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Summarium

45 (65) – 2016

ROBERT KUBLIKOWSKI

DEFINITIONS AND THE GROWTH OF KNOWLEDGE:

THE MAIN IDEAS*

Are definitions useful in an empirical knowledge-gaining process? What

roles do definitions play in the process of the growth of empirical knowl-

edge? Two attitudes towards definitions can be distinguished in the history of

the theory of definitions. According to the first and positive one, definitions

have been useful in science. The second attitude has been a critical one.

I try to defend the view about the usefulness of definitions, on the one

hand, by application of Hilary Putnam’s theory of reference of natural kind

terms. On the other hand, Karl Popper’s fallibilism is implemented to the

theory of definitions, especially to the theory of real definitions.

The structure of this text is as follows: (I) the origin and the development

of the theory of definitions, (II) Popperian antidefinitionism, (III) the theory

of definitions and the Putnamian theory of meaning and (IV) the theory of

stipulative, lexical and persuasive definitions.

I. THE ORIGIN AND THE DEVELOPMENT

OF THE THEORY OF DEFINITIONS

The known reflection on definitions began with Aristotle.

He distin-

guished two types of definitions — of a thing and of a name. The definition

of a thing was acknowledged as the most important one. It was called the

real definition by genus and differentia (the genus-differentia definition). Its

ROBERT KUBLIKOWSKI, PhD — Assistant Professor, The Department of Methodology of

Science, Faculty of Philosophy, The John Paul II Catholic University of Lublin; associate mem-

ber of the Faculty of Philosophy of TN KUL; address: Al. Racławickie 14, 20–950 Lublin,

Poland, e-mail: robe[email protected]

* The text is a changed version of the English summary of the book K

UBLIKOWSKI 2013.

The ancient, medieval and modern history of the theory of definitions see: KAMIŃSKI 1955-

57; 1958a; 1958b; 1992; 1994; 1997. See also BOCHEŃSKI 1961.

ROBERT KUBLIKOWSKI

goal is to fix the class of objects — so called the species-class — in other

words, the extension of the term which is being defined (definiendum). The

definition is built by characterising a large class of objects (the genus-class),

which consists of the extension of definiendum (the species-class) and some

other species-classes. In order to obtain such a definition one needs to dis-

tinguish definiendum and some other species-classes by giving the specific

feature, characterising exclusively the objects belonging to definiendum. The

classical example is: Man is a rational animal, where “man” is the name of

the species-class, “animal” is the name of the genus-class and rationality is

the differentia, that is the important feature which characterises only objects

of the species-class.

Such a definition was believed to fix the essential qualities of a class of

things (Socrates, Plato, Aristotle). Such a standpoint is called the methodo-

logical essentialism. According to Aristotle, the essential definition can be

obtained by the method of induction (epagoge) and intellectual intuition.

The Aristotelian opinion on the role of a real definition in his concept of

scientific knowledge can be interpreted in either a radical or a moderate way.

The Aristotelian theory of science, strictly speaking, his theory of a scien-

tific knowledge (epistemology) is maximalist. In other words, the goal of the

cognitive process is to gain knowledge (epistéme) understood — in a maxi-

malist, absolutist way — as true and absolutely certain beliefs. Such knowl-

edge was believed to be fixed once and for all. So, if the scientific beliefs

are justified by true and completely certain premises, placed in a formally

correct syllogism, then beliefs — obtained in this way — also belong to

knowledge (epistéme), so they are absolutely certain (infallible). According

to Aristotle, real definitions by genus and differentia are premises in such

syllogisms.

The Aristotelian epistemology can also be interpreted in a moderate way.

According to this interpretation, Aristotle divided knowledge into

doxa and

epistéme which can be understood, on the one hand, as really obtainable sci-

entific knowledge and on the other hand, as idealised scientific knowledge.

Perhaps Aristotle believed that such idealised knowledge is not really possi-

ble to get, but it is only the theoretical ideal which directs our cognitive

process.

Apart from a real definition, Aristotle knew also a nominal definition. Its

goal is to clarify the meaning of a word (see also Euclid).

KWIATKOWSKI 1969. See also CHARLES 2005.

DEFINITIONS AND THE GROWTH OF KNOWLEDGE: THE MAIN IDEAS

Ancient thinkers, especially the medieval ones, were more and more con-

scious that real and nominal definitions were linguistic-cognitive formulas.

(But their subjects and goals are different: real definitions characterise

classes of objects and nominal definitions characterise the meanings of

words.)

Medieval logicians and philosophers generally accepted the Aristotelian

view of definitions, but their interest in a nominal definition was gradually

increasing. The theory of definition was developed by the explication that

a real definition has two forms: a real essential definition by genus and

differentia (in the Aristotelian sense) and a real descriptive definition (men-

tioned earlier by Cicero), which was to fix the non-essential, but charac-

teristic features of a kind of things.

In modern times some philosophers like Thomas Hobbes and others were

critical towards the Aristotelian concept of a real essential definition. Yet,

Hobbes’ criticism was radical in theory and moderate in practice. Namely,

he accepted nominal definitions understood as abbreviations, but their form

was identical with the form of real definitions. Hobbes enriched the theory

of definitions by the notion of a stipulative definition, which introduces

a new word into a language; a precising definition, which clarifies a vague

meaning of a word and a lexical definition (a dictionary definition), which

delivers the actual meaning of a word.

Blaise Pascal also preferred a nominal definition to a real definition. For

a nominal definition was applied in geometry, which was the ideal for the

whole science. Antoine Arnauld and Pierre Nicole accepted the traditional,

classical theory of definition. John Locke was not sure whether the cognition

of essential features of things was possible and consequently, whether real

essential definitions were obtainable. Gottfried Leibniz, Immanuel Kant, Jo-

seph D. Gergonne and John S. Mill began to characterise a real definition

not as true, certain and full, but as fallible, partial and developing.

II. POPPERIAN ANTIDEFINITIONISM

Karl R. Popper

was an anti-essentialist and anti-definitionalist. That is

why he criticised the cognitive role of Aristotelian real essential definitions

and their usefulness in empirical sciences. Aristotle believed that the intel-

lectual intuition justified the adequacy of such definitions. Popper called

POPPER 1979; 1994; 2002a; 2002b; 2002c; 2003a; 2003b.

ROBERT KUBLIKOWSKI

them essentialist definitions. He claimed that intuition was useful only in the

process of obtaining and testing fallible hypotheses. So he acknowledged

only a heuristic role of definitions. It seems that there is no possibility to

justify the claim that things have essential features. That is why he rather ig-

nored the issue of the existence of the essential features and the usefulness

of essential definitions in the procedures of scientific explanation. This point

of view is called the Popperian methodological anti-essentialism or the

modified essentialism.

Nevertheless Popper claimed, that a real definition — but not an essential

one — played a useful role as an abbreviation. Such a definition allows to

use a short name (definiendum) instead of a long description (definiens) of

an example representing a group of empirical objects.

This type of a real definition has an identical form as a nominal defini-

tion. They differ in their roles. Namely, the role of a real definition is to de-

liver the verbal characteristics of objects and not only the verbal character-

istics of the meaning of words as in the case of a nominal definition. But in

fact the characteristics of objects and of the meaning of words are intercon-

nected.

III. THE THEORY OF DEFINITIONS

AND THE PUTNAMIAN THEORY OF MEANING

It is useful to apply Hilary Putnam’s

theory of reference to the theory of

definition, especially to the theory of a real definition. Namely, the role of

its definiendum is to designate of something or someone. In other words, de-

finiendum is used as an expression which has a relatively stable reference.

The Putnamian theory, which is applied here, aims at explaining how it is

possible to give meaning to terms, including the scientific ones. This process

runs as follows: the first step is that, on the basis of observation, people in-

troduce terms to their languages, including natural kind terms. Such terms

designate the observed empirical objects, which belong to natural classes

(i.e. to classes in nature, in the world). Such a procedure of designating

(a naming ceremony) is done in an introducing event.

Ostensive definitions and descriptions (descriptive definitions) are useful

methods in this procedure. The first use of a natural kind term — by pointing

out an object — fixes a causal-historical chain, which connects the usage of

PUTNAM 1975; 1979; 1981; 1983; 1987; 1988; 1990; 1994.

DEFINITIONS AND THE GROWTH OF KNOWLEDGE: THE MAIN IDEAS

the term in the introducing event and all other future uses of that term. That

is why according to the presented theory, a natural kind term has a relatively

stable reference. The meaning of a term is fixed not only by a causal-histori-

cal chain of usage of the term, which refers to its object, in fact, to the class

of objects. The component of its meaning is also the intention of users of

this term (of the first user and of the subsequent ones). Their intention is to

talk about the same objects, for example, the samples of a lemon, which be-

long to the extension of the same natural kind term “lemon.”

Empirically obtained descriptions and the theoretical definitions fixed on

their basis are only approximately correct (adequate) and definite (complete)

descriptions: some of them are not correct at all, some are less or more cor-

rect. Average users of a language can compare their descriptions of objects

(descriptive definitions) with the official, standard descriptions (stereotypes)

delivered by experts. That is why the meaning of natural kind terms like

“gold,” “water,” “acid,” “lemon,” “tiger” etc. is fixed within a community in

which there is the division of linguistic and cognitive work (roles). There are

some other components of the meaning of such terms: a syntactic marker

(mass noun, concrete etc.), a semantic marker (natural kind) and an exten-

sion. If these additional components are taken into account then the causal-

historical theory of reference becomes the causal-historical-sociolinguistic

theory of reference.

The application of the Putnamian theory of reference of natural kind

terms explicates the problems of the traditional theory of definition, espe-

cially the theory of a real definition. First of all, the traditional theory does

not explain how definiendum and definiens, which contains the description

of a class of objects, refer to these objects. But the Putnamian theory helps

to solve this problem. Secondly, a real definition is also problematic because

the general name, which is introduced in an ostensive way, for example, the

natural kind term “lemon” — may be connected with a sample which is not

representative for the defined class of objects. Such a case occurs if an un-

usual, nonstandard sample is taken into consideration. In this situation a de-

finition would not refer to standard, normal lemons, but to abnormal ones.

The Putnamian theory of reference is connected with his essentialism: the

essence of a class of things is a feature which is important and useful in sci-

ence. It is the important feature because all the other features depend on it.

Discovering of essential features is useful in the procedure of explaining

things (how they react or behave etc.). But Putnam distinguished the relative

essence of a class of things, the essence which partially depends on the im-

plicit structure of things (the contribution of the environment), and partially

ROBERT KUBLIKOWSKI

on the human, cognitive points of view, needs and interests. It can be noticed

that it is not the Aristotelian type of essentialism.

The application of the Putnamian theory of reference of natural kind

terms to the theory of definition helps to notice the specifics of the Aristote-

lian theory of a real essential definition. The Aristotelian name of the spe-

cies-class (definiendum) is not the same as the Putnamian natural kind term.

Putnam did not write explicite about the nesting of the species-classes in the

nearest genus-classes or about the hierarchy of all objects divided into spe-

cies-classes belonging to the nearest genus-classes. He just mentioned the

names of biological species as examples of natural kind terms. But he under-

stood a “natural kind term” in a broad sense, as more general than a “name

of a biological species.” Namely, the natural kind terms are also names of

chemical elements or acids etc.

Putnam, like Popper, questioned that the intellectual intuition played the

role of justification in the cognition of the empirical objects which are des-

ignated by natural kind terms. But Putnam gave a different argument sup-

porting the claim about the existence of essential features and natural kinds.

Namely, there are some descriptions (stereotypes) of natural kinds in our

languages. Such descriptions (descriptive definitions) are the obligatory

ways of conceptualisation in a linguistic community. If all descriptions or

the majority of them were not adequate, then the communication would not

occur. But in fact, a relatively successful and fluent communication occurs.

So — on the basis of modus tollendo tollens — at least some of such descrip-

tions (descriptive definitions) are adequate.

There is another argument for the existence of natural kinds. The growth

of science is an unquestionable fact described in the history of science. One

of the causes of this growth is the acceptance of the assumption about the

existence of natural kinds. Such assumption is useful in the procedure of

relatively correct scientific explanation of past facts and also in forecasting

the future (Putnam, Richard Boyd,

Hilary Kornblith

A difference can be noticed between the traditional theory of definition

and the contemporary one.

On the basis of the texts of such contemporary

philosophers as Popper, Putnam or Anil Gupta

it is possible to form a claim

BOYD 1991; 2000.

KORNBLITH 1993.

ROBINSON 1950; GORSKY 1981. See also WEINGARTNER 1989; 1991; FETZER, SHATZ,

CHLESINGER 1991; DAVID 1993; WIGGINS 2007.

GUPTA, BELNAP 1993; GUPTA 2006; 2011. See https://plato.stanford.edu/entries/definitions.

See also CHAPUIS, GUPTA 2000; KUBLIKOWSKI 2005; 2009; 2016.

DEFINITIONS AND THE GROWTH OF KNOWLEDGE: THE MAIN IDEAS

that definitions play useful, linguistic and cognitive roles, but they are not

real essential infallible (certain) definitions, fixed once and for all. They are

fallible definitions which are subject to revision and change in the context of

further growth of empirical sciences.

The proposed theory of definition is dependent on the twentieth century

fallibilistic philosophy of science (epistemology). The change of the account

concerning science has caused the change of the theory of scientific method

and knowledge. That is why the theory of a definition has also been

changed. According to epistemological fallibilism, beliefs and scientific

theories may be revised, changed, modified, or even falsified (refuted). That

is why definitions, including real definitions — used in scientific, empirical

theories — may also be subject to revision and change. An example of such

a process is the revision of the definition of a chemical element

or of an

acid,

described in the history of chemistry. Revisions are caused by the fact

that not all information about objects and their features—including the fea-

tures acknowledged as essential ones—is available in a specific period of the

growth of science. That is why new data correct scientific definitions. Defi-

nitions are accepted as adequate (true) and useful in the context of the actual

state of empirical knowledge. The acceptance of this or that definition is made

from the fallibilistic point of view: the previous definitions were formed and

accepted because of the previous knowledge. They were subject to revision in

the context of a new knowledge. Fallibilism suggests being critical and careful

towards the present and future scientific, empirical theories and definitions as

they may also be revised and changed. That is why they should not be

acknowledged as definite, absolutely certain and unchangeable ones.

In the traditional theory of definition objects like gold, water, lemon, tiger

are defined by fixing in a definiens a description expressing the features of the

objects. So a definition, for example, of a lemon would be like this: A lemon

is a fruit with a yellow colour, a thick peel, a sharp taste, a specific DNA

(from a biological point of view) etc. But Putnam questioned such a descrip-

tion because it was not complete. That is why such a definition cannot be

acknowledged as a full definition. It is not fixed once and for all. The de-

finiens of such a definition characterises only partially its definiendum. The

solution of this difficulty is to see this formula as a partial definition

under-

See e.g. https://www.britannica.com/science/chemical-element.

See e.g. https://www.britannica.com/science/acid.

In the case of a partial definition understood in a broad sense its definiens characterises its

definiendum only in a partial way. Such a definiens does not describe all, but only some objects

belonging to the definiendum.

ROBERT KUBLIKOWSKI

stood in a broad sense. It is adapted to an actual, but changeable state of em-

pirical research.

According to the proposed concept, the scientific, theoretical definitions

are not full (complete), but partial in a broad sense. It is caused by the fact

that the discovery of the features of empirical objects is a difficult, perhaps

unending process. It is not possible to obtain an adequate and complete

knowledge about empirical reality. In other words, it is not possible to get to

know all features of the objects of a class. Theories, including definitions,

are tested in the context of new research and if it is needed, they are changed

— completed, corrected or refused.

IV. THE THEORY OF STIPULATIVE, LEXICAL

AND PERSUASIVE DEFINITIONS

The role of a real stipulative definition

is to introduce an expression

(definiendum) into a language. If such a definiendum is a general term,

strictly speaking a natural kind term, then it has a reference. Such a defini-

endum is also a notational abbreviation. It is handy, useful and arbitrary in

the aspect of its graphical form (shape). The definiendum is handy because it

is shorter than the definiens containing a partial, actual scientific description

of a class of objects. (This standpoint was called by Popper as defining

“from the right to the left”). The definition understood in this way is cogni-

tively useful because it is the element of a theory which plays an explanatory

role in science. The form of such a definiendum is arbitrary. Namely, it is up

to someone to use a particular graphical form as a definiendum. For example,

instead of the English term “lemon” to designate objects traditionally called

in English “lemons,” a different graphical form could be used, let us say,

“ABC.” But the definition of a natural kind term “lemon,” in other words,

the description of lemons, is not arbitrary. It is based on experience, on a re-

liable and actual biological knowledge concerning the class of objects tradi-

tionally called “lemons.”

If a real stipulative definition is introduced into a language, then it be-

comes a lexical (dictionary) definition. Its role is to characterise an actual

meaning of a word fixed on the basis of actual empirical research (Popper

called it defining “from the left to the right”). But it is important to remem-

ber that such a real lexical definition — belonging to a scientific empirical

AJDUKIEWICZ 1958; 1960; 1974; 1984; 1985a; 1985b. See also MATTHEWS 1998.

DEFINITIONS AND THE GROWTH OF KNOWLEDGE: THE MAIN IDEAS

theory — is fallible, so it may be revised and changed in the context of fur-

ther empirical research and discoveries.

Natural kind terms are only syntactical, but not semantical abbreviations

for the most reliable scientific descriptions. In other words, such definitions

are not analytic sentences — in which there is the meaning equivalence be-

tween definiendum and definiens. The introduced natural kind terms (defini-

endum) are not synonyms of scientific descriptions (definiens). Such de-

scriptions are only approximately adequate. They are fallible and partial.

That is why the full extensions of natural kind terms are not known. Their

meanings (extensions) are modified in the course of successive empirical re-

search.

The fact of revisions and changes — modifications or refutations — of real

definitions may raise an objection that such definitions are just nominal per-

suasive definitions which depend on an actual social context: actual cogni-

tive needs or practical interests (Edward Schiappa

). But it is important to

emphasise that such definitions are formed on the basis of the most reliable

and actual empirical knowledge (see Douglas Walton

). Revisions of defini-

tions are caused by the factor that human methods and knowledge are falli-

ble according to the fallibilistic philosophy of science.

CONCLUSIONS

To sum up, the main historical and systematic accounts of definitions

have been presented, analysed and explicated. A new view of definitions has

been also proposed.

In the outline of the history of the theory of definitions I have put in order

the standpoints of the philosophers who have accepted the use of definitions

and those who have been critical towards definitions.

The Putnamian philosophical semantics of reference has been applied to

the theory of definition and in this way I have emphasised the relationship

between the theories of meaning (reference) and definition.

I have also explicated and stressed the connection between the theory of

definition and the epistemological distinction: infallible and certain beliefs

(epistéme) versus fallible, uncertain and probable beliefs (doxa). In the main

claim — a leitmotiv of this text — I have argued that definitions have played

SCHIAPPA 2003.

WALTON 2001; 2005; 2008; WALTON, MACAGNO 2008; MACAGNO, WALTON 2008a; 2008b.

ROBERT KUBLIKOWSKI

useful linguistic and cognitive roles. Nevertheless, such definitions are not

real essential infallible and completely certain definitions, fixed once and for

all, but they are fallible. They are subject to revision and change in the

course of the growth of empirical science which is described in the history

of science.

Casimir Ajdukiewicz claimed that the extensions of the expressions “real

definition” and “nominal definition” overlapped. The explication of the

claim showed that it is impossible to put these definitions in order by means

of classification. In this context some relationships between different kinds

and types of definitions can be distinguished. Namely, real or nominal defi-

nition can be full or partial and they can also be stipulative, lexical or per-

suasive.

I have worked out the concept of a real stipulative non-arbitrary defini-

tion. Its role is to introduce into a language a new expression which has its

reference. The result of such a definition is a synthetic sentence. On the

other hand, a nominal stipulative arbitrary definition — a meaning postulate

— delivers an analytic sentence into a language.

A stipulative definition — after its introduction into a language — be-

comes a lexical (dictionary) definition, which can be a synthetic sentence (a real

lexical definition) or an analytic sentence (a nominal lexical definition).

I have also explicated the distinction: a manipulative definition versus

a non-manipulative persuasive definition.

The proposed view is the attempt of a contemporary, new look at the tra-

ditional theory of definition and it can be helpful for linguists, psychologists,

sociologists or philosophers of language and science and also for those who

are interested in semiotics, methodology and epistemology.

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NETOGRAPHY

Acid. Available online: https://www.britannica.com/science/acid (Accessed on 25 February 2017).

Chemical element. Available online: https://www.britannica.com/science/chemical-element (Ac-

cessed on 25 February 2017).

Definitions. Available online: https://plato.stanford.edu/entries/definitions (Accessed on 25 Febru-

ary 2017).