The Classical Theory of Concepts

The classical theory of concepts is one of the five primary theories
of concepts, the other four being prototype or exemplar theories,
atomistic theories, theory-theories, and neoclassical theories. The
classical theory implies that every complex concept has a classical
analysis, where a classical analysis of a concept is a proposition
giving metaphysically necessary and jointly sufficient conditions for
being in the extension across possible worlds for that concept. That
is, a classical analysis for a complex concept C gives a set of
individually necessary conditions for being a C (or conditions that
must be satisfied in order to be a C) that together are sufficient for
being a C (or are such that something's satisfying every member of
that set of necessary conditions entails its being a C). The classical
view also goes by the name of "the definitional view of concepts," or
"definitionism," where a definition of a concept is given in terms of
necessary and jointly sufficient conditions.

This article provides information on the classical theory of concepts
as present in the historical tradition, on concepts construed most
generally, on the nature of classical conceptual analysis, and on the
most significant of the objections raised against the classical view.

1. Historical Background and Advantages of the Classical View

The classical view can be traced back to at least the time of
Socrates, for in many of Plato's dialogues Socrates is clearly seeking
a classical analysis of some notion or other. In the Euthyphro, for
instance, Socrates seeks to know the nature of piety: Yet what he
seeks is not given in terms of, for example, a list of pious people or
actions, nor is piety to be identified with what the gods love.
Instead, Socrates seeks an account of piety in terms of some
specification of what is shared by all things pious, or what makes
pious things pious—that is, he seeks a specification of the essence of
piety itself. The Socratic elenchus is a method of finding out the
nature or essence of various kinds of things, such as friendship
(discussed in the Lysis), courage (the Laches), knowledge (the
Theatetus), and justice (the Republic). That method of considering
candidate definitions and seeking counterexamples to them is the same
method one uses to test candidate analyses by seeking possible
counterexamples to them, and thus Socrates is in effect committed to
something very much like the classical view of concepts.

One sees the same sort of commitment throughout much of the Western
tradition in philosophy from the ancient Greeks through the present.
Clear examples include Aristotle's notion of a definition as "an
account [or logos] that signifies the essence" (Topics I) by way of a
specification of essential attributes, as well as his account of
definitions for natural kinds in terms of genus and difference.
Particular examples of classical-style analyses abound after
Aristotle: For instance, Descartes (in Meditation VI) defines body as
that which is extended in both space and time, and mind as that which
thinks. Locke (in the Essay Concerning Human Understanding, Ch. 21)
defines being free with respect to doing an action A as
choosing/willing to do A where one's choice is part of the cause of
one's actually doing A. Hume defines a miracle (in Enquiry Concerning
Human Understanding, §X) as an event that is both a violation of the
laws of nature and caused by God. And so on. The classical view looks
to be a presumption of the early analytic philosophers as well (with
Wittgenstein being a notable exception). The classical view is present
in the writings of Frege and Russell, and the view receives its most
explicit treatment by that time in G.E. Moore's Lectures on Philosophy
and other writings. Moore gives a classical analysis of the very
notion of a classical analysis, and from then on the classical view
(or some qualified version of it) has been one of the pillars of
analytic philosophy itself.

One reason the classical view has had such staying power is that it
provides the most obvious grounding for the sort of inquiry within
philosophy that Socrates began. If one presumes that there are answers
to What is F?-type questions, where such questions ask for the nature
of knowledge, mind, goodness, etc., then that entails that there is
such a thing as the nature of knowledge, mind, goodness, etc. The
nature of knowledge, for example, is that which is shared by all cases
of knowledge, and a classical analysis of the concept of knowledge
specifies the nature of knowledge itself. So the classical view fits
neatly with the reasonable presumption that there are legitimate
answers to philosophical questions concerning the natures or essences
of things. As at least some other views of concepts reject the notion
that concepts have metaphysically necessary conditions, accepting such
other views is tantamount to rejecting (or at least significantly
revising) the legitimacy of an important part of the philosophical
enterprise.

The classical view also serves as the ground for one of the most basic
tools of philosophy—the critical evaluation of arguments. For
instance, one ground of contention in the abortion debate concerns
whether fetuses have the status of moral persons or not. If they do,
then since moral persons have the right not to be killed, generally
speaking, then it would seem to follow that abortion is immoral. The
classical view grounds the natural way to address the main contention
here, for part of the task at hand is to find a proper analysis of the
concept of being a moral person. If that analysis specifies features
such that not all of them are had by fetuses, then fetuses are not
moral persons, and the argument against the moral permissibility of
abortion fails. But without there being analyses of the sort
postulated by the classical view, it is far from clear how such
critical analysis of philosophical arguments is to proceed. So again,
the classical view seems to underpin an activity crucial to the
practice of philosophy itself.

In contemporary philosophy, J. J. Katz (1999), Frank Jackson (1994,
1998), and Christopher Peacocke (1992) are representative of those who
hold at least some qualified version of the classical view. There are
others as well, though many philosophers have rejected the view (at
least in part due to the criticisms to be discussed in section 4
below). The view is almost universally rejected in contemporary
psychology and cognitive science, due to both theoretical difficulties
with the classical view and the arrival of new theories of concepts
over the last quarter of the twentieth century.

2. Concepts in General

The issue of the nature of concepts is important in philosophy
generally, but most perspicuously in philosophy of language and
philosophy of mind. Most generally, concepts are thought to be among
those things that count as semantic values or meanings (along with
propositions). There is also reason to think that concepts are
universals (along with properties, relations, etc.), and what general
theory of universals applies to concepts is thus a significant issue
with respect to the nature of concepts. Whether concepts are
mind-dependent or mind-independent is another such issue. Finally,
concepts tend to be construed as the targets of analysis. If one then
treats analysis as classical analysis, and holds that all complex
concepts have classical analyses, then one accepts the classical view.
Other views of concepts might accept the thesis that concepts are
targets of analysis, but differ from the classical view over the sort
of analysis that all complex concepts have.

a. Concepts as Semantic Values

As semantic values, concepts are the intensions or meanings of
sub-sentential verbal expressions such as predicates, adjectives,
verbs, and adverbs. Just as the sentence "The sun is a star" expresses
the proposition that the sun is a star, the predicate "is a star"
expresses the concept of being a star (or [star], to introduce
notation to be used in what follows). Further, just as the English
sentence "Snow is white" expresses the proposition that snow is white,
and so does the German sentence "Schnee ist Weiss," the predicates "is
white" in English and "ist Weiss" in German both express the same
concept, the concept of being white (or [white]). The intension or
meaning of a sentence is a proposition. The intensions or meanings of
many sub-sentential entities are concepts.

b. Concepts as Universals

Concepts are also generally thought to be universals. The reasons for
this are threefold:

(1) A given concept is expressible using distinct verbal expressions.
This can occur in several different ways. My uttering "Snow is white"
and your uttering "Snow is white" are distinct utterances, and their
predicates are distinct expressions of the same concept [white]. My
uttering "Snow is white" and your uttering "Schnee ist Weiss" are
distinct sentences with their respective predicates expressing the
same concept ([white], again). Even within the same language, my
uttering "Grisham is the author of The Firm" and your uttering
"Grisham is The Firm's author" are distinct sentences with distinct
predicates, yet their respective predicates express the same concept
(the concept [the author of The Firm], in this case).

(2) Second, different agents can possess, grasp, or understand the
same concept, though such possession might come in degrees. Most
English speakers possess the concept [white], and while many possess
[neutrino], not many possess that concept to such a degree that one
knows a great deal about what neutrinos themselves are.

(3) Finally, concepts typically have multiple exemplifications or
instantiations. Many distinct things are white, and thus there are
many exemplifications or instances of the concept [white]. There are
many stars and many neutrinos, and thus there are many instances of
[star] and [neutrino]. Moreover, distinct concepts can have the very
same instances. The concepts [renate] and [cardiate] have all the same
actual instances, as far as we know, and so does [human] and [rational
animal]. Distinct concepts can also have necessarily all of the same
instances: For instance, the concepts [triangular figure] and
[trilateral figure] must have the same instances, yet the predicates
"is a triangular figure" and "is a trilateral figure" seem to have
different meanings.

As universals, concepts may be treated under any of the traditional
accounts of universals in general. Realism about concepts (considered
as universals) is the view that concepts are distinct from their
instances, and nominalism is the view that concepts are nothing over
and above, or distinct from, their instances. Ante rem realism (or
platonism) about concepts is the view that concepts are ontologically
prior to their instances—that is, concepts exist whether they have
instances or not. In re realism about concepts is the view that
concepts are in some sense "in" their instances, and thus are not
ontologically prior to their instances. Conceptualism with respect to
concepts holds that concepts are mental entities, being either
immanent in the mind itself as a sort of idea, as constituents of
complete thoughts, or somehow dependent on the mind for their
existence (perhaps by being possessed by an agent or by being
possessible by an agent). Conceptualist views also include imagism,
the view (dating from Locke and others) that concepts are a sort of
mental image. Finally, nominalist views of concepts might identify
concepts with classes or sets of particular things (with the concept
[star] being identified with the set of all stars, or perhaps the set
of all possible stars). Linguistic nominalism identifies concepts with
the linguistic expressions used to express them (with [star] being
identified with the predicate "is a star," perhaps). Type linguistic
nominalism identifies concepts with types of verbal expressions (with
[star] identified with the type of verbal expression exemplified by
the predicate "is a star").

c. Concepts as Mind-Dependent or Mind-Independent

On many views, concepts are things that are "in" the mind, or "part
of" the mind, or at least are dependent for their existence on the
mind in some sense. Other views deny such claims, holding instead that
concepts are mind-independent entities. Conceptualist views are
examples of the former, and platonic views are examples of the latter.
The issue of whether concepts are mind-dependent or mind-independent
carries great weight with respect to the clash between the classical
view and other views of concepts (such as prototype views and
theory-theories). If concepts are immanent in the mind as mental
particulars, for instance, then various objections to the classical
view have more force; if concepts exist independently of one's ideas,
beliefs, capacities for categorizing objects, etc., then some
objections to the classical view have much less force.

d. Concepts as the Targets of Analysis

Conceptual analysis is of concepts, and philosophical questions of the
form What is F? (such as "What is knowledge?," "What is justice?,"
"What is a person?," etc.) are questions calling for conceptual
analyses of various concepts (such as [knowledge], [justice],
[person], etc.). Answering the further question "What is a conceptual
analysis?" is yet another way to distinguish among different views of
concepts. For instance, the classical view holds that all complex
concepts have classical analyses, where a complex concept is a concept
having an analysis in terms of other concepts. Alternatively,
prototype views analyze concepts in terms of typical features or in
terms of a prototypical or exemplary case. For instance, such a view
might analyze the concept of being a bird in terms of such typical
features as being capable of flight, being small, etc., which most
birds share, even if not all of them do. A second sort of prototype
theory (sometimes called "the exemplar view") might analyze the
concept of being a bird in terms of a most exemplary case (a robin,
say, for the concept of being a bird). So-called theory-theories
analyze a concept in terms of some internally represented theory about
the members of the extension of that concept. For example, one might
have an overall theory of birds, and the concept one expresses with
one's use of 'bird' is then analyzed in terms of the role that concept
plays in that internally represented theory. Neoclassical views of
concepts preserve one element of the classical view, namely the claim
that all complex concepts have metaphysically necessary conditions (in
the sense that, for example, being unmarried is necessary for being a
bachelor), but reject the claim that all complex concepts have
metaphysically sufficient conditions. Finally, atomistic views reject
all notions of analysis just mentioned, denying that concepts have
analyses at all.

e. The Classical View and Concepts in General

The classical view claims simply that all complex concepts have
classical analyses. As such, the classical view makes no claims as to
the status of concepts as universals, or as being mind-dependent or
mind-independent entities. The classical view also is consistent with
concepts being analyzable by means of other forms of analysis. Yet
some views of universals are more friendly to the classical view than
others, and the issue of the mind-dependence or mind-independence of
concepts is of some importance to whether the classical view is
correct or not. For instance, if concepts are identical to ideas
present in the mind (as would be true on some conceptualist views),
then if the contents of those ideas fail to have necessary and
sufficient defining conditions, then the classical view looks to be
false (or at least not true for all concepts). Alternatively, on
platonic views of concepts, such a lack of available necessary and
jointly sufficient conditions for the contents of our own ideas is of
no consequence to the classical view, since ideas are not concepts
according to platonic accounts.

3. Classical Analyses

There are two components to an analysis of a complex concept (where a
complex concept is a concept that has an analysis in terms of other
"simpler" concepts): The analysandum, or the concept being analyzed,
and the analysans, or the concept that "does the analyzing." For a
proposition to be a classical analysis, the following conditions must
hold:

(I) A classical analysis must specify a set of necessary and jointly
sufficient conditions for being in the analysandum's extension (where
a concept's extension is everything to which that concept could
apply). (Other classical theorists deny that all classical analysis
specify jointly sufficient conditions, holding instead that classical
analyses merely specify necessary and sufficient conditions.)

(II) A classical analysis must specify a logical constitution of the
analysandum.

Other suggested conditions on classical analysis are given below.

a. Necessary and Sufficient Conditions

Consider an arbitrary concept [F]. A necessary condition for being an
F is a condition such that something must satisfy that condition in
order for it to be an F. For instance, being male is necessary for
being a bachelor, and being four-sided is necessary for being a
square. Such characteristics specified in necessary conditions are
shared by, or had in common with, all things to which the concept in
question applies.

A sufficient condition for being an F is a condition such that if
something satisfies that condition, then it must be an F. Being a
bachelor is sufficient for being male, for instance, and being a
square is sufficient for being a square.

A necessary and sufficient condition for being an F is a condition
such that not only must a thing satisfy that condition in order to be
an F, but it is also true that if a thing satisfies that condition,
then it must be an F. For instance, being a four-sided regular figure
is both necessary and sufficient for being a square. That is, a thing
must be a four-sided regular figure in order for it to be a square,
and if a thing is a four-sided regular figure, then it must be a
square.

Finally, for a concept [F], necessary and jointly sufficient
conditions for being an F is a set of necessary conditions such that
satisfying all of them is sufficient for being an F. The conditions of
being four-sided and of being a regular figure are each necessary
conditions for being a square, for instance, and the conjunction of
them is a sufficient condition for being a square.

b. Logical Constitution

A classical analysis also gives a logical constitution of the concept
being analyzed, in keeping with Moore's idea that an analysis breaks a
concept up into its components or constituents. In an analysis, it is
the logical constituents that an analysis specifies, where a logical
constituent of a concept is a concept entailed by that concept. (A
concept entails another concept when being in the extension of the
former entails being in the extension of the latter.) For instance,
[four-sided] is a logical constituent of [square], since something's
being a square entails that it is four-sided.

For a logical constitution specified by a classical analysis, a
logical constitution of a concept [F] is a collection of concepts,
where each member of that collection is entailed by [F], and where [F]
entails all of them taken collectively.

Most complex concepts will have more than one logical constitution,
given that there are different ways of analyzing the same concept. For
instance, "A square is a four-sided regular figure" expresses an
analysis of [square], but so does "A square is a four-sided, closed
plane figure having sides all the same length and having neighboring
sides orthogonal to one another." The first analysis gives one logical
constitution for [square], and the second analysis seems to give
another.

c. Other Conditions on Classical Analyses

In addition to conditions (I) and (II), other conditions on classical
analyses have been proposed. Among them are the following:

(III) A classical analysis must not include the analysandum as either
its analysans or as part of its analysans. That is, a classical
analysis cannot be circular. "A square is a square" does not express
an analysis, and neither does "A true sentence is a sentence that
specifies a true correspondence between the proposition it expresses
and the world."

(IV) A classical analysis must not have its analysandum be more
complex than its analysans. That is, while "A square is a four-sided
regular figure" expresses an analysis, "A four-sided regular figure is
a square" does not. While the latter sentence is true, it does not
express an analysis of [four-sided regular figure]. The concept
[four-sided regular figure] analyzes [square], not the other way
around.

(V) A classical analysis specifies a precise extension of the concept
being analyzed, in the sense of specifying for any possible particular
whether it is definitely in or definitely not in that concept's
extension.

(VI) A classical analysis does not include any vague concepts in
either its analysandum or its analysans.

The last two conditions concern vagueness. It might be thought that an
analysis has to specify in some very precise way what is, and what is
not, in that concept's extension (condition (V)), and also that an
expression of an analysis itself cannot include any vague terms
(condition (VI)).

d. Testing Candidate Analyses

In seeking a correct analysis for a concept, one typically considers
some number of so-called candidate analyses. A correct analysis will
have no possible counterexamples, where such counterexamples might
show a candidate analysis to be either too broad or too narrow. For
instance, let

"A square is a four-sided, closed plane figure"

express a candidate analysis for the concept of being a square. This
candidate analysis is too broad, since it would include some things as
being squares that are nevertheless not squares. Counterexamples
include any trapezoid or rectangle (that is not itself a square, that
is).

On the other hand, the candidate analysis expressed by

"A square is a red four-sided regular figure"

is too narrow, as it rules out some genuine squares as being squares,
as it is at least possible for there to be squares other than red
ones. Assuming for sake of illustration that squares are the sorts of
things that can be colored at all, a blue square counts as a
counterexample to this candidate analysis, since it fails one of the
stated conditions that a square be red.

It might be wondered as to why correct analyses have no possible
counterexamples, instead of the less stringent condition that correct
analyses have no actual counterexamples. The reason is that analyses
are put forth as necessary truths. An analysis of a concept like the
concept of being a mind, for instance, is a specification of what is
shared by all possible minds, not just what is in common among those
minds that actually happen to exist. Similarly, in seeking an analysis
of the concept of justice or piety (as Socrates sought), what one
seeks is not a specification of what is in common among all just
actions or all pious actions that are actual. Instead, what one seeks
is the nature of justice or piety, and that is what is in common among
all possible just actions or pious actions.

e. Apriority and Analyticity with respect to Classical Analyses

Classical analyses are commonly thought to be both a priori and
analytic. They look to be a priori since there is no empirical
component essential to their justification, and in that sense
classical analyses are knowable by reason alone. In fact, the method
of seeking possible counterexamples to a candidate analysis is a
paradigmatic case of justifying a proposition a priori. Classical
analyses also appear to be analytic, since on the rough construal of
analytic propositions as those propositions "true by meaning alone,"
classical analyses are indeed that sort of proposition. For instance,
"A square is a four-sided regular figure" expresses an analysis, and
if "square" and "four-sided regular figure" are identical in meaning,
then the analysis is true by meaning alone. On an account of
analyticity where analytic propositions are those propositions where
what is expressed by the predicate expression is "contained in" what
is expressed in the subject expression, classical analyses turn out to
be analytic. If what is expressed by "four-sided regular figure" is
contained in what is expressed by "square," then "A square is a
four-sided regular figure" is such that the meaning of its predicate
expression is contained in what its subject expresses. Finally, on an
account of analyticity treating analytic propositions as those where
substitution of codesignating terms yields a logical truth, classical
analyses turn out to be analytic propositions once more. For since
"square" and "four-sided regular figure" have the same possible-worlds
extension, then substituting "square" for "four-sided regular figure"
in "A square is a four-sided regular figure" yields "A square is a
square," which is a logical truth. (For a contrary view holding that
analyses are synthetic propositions, rather than analytic, see
Ackerman 1981, 1986, and 1992.)

4. Objections to the Classical View

Despite its history and natural appeal, in many circles the classical
view has long since been rejected for one reason or another. Even in
philosophy, many harbor at least some skepticism of the thesis that
all complex concepts have classical analyses with the character
described above. A much more common view is that some complex concepts
follow the classical model, but not all of them. This section
considers six fairly common objections to the classical view.

a. Plato's Problem

Plato's problem is that after over two and a half millennia of seeking
analyses of various philosophically important concepts, few if any
classical analyses of such concepts have ever been discovered and
widely agreed upon as fact. If there are classical analyses for all
complex concepts, the critics claim, then one would expect a much
higher rate of success in finding such analyses given the effort
expended so far. In fact, aside from ordinary concepts such as
[bachelor] and [sister], along with some concepts in logic and
mathematics, there seems to be no consensus on analyses for any
philosophically significant concepts. Socrates' question "What is
justice?," for instance, has received a monumental amount of attention
since Socrates' time, and while there has been a great deal of
progress made with respect to what is involved in the nature of
justice, there still is not a consensus view as to an analysis of the
concept of justice. The case is similar with respect to questions such
as "What is the mind?," "What is knowledge?," "What is truth?," "What
is freedom?," and so on.

One might think that such an objection holds the classical view to too
high a standard. After all, even in the sciences there is rarely
universal agreement with respect to a particular scientific theory,
and progress is ongoing in furthering our understanding of entities
such as electrons and neutrinos, as well as events like the Big
Bang—there is always more to be discovered. Yet it would be
preposterous to think that the scientific method is flawed in some way
simply because such investigations are ongoing, and because there is
not universal agreement with respect to various theories in the
sciences. So why think that the method of philosophical analysis, with
its presumption that all complex concepts have classical analyses, is
flawed in some way because of the lack of widespread agreement with
respect to completed or full analyses of philosophically significant
concepts?

Yet while there are disagreements in the sciences, especially in cases
where a given scientific theory is freshly proposed, such
disagreements are not nearly as common as they are in philosophy. For
instance, while there are practicing scientists that claim to be
suspicious of quantum mechanics, of the general theory of relativity,
or of evolution, such detractors are extremely rare compared to what
is nearly a unanimous opinion that those theories are correct or
nearly correct. In philosophy, however, there are widespread
disagreements concerning even the most basic questions in philosophy.
For instance, take the questions "Are we free?" and "Does being free
require somehow being able to do otherwise?" The first question asks
for an analysis of what is meant by "free," and the second asks
whether being able to do otherwise is a necessary condition on being
free. Much attention has been paid to such basic questions, and the
critics of the classical view claim that one would expect some sort of
consensus as to the answers to them if the concept of freedom really
has a classical analysis. So there is not mere disagreement with
respect to the answers to such questions, but such disagreements are
both widespread and involve quite fundamental issues as well. As a
result, the difficulty in finding classical analyses has led many to
reject the classical view.

b. The Argument from Categorization

There are empirical objections to the classical view as well. The
argument from categorization takes as evidence various data with
respect to our sorting or categorizing things into various categories,
and infers that such behavior shows that the classical view is false.
The evidence shows that we tend not to use any set of necessary and
sufficient conditions to sort things in to one category or another,
where such sorting behavior is construed as involving the application
of various concepts. It is not as if one uses a classical analysis to
sort things into the bird category, for instance. Instead, it seems
that things are categorized according to typical features of members
of the category in question, and the reason for this is that more
typical members of a given category are sorted into that category more
quickly than less typical members of that same category. Robins are
sorted into the bird category more quickly than eagles, for instance,
and eagles are sorted into the bird category more quickly than
ostriches. What this suggests is that if concepts are used for acts of
categorization, and classical analyses are not used in all such
categorization tasks, then the classical view is false.

One presumption of the argument is that when one sorts something into
one category or another, one uses one's understanding of a conceptual
analysis to accomplish the task. Yet classical theorists might
complain that this need not be the case. One might use a set of
typical features to sort things into the bird category, even if there
is some analysis not in terms of typical features that gives the
essential features shared by all birds. In other words (as Rey (1983)
points out), there is a difference between what it is to look like a
bird and what it is to be a bird. An analysis of a concept gives the
conditions on which something is an instance of that concept, and it
would seem that a concept can have an analysis (classical or
otherwise) even if agents use some other set of conditions in acts of
categorization.

Whether this reply to the argument from categorization rebuts the
argument remains to be seen, but many researchers in cognitive
psychology have taken the empirical evidence from acts of
categorization to be strong evidence against the classical view. For
such evidence also serves as evidence in favor of a view of concepts
in competition with the classical view: the so-called prototype view
of concepts. According to the prototype view, concepts are analyzed
not in terms of necessary and jointly sufficient conditions, but in
terms of lists of typical features. Such typical features are not
shared by all instances of a given concept, but are shared by at least
most of them. For instance, a typical bird flies, is relatively small,
and is not carnivorous. Yet none of these features is shared by all
birds. Penguins don't fly, albatrosses are quite large, and birds of
prey are carnivores. Such a view of concepts fits much more neatly
with the evidence concerning our acts of categorization, so such
critics reject the classical view.

c. Arguments from Vagueness

Vagueness has also been seen as problematic for the classical view.
For one might think that in virtue of specifying necessary and jointly
sufficient conditions, a classical analysis thus specifies a precise
extension for the concept being analyzed (where a concept C has a
precise extension if and only if for all x, x is either definitely in
the extension of C or definitely not in the extension of C). Yet most
complex concepts seem not to have such precise extensions. Terms like
"bald," "short," and "old" all seem to have cases where it is unclear
whether the term applies or not. That is, it seems that the concepts
expressed by those terms are such that their extensions are unclear.
For instance, it seems that there is no precise boundary between the
bald and the non-bald, the short and the non-short, and the old and
the non-old. But if there are no such precise boundaries to the
extensions for many concepts, and a classical analysis specifies such
precise boundaries, then there cannot be classical analyses for what
is expressed by vague terms.

Two responses deserve note. One reply on behalf of the classical view
is that vagueness is not part of the world itself, but instead is a
matter of our own epistemic shortcomings. We find unclear cases simply
because we don't know where the precise boundaries for various
concepts lie. There could very well be a precise boundary between the
bald and the non-bald, for instance, but we find "bald" to be vague
simply because we do not know where that boundary lies. Such an
epistemic view of vagueness would seem to be of assistance to the
classical view, though such a view of vagueness needs a defense,
particularly given the presence of other plausible views of vagueness.
The second response is that one might admit the presence of unclear
cases, and admit the presence of vagueness or "fuzziness" as a feature
of the world itself, but hold that such fuzziness is mirrored in the
analyses of the concepts expressed by vague terms. For instance, the
concept of being a black cat might be analyzed in terms of [black] and
[cat], even if "black" and "cat" are both vague terms. So classical
theorists might reply that if the vagueness of a term can be mirrored
in an analysis in such a way, then the classical view can escape the
criticisms.

d. Quine's Criticisms

A family of criticisms of the classical view is based on W.V.O.
Quine's (1953/1999, 1960) extensive attack on analyticity and the
analytic/synthetic distinction. According to Quine, there is no
philosophically clear account of the distinction between analytic and
synthetic propositions, and as such there is either no such
distinction at all or it does no useful philosophical work. Yet
classical analyses would seem to be paradigmatic cases of analytic
propositions (for example, [bachelors are unmarried males], [a square
is a four-sided regular figure]), and if there are no analytic
propositions then it seems there are no classical analyses.
Furthermore, if there is no philosophically defensible distinction
between analytic and synthetic propositions, then there is no
legitimate criterion by which to delineate analyses from non-analyses.
Those who hold that analyses are actually synthetic propositions face
the same difficulty. If analyses are synthetic, then one still needs a
principled difference between analytic and synthetic propositions in
order to distinguish between analyses and non-analyses.

The literature on Quine's arguments is vast, and suffice it to say
that criticism of Quine's arguments and of his general position is
widespread as well. Yet even among those philosophers who reject
Quine's arguments, most admit that there remains a great deal of
murkiness concerning the analytic/synthetic distinction, despite its
philosophical usefulness. With respect to the classical view of
concepts, the options available to classical theorists are at least
threefold: Either meet Quine's arguments in a satisfactory way, reject
the notion that all analyses are analytic (or that all are synthetic),
or characterize classical analysis in a way that is neutral with
respect to the analytic/synthetic distinction.

e. Scientific Essentialist Criticisms

Scientific essentialism is the view that the members of natural kinds
(like gold, tiger, and water) have essential properties at the
microphysical level of description, and that identity statements
between natural kind terms and descriptions of such properties are
metaphysically necessary and knowable only a posteriori. Some versions
of scientific essentialism include the thesis that such identity
statements are synthetic. That such statements are a posteriori and
synthetic looks to be problematic for the classical view. For sake of
illustration, let "Water is H2O" express an analysis of what is meant
by the natural kind term "water." According to scientific
essentialism, such a proposition is metaphysically necessary in that
it is true in all possible worlds, but it is a necessary truth
discovered via empirical science. As such, it is not discovered by the
a priori process of seeking possible counterexamples, revising
candidate analyses in light of such counterexamples, and so on. But if
water's being H2O is known a posteriori, this runs counter to the
usual position that all classical analyses are a priori. Furthermore,
given that what is expressed by "Water is H2O" is a posteriori, this
entails that it is synthetic, rather than analytic as the classical
view would normally claim.

Again, the literature is vast with respect to scientific essentialism,
identity statements involving natural kind terms, and the epistemic
and modal status of such statements. For classical theorists, short of
denying the basic theses of scientific essentialism, some options that
save some portion of the classical view include holding that the
classical view holds for some concepts (such as those in logic and
mathematics) but not others (such as those expressed by natural kind
terms), or characterizing classical analysis in a way that is neutral
with respect to the analytic/synthetic distinction. How successful
such strategies would be remains to be seen, and such a revised
classical view would have to be weighed against other theories of
concepts that handle all complex concepts with a unified treatment.

5. References and Further Reading

Ackerman, D. F. 1981. "The Informativeness of Philosophical Analysis."
In P. French, et al. (Eds.), Midwest Studies in Philosophy, vol. 6.
Minneapolis, Minnesota: University of Minnesota Press, 313-320.

Ackerman, D. F. 1986. "Essential Properties and Philosophical
Analysis." In P. French, et al. (Eds.), Midwest Studies in Philosophy,
vol. 11. Minneapolis, Minnesota: University of Minnesota Press,
304-313.

Ackerman, D. F. 1992. "Analysis and Its Paradoxes." In E.
Ullman-Margalit (Ed.), The Scientific Enterprise: The Israel
Colloquium Studies in History, Philosophy, and Sociology of Science,
vol. 4. Norwell, Massachusetts: Kluwer.

Bealer, George. 1982. Quality and Concept. Oxford: Clarendon Press.

Bealer, George. 1996. "A Priori Knowledge and the Scope of
Philosophy." Philosophical Studies 81, 121-142.

Bonjour, Laurence. 1998. In Defense of Pure Reason: A Rationalist
Account of A Priori Justification. Cambridge: Cambridge University
Press.

Chalmers, David J. and Jackson, Frank. 2001. "Conceptual Analysis and
Reductive Explanation" [On-line]. Available:
http://www.u.arizona.edu/~chalmers/papers/analysis.html

Donnellan, Keith. 1983. "Kripke and Putnam on Natural Kind Terms." In
C. Ginet and S. Shoemaker (Eds.), Knowledge and Mind. Oxford: Oxford
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Fodor, Jerry A. 1998. Concepts: Where Cognitive Science Went Wrong.
Oxford: Clarendon Press.

Fodor, Jerry A., Garrett, M. F., Walker, E. C. T., and Parkes, C. H.
1980/1999. "Against Definitions." In Margolis and Laurence 1999,
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Grice, H. P. and Strawson, P. F. 1956. "In Defense of a Dogma." The
Philosophical Review 65 (2), 141-158.

Hanna, Robert. 1998. "A Kantian Critique of Scientific Essentialism."
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Harman, Gilbert. 1999. "Doubts About Conceptual Analysis." In Gilbert
Harman, Reasoning, Meaning, and Mind, Oxford: Oxford University Press,
138-143.

Jackson, Frank. 1994. "Armchair Metaphysics." In M. Michael and J.
O'Leary-Hawthorne (Eds.), Philosophy in Mind. Dordrecht: Kluwer.

Jackson, Frank. 1998. From Metaphysics to Ethics: A Defence of
Conceptual Analysis. Oxford: Clarendon Press.

Katz, J. J. 1999.

Keefe, Rosanna and Smith, Peter (Eds.). 1999. Vagueness: A Reader.
Cambridge, Massachusetts: M.I.T. Press.

King, Jeffrey C. 1998. "What is a Philosophical Analysis?"
Philosophical Studies 90, 155-179.

Kripke, Saul A. 1980. Naming and Necessity. Cambridge, Massachusetts:
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Kripke, Saul A. 1993. "Identity and Necessity." In A. W. Moore,
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Langford, C. H. 1968. "The Notion of Analysis in Moore's Philosophy."
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Laurence, Stephen and Margolis, Eric. 1999. "Concepts and Cognitive
Science." In Margolis and Laurence 1999, 3-81.

Margolis, Eric and Laurence, Stephen (Eds.). 1999. Concepts: Core
Readings. M.I.T. Press.

Moore, G. E. 1966. Lectures on Philosophy. Ed. C. Lewy. London:
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Moore, G. E. 1968. "A Reply to My Critics." In Schlipp 1968, 660-677.

Murphy, Gregory L. 2002. The Big Book of Concepts. Cambridge: M.I.T. Press.

Peacocke, Christopher. 1992. A Study of Concepts. Cambridge: M.I.T. Press.

Pitt, David. 1999. "In Defense of Definitions." Philosophical
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Plato. 1961a. The Collected Dialogues of Plato. Ed. Edith Hamilton and
Huntington Cairns. Princeton, New Jersey: Princeton University Press.

Plato. 1961b. Euthyphro. Trans. L. Cooper. In Plato 1961a, 169-185.

Plato. 1961c. Laches. Trans. L. Cooper. In Plato 1961a, 123-144.

Plato. 1961d. Lysis. Trans. L. Cooper. In Plato 1961a, 145-168.

Plato. 1961e. Theatetus. Trans. L. Cooper. In Plato 1961a, 845-919.

Plato. 1992. Republic. Trans. G. M. A. Grube. Indianapolis, Indiana: Hackett.

Prinz, Jesse J. 2002. Furnishing the Mind: Concepts and Their
Perceptual Basis. Cambridge: M.I.T. Press.

Putnam, Hilary. 1962. "It Ain't Necessarily So." Journal of Philosophy
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Putnam, Hilary. 1966. "The Analytic and the Synthetic." In H. Feigl
and G. Maxwell, eds., Minnesota Studies in the Philosophy of Science,
vol. III. Minneapolis, Minnesota: University of Minnesota Press,
358-397. Putnam,

Hilary. 1970. "Is Semantics Possible?" In H. Keifer and M. Munitz,
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Putnam, Hilary. 1975. "The Meaning of 'Meaning'." In Keith Gunderson
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Putnam, Hilary. 1983. "'Two Dogmas' Revisited." In Hilary Putnam,
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Putnam, Hilary. 1990. "Is Water Necessarily H2O?" In James Conant
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Quine, W. V. O. 1953/1999. "Two Dogmas of Empiricism." In Margolis and
Laurence 1999, 153-170.

Quine, W. V. O. 1960. Word and Object. Cambridge: The M.I.T. Press.

Ramsey, William. 1992. "Prototypes and Conceptual Analysis." Topoi 11, 59-70.

Rey, Georges. 1983. "Concepts and Stereotypes." Cognition 15, 237-262.

Rey, Georges. 1985. "Concepts and Conceptions: A Reply to Smith, Medin
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Rosch, Eleanor. 1999. "Principles of Categorization." In Margolis and
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Schlipp, P. (Ed.). 1968. The Philosophy of G. E. Moore. LaSalle,
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Smith, Edward E. 1989. "Three Distinctions About Concepts and
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Smith, Edward E., and Medin, Douglas L. 1981. Categories and Concepts.
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Smith, Edward E. 1999. "The Exemplar View." In Margolis and Laurence
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Smith, Edward E., Medin, Douglas L., and Rips, Lance J. 1984. "A
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Sosa, Ernest. 1983. "Classical Analysis." Journal of Philosophy 80
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Stalnaker, Robert. 2001. "Metaphysics Without Conceptual Analysis."
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Williamson, Timothy. 1994. Vagueness. New York: Routledge. Williamson,
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