \(M\) of \(L\) can be expanded to an interpretation \(M^{+}\) of \(L^{+}\).

In other words, a definition is strongly semantically conservative if it does not rule out any previously available interpretations of the original language.

Observe that the satisfaction of Conservativeness and Eliminability criteria, whether in their semantic or their syntactic formulation, is not an absolute property of a definition; the satisfaction is relative to the ground language. Different ground languages can have associated with them different systems of proof and different classes of interpretations. Hence, a definition may satisfy the two criteria when added to one language, but may fail to do so when added to a different language. For further discussion of the criteria, see Suppes 1957 and Belnap 1993.

For concreteness, let us fix the ground language \(L\) to be a classical first-order language with identity. The proof system of \(L\) may contain some non-logical axioms \(T\); the interpretations of \(L\) are then the classical models of \(T\). As before, \(L^{+}\) is the expanded language that results when a definition \(\mathcal{D}\) of a non-logical constant \(X\) is added to \(L\); hence, \(X\) may be a name, a predicate, or a function-symbol. Call two definitions equivalent iff they yield the same theorems in the expanded language. Then, it can be shown that if \(\mathcal{D}\) meets the criteria of Conservativeness and Eliminability then \(\mathcal{D}\) is equivalent to a definition in normal form as specified below. [ 6 ] Since definitions in normal form meet the demands of Conservativeness and Eliminability, the traditional account implies that we lose nothing essential if we require definitions to be in normal form.

The normal form of definitions can be specified as follows. The definitions of names \(a, n\)-ary predicates \(H\), and \(n\)-ary function symbols \(f\) must be, respectively, of the following forms:

where the variables \(x_{1}\), …, \(x_{n}\), \(y\) are all distinct, and the definiens in each case satisfies conditions that can be separated into a general and a specific part. [ 7 ] The general condition on the definiens is the same in each case: it must not contain the defined term or any free variables other than those in the definiendum. The general conditions remain the same when the traditional account of definition is applied to non-classical logics (e.g., to many-valued and modal logics). The specific conditions are more variable. In classical logic, the specific condition on the definiens \(\psi(x)\) of (7) is that it satisfy an existence and uniqueness condition: that it be provable that something satisfies \(\psi(x)\) and that at most one thing satisfies \(\psi(x)\). [ 8 ] There are no specific conditions on (8), but the condition on (9) parallels that on (7). An existence and uniqueness claim must hold: the universal closure of the formula

must be provable. [ 9 ]

In a logic that allows for vacuous names, the specific condition on the definiens of (7) would be weaker: the existence condition would be dropped. In contrast, in a modal logic that requires names to be non-vacuous and rigid, the specific condition would be strengthened: not only must existence and uniqueness be shown to hold necessarily, it must be shown that the definiens is satisfied by one and the same object across possible worlds.

Definitions that conform to (7)–(9) are heterogeneous; the definiendum is sentential, but the defined term is not. One source of the specific conditions on (7) and (9) is their heterogeneity. The specific conditions are needed to ensure that the definiens, though not of the logical category of the defined term, imparts the proper logical behavior to it. The conditions thus ensure that the logic of the expanded language is the same as that of the ground language. This is the reason why the specific conditions on normal forms can vary with the logic of the ground language. Observe that, whatever this logic, no specific conditions are needed for regular homogeneous definitions.

The traditional account makes possible simple logical rules for definitions and also a simple semantics for the expanded language. Suppose definition \(\mathcal{D}\) has a sentential definiendum. (In classical logic, all definitions can easily be transformed to meet this condition.) Let \(\mathcal{D}\) be

where \(x_{1}\), …, \(x_{n}\) are all the variables free in either \(\phi\) or \(\psi\). And let \(\phi(t_{1},\ldots,t_{n})\) and \(\psi(t_{1},\ldots,t_{n})\) result by the simultaneous substitution of terms \(t_{1}\), …, \(t_{n}\) for \(x_{1}\), …, \(x_{n}\) in, respectively, \(\phi(x_{1},\ldots, x_{n})\) and \(\psi(x_{1},\ldots, x_{n})\); changing bound variables as necessary. Then the rules of inference governing \(\mathcal{D}\) are simply these:

The semantics for the extended language is also straightforward. Suppose, for instance, \(\mathcal{D}\) is a definition of a name \(a\) and suppose that, when put in normal form, it is equivalent to (7). Then, each classical interpretation \(M\) of \(L\) expands to a unique classical interpretation \(M^{+}\) of the extended language \(L^{+}\). The denotation of \(a\) in \(M^{+}\) is the unique object that satisfies \(\psi(x)\) in \(M\); the conditions on \(\psi(x)\) ensure that such an object exists. The semantics of defined predicates and function-symbols is similar. The logic and semantics of definitions in non-classical logics receive, under the traditional account, a parallel treatment.

Note that the inferential force of adding definition (10) to the language is the same as that of adding as an axiom, the universal closure of

However, this similarity in the logical behavior of (10) and (11) should not obscure the great differences between the biconditional (‘\(\leftrightarrow\)’) and definitional equivalence (‘\(\eqdf\)’). The former is a sentential connective, but the latter is trans-categorical: not only formulas, but also predicates, names, and items of other logical categories can occur on the two sides of ‘\(\eqdf\)’. Moreover, the biconditional can be iterated—e.g., \(((\phi \leftrightarrow \psi) \leftrightarrow \chi)\)—but not definitional equivalence. Finally, a term can be introduced by a stipulative definition into a ground language whose logical resources are confined, say, to classical conjunction and disjunction. This is perfectly feasible, even though the biconditional is not expressible in the language. In such cases, the inferential role of the stipulative definition is not mirrored by any formula of the extended language.

The traditional account of definitions should not be viewed as requiring definitions to be in normal form. The only requirements that it imposes are (i) that the definiendum contain the defined term; (ii) that the definiendum and the definiens belong to the same logical category; and (iii) the definition satisfies Conservativeness and Eliminability. So long as these requirements are met, there are no further restrictions. The definiendum, like the definiens, can be complex; and the definiens, like the definiendum, can contain the defined term. So, for example, there is nothing formally wrong if the definition of the functional expression ‘the number of’ has as its definiendum the formula ‘the number of \(F\)s is the number of \(G\)s’. The role of normal forms is only to provide an easy way of ensuring that definitions satisfy Conservativeness and Eliminability; they do not provide the only legitimate format for stipulatively introducing a term. Thus, the reason why (4) is, but (6) is not, a legitimate definition is not that (4) is in normal form and (6) is not.

The reason is that (4) respects, but (6) does not, the two criteria. (The ground language is assumed here to contain ordinary arithmetic; under this assumption, the second definition implies a contradiction.) The following two definitions are also not in normal form:

But both should count as legitimate under the traditional account, since they meet the Conservativeness and Eliminability criteria. It follows that the two definitions can be put in normal form. Definition (12) is plainly equivalent to (4), and definition (13) is equivalent to (14):

Observe that the definiens of (13) is not logically equivalent to any \(G\)-free formula. Nevertheless, the definition has a normal form.

Similarly, the traditional account is perfectly compatible with recursive (a.k.a.: inductive ) definitions such as those found in logic and mathematics. In Peano Arithmetic, for example, exponentiation can be defined by means of the following equations:

Here the first equation—called the base clause—defines the value of the function when the exponent is 0. And the second clause—called the recursive clause—uses the value of the function when the exponent is \(n\) to define the value when the exponent is \(n + 1\). This is perfectly legitimate, according to the traditional account, because a theorem of Peano Arithmetic establishes that the above definition is equivalent to one in normal form. [ 10 ] Recursive definitions are circular in their format, and indeed it is this circularity that renders them perspicuous. But the circularity is entirely on the surface, as the existence of normal forms shows. See the discussion of circular definitions below.

It is a part of our ordinary practice that we sometimes define terms not absolutely but conditionally. We sometimes affirm a definition not outright but within the scope of a condition, which may either be left tacit or may be set down explicitly. So, for example, we may define F ( x , y ) to express the notion “first cousin once removed” by stipulating that

where it is understood that the variables range over humans. For another example, when defining division, we may explicitly set down as a condition on the definition that the divisor not be 0. We may stipulate that

but with the proviso that \( x \neq 0 \). This practice may appear to violate the Eliminability criterion, for it appears that conditional definitions do not ensure the eliminability of the defined terms in all sentences. Thus (16) does not enable us to prove the equivalence of

with any F -free sentence because of the tacit restriction on the range of variables in (16). Similarly (17) does not enable us to eliminate the defined symbol from

However, if there is a violation of Eliminability here, it is a superficial one, and it is easily corrected in one of two ways. The first way—the way that conforms best to our ordinary practices—is to understand the enriched languages that result from adding the definitions to exclude sentences such as (18) and (19). For when we stipulate a definition such as (16), it is not our intention to speak about the first cousins once removed of numbers; on the contrary, we wish to exclude all such talk as improper. Similarly, in setting down (17), we wish to exclude talk of division by 0 as legitimate. So, the first way is to recognize that a conditional definition such as (16) and (17) brings with it restrictions on the enriched language and, consequently, respects the Eliminability criterion once the enriched language is properly demarcated. This idea can be implemented formally by seeing conditional definitions as formulated within languages with sortal quantification.

The second way—the way that conforms best to our actual formal practices—is to understand the applications of the defined term in cases where the antecedent condition fails as “don’t care cases” and to make a suitable stipulation concerning such applications. So, we may stipulate that nothing other than a human has first cousins once removed, and we may stipulate that the result of dividing any number by 0 is 0. Thus we may replace (17) by

The resulting definitions satisfy the Eliminability criterion. The second way forces us to exercise care in reading sentences with defined terms. So, for example, the sentence

though true when division in defined as in (20), does not express an interesting mathematical truth but one that is merely a byproduct of our treatment of the “don’t care cases.” Despite this cost, the gain in simplicity in the notion of proof may well warrant, in some contexts, the move to a definition such as (20).

See Suppes 1957 for a different perspective on conditional definitions.

The above viewpoint allows the traditional account to bring within its fold ideas that might at first sight seem contrary to it. It is sometimes suggested that a term \(X\) can be introduced axiomatically, that is, by laying down as axioms certain sentences of the expanded language \(L^{+}\). The axioms are then said to implicitly define \(X\). This idea is easily accommodated within the traditional account. Let a theory be a set of sentences of the expanded language \(L^{+}\). Then, to say that a theory \(T^*\) is an implicit ( stipulative ) definition of X is to say that \(X\) is governed by the definition

where \(\phi\) is the conjunction of the members of \(T^*\). (If \(T^*\) is infinite then a stipulation of the above form will be needed for each sentence \(\psi\) in \(T^*\).) [ 11 ] The definition is legitimate, according to the traditional account, so long as it meets the Conservativeness and Eliminability criteria. If it does meet these criteria, let us call \(T^*\) admissible ( for a definition of X ). So, the traditional account accommodates the idea that theories can stipulatively introduce new terms, but it imposes a strong demand: the theories must be admissible. [ 12 ]

Consider, for concreteness, the special case of classical first-order languages. Let the ground language \(L\) be one such, and let its interpretations be models of some sentences \(T\). Let us say that

\(T^*\) is an implicit semantic definition of X iff, for each interpretation \(M\) of \(L\), there is a unique model \(M^{+}\) of \(T^*\) such that \(M^{+}\) is an expansion of \(M\).

Then, from the normal form theorem, the following claim is immediate:

If \(T^*\) is admissible then \(T^*\) is an implicit semantic definition of \(X\).

That is, an admissible theory fixes the semantic value of the defined term in each interpretation of the ground language. This observation provides one natural method of showing that a theory is not admissible:

Padoa’s method . To show that \(T^*\) is not admissible, it suffices to construct two models of \(T^*\) that are expansions of one and the same interpretation of the ground language \(L\). (Padoa 1900)

Here is a simple and philosophically useful application of Padoa’s method. Suppose the proof system of \(L\) is Peano Arithmetic and that \(L\) is expanded by the addition of a unary predicate \(Tr\) (for “Gödel number of a true sentence of \(L\)”). Let \(\mathbf{H}\) be the theory consisting of all the sentences (the “Tarski biconditionals”) of the following form:

where \(\psi\) is a sentence of \(L\) and \(s\) is the canonical name for the Gödel number of \(\psi\). Padoa’s method implies that \(\mathbf{H}\) is not admissible for defining \(Tr\). For \(\mathbf{H}\) does not fix the interpretation of \(Tr\) in all interpretations of \(L\). In particular, it does not do so in the standard model, for \(\mathbf{H}\) places no constraints on the behavior of \(Tr\) on those numbers that are not Gödel numbers of sentences. (If the coding renders each natural number a Gödel number of a sentence, then a non-standard model of Peano Arithmetic provides the requisite counterexample: it has infinitely many expansions that are models of \(\mathbf{H}\).) A variant of this argument shows that Tarski’s theory of truth, as formulated in \(L^{+}\), is not admissible for defining \(Tr\).

What about the converse of Padoa’s method? Suppose we can show that in each interpretation of the ground language, a theory \(T^*\) fixes a unique semantic value for the defined term. Can we conclude that \(T^*\) is admissible? This question receives a negative answer for some semantical systems, and a positive answer for others. (In contrast, Padoa’s method works so long as the semantic system is not highly contrived.) The converse fails for, e.g., classical second-order languages, but it holds for first-order ones:

Beth’s Definability Theorem . If \(T^*\) is an implicit semantic definition of \(X\) in a classical first-order language then \(T^*\) is admissible.

Note that the theorem holds even if \(T^*\) is an infinite set. For a proof of the theorem, see Boolos, Burgess, and Jeffrey 2002; see also Beth 1953.

The idea of implicit definition is not in conflict, then, with the traditional account. Where conflict arises is in the philosophical applications of the idea. The failure of strict reductionist programs of the late-nineteenth and early-twentieth century prompted philosophers to explore looser kinds of reductionism. For instance, Frege’s definition of number proved to be inconsistent, and thus incapable of sustaining the logicist thesis that the principles of arithmetic are analytic. It turns out, however, that the principles of arithmetic can be derived without Frege’s definition. All that is needed is one consequence of it, namely, Hume’s Principle:

Hume’s Principle . The number of \(F\)s = the number of \(G\)s iff there is a one-to-one correspondence between the \(F\)s and \(G\)s.

If we add Hume’s Principle to axiomatic second-order logic, then we obtain a consistent theory from which we can analytically derive second-order Peano Arithmetic. (The essentials of the argument are found already in Frege 1884.) It is a central thesis of Neo-Fregeanism that Hume’s Principle is an implicit definition of the functional expression ‘the number of’ (see Hale and Wright 2001). If this thesis can be defended, then logicism about arithmetic can be sustained. However, the neo-Fregean thesis is in conflict with the traditional account of definitions, for Hume’s Principle violates both Conservativeness and Eliminability. The principle allows one to prove, for arbitrary \(n\), that there are at least \(n\) objects.

Another example: The reductionist program for theoretical concepts (e.g., those of physics) aimed to solve epistemological problems that these concepts pose. The program aimed to reduce theoretical sentences to (classes of) observational sentences. However, the reductions proved difficult, if not impossible, to sustain. Thus arose the suggestion that perhaps the non-observational component of a theory can, without any claim of reduction, be regarded as an implicit definition of theoretical terms. The precise characterization of the non-observational component can vary with the specific epistemological problem at hand. But there is bound to be a violation of one or both of the two criteria, Conservativeness and Eliminability. [ 13 ]

A final example: We know by a theorem of Tarski that no theory can be an admissible definition of the truth predicate, \(Tr\), for the language of Peano Arithmetic considered above. Nonetheless, perhaps we can still regard theory \(\mathbf{H}\) as an implicit definition of \(Tr\). (Paul Horwich has made a closely related proposal for the ordinary notion of truth.) Here, again, pressure is put on the bounds imposed by the traditional account. \(\mathbf{H}\) meets the Conservativeness criterion, but not that of Eliminability.

In order to assess the challenge these philosophical applications pose for the traditional account, we need to resolve issues that are under current philosophical debate. Some of the issues are the following. (i) It is plain that some violations of Conservativeness are illegitimate: one cannot make it true by a stipulation that, e.g., Mercury is larger than Venus. Now, if a philosophical application requires some violations of Conservativeness to be legitimate, we need an account of the distinction between the two sorts of cases: the legitimate violations of Conservativeness and the non-legitimate ones. And we need to understand what it is that renders the one legitimate, but not the other. (ii) A similar issue arises for Eliminability. It would appear that not any old theory can be an implicit definition of a term \(X\). (The theory might contain only tautologies.) If so, then again we need a demarcation of theories that can serve to implicitly define a term from those that cannot. And we need a rationale for the distinction. (iii) The philosophical applications rest crucially on the idea that an implicit definition fixes the meaning of the defined term. We need therefore an account of what this meaning is, and how the implicit definition fixes it. Under the traditional account, formulas containing the defined term can be seen as acquiring their meaning from the formulas of the ground language. (In view of the primacy of the sentential, this fixes the meaning of the defined term.) But this move is not available under a liberalized conception of implicit definition. How, then, should we think of the meaning of a formula under the envisioned departure from the traditional account? (iv) Even if the previous three issues are addressed satisfactorily, an important concern remains. Suppose we allow that a theory \(T\), say, of physics can stipulatively define its theoretical terms, and that it endows the terms with particular meanings. The question remains whether the meanings thus endowed are identical to (or similar enough to) the meanings the theoretical terms have in their actual uses in physics. This question must be answered positively if implicit definitions are to serve their philosophical function. The aim of invoking implicit definitions is to account for the rationality, or the apriority, or the analyticity of our ordinary judgments, not of some extraordinary judgments that are somehow assigned to ordinary signs.

The literature on neo-Fregeanism presents an interesting case study in respect of these issues. Much of the debate concerning the neo-Fregean thesis can fruitfully be viewed as a debate over the extent and precise formulation of the criteria of Conservativeness and Use. For example, the so-called Julius Caesar objection (due to Frege 1884) urges that Hume’s Principle cannot be a legitimate definition of ‘the number of’ because it does not determine the use of this expression in mixed identity contexts, such as ‘\(\text{the number of }F\text{s} = \text{Julius Caesar}\)’. Other classic objections (Field 1984, Boolos 1997) focus on the non-conservativeness of Hume’s Principle. Boolos 1990 raises a particularly sharp point, known as the Bad Company problem. Definitions of the same kind as Hume’s Principle are known as abstraction principles. Boolos exhibits an abstraction principle that is consistent by itself, but inconsistent in conjunction with Hume’s Principle. This pathological situation never arises with conservative definitions. So, the Bad Company problem illustrates what can go wrong when the Conservativeness requirement is violated.

Friends of neo-Fregeanism have responded to these objections in various ways. Wright 1997 argues that abstraction principles need only satisfy a restricted version of Conservativeness, and needn’t satisfy Eliminability at all. (However, Wright’s proposal suffered the revenge of the Bad Company problem: see Weir 2003.) By contrast, Linnebo 2018 argues for much more stringent requirements on abstraction principles. He countenances only predicative abstraction principles, which satisfy both Conservativeness and Eliminability in suitable contexts. Mackereth and Avigad (forthcoming) defend an intermediate position. They hold that abstraction principles must satisfy Conservativeness in an unrestricted sense, but needn’t satisfy Eliminability. Furthermore, Mackereth and Avigad show that in the absence of Eliminability, the precise formulation of Conservativeness (syntactic vs. semantic, etc.) makes a big difference. In particular, it is possible to get impredicative versions of Hume’s Principle that are semantically conservative, but the same does not appear to be true for syntactic conservativeness.

For further discussion of these issues, see Horwich 1998, especially chapter 6; Hale and Wright 2001, especially chapter 5; and the works cited there.

Another departure from the traditional theory begins with the idea not that the theory is too strict, but that it is too liberal, that it permits definitions that are illegitimate. Thus, the traditional theory allows the following definitions of, respectively, “liar” and the class of natural numbers \(\mathbf{N}\):

Russell argued that such definitions involve a subtle kind of vicious circle. The definiens of the first definition invokes, Russell thought, the totality of all propositions, but the definition, if legitimate, would result in propositions that can only be defined by reference to this totality. Similarly, the second definition attempts to define the class \(\mathbf{N}\) by reference to all classes, which includes the class \(\mathbf{N}\) that is being defined. Russell maintained that such definitions are illegitimate. And he imposed the following requirement—called, the “Vicious-Circle Principle”—on definitions and concepts. (Henri Poincaré had also proposed a similar idea.)

Vicious-Circle Principle . “Whatever involves all of a collection must not be one of the collection (Russell 1908, 63).”

Another formulation Russell gave of the Principle is this:

Vicious-Circle Principle (variant formulation) . “If, provided a certain collection had a total, it would have members only definable in terms of that total, then the said collection has no total (Russell, 1908, 63).”

In an appended footnote, Russell explained, “When I say that a collection has no total, I mean that statements about all its members are nonsense.”

Russell’s primary motivation for the Vicious-Circle Principle were the logical and semantic paradoxes. Notions such as “truth,” “proposition,” and “class” generate, under certain unfavorable conditions, paradoxical conclusions. Thus, the claim “Cheney is a liar,” where “liar” is understood as in (16), yields paradoxical conclusions, if Cheney has asserted that he is a liar, and all other propositions asserted by him are, in fact, false. Russell took the Vicious-Circle Principle to imply that if “Cheney is a liar” expresses a proposition, it cannot be in the scope of the quantifier in the definiens of (16). More generally, Russell held that quantification over all propositions, and over all classes, violates the Vicious-Circle Principle and is thus illegitimate. Furthermore, he maintained that expressions such as ‘true’ and ‘false’ do not express a unique concept—in Russell’s terminology, a unique “propositional function”—but one of a hierarchy of propositional functions of different orders. Thus the lesson Russell drew from the paradoxes is that the domain of the meaningful is more restricted than it might ordinarily appear, that the traditional account of concepts and definitions needed to be made more restrictive in order to rule out the likes of (16) and (17).

In application to ordinary, informal definitions, the Vicious-Circle Principle does not provide, it must be said, a clear method of demarcating the meaningful from the meaningless. Definition (16) is supposed to be illegitimate because, in its definiens, the quantifier ranges over the totality of all propositions. And we are told that this is prohibited because, were it allowed, the totality of propositions “would have members only definable in terms of the total.” However, unless we know more about the nature of propositions and of the means available for defining them, it is impossible to determine whether (16) violates the Principle. It may be that a proposition such as “Cheney is a liar”—or, to take a less contentious example, “Either Cheney is a liar or he is not”— can be given a definition that does not appeal to the totality of all propositions. If propositions are sets of possible worlds, for example, then such a definition would appear to be feasible.

The Vicious-Circle Principle serves, nevertheless, as an effective motivation for a particular account of legitimate concepts and definitions, namely that embodied in Russell’s Ramified Type Theory. The idea here is that one begins with some unproblematic resources that involve no quantification over propositions, concepts, and such. These resources enable one to define, for example, various unary concepts, which are thereby assured of satisfying the Vicious-Circle Principle. Quantification over these concepts is thus bound to be legitimate, and can be added to the language. The same holds for propositions and for concepts falling under other types: for each type, a quantifier can be added that ranges over items (of that type) that are definable using the initial unproblematic resources. The new quantificational resources enable the definition of further items of each type; these, too, respect the Principle, and again, quantifiers ranging over the expanded totalities can legitimately be added to the language. The new resources permit the definition of yet further items. And the process repeats. The result is that we have a hierarchy of propositions and of concepts of various orders. Each type in the type hierarchy ramifies into a multiplicity of orders. This ramification ensures that definitions formulated in the resulting language are bound to respect the Vicious-Circle Principle. Concepts and classes that can be defined within the confines of this scheme are said to be predicative (in one sense of this word); the others, impredicative .

For further discussion of the Vicious-Circle Principle, see Russell 1908, Whitehead and Russell 1925, Gödel 1944, and Chihara 1973. For a formal presentation of Ramified Type Theory, see Church 1976; for a more informal presentation, see Hazen 1983. See also the entries on type theory and Principia Mathematica , which contain further references.

The paradoxes can also be used to motivate a conclusion that is the very opposite to Russell’s. Consider the following definition of a one-place predicate \(G\):

This definition is essentially circular; it is not reducible to one in normal form. Still, intuitively, it provides substantial guidance on the use of \(G\). The definition dictates, for instance, that Socrates falls under \(G\), and that nothing apart from the three ancient philosophers mentioned does so. The definition leaves unsettled the status of only two objects, namely, Plato and Aristotle. If we suppose that Plato falls under \(G\), the definition yields that Plato does fall under \(G\) (since Plato satisfies the definiens), thus confirming our supposition. The same thing happens if we suppose the opposite, namely, that Plato does not fall under \(G\); again our supposition is confirmed. With Aristotle, any attempt to decide whether he falls under \(G\) lands us in an even more precarious situation: if we suppose that Aristotle falls under \(G\), we are led to conclude by the definition that he does not fall under \(G\) (since he does not satisfy the definiens); and, conversely, if we suppose that he does not fall under \(G\), we are led to conclude that he does. But even on Plato and Aristotle, the behavior of \(G\) is not unfamiliar: \(G\) is behaving here in the way the concept of truth behaves on the Truth Teller (“What I am now saying is true”) and the Liar (“What I am now saying is not true”). More generally, there is a strong parallel between the behavior of the concept of truth and that of concepts defined by circular definitions. Both are typically well defined on a range of cases, and both display a variety of unusual logical behavior on the other cases. Indeed, all the different kinds of perplexing logical behavior found with the concept of truth are found also in concepts defined by circular definitions. This strong parallelism suggests that since truth is manifestly a legitimate concept, so also are concepts defined by circular definitions such as (18). The paradoxes, according to this viewpoint, cast no doubt on the legitimacy of the concept of truth. They show only that the logic and semantics of circular concepts is different from that of non-circular ones. This viewpoint is developed in the revision theory of definitions .

In this theory, a circular definition imparts to the defined term a meaning that is hypothetical in character; the semantic value of the defined term is a rule of revision , not as with non-circular definitions, a rule of application . Consider (18) again. Like any definition, (18) fixes the interpretation of the definiendum if the interpretations of the non-logical constants in the definiens are given. The problem with (18) is that the defined term \(G\) occurs in the definiens. But suppose that we arbitrarily assign to \(G\) an interpretation—say we let it be the set \(U\) of all objects in the universe of discourse (i.e., we suppose that \(U\) is the set of objects that satisfy \(G)\). Then it is easy to see that the definiens is true precisely of Socrates and Plato. The definition thus dictates that, under our hypothesis, the interpretation of \(G\) should be the set \(\{ \text{Socrates}, \text{Plato}\}\). A similar calculation can be carried out for any hypothesis about the interpretation of \(G\). For example, if the hypothesis is \(\{\text{Xenocrates}\}\), the definition yields the result \(\{\text{Socrates}, \text{Aristotle}\}\). In short, even though (18) does not fix sharply what objects fall under \(G\), it does yield a rule or function that, when given a hypothetical interpretation as an input, yields another one as an output. The fundamental idea of the revision theory is to view this rule as a revision rule: the output interpretation is better than the input one (or it is at least as good; this qualification will be taken as read). The semantic value that the definition confers on the defined term is not an extension—a demarcation of the universe of discourse into objects that fall under the defined term, and those that do not. The semantic value is a revision rule.

The revision rule explains the behavior, both ordinary and extraordinary, of a circular concept. Let \(\delta\) be the revision rule yielded by a definition, and let \(V\) be an arbitrary hypothetical interpretation of the defined term. We can attempt to improve our hypothesis \(V\) by repeated applications of the rule \(\delta\). The resulting sequence,

is a revision sequence for \(\delta\). The totality of revision sequences for \(\delta\), for all possible initial hypotheses, is the revision process generated by \(\delta\). For example, the revision rule for (18) generates a revision process that consists of the following revision sequences, among others:

Observe the behavior of our four ancient philosophers in this process. After some initial stages of revision, Socrates always falls in the revised interpretations, and Xenocrates always falls outside. (In this particular example, the behavior of the two is fixed after the initial stage; in other cases, it may take many stages of revision before the status of an object becomes settled.) The revision process yields a categorical verdict on the two philosophers: Socrates categorically falls under \(G\), and Xenocrates categorically falls outside \(G\). Objects on which the process does not yield a categorical verdict are said to be pathological ( relative to the revision rule, the definition, or the defined concept). In our example, Plato and Aristotle are pathological relative to (18). The status of Aristotle is not stable in any revision sequence. It is as if the revision process cannot make up its mind about him. Sometimes Aristotle is ruled as falling under \(G\), and then the process reverses itself and declares that he does not fall under \(G\), and then the process reverses itself again. When an object behaves in this way in all revision sequences, it is said to be paradoxical . Plato is also pathological relative to \(G\), but his behavior in the revision process is different. Plato acquires a stable status in each revision sequence, but the status he acquires depends upon the initial hypothesis.

Revision processes help provide a semantics for circular definitions. [ 14 ] They can be used to define semantic notions such as “categorical truth” and logical notions such as “validity.” The characteristics of the logical notions we obtain depend crucially on one aspect of revision: the number of stages before objects settle down to their regular behavior in the revision process. A definition is said to be finite iff, roughly, its revision process necessarily requires only finitely many such stages. [ 15 ] For finite definitions, there is a simple logical calculus, \(\mathbf{C}_{0}\), that is sound and complete for the revision semantics. [ 16 ] With non-finite definitions, the revision process extends into the transfinite. [ 17 ] And these definitions can add considerable expressive power to the language. (When added to first-order arithmetic, these definitions render all \(\Pi^{1}_{2}\) sets of natural numbers definable.) Because of the expressive power, the general notion of validity for non-finite circular definitions is not axiomatizable (Kremer 1993). We can give at best a sound logical calculus, but not a complete one. The situation is analogous to that with second-order logic.

Let us observe some general features of the revision theory of definitions. (i) Under this theory, the logic and semantics of non-circular definitions—i.e., definitions in normal form—remain the same as in the traditional account. The introduction and elimination rules hold unrestrictedly, and revision stages are dispensable. The deviations from the traditional account occur only over circular definitions. (ii) Under the theory, circular definitions do not disturb the logic of the ground language. Sentences containing defined terms are subject to the same logical laws as sentences of the ground language. (iii) Conservativeness holds. No definition, no matter how vicious the circularity in it, entails anything new in the ground language. Even the utterly paradoxical definition

respects the Conservativeness requirement. (iv) Eliminability fails to hold. Sentences of the expanded language are not, in general, reducible to those of the ground language. This failure has two sources. First, revision theory fixes the use, in assertion and argument, of sentences of the expanded language but without reducing the sentences to those of the ground language. The theory thus meets the Use criterion, but not the stronger one of Eliminability. Second, in this theory, a definition can add logical and expressive power to a ground language. The addition of a circular definition can result in the definability of new sets. This is another reason why Eliminability fails.

It may be objected that every concept must have an extension, that there must be a definite totality of objects that fall under the concept. If this is right then a predicate is meaningful—it expresses a concept—only if the predicate necessarily demarcates the world sharply into those objects to which it applies and those to which it does not apply. Hence, the objection concludes, no predicate with an essentially circular definition can be meaningful. The objection is plainly not decisive, for it rests on a premiss that rules out many ordinary and apparently meaningful predicates (e.g., ‘bald’). Nonetheless, it is noteworthy because it illustrates how general issues about meaning and concepts enter the debate on the requirements on legitimate definitions.

The principal motivation for revision theory is descriptive. It has been argued that the theory helps us to understand better our ordinary concepts such as truth, necessity, and rational choice. The ordinary as well as the perplexing behavior of these concepts, it is argued, has its roots in the circularity of the concepts. If this is correct, then there is no logical requirement on descriptive and explicative definitions that they be non-circular.

For more detailed treatments of these topics, see Gupta 1988/89, Gupta and Belnap 1993, and Chapuis and Gupta 1999. See also the entry on the revision theory of truth . For critical discussions of the revision theory, see the papers by Vann McGee and Donald A. Martin, and the reply by Gupta, in Villanueva 1997. See also Shapiro 2006.

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• –––, 2019, Conscious Experience: A Logical Inquiry , Cambridge, MA: Harvard University Press.
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• Hazen, A., 1983, “Predicative Logics,” in Handbook of Philosophical Logics: Volume I: Elements of Classical Logic , edited by D. Gabbay and F. Guenthner, Dordrecht: Reidel, pp. 331–407.
• Hodges, W., 1993, “Tarski’s Theory of Definition,” in New Essays on Tarski and Philosophy , edited by D. Patterson, Oxford: Oxford University Press, pp. 94–132.
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• Kremer, P., 1993, “The Gupta-Belnap systems \(\mathbf{S}^{\#}\) and \(\mathbf{S}^{*}\) are not axiomatisable,” Notre Dame Journal of Formal Logic , 34: 583–596.
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• Tarski, A., 1983, Logic, Semantics, Metamathematics: Papers from 1923 to 1938 , second edition, edited by J. Corcoran, Indianapolis: Hackett Publishing Company.
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How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Definitions, Dictionaries, and Meanings , notes by Norman Swartz, Simon Fraser University

analytic/synthetic distinction | Aristotle, General Topics: logic | descriptions | Frege, Gottlob: theorem and foundations for arithmetic | logical constants | Tarski, Alfred: truth definitions | truth: revision theory of | type theory

Acknowledgments

The authors would like to thank Edward Zalta and any anonymous editor for helpful suggestions for improving this entry.

Copyright © 2023 by Anil Gupta < agupta @ pitt . edu > Stephen Mackereth < sgmackereth @ gmail . com >

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Stipulative Definitions in English

George Rose / Getty Images

• An Introduction to Punctuation
• Ph.D., Rhetoric and English, University of Georgia
• M.A., Modern English and American Literature, University of Leicester
• B.A., English, State University of New York

A stipulative is a definition that assigns meaning to a word, sometimes without regard for common usage . The term stipulative definition is often used in a pejorative sense to refer to a definition that appears to be deliberately misleading . Stipulative definitions are also known as Humpty-Dumpty words or legislative definitions.

Examples and Observations

Michael Ghiselin

"A lexical definition, such as one that occurs in a dictionary (a ' lexicon '), is a kind of report on how language is used. A stipulative definition proposes ('stipulates') that language shall be used in a given way." – Metaphysics and the Origin of Species . SUNY Press, 1997

Trudy Govier

"Words in a language are public instruments for communication in that language, and a stipulative definition is useful only if it sets out predictable and comprehensible standards of use that are workable for the purpose at hand. If a stipulated definition becomes popular, the word defined in its new sense then becomes part of public language, and it is open to changes and variations in use just as other words are." – A Practical Study of Argument , 7th ed. Wadsworth, 2010

Patrick J. Hurley

"Stipulative definitions are misused in verbal disputes when one person covertly uses a word in a peculiar way and then proceeds to assume that everyone else uses that word in the same way. Under these circumstances that person is said to be using the word 'stipulatively.' In such cases the assumption that the other person use the word in the same way is rarely justified." – A Concise Introduction to Logic , 11th ed. Wadsworth, 2012

Jon Stratton

"Stipulative definitions that slant or bias meanings are called 'persuasive definitions.' They are meant to persuade and to manipulate people, not to clarify meaning and encourage communication. Persuasive definitions are sometimes encountered in advertising, political campaigns, and in discussions about moral and political values. For example the definition, 'A caring mother is one who uses Softness brand disposable diapers,' is persuasive because it unfairly stipulates the secondary designation 'Softness user.' The term 'caring mother' is much more significant than that!" – Critical Thinking for College Students . Rowman & Littlefield, 1999

Use in Literature

“There’s glory for you!”

“I don’t know what you mean by ‘glory,’" Alice said.

Humpty Dumpty smiled contemptuously. “Of course you don’t–till I tell you. I meant ‘there’s a nice knock-down argument for you!’”

“But ‘glory’ doesn’t mean ‘a nice knock-down argument,’” Alice objected.

“When I use a word,” Humpty Dumpty said, in rather a scornful tone, “it means just what I choose it to mean–neither more nor less.”

“The question is,” said Alice, “whether you can make words mean so many different things.”

“The question is,” said Humpty Dumpty, “which is to be master–that’s all.”

Alice was too much puzzled to say anything; so after a minute Humpty Dumpty began again. “They’ve a temper, some of them–particularly verbs, they’re the proudest–adjectives you can do anything with, but not verbs–however, I can manage the whole lot of them! Impenetrability! That’s what I say!”

“Would you tell me, please,” said Alice, “what that means?”

“Now you talk like a reasonable child,” said Humpty Dumpty, looking very much pleased. “I meant by ‘impenetrability’ that we’ve had enough of that subject, and it would be just as well if you’d mention what you mean to do next, as I suppose you don’t mean to stop here all the rest of your life.”

“That’s a great deal to make one word mean,” Alice said in a thoughtful tone.

“When I make a word do a lot of work like that,” said Humpty Dumpty, “I always pay it extra.” –Lewis Carroll, Through the Looking-Glass , 1871

Use in Film

Nancy: Can you, like, define the meaning of love?

Fielding Mellish: What do you... define... it's love! I love you! I want you in a way of cherishing your totality and your otherness, and in the sense of a presence, and a being and a whole, coming and going in a room with great fruit, and love of a thing of nature in a sense of not wanting or being jealous of the thing that a person possesses.

Nancy: Do you have any gum? –Louise Lasser and Woody Allen in Bananas , 1971

• Humpty Dumpty's Philosophy of Language
• Writers on Words
• Free Variation in Phonetics
• Broadening (Semantic Generalization)
• What Are Word Blends?
• Sound Symbolism in English: Definition and Examples
• What Is an Ideogram? Definition and Examples
• The Top 20 Figures of Speech
• Amelioration (word meanings)
• The Meaning of Innuendo
• Pun: Definition and Examples in English
• lexeme (words) Definition, Etymology and Examples
• Definition of Usage Labels and Notes in English Dictionaries
• The Etymology of Words and Their Surprising Histories
• Meaning Semantics
• What Is a Synonym? Definition and Examples

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9 The Concept of an Argument

David hitchcock, 1. introduction [1] , [2].

The concept of an argument for which I propose an analysis is the reason-giving sense in which one speaks, for example, about Daniel Kahneman’s argument (2011, pp. 334-335) that the tendency of most people to be risk averse about gains but risk-seeking about losses is irrational. This sense of the word ‘argument’ should be sharply distinguished from the disputational sense in which one speaks about two people having an argument, discussed in Chapter 8. That these are two different senses is clear from the fact that languages other than English use two different words for the two senses. For example, in French, ‘to argue’ in the sense of quarrelling is ‘ disputer ’, whereas ‘to argue’ in the sense of giving reasons for or against is ‘ argumenter ’.

We could give a rough lexical definition of the word ‘argument’ in this sense by quoting the definition by the Hellenistic Stoics of an argument as “a system composed of premisses [3] and a conclusion” ( systêma ek lêmmatôn kai epiphoras , Diogenes Laertius 1925/ca. 210-240, 7.45). Aside from its idiosyncratic failure to recognize one-premiss arguments, this definition is an acceptable starting point for a conceptual analysis. That analysis would need to answer a number of questions raised by the lexical definition. What is a premiss? What is a conclusion? What sorts of entities can function as a premiss? What sorts can function as a conclusion? How do premisses and a conclusion form a unified system? Does such a system have an intrinsic function or purpose, or on the contrary can it be used for various purposes? What about complex arguments?

We should recognize that arguments are not necessarily the content or product of argumentation—that is, of communications in which arguments are exchanged. One can consider an argument for a certain position or policy even if nobody has ever used that argument. One can imagine crazy arguments that no sane person would ever put forward. One can apply the term ‘argument’ to unified stretches of solo reasoning where some conclusion is reached on the basis of reasons, as when one considers mentally various aspects of a situation and then describes “the argument that finally convinced me”. Indeed, it seems consistent with our ordinary use of the term ‘argument’ in its reason-giving sense to say that there are arguments that nobody has ever thought of and nobody ever will. The most we can demand is that an argument must be thinkable and expressible. Arguments as a class thus have no common function or purpose. They are not necessarily used to justify or establish something. Nor are they necessarily used to persuade anybody.

Thus, critical thinking textbooks that define ‘argument’ as “rational persuasion—an attempt to influence another or others using reasons” are actually describing one use of arguments, not the concept itself.

2. Simple arguments

Begin by considering simple arguments, in the sense of single-inference systems that consist of one or more premisses and one conclusion. Of what sorts of entities are such arguments composed? That is, what kind of object can function as a premiss, and what kind can function as a conclusion? A common answer is that these components are propositions, in the sense of postulated timeless and non-located entities that can be expressed linguistically (or in some other way) and that can be objects of belief or knowledge. Propositions however are not the right candidates to be premisses or conclusions.

As to premisses, consider the following two arguments:

(1)  Suppose that there is life on other planets in the universe. Then it makes sense to look for it.

(2)  There is life on other planets in the universe. So it makes sense to look for it.

These arguments have the same conclusion, but different premisses. But both premisses express the same proposition, that there is life on other planets in the universe. The difference is in the illocutionary act performed by someone who utters the premiss in standard contexts. In uttering argument (1), the author hypothesizes the propositional content of the premiss. In uttering argument (2), on the other hand, the author asserts the proposition. The difference makes a difference to the evaluation of the two arguments: argument (2) requires a stricter condition of premiss adequacy than argument (1).

If arguments need not be expressed but their premisses are illocutionary acts, the premisses must be illocutionary act-types rather than illocutionary act-tokens. Sometimes the type may have no actual tokens. Someone can use the same argument on different occasions, and different people can use the same argument. A premiss can be a supposition or an assertive or any other member of the class of illocutionary acts that Searle (1976) grouped under the label ‘representatives’, and which he defined (p. 10) as acts whose point is to commit the speaker, perhaps hypothetically or guardedly, to something’s being the case. It cannot be any other kind of illocutionary act, as we can see by noting the peculiarity of putting examples (taken from Hitchcock 2006, pp. 103-104) of the other kinds of illocutionary acts in premissary position before an inferential ‘therefore’:

(3) * What time is it? Therefore, you must go home .

(4) ? I promise to pick up some milk on the way home. Therefore, you don’t need to get it.

(5) * Congratulations on your anniversary. Therefore, you are married.

(6) * I hereby sentence you to two years less a day. Therefore, the guards will now take you to prison.

In standard contexts, the utterances in the premissary position are respectively (3) a directive (in particular, a request for information), (4) a commissive (in particular, a promise), (5) an expressive (in particular, a congratulation), and (6) a declarative (in particular, a judicial verdict). The inappropriateness of these pairings reveal the general inability of illocutionary acts other than representatives to function as premisses. The premiss in (4) is a borderline case, because a promise can be taken to imply a prediction (that the promise will be kept) and a prediction is a kind of assertion. It is the implicit prediction rather than the commitment that makes it possible to construe example (4) as an argument.

Among conclusions, we find a greater variety of illocutionary acts than among premisses. We have already seen two examples ((1) and (2) above) in which the conclusion is a representative. Conclusions (and premisses too) can be hedged by such qualifiers as ‘probably’, ‘presumably’, ‘possibly’, and the like, which are best given a speech-act interpretation. [4] Thus a wide range of representatives can be conclusions of arguments. But the other main kinds of illocutionary acts can also be conclusions, as we can see from the following examples (taken from Hitchcock 2006, p. 105):

(7) There is a forecast of thundershowers, so let’s cancel the picnic.

(8) I know how difficult it will be for you to get the milk, so I pro m ise you that I will pick it up on the way home.

(9) My conduct was inexcusable, so I apologize most sincerely.

(10) The evidence establishes beyond a reasonable doubt that you committed the crime of which you are accused, so I hereby find you guilty as charged.

When these arguments are expressed in standard contexts, their conclusions are respectively (7) a directive, (8) a commissive, (9) an expressive, and (10) a declarative. Thus the conclusion of an argument can be an illocutionary act type of any kind: a representative, a directive, a commissive, an expressive, or a declarative.

A reason can be advanced as a reason against some claim as well as a reason for it. Consider the following example:

(11) Proponent: We need a concerted global reduction of greenhouse gas emissions to mitigate future climate disruption. Opponent: A cost-benefit analysis needs to be done first to dete r mine whether it makes more sense to adapt to future climate disruption rather than to mitigate it.

Here the opponent’s reason is put forward as a reason against the proponent’s claim. The exchange has an inferential structure that is quite parallel to that in which a reason is put forward in support of a claim. In general, objections and criticisms seem to have just the same inferential structure as supports. In other words, there can be arguments against something as well as arguments for something. Consider an example. In the 11th century the monk Gaunilon objected to Anselm’s ontological argument for the existence of God that by the same reasoning one could prove the existence of a perfect island (Anselm 1903/1077-78). Gaunilon’s objection is an argument against the cogency of Anselm’s argument. It would involve needless and misleading subtlety to recast his objection as an argument in support of some claim. It is better to follow a number of authors who have recognized that there can be arguments against as well as arguments for (Johnson 2000; Rahwan et al. 2009; Freeman 2010; Wohlrapp 2014/2008).

In fact, the same reason can be adduced for a claim by one person and against the same claim by another person. For example, some people use the principle of self-determination as a reason for legalizing voluntary euthanasia, whereas others use it as a reason against legalizing voluntary euthanasia (Wohlrapp 2014/2008, pp. 264-265 [5] ). Each group advances an argument, and the two arguments clearly differ from each other. Thus it makes sense to add to the conception of an argument as a premiss-conclusion or claim-reason complex a third component indicating whether the reasons are to count for or against the claim. Further, to accommodate the existence of arguments against as well as arguments for, I shall hereafter use the term ‘target’ rather than ‘conclusion’ or ‘claim’ for the part of an argument to which its reasons are directed.

We are now in a position to say what a simple argument is:

A simple argument consists of one or more of the types of expression that can function as reasons, a “target” (any type of expression), and an indicator of whether the reasons count for or against the target. [6]

There may be no tokens of the component illocutionary act types. In other words, simple arguments as just defined are abstract structures that are not necessarily actually realized. We need impose no further restrictions on what can count as a simple argument, thus widening the class of arguments to the craziest combinations that one can imagine.

What gives such a set unity as a single argument is that someone puts forward or entertains, that is—adduces—its reasons as support for its target. In doing so, the person considers that the reasons, if true or otherwise acceptable, provide grounds for accepting or rejecting the target (to an extent indicated). Normally, the assumption motivating adducing the argument is that the person addressed by, or who considers, the argument did not previously think that the reasons provide the claimed support for, or opposition to, the target.

Goddu (2018) has objected to this way of securing the unity of an actualized argument. He contends that a person can entertain an argument mentally without supposing that its reasons support (or oppose) its target. One can for example wonder whether the reasons in an argument one is considering actually support the target. This is true, but in such a case the person considering the argument is viewing it as an argument that someone might or could adduce, i.e., as a hypothetical argument, a possible complex of reasons, indicator, and target.

Someone who adduces reasons as counting for or against a target must express the indicator, and must be the author of either the reasons or the target. But such an adducer need not be the author of both reasons and target. One can draw a conclusion from something someone else has said, in which case the person who draws the conclusion adduces what the other person said as supporting the conclusion drawn. One can provide reasons against someone else’s claim, in which case the person who provides the reasons adduces them as opposing the other person’s claim. In any situation where an argument is expressed, the adducer is the person who articulates the inferential claim conveyed by the indicator that points to the argument’s target.

3. Complex arguments

So far this conception of an argument accommodates only simple arguments, i.e. single-inference arguments with a set of one or more reasons, a target, and an indication of whether the reasons count for or against the target. We need to allow as well for complex arguments that involve a chain of reasoning or embedded suppositional reasoning.

3.1 Chain of reasoning arguments

In chained arguments, a reason of one argument (which I will call ‘the superordinate argument’) is the target of another (which I will call ‘the subordinate argument’ or ‘sub-argument’). Since only representatives can be reasons, the target of any subordinate argument must be a representative. There is no limit to the depth of chaining. The ultimate target in a chain of reasoning is supported or opposed by one or more reasons, each of which may be the target of one or more reasons in a sub-argument, each of which in turn may be the target of one or more reasons in a sub-sub-argument, and so on indefinitely. In an expressed sub-argument at any level, the reasons must be adduced in support of the target. Otherwise the target would have to be the complement of the reason in the superordinate argument to which it was linked. But it is hard to define the complement of a representative illocutionary act. What, for example, is the complement of a hedged assertion of the form ‘probably p ’? Representatives incompatible with ‘probably p ’ include ‘definitely p ’, ‘probably p ′ ’, and ‘definitely p ′ ’, where p ′ is a contradictory of p . An argument against some target that was used to support a reason of the form ‘probably p ’ would therefore need an unwieldy disjunction as its target, for which it would be difficult if not impossible to formulate a set of reasons that successfully opposed each disjunct simultaneously. Since subordinate simple arguments in an expressed complex argument make sense only if their reasons are presented in support of their target, it makes sense to limit unexpressed subordinate simple arguments in the same way.

The natural way to accommodate the indefinite complexity of chained arguments is to use a recursion clause that can be applied again and again so as to build up arguments of increasing complexity. The process is analogous to that by which one defines what a person’s ancestor is by saying that a parent of a person is an ancestor of that person and that a parent of any ancestor of that person is also an ancestor of that person. This definition allows one to construct the class of a person’s ancestors, starting with the person’s parents, then adding the grandparents, then the great-grandparents, and so on without end.

In defining recursively what an argument is, one needs to take some care in constructing the recursion clause for chaining arguments. The most sensible way to do so seems to be to add one at a time a simple argument for a reason in an already constructed argument. One can conceive of a simple argument, which is a triple, as a unit set, a set with one member. One can combine it with a simple argument whose target is a reason in the first argument by taking the union of the two sets, i.e., the set whose members are all the triples that are members of either set. And then one can combine this set of two triples with a third simple argument whose target is a reason in one of the first two triples. And so on. Let us call a reason in any triple in a set of such triples a ‘reason in the argument’. The recursion clause might then read as follows:

If in an argument something is a reason but is not a target, then the union of that argument with a simple argument whose target is that reason and whose indicator is positive is also an argument.

As with the definition of simple arguments, this clause allows that the most fantastic and crazy combinations are arguments in the abstract sense. The condition that the reason is not already a target is meant to exclude from being a single argument structures in which a reason is the target of more than one simple argument. Just as multiple arguments for or against the same ultimate target do not constitute a single argument, so too multiple arguments for the same intermediate target cannot be components of a single complex argument.

3.2 Embedded suppositional reasoning

Chaining is one of two ways to construct complex arguments. The other is embedding, where suppositional reasoning is used to support or oppose a target, with one or more of its suppositions being “discharged” in the process. (E.g., “Suppose the U.S. did not use the atomic bombs in WWII. Had that been the case, then probably…” or “Suppose we take on the debt of a big mortgage and buy a house. If we were to do that, then …”.) Any line of suppositional reasoning is an argument according to the recursive definition of argument developed so far. To allow for embedding one or more such lines of suppositional reasoning, we need to allow that a line of suppositional reasoning can count as something like a reason. [7] One way to do so is to take the line of suppositional reasoning as an implicit assertion that the ultimate target of the line of suppositional reasoning follows from its ultimate supposition in combination with any other ultimate reasons used in derivation of the ultimate target. (The assertion may be qualified, if either an inference or an ultimate reason in the suppositional reasoning is qualified.)

When the suppositional reasoning is embedded in a larger context, the target external to this line of reasoning is a representative, which in the case of nested suppositional reasoning may itself have a suppositional status. The recursion clause allowing embedding of suppositional reasoning thus needs to allow for the dual complexity of chains of reasoning from suppositions and nesting of suppositional reasoning inside suppositional reasoning. It also needs to allow that a line of suppositional reasoning can be used in opposition to a target as well in support of one. If the target of a line of suppositional reasoning is a reason in a sub-argument, however, then the expression of such a complex argument makes sense only if the suppositional reasoning is adduced in support of the target, for the same reason that an expressed chained simple sub-argument makes sense only if its reasons are adduced in support of its target: an opposed target would have to be too complex to count as the complement of the reason in the superordinate argument that is being indirectly supported by opposition to the target of the suppositional reasoning.

In general, too, it makes sense to use a line of suppositional reasoning only if its internal ultimate target is argued for rather than against, since all the recognized legitimate ways of discharging a supposition assume that the supposition is used to support the ultimate target. Similar restrictions to arguments with a positive indicator are therefore appropriate for abstract arguments that need not be expressed. It seems an unnecessary further complication, however, to incorporate in a clause allowing embedding the specific ways in which a supposition in a piece of suppositional reasoning may legitimately be discharged. [8] The abstract definition of an argument will thus allow for embedding pieces of suppositional reasoning in totally illegitimate ways.

The following is a possible recursion clause allowing embedding;

A triple is an argument if its first member is a set whose members include at least one argument with a suppositional ultimate reason, whose third member (the target) is an illocutionary act of any kind, and whose second member is an indicator of whether the members of the set count for or against the target.

As is usual with recursive definitions, there needs to be a final closure clause to the effect that nothing is an argument unless it is an argument according to the base clause and the recursion clauses. [9] One can illustrate and test the resulting definition by using its clauses to construct complex arguments as they appear in argumentative texts.

As with the abstract concept of a single argument, we need a basis for the unity of an expressed complex argument. An expressed chaining of two arguments is a complex illocutionary act of adducing the resulting chain of reasoning as supporting or opposing the ultimate target of the superordinate argument in the chain (i.e. the argument that has a reason which the subordinate simple argument targets). The essence of adducing in this case is that the utterance of the adducer counts as a claim that in each link of the chain the reasons if true or otherwise acceptable would provide epistemic support for the target or as a claim that the reasons if true or otherwise acceptable would provide epistemic opposition to the target. An embedding of an argument is a complex act of adducing the embedded suppositional reasoning, possibly along with one or more reasons, as support for or opposition to the target of the argument in which the suppositional reasoning is embedded. The essence of adducing in this case is that the utterance of the adducer counts as a claim that the suppositional reasoning would if the additional reasons (if any) were true or otherwise acceptable provide epistemic support for the target or as a claim that the suppositional reasoning would if the additional reasons (if any) were true or otherwise acceptable provide epistemic opposition to the target. The content conditions, preparatory conditions and sincerity conditions for these more complex acts of adducing are a function of the content, preparatory and sincerity conditions for the simple acts of adducing from which they are constituted.

As with simple expressed arguments, we can accommodate complex arguments that are merely considered by a hypothetically possible act of adducing. If one is considering a complex abstract argument as a whole that could be used to adduce the reasons as supporting or opposing its ultimate target, then one is considering an argument.

The conception of an argument that I propose has the following distinctive features:

• It takes the ultimate constituents of arguments to be illocutionary act types rather than propositions, statements, utterances, and the like.
• It allows for arguments against something as well as arguments for something.
• It allows the reasons in an argument to be any kind of representative illocutionary act.
• It allows arguments to have as their target any kind of illocutionary act.
• It distinguishes arguments as abstract structures that may never be expressed or even thought of from expressed arguments.
• It locates the unity of an expressed or mentally entertained argument in a second-order illocutionary act of adducing, which may be actual or merely hypothetically entertained.
• It allows for a variety of uses of arguments, since neither the abstract conception of an argument nor the act of adducing that constitutes a complex of illocutionary act types as a single argument includes any conception of the purpose or function of an argument.
• It provides explicitly for complex arguments to be constructed recursively by steps of chaining and embedding.

Anselm, Saint (1903/1077-78). Proslogium ; Monologium : An appendix in behalf of the fool by Gaunilo ; and Cur deus homo , translated from the Latin by Sidney Norton Deane, B.A. with an introduction, bibliography, and reprints of the opinions of leading philosophers and writers on the ontological argument. Chicago: Open Court. Latin original of the Proslogium written in 1077-78.

Diogenes Laertius (1925/ca. 210-240). Lives of eminent philosophers , with an English translation by R. D. Hicks, 2 vols. Loeb Classical Library 184 and 185. Cambridge, Mass.: Harvard University Press. First published ca. 210-240 CE.

Ennis, Robert H. (2006). ‘Probably’. In David Hitchcock & Bart Verheij (Eds.), Arguing on the Toulmin model: New essays on argument analysis and evaluation (pp. 145-164). Dordrecht: Springer.

Freeman, James B. (2010). Commentary on Geoffrey C. Goddu’s “Refining Hitchcock’s definition of ‘argument’”. In Juho Ritola (Ed.), Argument cu l tures: Proceedings of OSSA 09 , CD-ROM (pp. 1-10). Windsor, ON: OSSA. Available at http://scholar.uwindsor.ca/cgi/viewcontent.cgi?article=1141&context=ossaarchive .

Goddu, Geoffrey C. (2018). Against the intentional definition of argument. In Steve Oswald and Didier Maillat (Eds .), Proceedings of the Second E u ropean Conference on Argumentation, University of Fribourg, Switzerland, 20-23 June 2017 , Vol. II (pp. 337-346). London: College Publications.

Hitchcock, David (2006). Informal logic and the concept of argument. In Dale Jacquette (Ed.), Philosophy of logic , volume 5 of Dov M. Gabbay, Paul Thagard & John Woods (Eds.), Handbook of the philosophy of sc i ence (pp. 101-129). Amsterdam: North Holland.

Hitchcock, David (2017). The concept of argument. In David Hitchcock, On reasoning and argument: Essays in informal logic and on critical thinking (pp. 518-529). Dordrecht: Springer.

Johnson, Ralph H. (2000). Manifest rationality: A pragmatic theory of a r gument . Mahwah, NJ: Lawrence Erlbaum Associates.

Kahneman, Daniel (2011). Thinking, fast and slow . New York: Farrar, Straus and Giroux.

Rahwan, Iyad, & Chris Reed (2009). The Argument Interchange Format. In Guillermo R. Simari (Ed.), Argumentation in artificial intelligence (pp. 383-402). Boston: Springer.

Searle, John R. (1976). A classification of illocutionary acts. Language in Society , 5(1): 1-23.

Toulmin, Stephen Edelston (1958). The uses of argument . Cambridge: Cambridge University Press.

Wohlrapp, Harald R. (2014/2008). The concept of argument: A philosoph i cal foundation . Dordrecht: Springer. German original first published in 2008.

• © David Hitchcock ↵
• This chapter uses material from “The concept of argument” (Hitchcock 2017, pp. 518-529; © Springer International Publishing AG 2017), with permission of Springer. ↵
• ‘Premise’ and ‘premiss’ are both acceptable spellings of the word. Some authors prefer the first, which is more common in the USA; some prefer the second, which is found more often in Great Britain. ↵
• As Toulmin (1958, pp. 47-62) and Ennis (2006, pp. 145-164) have argued. ↵
• Wohlrapp argues that if voluntary euthanasia becomes legal on the basis that self-determination requires it, those whose condition might qualify them for approval to be euthanized but who want merely to live out the remainder of their natural lives are pressured by appeals to self-determination to submit to euthanasia. The supposedly liberating value becomes coercive. ↵
• More precisely: A simple argument is a triple whose first member is a set of one or more representative illocutionary act types (called ‘the reasons’), whose third member (called ‘the target’) is an illocutionary act type of any kind, and whose second member is an indicator of whether the reasons count for or against the target. ↵
• It won’t do, however, to count it as a reason in the same sense as that in which a representative is a reason. Otherwise the recursion clause for chaining would allow for arguments that are subordinate to a line of suppositional reasoning, which makes no sense. ↵
• One way of legitimately discharging a supposition is conditional proof, in which one derives a conditional from a line of suppositional reasoning that starts from the supposition of the conditional’s antecedent and ends with the conditional’s consequent. A variant form of conditional proof starts from the supposition of a contradictory of a conditional’s consequent and ends with a contradictory of its antecedent. Another way to legitimately discharge a supposition is reductio ad absurdum, in which one uses a line of reasoning from a supposition to some absurdity as a reason for denying the supposed proposition. Another is argument by cases, in which one considers an allegedly exhaustive set of possible cases, deriving the same ultimate target from the supposition of each case, and then drawing this ultimate target as a conclusion. Another is to argue for a proposition in a proof by mathematical induction by supposing at the inductive step that the proposition holds for the number n (or for every number up to and including n) and deriving from this supposition that then it also holds for the number n 1. Another is universal generalization, in which one derives a universal generalization about a kind by reasoning from the supposition that some individual is of that kind to the conclusion that the generalization holds for this individual, without using any other assumption about the individual. ↵
• One can express the recursive definition in the customary form of a statement in which there appears in the first part the term to be defined, in the last part the defining part of the definition, and in between these two parts an indicator (such as ‘means’, ‘=df’, ‘if and only if’, or ‘is a’) that the defining part states the meaning of the defined term. For example, one could say that something is an argument if and only if it belongs to every set that includes everything that satisfies the base clause, as well as everything that can be constructed from its members using the recursion clauses for chaining and embedding. ↵

Studies in Critical Thinking Copyright © by David Hitchcock is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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• Published: 03 February 2021

Exploring linguistic features, ideologies, and critical thinking in Chinese news comments

• Yang Gao   ORCID: orcid.org/0000-0001-5888-6033 1 &
• Gang Zeng 1  

Humanities and Social Sciences Communications volume  8 , Article number:  39 ( 2021 ) Cite this article

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• Cultural and media studies
• Language and linguistics

This study explores linguistic features, ideological beliefs, and critical thinking in news comments, which are defined as the comments from readers to news posts on social media or platforms. Within the overarching framework of critical discourse analysis, a sociocognitive approach was adopted to provide detailed analyses of the studied constructs in sampled news comments. In terms of the data collection and analysis, sampled social media, news columns, and news comments were selected, and then 19 college students were interviewed for their responses to different news topics. The primary findings of the study include: (1) personal and social opinions are representations of ideological beliefs and are fully presented through news comments, (2) these personal and social ideological beliefs may diverge or converge due to critical thinking, (3) critical thinking helps commenters form their personal and social ideologies, and then helps them choose the linguistic forms they believe fit their news comments, (4) news topics, however, vary in informing commenters’ critical thinking ability. Finally, a sociocognitive model for studying linguistic forms, ideologies, and critical thinking was proposed in the study.

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Introduction.

Over the decades, the majority of the existing literature on news text has focused on how the news is framed from an author’s perspective; however, research on news text from commenters is far less developed. Therefore, we chose a specific type of underdeveloped news text, i.e., news comment, as the focal text for this study. In the study, news comments were not defined as the long commentary articles professionals or journalists write to comment on specific news; instead they were the real-time, short comments or prompts from readers. We took the theoretical premise from van Dijk ( 1997 ) that news text is ideological in nature (p. 197) and explored how critical thinking and linguistic forms, as different constructs, may inform the commenters of revealed ideologies through a specific news text. Before we elaborate on the theoretical framework, we present some synopses of the terms or constructs, i.e., ideology and critical thinking, the focal components of the study.

Van Dijk ( 2006 ) defined ideologies as “systems of ideas” and sociocognitively “shared representations of social groups, and more specifically as the axiomatic principles of such representations” (p. 115). Ideologies are thus “the basic frameworks for organizing the social cognitions shared by members of social groups, organizations or institutions” (van Dijk, 1997 , p. 18) and penetrate all discourse and communication, including media text as one of the predominant forms. From a critical literacy perspective, Tolson ( 2001 ) argued that the informational content conveyed through the mass media is ideology-based; it reproduces and strengthens social relations between the oppressed and the oppressors. Therefore, news commentary, as one type of media text, shows the audience’s attitudes towards a particular news, topic, or event; it conveys the ideological beliefs that audiences hold about the news, topics, or events. Fairclough ( 2006 ) argued that understanding how audiences interpret and respond to the news is helpful to analyze their ideologies. However, the explicitness or vagueness of the ideological beliefs revealed through media discourse or news text makes research on this topic difficult.

Ideologies include cognitive and social ideologies and these two types of ideologies may converge or diverge. We argue that the convergence or divergence of these two types of ideologies depends on critical thinking, another construct that we explore in the study. The notion of critical thinking may be traced to different fragmented tenets of critical discourse analysis (CDA). At the same time, it is one of the core components in interpreting discourse and text (Fairclough, 2006 ). Critical thinking is related to the notion of reflexivity in some classic CDA works; it may refer to both a general principle of doing scientific research and a property of language use, subjectivity, or practice (Chouliaraki and Fairclough, 1999 ; Feustel et al., 2014 ; Zienkowski, 2017 ). For example, Fairclough ( 2010 ) stated that

“Late modernity is characterized by increasing reflexivity including language reflexivity, and people need to be equipped both for the increasing knowledge-based design of discursive practices within economic and governmental systems, and for critique and redesign of these designed and often globalized practices” (p. 603).

Multiple approaches have been used to study linguistic features, ideologies, and critical thinking. Studying these constructs is a challenging task. Because the complex world is dynamic and changes regularly, a specific and individual framework may not be able to interpret or explain the constructs thoroughly. Furthermore, some the focal components or tenets of some theories or frameworks may overlap, which complicates the selection of a theoretical framework. For the current study, we decided to pinpoint our focal constructs and then align these constructs with appropriate theories. While CDA has been applied to studies on language and ideology for decades, it has rarely been considered with regard to news comments, particularly in the Chinese context. This research thus aims to study the linguistic features of news comments through major social media in China and to further explore ideological and critical thinking incidents in these commentary responses. Specifically, we attempt to explore the following issues: (1) the typical linguistic forms, ideologies, and critical thinking in news comments and (2) how these constructs inform each other in news comments.

Theoretical considerations

Under the overarching concept of CDA, different focal approaches or schools have developed over the years, including but not limited to: Fairclough’s Critical Approach, Wodak’s Discourse-historical Approach, and van Dijk’s sociocognitive approach (SCA). Fairclough’s approach has been regarded as the foundational and most classic approach. It perceives language as a social process in which discourse produces and interprets text; however, this process is not random or free but is socially conditioned. Fairclough’s approach has infrequently focused on media text, which then has been extended and developed by Wodak and van Dijk. Unlike Fairclough’s approach, Wodak’s approach focuses on a macroperspective as national identity and is concerned with strategies that can be adapted to achieve specific political and psychological goals. To understand this bigger picture, Wodak’s approach includes historical analysis and considers the sociocultural background of the text studied. In terms of media text study, Wodak and Busch ( 2004 ) analyzed different approaches in media text, from mapping out historical development in CDA to advanced qualitative approaches in critical linguistics and CDA.

SCA resembles Fairclough’s approach in connecting the microstructure of language to the macrostructure of society (Kintsch and van Dijk, 1978 ). However, van Dijk ( 1993 ) extended the field by transplanting social cognition as the mediating tool between text and society. He defined social cognitions as “socially shared representations of societal arrangements, groups, and relations, as well as mental operations such as interpretation, thinking and arguing, inferencing and learning” (p. 257). Similar to Wodak, van Dijk ( 1991 ) applied his approach of discourse analysis to media texts and firmly believed that one area in which discourse can play an important role is in the (re)production of racism inequality through discourse. The major point of his work is that “racism is a complex system of social and political inequality that is also reproduced by discourse” (van Dijk, 2001 , p. 362). Van Dijk’s SCA thus focuses on the schemata through which minorities are perceived and illustrated as well as in headlines in the press.

We firmly believe that no single approach mentioned above perfectly fits all the constructs to be studied in the research, but tenets of different approaches work in different ways to inform the findings of the study. We went deeper into these frameworks and determined that an SCA approach under CDA may better inform the study and thus serve as the theoretical foundation of the study; it works better than other approaches in mapping out relationships among language, cognition in which critical thinking is embedded, and ideologies. However, we did not adhere to a specific school or approach in CDA but instead incorporated different tenets among three different schools in CDA into our study. For example, we referred to a textual analysis perspective from the three-dimensional framework (Fairclough, 1995 ) and extended and interpreted our findings by incorporating social and national ideologies from Wodak ( 2007 ) and social/personal cognition from van Dijk ( 1997 ).

In addition, we reinterpreted CDA from an audience or commenter perspective rather than the author perspective. Our rationale is that the text an author or speaker has framed may serve discursive and social purposes. The author or speaker in this way serves as the initiator of the discursive and social practices. However, this is not the case from an audience or reader perspective. An audience or reader is not the initiator of the actions or practices; he or she may be the person who accepts or rejects the practices. Therefore, we argue that examining ideological and critical thinking constructs in news comments may reveal audiences’ perceptions of and attitudes towards certain practices and even the power behind these practices.

Research methodology

Wodak and Meyer ( 2015 ) concluded that “CDA does not constitute a well-defined empirical method but rather a bulk of approaches with theoretical similarities and research questions of a specific kind” (p. 27). They further explained that methodologies under CDA typically fall into a hermeneutic rather than an analytical-deductive approach. The hermeneutic style requires detailed analyses and reasoning that fit the theoretical framework in the study.

While it might be a challenging task to pinpoint a specific methodology, we followed appropriate guidance in conducting this CDA study. As classic methodological guidance, Wodak and Meyer ( 2015 ) provided a diagrammed process for conducting CDA studies, including theory , operationalization , discourse/text , and interpretation . Theories provide the soil for the conceptualization and selection of theoretical frameworks; operationalization demands specific procedures and instruments; discourse/text is a platform to convey the information; and interpretation is the stage to examine assumptions. One of the major components that guide the methodological design and selection is operationalization, which requires specific procedures and instruments. Therefore, we first selected social media and sampled news and then conducted interviews among 19 college students in a typical research-based university in Northeast China.

Selection of the social media and news columns

Liu ( 2019 ) synthesized social media user reports in the first quarter of 2018 and listed the top 10 social media software and apps that people used in China, which included payment apps (e.g., Alipay), shopping platforms and/or apps (e.g., Taobao), and other platforms and/or apps for entertainment or regular social purposes (e.g., WeChat, Baidu, Sina). According to the poll, we selected WeChat (1040 million users), Baidu search (700 million users), and Sina vlog (392 million users) as the three social media we used for the current study.

Among the three largest social media platforms, Baidu News has a specific classification of 12 news columns, which include domestic affairs, international affairs, military and army, finance and economics, entertainment, sports, internet, technology, gaming, and beauty. The column military and army was an outlier in the selection because it is heavily political or ideological in the context; gaming and beauty were also regarded as two outliers that were highly gender-oriented. After a screening process, we thus deleted and synthesized these columns into six, including domestic/international affairs, finance, entertainment, sports, technology, and game.

Then, one or two news samples were selected under each topic, considering whether the samples might solicit rich information from the interviewees or commenters. For analysis purposes, we collected representative responses with high recognition of the selected news samples. We then conducted a rough analysis of the selected news and corresponding comments and discussed the appropriateness of the news samples. We finalized 12 sampled news items with more than 30 comments and charted them in Table 1 .

Participants

Participants in the study included both public users of social media and undergraduates from an eastern university in China. First, representative news reviews in six categories, including finance, sports, international, domestic, entertainment, and technology, were collected. The comment publishers were social media users from Baidu, Sina Weibo, Surging News, etc.

Additionally, we conducted individual interviews with 19 undergraduates from a university in Northeast China. The interviews focused on the research participants’ opinions on the news. Among the participants, there were three freshmen, 14 sophomores, and two juniors. The ratio of males to females was 9/10. The research participants were from eight different schools: the Law School, the School of Foreign Languages, the School of Sciences, the School of Maritime Electrical Engineering, the School of Transportation Engineering, the Navigation School, the School of Information Science and Technology, and the School of Public Management and Liberal Arts (see Table 2 ).

We conducted one-on-one interviews with 19 undergraduates from a research-based university in Northeast China. The participants of the research were from diverse backgrounds, and the interviews mainly focused on the participants’ views on the news. To ensure the reliability of the results, the participants were not informed until the interview began on site. We conducted the interviews in a casual, conversational format. Each interview lasted ~20 min and aimed to solicit the students’ prompt, real-time responses to the column news. All the interviews were recorded and transcribed for data collection and analysis purposes.

An interview protocol was designed based on the sampled news analysis. The interview protocol consisted of news subjects and guiding sentences. The news subjects were the originally quoted news, while the guiding sentences were directed to each individual news sample. The protocol questionnaire was used to guide the participants to go through the news and then make an instant response.

Data collection and analysis

With the designed interview protocol, corresponding interviews were conducted with 19 college students in the form of casual conversations. Through the WeChat platform and other media, university students’ personal thoughts about specific news were recorded because most of the interviewees had chosen to use text and audio records in WeChat to express themselves. The researchers collected and organized the obtained information and added it to the information charts after acquiring the permission of the interviewees, who were selected from different year levels and faculties. Preliminarily, there were a total of 25 participants who attended the interview and provided nearly 50 pieces of interview information. The researchers finalized the participant size to 19 by deleting some outlier responses. Finally, data collected from the two primary methods were integrated by the researchers and then categorized into four sections, including news content, typical responses, interview responses, and analyses.

Detailed analyses from SCA worked to guide the specific methodology used for the current study due to its theoretical foundation and constructs, including linguistic forms, ideology, and critical thinking, which we wanted to explore. Specifically, SCA suggests six steps of analyses, including semantic macrostructures (topics and macro propositions), local meanings, “subtle” formal structures, global and local discourse forms or formats, linguistic realizations, and the context (Wodak and Meyer, 2015 ). Some types of analyses focus on linguistic forms and figures of speech analysis, some of the analyses focus on literal or connotative meanings, and others on context. It is worth mentioning that not all the analyses can be completely conducted in one single study because some analyses do not fit a specific study. However, these analyses offered methodological insights for the current study. We took steps in collecting different sources of data and analyzed the data in different ways.

Linguistics: lexical, syntactic, and figurative speech features

Van Dijk ( 1995 ) argued that the first step for analysts in CDA studies is to “explore the structures and strategies of text and talk to attend in order to discover patterns of elite dominance or manipulation ‘in’ texts” (p. 19). As van Dijk ( 2006 ) stated, “Although general properties of language and discourse are not, as such, ideologically marked, systematic discourse analysis offers powerful methods to study the structures and functions of underlying ideologies” (p. 115). Therefore, linguistic forms are excellent representations and tools to study ideologies in text. Linguistic features of the text, as a formal property of the text (Fairclough, 1989 , p. 26), are explored in the descriptive stage. One of the features is that idioms, as a way to show respondents’ attitudes and ideologies through the linguistic form, are widely used in the news comments. Idioms are generally used among people with certain cultural capitals. They are socially conditioned, and outgroup people may find them difficult to comprehend. By using idioms, news respondents present shared sociocultural knowledge that can only be easily processed among ingroup people. In the study, many idioms were found in the news comments, such as “ hai ren zhi xin bu ke you, fang ren zhi xin bu ke wu (guard against all intents to harm you, but harbor no intention to harm others)”, “ yan zhen yi dai (be on guard)”, “ jing dai hua kai (wait for the blossom)”, “ zuo wu xu xi (be fully seated)”, and “ qi er yi ju (an effortless job to do)”. The idiomatic expression resonates with what SCA argues are local meanings (Wodak and Meyer, 2015 ) because it focuses on the meanings in the specific, local context.

In addition, connotative meanings of the lexical terms that were connected with figure-of-speech usage appeared in the news commentary, such as, “It might not be good to comment on people’s backyard if one had never lived in Hong Kong.” The backyard in the sentence has a connotative meaning and is used as a metonymy. The feature relates to dialectical and regional terms; some of these cultural capitals behind these terms are deeply rooted in particular regions. Again, the lexical choice, e.g., the backyard, indicates an ingroup–outgroup dichotomy and thus embodies certain personal or social ideologies. A typical SCA approach suggests that language realization analysis requires a figure of speech analysis, which helps map out the local and global meanings of a specific excerpt (van Dijk, 1995 ; Wodak and Meyer, 2015 ).

In terms of the syntactic structure, the research showed that social media platforms and interviewees mainly used relatively complex, notably parallel sentence structures. Examples are the use of the metaphor in “Martial art is not equal to Kungfu. Art involves manifestation and form, while Kungfu involves speed and flexibility. Basketball is a kind of Kungfu, not martial arts. Chinese athletes lack Kungfu but have little success in martial arts” (News, Responsible for the Failure of the Chinese Men’s Basketball Team? A Dejiang, He is a Man, Zhou Qi Needs Care ) or “Like art, the sport has no borders” (News, After Chinese Netizens, Boycotted the NBA, the NBA China Game is Still Fully Seated, and Some People Even Let the Player Sign on the Chinese Flag ). The use of rhetorical techniques, such as metaphors, also increased the complexity of the syntactic structure.

The parallel structure served two primary purposes: it restated the points that the news respondents or the college students attempted to emphasize, and it fostered either a provoking or an emotional context that resonated with the news commentary readers. For example, “Since the start of the match, the Chinese women’s volleyball team has defeated South Korea, vanquished Cameroon, edged out Russia, knocked out Japan, and beaten Brazil” (News: The Chinese Women’s Volleyball Team beat Brazil, Warming up before the Sino-U.S. Confrontation ). Another example with repeated terms and concepts was “Ball, the ball, is just a ball; the country is always behind you” (News: After Chinese Netizens Boycotted the NBA, the NBA China Game is Still Fully Seated, and Some People Even Let the Player Sign on the Chinese Flag ). In the responses in the first example, repetitive verb forms fostered an accelerating sense of excitement for Chinese readers, who may feel proud to be a member of that winning country. In the other example, the repeated term ball puts readers at the front of national and personal interests and may cause a provoking sense of quitting the game for the sake of national interests.

Ideological and critical thinking accounts

Van Dijk ( 1995 ) argued,

“[T]he social functions of ideologies are, among others, to allow members of a group to organize (admission to) their group, coordinate their social actions and goals, to protect their (privileged) resources, or, conversely, to gain access to such resources in the case of dissident or oppositional groups” (p. 19).

We argue that linguistic features as mentioned above did not directly form or express the ideologies of news commenters or interviewees; instead, they indirectly indicated or expressed the ideologies of these commenters and interviewees. This may result from the nature of news commentary, which is a way to represent commenters’ views or opinions and presents certain personal or social ideologies. Through the textual analysis, we found that the way the news is framed may arouse commenters’ acceptance or rejection of the content of news text, which indicates their sense of group relations and structures (van Dijk, 1995 ). For example, a strong sense of ingroup affiliation was revealed through most of the news commentary and interviewee responses. News commenters and interviewees had a strong sense of pride and praise for news related to the economic or political power of China. Exemplar sentences of pride and praise for China’s strength included, “The increase in the creativity of Chinese companies in recent years shows the great potential of China’s high-tech industry,” “Support domestic products!” and “The Chinese Women’s Volleyball Team won the 13th Women’s Volleyball World Cup with a record of 11 wins….” Van Dijk ( 1995 ) argued, “The contents and schematic organization of group ideologies in the social mind shared by its members are a function of the properties of the group within the societal structure” (p. 19). This is true even when social cognition may conflict with personal cognition. In this study, most interviewees had a strong sense of honor in their home country even when facing conflicts between personal interests and national interests.

While ideologies define and explain the similarities in the social practices of social members, they also leave room for individual variation and differences, which contributes to a “dynamic and dialectic” relationship between social ideology and personal cognition (van Dijk, 1995 , p. 19). Personal cognition or ideology thus becomes an embodiment of critical thinking (van Dijk, 2006 ). Van Dijk ( 2006 ) explained that the analysis of ideologies is actually a critical analysis because ideologies may be used as a foundation to study critical thinking. Studying whether certain ideologies and personal cognition diverge or converge may indicate how critical thinking works. In our study, we found the emergence of critical thinking in the form of multiple, diverse perspectives in news reviews, comments, or responses. For example, the news responders were able to interpret news based on the pros and cons or multiple perspectives; we connect that multiperspective analysis with their critical thinking ability. The analysis of critical thinking is above the ideological analysis in the news commentary; it helped the researchers evaluate whether the respondents’ or commenters’ patriotism was rational. For example, in the commentary “we should not pursue foreign products too much, but the advanced technology contained in the foreign products is something we can learn from,” instead of being blindly patriotic, the respondent may show a sense of rationalism in his/her response: stopping the purchase of foreign products is hardly equal to stopping the learning of advanced technology in designing or manufacturing these products. Another example is “Sports, like art, has no national boundaries, but one should stand firmly on the side of the nation as a Chinese when national political issues are involved in sports.”

Topics and news comments

We also found that news topics may inform linguistic features, ideological beliefs, and critical thinking accounts in the news comments in different ways. Wodak and Meyer ( 2015 ) explained that topics are an important semantic macrostructure to be addressed in SDA analyses.

Topics and languages

Generally, news topics varied in their power to generate lexical and syntactical structures. Some topics on politics, the economy, and technology led the commenters to be more rigorous in their wording and phrasing, and their commentary language was more professional and formal than it was for other topics from entertainment and sports. The following example is one response to the news on China’s development of 5G technology: “First, it shows the progress China has made in science and technology in recent years, and the relevant policies are effective… second, ….” The responder provided more details and even listed points for the reasoning. The commentary was not simply in a narrative or colloquial format but instead was organized in a logical way. The same type of commentary was revealed through the news on “The Giant Carrefour Lost to China….” Sample responses included the following: “With the development of the commodity retail industry, there is a need for consumers’ needs to be met in the first place. The consumer values quality, cost efficiency, and then brands. To keep consumers within long-term development, service is another vital part. Next….” The sampled interview response also indicated the interviewed responder’s analysis of the rationale for why Carrefour had lost its market shares in China.

On the other hand, we found that comments on entertainment topics were presented in a more informal way than other issues. For example, when some responders were interviewed about their responses to news related to stars or celebrities’ clothing or behavior, they directly expressed their belief that it was not their business or was a personal issue for the stars or celebrities. The closer the topic was to life, the simpler the language was in terms of wording and expressions.

Topics, ideologies, and critical thinking

In terms of how topics related to or informed ideological beliefs in news commentary, we found that the research samples presented significant patriotic tendencies in news comments on science and technology, sports, and international and domestic affairs. These topics included national infrastructure and economic development, national interests, and sports competitions with other countries, which might easily inspire the national self-esteem and national self-confidence of newsreaders and respondents. The responses to these news topics in the sample reflected strong support for the home country. Most of these responses were affirmative and positive, showing the commenters’ chauvinistic attitudes towards specific nationalist characteristics or stating factual evidence of China’s progress in a positive way. For example, responses to the news “China has the world’s first 5G standard necessary patents” were mostly positive and affirming, with the majority applauding and supporting the development of the technology in China. A few comments presented a critical, dialectical analysis on its advantages and disadvantages. A critical, dialectical analysis serves as a principal way to motivate and probe a thinker, with its goal to push the thinker go beyond the ideas and values, their significance, and their limitations. Dialectical thinking is a way of thinking that replaces or serves as a counterpart of logical thinking. Originally derived from the tenets of German philosopher Hegel (e.g., 1971 , 1975 ), dialectical thinking promotes tenets including being self-critical and taking nothing for granted. Dialectical thinking focuses on how reflectivity helps a thinker extend the dimensions of his/her repertoire of a certain concept or thing. Among ways of dialectical thinking is the Marxist dialectic which applies to the study of historical materialism and deeply influences Asian culture.

Marxist materialism is melded to the Hegelian dialectic (e.g., Marx, 1975 ). Marx opposes metaphysics, which he considered unscientific but instead asserted that reality was directly perceived by the observer without an intervening conceptual apparatus. He then used the dialectic, a metaphysical system which he thought to be empirically true. The Marxist dialectic considers theory and practice to be a single entity and that what men actually do demonstrates the truth. In the same vein, Dewey’s logic including learning by doing is also influenced by Hegel’s dialectical thinking, which highlights the experimental situation rather than from an externally validated formal system (Rytina and Loomis, 1970 ).

In the current study, we argued that Marxist dialectical analysis or thinking helps commenters or readers think about and interpret news from a multidimensional, unstable, and empirical way. We did find in a critical, dialectical way of thinking in a few news comments. Specifically, regarding the way topics related to or informed critical thinking in news commentary, we found that responses to news topics on entertainment and domestic topics diverged, which indicated different voices or perspectives on the news. Respondents tended to provide more critical thinking accounts on the news. The awareness of critical thinking is mainly reflected in the fact that the commenter can analyze the event from multiple aspects rather than interpreting the problem in isolation or can be aware that his or her point of view starts from only one perspective. For example, responses to the news on Wang Yuan smoking in public places and Rayza’s airport look diverged in the different opinions of the respondents. Some believed stars or celebrities should have their own privacy and identity, whereas others believed they should set good examples for the public and avoid traditionally defined misbehaviors. Another example was found in the news comments that stated that how much a person earns could lead to financial independence or help people be self-sufficient. The following is a sampled response:

“Simply talking about financial freedom is not rational, as it is hard to define what is it. Financial freedom may come from one’s inner satisfaction. For example, successful businessmen have tons of money, but there are also many things for them to consider, including social responsibility and company operation. Money, for them, cannot be spent at will….”

We detected rational analysis from the responder, who was able to analyze the news from multiple perspectives in a logical and rational way. Examples in the responder’s commentary made sense, suggesting that one’s self-sufficiency cannot be measured simply by how much he/she earns or possesses.

Linguistic features, discursive practice, and social practice

Drawing upon systemic functional grammar (Halliday, 1978 ), Fairclough acknowledged that language is, to some extent, a social practice. The reason why the form of language is mainly determined by its social function is revealed in the perspective of the social communication function of discourse. Discourse is not only seen as a form of language but is also embodied as a social practice. CDA essentially studies society from a linguistic perspective and links linguistic analysis with social commentary.

News comments in the study indicate the respondents’ attitudes, which may render any discursive practice in the form of speech acts (Fairclough, 1989 , 1995 ). For example, some commenters held subjective views against smoking in public places, dissatisfaction with cyber violence specific to women’s clothing, and positive support and encouragement of the Chinese Women’s Volleyball Team and the Chinese Men’s Basketball Team. The social participation of the respondents was revealed through the text, which represents discursive and social practice. The commenters whose comments reflected multifaceted and multilayered thinking or ideology had a high degree of social participation, and those whose comments had explicit attitudes towards real life had a high degree of social participation. In addition to ideology, the responses served a social function (van Dijk, 1995 ). For instance, “smoking in public is not appropriate” was a manifestation of social care that was generally accepted by the public, while “living in other people’s eyes” was a manifestation of guiding citizens to have their own judgments and values and to advocate for ideological improvement. The comments on 5G and Apple showed that people paid close attention to the development of science and technology in the country and the need for high-tech ways to improve life. Support and encouragement for the Chinese women’s volleyball team and the men’s basketball team played a social role in increasing patriotism.

The younger generation’s ideology in China

One of the hidden themes in the study is the young generation’s language or new literacy, with sample features such as slang or buzzwords they use in daily life. For example, “ liang liang (failure),” “ sha diao (idot),” “ zhong cao (attractive),” “ di biao zui qiang (the most powerful one),” and “ shen xian da jia (competition among the elites)” were frequently cited in their comments; some of these terms are from movies or social media, while some are terms coined in their peer communication. These terms represent their generation and show their uniqueness and differences from their parents’ generations. Behind these terms stand their personal beliefs and ideologies.

In addition, by analyzing the critical thinking ability of college students’ news reviews, the researchers found that college students were prone to express their views and value all civil rights and national sovereignty in their news commentary. Students’ comments were relatively independent, rational, and critical. Fairclough ( 1995 ) argued that the undiscovered information of power, ideology, and language in news reports could be investigated and explained through institutional context and societal context. Because the Chinese ideology is deeply rooted in culture, the power of patriotism or populism was reflected in the college students’ comments:

“It is not about the freedom of the speech. It is about the justice and fairness of one’s comments. The higher a person’s status is, the more responsible he/she should be for his/her words. It may not be a good thing to comment on one’s backyard if one has never lived there (i.e. in China or Hong Kong), right?” (selected comment to the NBA Game news).

“I think the arena being fully seated is a matter of personal choice which cannot be attributed to …, while it is a bit inappropriate to ask the player to sign on the flag of China, as that represents the national identity” (selected comment to the NBA Game news).

From news interviews, the researchers also found that college students’ comments on news generally presented an awareness of social justice, which may represent the younger generation’s attitudes, beliefs, and values in either personal or social cognition (van Dijk, 1995 ). They emphasized objectivity and fairness over subjectivity to no small extent. For example, regarding the news of whether the NBA game tickets were refundable, the students’ comments respected the individual’s right to make decisions. Nevertheless, they also explained that it was inappropriate to sign on the flag of China. Students’ comments on the news Rayza’s airport look were even more concerned with social justice. Moreover, they analyzed the issue from an objective perspective instead of an individual perspective and extended it to the social level, which further showed that current college students are more inclined to social justice.

Critical thinking informing ideological and linguistic choices

One of the most important findings of this study is the complex relationships among critical thinking, ideological beliefs, and linguistic features. We present these complex relationships as shown in Fig. 1 .

*p: personal ideologies; s: social ideologies.

By mapping out different comments, we find that critical thinking works as an analytical and filtering tool to guide commenters to select their ideological beliefs, either personal or social. These personal and social ideological beliefs may diverge or converge. The divergence or convergence of personal and social ideological beliefs may indicate the strength of critical thinking, which, however, may not equal the quality of critical thinking. To be more specific, critical thinking may help commenters present a different perspective from the commonly accepted social perspective, which shows efforts in analyzing a news article and offering their opinions. However, the opinions that differ from widely accepted views may not be weighed as right or wrong or un/acceptable; they may just be different voices.

We argue that these personal and social opinions are representations of ideological beliefs and are fully presented through news comments; news comments are ideology-based. Critical thinking helps commenters choose their personal and social ideologies and then helps them choose linguistic forms they believe fit their news comments. While critical thinking plays a crucial role in choosing specific ideological beliefs and linguistic forms, news topics vary in informing commenters’ critical thinking ability. In the study, we found that some topics may inform divergence between personal and social ideological beliefs, whereas other topics may inform the convergence of the two constructs. We also propose that the way a specific piece of news is framed informs the linguistic form of the news comments, which may arouse a certain sense in the commenters (e.g., a sense of belonging as in/out-group members). Reading these news pieces may stimulate commenters’ critical thinking and then work on the linguistic forms in news comments.

The present study provided an overall account of how linguistic features, ideological beliefs, and critical thinking accounts are revealed through news comments. News comments in China present value propositions and ways of thinking through complex lexical and syntactical structures. The respondents presented power, ideology, inequality, and social justice through their responses to the news, which informed news commentary as a way to serve the social function of the language. The responses also presented the younger generation’s personal ideology through the news comments. However, topics were important in informing these constructs and caused divergences among different comments. One of the critiques that this study, and the CDA studies in general, may receive is the simplistic or even vague description of the methodology (Wodak, 2006 ) because there is currently “no accepted canon of data collection” (Wodak and Meyer, 2015 ). Instead, we tried to provide careful systemic analysis and separated description and interpretation (Wodak and Meyer, 2015 ). For future studies, we believe that further analysis of how critical thinking may work with personal and social ideologies is necessary. Additionally, it is worthwhile to study the effects of other cognitive attributes on language and ideologies to extend the SCA domain.

Data availability

The data analyzed and generated are included in the paper.

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Acknowledgements

The paper is funded through Graduate Program Research Fund (# YJG2020403) at Dalian Maritime University. In addition, it is also partially funded through DMU Xinhai Scholar Research Fund (#02500805). Our sincere thanks go to our undergraduate and graduate students who were keen on helping us with data collection and analysis.

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YG made substantial contributions to the conception, design, and implementation of the work; He also drafted, revised, and finalized the work during the whole process. GZ was involved in the drafting and proofreading process of the work and also accountable for all the aspects of the work ensuring its accuracy and integrity.

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Gao, Y., Zeng, G. Exploring linguistic features, ideologies, and critical thinking in Chinese news comments. Humanit Soc Sci Commun 8 , 39 (2021). https://doi.org/10.1057/s41599-021-00715-y

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Critical thinking definition

Critical thinking, as described by Oxford Languages, is the objective analysis and evaluation of an issue in order to form a judgement.

Active and skillful approach, evaluation, assessment, synthesis, and/or evaluation of information obtained from, or made by, observation, knowledge, reflection, acumen or conversation, as a guide to belief and action, requires the critical thinking process, which is why it's often used in education and academics.

Some even may view it as a backbone of modern thought.

However, it's a skill, and skills must be trained and encouraged to be used at its full potential.

People turn up to various approaches in improving their critical thinking, like:

• Developing technical and problem-solving skills
• Engaging in more active listening
• Actively questioning their assumptions and beliefs
• Seeking out more diversity of thought
• Opening up their curiosity in an intellectual way etc.

Is critical thinking useful in writing?

Critical thinking can help in planning your paper and making it more concise, but it's not obvious at first. We carefully pinpointed some the questions you should ask yourself when boosting critical thinking in writing:

• What information should be included?
• Which information resources should the author look to?
• What degree of technical knowledge should the report assume its audience has?
• What is the most effective way to show information?
• How should the report be organized?
• How should it be designed?
• What tone and level of language difficulty should the document have?

Usage of critical thinking comes down not only to the outline of your paper, it also begs the question: How can we use critical thinking solving problems in our writing's topic?

Let's say, you have a Powerpoint on how critical thinking can reduce poverty in the United States. You'll primarily have to define critical thinking for the viewers, as well as use a lot of critical thinking questions and synonyms to get them to be familiar with your methods and start the thinking process behind it.

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Lexical Definitions Show How a Word Is Used

Explaining How a Word is Used In General Contexts

• Belief Systems
• Key Figures in Atheism
• M.A., Princeton University
• B.A., University of Pennsylvania

Most of the time when encountering a definition , you are looking at a lexical definition. A lexical definition (sometimes also called a reportive definition) is any definition which explains how a word is actually used. It is thus distinct from stipulative definitions which simply propose a possible way to use a word and which may or may not be accepted. Therefore, lexical definitions are capable of being true or false, of being accurate or inaccurate.

If there are choices between different types of definitions, the lexical definition is commonly thought of as the real definition. Because it describes how words are genuinely used, there is some basis for this judgment. Lexical definitions have a serious drawback, however, because they are often vague or ambiguous. This is not surprising because they reflect the real-world usage of words, and that is rife with vagueness and ambiguity.

Vagueness and Ambiguity in Lexical Definitions

Although vagueness and ambiguity are often used interchangeably, the two terms are nonetheless distinct. A word is vague when there are borderline cases which might or might not fit in the definition and it isn't easy to tell how to classify them. The word fresh is vague because it isn't clear at what point a sample of, say, fruit will qualify as fresh and at what point it stops being fresh.

Ambiguity occurs when there are a number of completely distinct ways in which the term can be used. Words that can be ambiguous include right and light. The right may be an adjective, adverb, noun, verb, or simple exclamation. As an adjective alone it may mean being correct, objectively and factually true, morally good, justifiable, virtuous, ethical, proper, honest, or socially acceptable. Those are many gradations when it comes to ethics and religion. You may need to seek further clarification of what the author or speaker means when using the term right.

The term light can be both vague and ambiguous. It is ambiguous because it might be "radiant energy" or "of little weight." If the latter, it is vague because it is unclear at what point something starts being light and stops being heavy. A good lexical definition will seek to reduce ambiguity by highlighting only the sense that is truly relevant.

Examples of Lexical Definitions

Here are two examples of lexical definitions of the word atheist:

1. atheist: one who disbelieves in or denies the existence of God or gods. 2. atheist: one who knows that God exists, but is in denial for some reason.

The first is a correct definition in the lexical sense because it accurately describes how the term atheist is used in a wide variety of contexts.

The second, however, is an incorrect definition in the lexical sense. You won't find it in any dictionaries or in widespread use, but it is a definition used in narrow circles of evangelical Christians. Rather than a lexical definition, this more properly an example of a persuasive definition.

• Religion vs. Religious
• What Does it Mean to Say "I Believe" Something Is True?
• Beliefs and Choices: Do You Choose Your Religion?
• Defining the Characteristics of Religion
• Logic: What is a Non-Argument?
• Fallacy of Amphiboly
• What Is the Difference Between Denotation and Connotation?
• Is Astrology a Pseudoscience?
• What Is the Fallacy of Accent?
• The Criteria for Science and Scientific Theories
• Theoretical Definitions
• Atheism and Skepticism in Ancient Greece
• What Is Open Mindedness in Critical Thinking?
• Albert Einstein on Science, God, and Religion
• Should You Reveal Your Atheism to Family?
• Types of Truths