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What are Concepts?
Hans-Johann Glock
Summary: The article argues that a reasonably unied
account of the established use of `concept' and its cogna-
tes can be provided by a cognitivist approach. Such an
approach starts out from the role the ascription of con-
cepts plays in characterizing certain cognitive operations
and abilities, yet without treating concepts as symbolic
representations or particulars in the minds of individu-
als. In particular, it explores the idea that concepts are
rules or principles of classication and inference. At the
end I argue that a cognitivist account can deal not just
with the role of concepts in cognition, but also with the
idea that they are components of propositions.
This article aims to elucidate the established use or uses of the
term `concept', and those of its equivalents and cognates. This
established use includes everyday uses: like some related terms
with a philosophical provenance notably `idea' but unlike
others notably `universal' `concept' is widely employed in
everyday parlance.
1
But it also comprises the established uses
of these terms in special disciplines like the history of ideas,
psychology, logic and philosophy.
Within these disciplines, one encounters numerous theoretical
judgements or prejudices about concepts, for instance that they
contrast with intuitions (Kant), are tied to language (rationalist
tradition), are unsaturated entities (Frege), are compositional
1
Quotidian contexts are particularly signicant for the German Be-
gri, since the humdrum verb begreifen covers all types of compre-
hension. In a lecture, the late Michael Dummett once illustrated the
pervasiveness of Begri by relating how struck he was on his rst
visit to Germany when reading a sign at a railway station mentio-
ning `Gepckstcke, die unter den Begri Koer fallen' that is,
pieces of luggage which fall under the concept suitcase.
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8 Hans-Johann Glock
(Fodor), must be amenable to naturalization (most philosophers
and cognitive scientists in the USA), are socially constituted
(most other North-American academics in the humanities), etc.
However, my account seeks to respect not such specic theories
about concepts, but rather fruitful uses of `concept' and its
cognates. It is salutatory to remember that even in specialised
disciplines the use of `concept' is rarely entirely stipulative or
unconnected to the everyday use, since these disciplines purport
to explain cognitive and semantic phenomena describable in
terms of concepts in ordinary discourse.
Philosophers and logicians talk of comparative (x is heavier
than y), quantitative (x weighs 20kg), individual (the author
of Atemschaukel), logical (negation, implication), spatial and
temporal concepts, including the concepts of space and of time.
My initial focus here will be on those concepts that have tended
to occupy centre stage, namely predicative concepts. These are
concepts that correspond to general terms of a particular kind,
namely to the verbs, adjectives or count-nouns that feature in
one-place predicates like `x runs', `x is radioactive' and `x is a
tool'. But I shall also consider the question whether suggested
denitions of concepts capture other types of concepts.
It is relatively uncontroversial that predicative concepts are
involved when rational creatures entertain thoughts like
(1) Dogs bark.
The nature of this involvement remains controversial, ho-
wever. In the history of philosophy, one can distinguish three
fundamental approaches to concepts. According to subjectivist
conceptions, concepts are mental phenomena, particular entities
or goings-on in the mind or in the head of individuals. According
to objectivist conceptions, concepts exist independently of human
minds, as self-subsistent abstract entities. Finally, there is an
intermediate position, which may be termed cognitivist. It agrees
with objectivism in denying that concepts are mental particulars,
while at the same time maintaining, with subjectivism, that
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What are Concepts? 9
they have an ineliminable mental or cognitive dimension. One
version of cognitivism is intersubjectivism. It holds that concepts
exist independently of individual rational subjects, but insists
that they are constituted by intersubjective linguistic practices.
Another version brackets the question of existence, yet holds
that what concepts are their essence, if you wish can be
explained only by reference to the operations and capacities of
rational subjects.
This article investigates whether the concept of a concept can
be given a fairly uniform explanation through a `cognitivist'
account of this second, less committal kind, one that accepts
that concepts may exist independently of individual subjects
or even linguistic communities, yet nonetheless invokes mental
achievements and capacities. I shall argue that (many) of
the established ways of using `concept' can be explained by
looking at the relationship between the concept of a concept
and cognitive notions like ability, way of thinking and rule. In
particular, I shall present a case for holding that a cognitivist
explanation can account not just for the connection between
concepts and human thinking and speaking but also for the idea
that they are components of thoughts (propositions). If we are
to situate concepts within the subjective/objective spectrum, it
is useful to distinguish at least ve philosophical questions that
can be raised about them:
Denition question: What are concepts?
Individuation question: How are concepts individuated?
Possession question: What is it to have a concept?
Function question: What is the role of concepts in cognition?
Once we keep apart these four questions, one further question
arises: Priority Question: Which of these questions denition,
individuation, possession or function is the most fundamental?
I have criticized prominent objectivist denitions of concepts el-
sewhere (2010b: 312-5), and shall take their failure for granted
here. Instead, I shall start by arguing against subjectivist ans-
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10 Hans-Johann Glock
wers to the denition question. These arguments point in the
direction of a cognitivist approach. Yet the most straightforward
cognitivist denition, which identies concepts and abilities, will
also be found wanting. On the other hand it will transpire that
the cognitivist tradition gives the right response to the possession
question, and that this response does not entail untenable ans-
wers to the individuation question. This result will also suggest
that cognitivism is right in according priority to the possession
question.
1 Concepts and general terms
In many everyday contexts, `concept' means roughly: general
term with a meaning.
2
This denition also ts the role of `con-
cept' in logic in so far as concepts have an extension and are
components of sentences (see below). Yet it does not capture
crucial uses in philosophy, logic and psychology. In psychology, in
particular, concepts are invoked to account for cognitive processes
that are not verbalised. And this chimes with common sense. We
do not express all of our thoughts in words- and thank goodness
for that. Equally, we sometimes say that p when we think that q.
A lingualist might reply that in such cases we talk to ourselves
in foro interno, and that thinking is a kind of internal monologue
(as Plato had suggested in Thaetetus: 189e). But Wittgenstein
and Ryle ought to have taught us that speaking to oneself in the
2
This is more felicitous than predicates with a meaning, since the
latter are supposed to involve the copula or its equivalents. The
concept of a dog corresponds to the general term `dog' rather than
the predicate `x is a dog'. A moot question which I shall not take up
here is whether the latter is more closely aligned to the concept or
property of being a dog. The addition `with a meaning' is superuous
if a term is understood as a symbol, part of an established language;
but it is required if a general term is understood as mere sign which
has been accorded a syntactic role but no specic meaning (some-
thing represented by a predicate-letter in an uninterpreted formal
language).
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What are Concepts? 11
imagination is no more sucient or necessary for thinking than
having mental images (see Glock 1997).
Now, one might grant this point, yet insist that genuinely concep-
tual thought must issue in `judgements', something in which the
subject consciously and explicitly applies a general term, whether
it be in overt or inner speech. This gambit would imply, however,
that human cognition involves much less conceptual thought than
commonly assumed; and it is not forced on us by the meaning of
concept in psychology or ordinary parlance (see Prior 1953: ch.
XI). Furthermore, the retreat to silent predication rules out ab
initio the possibility of concept-possession by non-linguistic crea-
tures, which is at least contentious (see Glock 2010a).
Even if these qualms could be waived, moreover, silent predica-
tion would not solve another problem. Talking to oneself in the
imagination is a process involving specic languages. By contrast,
in philosophy, logic and psychology concepts are standardly sup-
posed to cut across dierent languages, whether they be natural
languages or interpreted formal calculi. According to psycholo-
gists, it is the concept of a dog rather than general terms like
`dog' or `chien' that is involved in thinking (1). And a logical
concept like that of negation is expressed equally by logical par-
ticles from dierent languages: `not', `nicht', `ne pas', `~', etc. In
such contexts, `concept' is more closely aligned with `idea' than
with `word' or `term', which signify lexical items from specic
languages.
Now, there is a venerable tradition which would allow us to ex-
tend the denition of concepts as general terms to non-verbalised
cognitive processes and cognitive processes of non-linguistic crea-
tures, and which also lifts the restriction to particular languages.
This tradition postulates a mental language that is shared by
all creatures capable of conceptual thought, a universal mental
symbolism that underlies all specic languages. Concepts, the
story goes, are nothing other than the words of this language of
thought, a language that is thought by individuals rather than
spoken by linguistic communities. This is a version of subjecti-
vism. It goes back at least to Occam, and it ts Kant's claim
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12 Hans-Johann Glock
that a concept is a `predicate of a possible judgement' (Critique
of Pure Reason: A 69/B 94). Its most explicit and prominent ver-
sion, however, is Fodor's `representational theory of mind'. This
position will now be criticized.
2 Are concepts mental particulars or mental
representations?
According to Fodor, so-called propositional attitudes like belief
and desire are mental states, and they `are constituted by rela-
tions to mental representations', namely `thoughts' (Fodor 2003:
141, 10). Concepts are `the constituents of thoughts' (Fodor 1998:
25). They constitute a kind of `mental representation' and hence
a `kind of mental particular'. As mental particulars, they are `ob-
jects in the mind' or `in the head' of individuals; they are `concre-
te' rather than abstract; and they have causes and eects in the
physical world (Fodor 1998: 3, 7-8, 22; Fodor 2003: 13 and note).
As mental representations, they have `representational content'.
They contribute to the content of our propositional attitudes, to
what we believe, desire, etc. They do so by determining the con-
ditions under which our beliefs are true and our desires satised.
Any form of subjectivism faces a Fregean objection: concepts can-
not be phenomena in the minds or heads of individuals, since they
can be shared between dierent subjects. Now, `sharing' and its
cognates are used in a variety of ways. One paradigm is that of
dividing an object into parts, which themselves are not shared,
as in sharing a banana. But there is another, equally basic, para-
digm which does not imply division and extends well beyond ma-
terial objects. Dierent people can share bicycles, predilections,
insurance companies, heads of states, the credit for an invention,
beliefs, etc. It is in this sense that concepts are shareable. Two
individuals A and B can both have the same concept F, which
means that it is possible that both A and B have mastered and
employ F.
Shareability is a feature of the concept of a concept in both every-
day life and in disciplines like psychology and the history of ideas.
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What are Concepts? 13
One central use we make of `concept' and terms that are equiva-
lent in the relevant contexts (like `conception', `idea' or `notion')
is in claims about dierent individuals or even groups of indivi-
duals either sharing a concept, or failing to do so. For instance,
dierent political and religious traditions may or may not share
the same concept of freedom or of guilt. Such claims are equally
central to intellectual history, e.g. when it comes to comparing
the Greek concept of eudaimonia with our concept of happiness.
Fodor accepts shareability as a `non-negotiable condition', that
concepts are `the sorts of things that lots of people can, and do,
share' (Fodor 1998: 28). The obvious diculty is that mental
particulars contrast with concepts in that they are modes of in-
dividual minds or heads, and hence private to their owners. Fodor
thinks, however, that he can easily overcome this diculty by in-
troducing a distinction between type and token. Fodor's `language
of thought hypothesis' treats mental representations as symbols
of a `language of thought' or `Mentalese'. Thoughts, the larger
wholes formed by concepts, are the sentences of Mentalese, phy-
sical tokens of computational types. When we engage in concep-
tual thought, Mother Nature inscribes the words of a computer
programme into our brains. And concepts are nothing other than
the token-words of Mentalese, i.e. computationally identied pat-
terns of neural rings.
Consider the scenario in which Anne and Sarah both believe that
dogs bark and (improbably) utter `Dogs bark' in close succes-
sion. In that case we have two tokens of a single type-sentence
`Dogs bark', and two tokens of a single type-word `bark'. Similar-
ly, according to Fodor, in Anne's brain there occurs one neural
token-sentence, and in Sarah's brain there occurs another neural
token-sentence. Yet Anne and Sarah both believe the same thing,
namely that dogs bark, since both tokens instantiate the same
Mentalese type-sentence DOGS BARK. Finally, they share the
concept DOG, because both have tokens of one and the same
Mentalese type-word.
This position can account for shareability. It does so at a pri-
ce, however. The type/token distinction implies abandoning the
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14 Hans-Johann Glock
claim that concepts themselves are particulars. After all, Anne
and Sarah do not have a Mentalese token-word in common, what
they have in common is that their distinct token-words are of
the same type. What can be shared between dierent individuals
are representation-types; and these types, as Fodor duly acknow-
ledges, are `abstracta' rather than mental particulars (see 1998:
20-1, 28). To be more precise, types are repeatable universals and
hence abstract. Conversely, what can qualify as mental particu-
lars are representation-tokens; and these tokens are conned to
each individual rather than shareable. This leaves Fodor's positi-
on in tatters. On the one hand, the non-negotiable constraint on
concepts, namely that they be shareable, is satised only by the
abstract types which are neither particulars (mental, physical or
otherwise) nor concrete. On the other hand, his central claim, na-
mely that concepts are concrete particulars, applies only to the
tokens which are not shareable. If one persistently keeps apart
types and tokens, one is forced to abandon the subjectivist credo
that concepts are mental particulars that can enter into causal
relations. Concepts themselves the things that can be shared
by dierent individuals are not particulars.
As far as shareability is concerned, concepts might yet be mental
representations, namely of the type- rather than token-variety.
This is in line with Fodor's contention that `concepts are [Menta-
lese] symbols' (Fodor 1998: 28). But at the same time he is driven
to the claim that concepts are something that `mental representa-
tions . . . express', namely `word meanings' (Fodor 1998: 2; Fodor
2003: 13). Accordingly, he is committed to the inconsistent claim
that concepts are both mental words and the meanings of those
very same words. This inconsistency is no coincidence. Instead,
it is connected to a fundamental aw in the language of thought
hypothesis and a general problem with the idea that concepts or
thoughts are representations.
Following Peirce's theory of signs (1933), one can distinguish bet-
ween dierent types of representation:
Icons resemble what they represent
Symbols are related to what they represent by convention
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What are Concepts? 15
Indices are connected to what they `represent' by causal de-
pendencies or by other natural relations such as spatial or
temporal proximity.
Thus realist paintings are icons of what they represent. Linguistic
expressions, with the possible exception of onomatopoetic ones,
are symbols of what they represent. The word `dog', for example,
is connected to the animals not through any kind of resemblance,
but through an arbitrary convention. Smoke, nally, is an index
of re, because it is a causal result of re.
Given this distinction, one might deliver the following brief ver-
dict on the idea of a neurophysiological language of thought:
a) Patterns of neural rings are indices of external phenomena,
but only for suitably informed with neurophysiological mea-
suring equipment, not for ordinary subjects of thought;
b) they might be icons (but in fact not);
c) they cannot be symbols.
That neural rings are causal results of external events and cau-
sal preconditions of perception is agreed on all sides. The extent
to which there is, for example, a spatial resemblance between the
objects of perception and the neural activities that underlie per-
ception, is a matter for empirical investigation. For the most part,
no such iconic relation has been observed. Although experiments
like those of Hubel and Wiesel show that particular neurons are
involved in seeing lines of a particular orientation, there is no ico-
nic similarity between the lines and the pattern of ring neurons.
Finally, neural rings cannot be symbols because there is no one
who uses them to represent somehing in a conventional way (a
point to which I shall return). Accordingly, there can be no men-
tal symbols and hence no language of thought.
What about the more general idea that concepts are representati-
ons? According to an orthodoxy shared by Fodor, concepts must
be shareable because they are components of what people belie-
ve, of shareable thoughts or `propositional contents'. But as their
components, concepts can no more be representations or signs
than propositions themselves they are what is represented, the
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16 Hans-Johann Glock
content of thinking, not what represents, i.e. what expresses these
contents (Glock 2009 elaborates these objectioins to Fodor).
This lesson is in line with the common sense view that concepts
are expressed by signs such as predicates or logical operators. It
also follows from a more basic feature of the notion of represen-
tation.
Bona de representations, at least of an iconic or symbolic kind,
require a medium. That is to say, they have representational pro-
perties by virtue of having non-representational properties. For
instance, Rembrandt's self-portrait in the National Gallery of
Scotland represents a particular individual on account of more
basic properties, roughly the way in which it arranges colours
and shapes (see Hyman 2006). Similarly, the sign-token `Rem-
brandt Harmenszoon van Rijn' signies that same individual on
account of its typographic properties, which are subject to the
kind of conventions characteristic of symbols.
The idea that thoughts and concepts are (mental, computatio-
nal or neural) representations is incompatible with this dening
feature of representations. With apologies to Marshall McLuhan,
thoughts and by implication concepts are all message and no
medium! Or, with rather fewer apologies to Ludwig Wittgenstein,
thought is not a linguistic symbol requiring interpretation; it is
itself `the last interpretation' (1958: 34).
But couldn't one respond that concepts and propositions qua
sign-types of Mentalese do occur in a medium, namely a medium
of neural rings? The latter represent propositional or conceptu-
al contents on account of their non-representational physiological
or physical properties. According to Fodor, for instance, these
representations have certain syntactic properties properties de-
termining the way they are processed on account of their phy-
siological qualities, and they have certain semantic properties,
properties determining what they represent, on account of their
causal relations to the environment.
At this juncture, the epistemic or cognitive dimension of repre-
sentations comes into play. The non-representational properties
of representations must be accessible to the subject of representa-
-
What are Concepts? 17
tion. After all, a representation R is not just a sign of something
an object O, but a sign for someone a subject of representati-
on S someone to whom X is represented through R (again, the
point was epitomized by Peirce, in his famous semiotic triangle).
Yet neural tokens of computational types are entirely and in prin-
ciple inaccessible to the subject; they are `deeply unconscious', to
use Searle's (1997) critical label. By the same token, they cannot
be used by S intentionally or, a fortiori, with the specic intent
to represent something. Nor can the subject employ them accor-
ding to rules, as required for symbolic representation.
A possible response: neural signs are used by sub-personal sub-
jects, e.g. by the brain, its parts, or functionally dened modu-
les.
3
But this invites the charge of a `homunculus' or `mereological
fallacy' (Kenny 1984: ch. 9; Bennett/Hacker 2003). This is the
fallacy of explaining mental attributes of an animal or subject
in our case the capacity for conceptual thought by postulating
sub-personal subjects homunculi with the same or similar
mental capacities in this case the capacity for the intentional
employment of signs. The explanation is fallacious because these
capacities can only be attributed to the animal or subject S as
a whole, and not save metaphorically to its parts, whether
they be organs like S 's brain or capacities like S 's mind. Further-
more, even if it made sense to credit sub-personal instances with
symbolic understanding, this would only push back the problem.
One then needs to explain the representational capacities of these
postulated homunculi, which engenders a regress.
Yet surely, to anyone except die-hard behaviourists the very exis-
tence of cognitive phenomena shows that there are mental repre-
sentations! Doesn't thought require some kind of representation?
The answer is yes, but only if `representation' is divested from
the standard connection with a medium and understood in a mi-
3
Fodor himself does not fall back on this response. He grants that
`nobody ever interprets mental representations' (2008: 16). Yet this
concession removes any license for holding that these representations
are symbolic, and hence for speaking about a language of thought.
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18 Hans-Johann Glock
nimalist sense. On that understanding, our thoughts are repre-
sentations, simply because they have what are nowadays called
semantic properties:
a proposition that p is true or false
a singular representation a refers or fails to refer to an object x
a concept F applies or doesn't apply to an object x
However, representations in this minimalist sense cannot explain
thought. For to represent (that p or x or F s or things being F )
in this sense simply is to think (to think that p, about x, about
F s, or about things being F ).
4
Representationalism is reduced to
uninformative claims like:
to think that a is F is to represent a as being F,
and to think of F s qua F s is to represent F s, etc.
A non-representationalist (`cognitivist') approach at least holds
the promise of a genuine explanation of what thought amounts
to: what it is to think that p or about F s as F s is spelled out in
terms of the possession of certain cognitive abilities.
4
Austere representationalists such as Husserl (1900), have disassocia-
ted the idea of representation from any specic connotations, nota-
bly from the link with a particular medium whether it be mental
images or words crossing one's mind, neural rings or computational
symbols. But such positions once more face the task of explaining
what having a representation amounts to. In Husserl's case, for ex-
ample, we seem to be left with the idea that it is `just like' mental
picturing, only without mental images. But that simply boils down
to saying that having a representation of (an) F is to think about
(an) F, which means that the explanation of thought has moved
in a circle. A logical relation, thinking about (an) F, has rst been
construed as a pictorial one, and has then been robbed of the picto-
rial aspects which alone can give it any substance (Tugendhat 1976:
62-3, 276-7).
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What are Concepts? 19
3 Concepts and abilities
The most popular and straightforward cognitivist answer to the
denition question identies concepts with abilities. Thus, in re-
sponse to the question `Are concepts entities or are they dispo-
sitions?' Price states in no uncertain terms: `a concept is not an
entity [. . . ] but a disposition or capacity' (1953: 320, 348). In the
same vein Geach pronounces that concepts `are capacities exer-
cised in acts of judgement' (1957: 7, see also 13; Saporiti 2010).
The idea that concepts are abilities is also espoused by Millikan
from a very dierent, naturalistic perspective (2000: ch. 4). This
proposal respects several features of established use.
First, properties are objective, something possessed by things of
all kinds. By contrast, concepts are something possessed by ra-
tional subjects capable of classifying things according to their
properties. This is simply a crucial aspect of the cognitive dimen-
sion of concepts stressed by cognitivism.
Secondly, the identication of concepts and capacities does not
fall foul of the constraint that concepts must be shareable. As Ge-
ach points out, it does not entail that `it is improper to speak of
two people as having the same concept ', since dierent indivi-
duals can possess the same mental capacities (1957: 14). Thirdly,
concepts and abilities alike can be acquired, applied and lost, and
some of them may be innate.
Finally, to possess a concept is to possess a certain kind of mental
ability, capacity or disposition. In what follows, I refrain from de-
ciding which of these types of potentiality is the most appropriate
general category (see Glock 2010b: section 5). Barring that issue,
identifying concept-possession with an ability, capacity or dispo-
sition of some kind is inevitable. That concept-possession is an
ability of some kind is accepted, willy-nilly, even by Fodor, who
purports to contradict cognitivism (a.k.a. `pragmatism') on this
issue (2003: 19). The real bone of contention between representa-
tionalists like Fodor and those cognitivists that can properly be
called `concept pragmatists' in a wide sense e.g. Wittgenstein,
Ryle, Travis and concerns the question of whether concept-
possession is simply the ability to represent the property of being
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20 Hans-Johann Glock
F or F s as F s, or whether it should be explained as the ability to
classify things into those which are F s and those which aren't, or
to draw inferences from thoughts about F s. Concepts are involved
not just in occurrent thoughts or beliefs, but also in long-standing
or dispositional beliefs. Consequently, the possession of concepts
must be at least as stable as the possession of dispositional beliefs.
Put in Aristotelian terms, concept-possession must be a poten-
tiality of some kind, since it combines two features. On the one
hand, it is enduring rather than episodic. On the other hand, it
is something which manifests itself in certain episodes, notably of
overt or silent classication and inference.
In addition to respecting features of the established concept of
a concept, dening concepts as abilities has advantages when it
comes to explaining both the phylo- and the ontogenesis of con-
ceptual thought and of language. Of course, the denition itself
does not provide such a genetic explanation. But it claries how
we might be able to give a genetic account that avoids vicious
regress and circularity and thereby the paradoxical denial that
an explanation is impossible in principle. In particular, the abili-
ty approach is congenial to the following claims that facilitate a
genetic explanation of conceptual thought:
i. there are preconceptual forms of cognition, conation and in-
tentional action;
ii. these dier from the conceptual forms through the absence
of certain advanced cognitive abilities.
iii. abilities can be possessed in varying degrees, and they can be
acquired through a gradual process.
4 The individuation of concepts and abilities
Its attractions notwithstanding, the identication of concepts
with abilities faces the objection that it implies an untenable ans-
wer to the individuation question. Thus Fodor has alleged that
concepts are more nely individuated than abilities. For instance,
`creature with a kidney' and `creature with a heart' apply to all
and only the same things, but they express dierent concepts.
-
What are Concepts? 21
Furthermore, `equilateral triangle' and `equiangular triangle' ap-
ply necessarily to the same things, yet they still express dierent
concepts. In current jargon, concepts are not just `intensional'
but `hyperintensional'.
Now, an ability is individuated by reference to its exercise. But,
Fodor maintains, the same sorting and inferential performances
can manifest the possession of dierent concepts. Conning our-
selves to the ability to sort or discriminate, sorting equilateral tri-
angles from all other gures is also sorting equiangular triangles
from all other gures (Glock 2003: 256, 1436). It seems to fol-
low that concepts cannot be individuated by the exercise of an
ability, and hence that they cannot be individuated by reference
to abilities. In eect, Fodor's objection runs as follows:
P1 Abilities are individuated by their exercise (ability to =ability to i ing = ing).P2 In all possible situations, one and the same sorting activity
can manifest dierent concepts.
C: Concepts cannot be individuated through the abilities which
constitute their possession.
The argument is valid. Yet P2 is false: sorting triangles according
to lengths is not the same activity as sorting triangles according
to angles, even though the results are the same. The dierence in
the two activities can be displayed by linguistic creatures, who can
justify their sorting along dierent lines. It can even be manifes-
ted in non-linguistic behaviour. A creature that sorts on account
of comparing or measuring lengths applies equilateral triangle, a
creature that sorts on account of measuring angles applies equian-
gular triangle. These are dierent activities, manifesting dierent
abilities and thereby the possession of dierent concepts. And it
is obvious that one can have one of these abilities or concepts
without having the other. Indeed, most children actually learn
how to measure lengths before learning how to measure angles.
But individuation also poses another challenge to identifying con-
cepts with abilities. Many cognitivists grant that there is no pre-
cise way of individuating abilities. Thus Travis (2000) grants that
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22 Hans-Johann Glock
linking concepts to abilities may not be much help in individua-
ting concepts, since it is not clear how abilities are to be counted.
That concession needs to be put in perspective, however. Like
Travis, Geach (1957: 15) accepts that it is absurd to ask how
many abilities are exercised in a judgement. Yet he also insists,
rightly, that we can still distinguish between such abilities. More
generally, one must distinguish between the possibility of enume-
rating and the possibility individuating entities of a particular
kind (see Strawson 1997: ch. 1; Glock 2003: 4752). And this ge-
neral lesson applies equally to abilities.
Still a problem remains. It is prima facie plausible to hold that
we are able not only to distinguish the concept of a dog from that
of barking, but also to specify that precisely two concepts are in-
volved in judging that dogs bark. So concepts and abilities seem
to come apart on the issue of enumerability. This verdict can be
contested, however, on the grounds that it does not compare like
with like. The claim that the number of concepts involved in (1)
is determinate is only even remotely plausible if we conne oursel-
ves to predicative concepts (otherwise we have to add at least one
quantitative concept that corresponds to the plural in English; al-
ternatively, if we analyse (1) with the help of Fregean logic, we
need to add the logical concepts of universal quantication and
of material implication). But the very same consideration applies
to abilities. It is just as plausible to insist that precisely two pre-
dicative abilities are involved in judging that (1) namely that of
thinking about dogs and that of thinking about things that bark
as it is to maintain that precisely two predicative concepts are
involved in (1).
5 Dierences between concepts and abilities
The stumbling block for identifying concepts with abilities is not
individuation. It is rather that there are other respects in which
the established use of `concept' diers from that of `ability', not
least as regards the role or function of concepts.
First, one thing we do with concepts is to dene or explain them.
-
What are Concepts? 23
But to dene or explain a concept is not to dene or explain a
capacity. Normally, to explain an ability is to explain its causal
preconditions (causal explanation), whereas to explain a concept
is to explain its content (semantic explanation). Furthermore,
even when we dene an ability (i.e. explain its content), we
specify what it is an ability to do; as just mentioned, abilities
are individuated through their exercise. By contrast, to explain
a predicative concept is to specify the conditions that an object
must satisfy to fall under it.
Secondly, and relatedly, concepts can be instantiated or satised
by things; conversely, things instantiate, satisfy or fall under
concepts. These things cannot be said of abilities, or at least not
in the same sense.
Thirdly, and once more relatedly, concepts have an extension
(the set of objects which fall under them) and an intension
(the features which qualify objects for falling under them); yet
this cannot be said of abilities. Insofar as the ability linked to
possessing the concept F has an extension, it is not the range of
things that are F, but either the range of subjects that possess
F, or the range of situations in which these possessors can apply
or withhold F.
Fourthly, a concept can occur in a proposition or statement, but
an ability cannot. Of course, abilities can occur in propositions
in the sense of being mentioned in them, as in
(2) The ability to lie convincingly is a great asset in ban-
king.
But it seems that concepts occur in propositions in yet
another and more pervasive way, not just as topics or referents,
something the proposition is about, but as components. The
concept of being sweet occurs in the proposition that
(3) Sugar is sweet
even though no ability occurs in it.
-
24 Hans-Johann Glock
6 Tools
At this point it behoves us to return to the issue of concept
possession, since it provides the strongest argument in favour of
the identication. It starts out from
(I) to possess a concept is to possess a certain mental ability.
Next, it glosses (I) as
(I') to possess a concept = to possess a certain mental ability
It then invokes the additional premise
(II) to possess x = to possess y x = y
in order to reach the conclusion that
(III) a concept = a certain mental ability.
But this reasoning is problematic. First, it is unclear whe-
ther (I) is indeed an identity statement, as the paraphrase (I')
assumes. Often statements of the form `to is to ' merelyexpress a generality statement of the form `For all x, if x F s then
x Gs)'. The latter need not even be reversible (as in `to be a
Cretan is to be a liar'). Next, to be reversible, (I) and (I') would
have to specify a particular mental ability which is equivalent
to concept possession. This is far from trivial, as we shall see.
And even if this feat has been achieved, it will be insucient
to establish an identity. It will only mean that everyone who
possesses a concept also possesses this specic mental ability,
and vice versa.
Furthermore, it remains an open question whether (I) should
not instead be glossed as:
I* S has the concept F S has the ability of operating with F.
-
What are Concepts? 25
To be sure, someone who identies concepts with abilities will
resist that paraphrase and insist that the ability with which pos-
sessing the concept F is to be identied must be explained with-
out mentioning the concept F, an entity with which the subject
operates. But it is an alternative that her arguments do not rule
out. That alternative is based on the following line of thought. If
having a concept is an ability, it is an ability to operate with con-
cepts. In that case, however, the concept itself cannot be identical
with the ability. Rather, it is something employed in the exercise
of that ability.
A cognitivist conception which picks up this cue is the popular
idea that concepts are a kind of cognitive or linguistic tool. Con-
cepts are things employed in the exercise of conceptual abilities,
just as tools are things employed in the exercise of manual (tech-
nical) abilities.
Unfortunately, it is far from clear what kind of tool concepts
might be. Worse still, the analogy is misleading to begin with.
The idea that concepts are akin to tools in that they are objects
(concrete, mental or abstract) with which we operate in conceptu-
al thought amounts to a reication. There is a dierence between
the possession of a tool and the possession of the ability to em-
ploy the tool as I keep discovering to my cost when trying to
operate our electric drill. This distinction cannot be drawn in the
case of concepts. To possess a concept is ipso facto to possess the
ability to use the concept.
5
I now turn to two proposals that avoid the pitfall of treating
objects as if they were bona de objects.
7 Ways of thinking
First, the Neo-Fregean proposal that concepts are senses or `mo-
des of presentation' (Peacocke 1992; Knne 2005). Unfortunately,
the latter is merely a catch-phrase, and one Frege himself never
explained adequately, least of all with respect to concepts, which
5
In this respect, concepts resemble skills. To possess a skill is ipso
facto to possess the ability to apply the skill.
-
26 Hans-Johann Glock
he regarded as referents rather than senses of predicates. But we
can put some esh on it by treating concepts as ways of thin-
king about objects, though not in the adverbial sense of thinking
about them hard or longingly. More specically, concepts are ways
of thinking about or conceiving of objects as possessing certain
properties, without themselves being properties. To render that
suggestion viable, we need to avoid literal interpretations of the
Fregean idea that a sense is a `mode of presenting a referent'.
Strictly speaking, there can be no way of presenting a referent
unless there is a referent or extension. In the case of concepts,
this would rule out uninstantiated concepts, which is absurd. On
my construal, therefore, ways of thinking about objects are direc-
ted not just at those objects which possess the relevant properties,
but at all objects of which the relevant properties can be predi-
cated either truly or falsely. To put it dierently, a concept is a
way of thinking of objects from a suitable range as possessing or
lacking certain properties. This reintroduces the idea of classica-
tion. Finally, we can operationalize the idea of ways of thinking,
thereby further spelling out its cognitive dimension. The concept
expressed by a predicate is determined by the features to which
the subject refers in deciding whether a given object falls under
the concept, or would decide, if the question arose.
6
Neo-Fregeanism does justice to the cognitive dimension in several
respects. First, its answer to the possession question runs:
A subject S possesses the concept F i S is capable of
thinking of an object as being an F.
Secondly, the Neo-Fregean answer to the denition question has
it that concepts are `representational abstract entities' (Knne
2007: 346-7). Qua modes of presentation they are not linguistic
symbols predicates of a language of thought but things ex-
pressed by symbols. Yet they in turn are ways of thinking about
objects or of objects as having properties. Concepts are at the
same time representanda of the predicates of public languages
and representantia of properties. And they are subjective not in
6
For a more elaborate discussion of Neo-Fregeanism, see Glock 2011.
-
What are Concepts? 27
the sense of being inside the minds or brains of individuals, but
only in a sense related to the function question: it is essential to
concepts that they play a role in cognitive acts and operations.
Hurdles remain nonetheless when it comes to expatiating upon
the idea of thinking of an object as possessing certain properties.
For one thing, to accommodate even all employments of predica-
tive concepts Neo-Fregeans are driven to statements like
one thinks of something as F if one judges, that it is F,
when one hopes that it is F, when one wonders, whether it
is F, etc. for all propositional attitudes and acts. (Knne
2007: 343)
Alas, when I wonder whether Susan is well, I do not, normally,
think of her as being well. Accordingly, `thinking of something as
F ' cannot have its normal sense here, and hence cannot be used
to explain the Neo-Fregean notion of `way of thinking'. One might
respond that `thinking of something as F ' has a technical sense
here; it is something one does when one judges that x is F, hopes
that x is F, wonders whether it is F, etc. But this would once more
take us back to square one, namely the cognitive phenomena that
concepts were supposed to explain.
For another, `thinking of objects as possessing certain properties'
does not t all types of concept or conceptual thought. It directly
captures predicative concepts and classication. And perhaps the
idea can be extended to comparative, quantitative, spatial and
temporal concepts, and to individual concepts, provided that the
latter are welcomed as bona de concepts in the rst place. But
it does not capture logical concepts and inference. To possess
the concept of negation is not a `mode of presenting' or a `way of
thinking' about a putative logical object negation, or the property
of being negated, or even of negated propositions or a proposition
as negated. Instead, it is a way of operating with negation, e.g.
in negating propositions and drawing inferences.
-
28 Hans-Johann Glock
8 Techniques and rules
A nal cognitivist approach promises both more specicity and
greater generality. It also has the advantage of acknowledging
that a concept is something employed in conceptual thought
without reifying it. A concept is not an object, properly speaking,
the story goes, but a technique. Thus Wittgenstein maintained
that `a concept is a technique of using a word', or `the technique
of our use of an expression: as it were, the railway network that
we have built for it' (1988: 50 and 2000: MS 163: 56v). To master
or possess a technique is to master or possess an ability. Yet
techniques are not themselves abilities, but something which the
possessor of an ability uses in exercising the ability. There is a
dierence, for instance, between the ability to skin a rabbit and
the various techniques one might employ to this end.
Wittgenstein regarded concepts as linguistic techniques. But
his idea can be given a Kantian twist, in order to avoid the
potentially problematic implication that concepts are the
prerogative of linguistic creatures. One can tie concepts instead
to thought or understanding rather than language. Concepts are
techniques not just for using words, but for mental operations or
mental acts which may or may not be expressed in language. The
capacity for such mental operations may presuppose possession
of language, yet it can denitely be exercised by a subject that
does not engage in either overt or silent speech at the time (see
also section 1 above).
But what kind of mental operation? Here we face the question of
what function or functions concepts are supposed to full. The
most popular candidate, and the one that has preoccupied us so
far, is classication. Often classication is in turn spelled out as
an operation of discrimination, of sorting things into those that
do and those that do not fall under the concept. This elaboration
invites an objection, however. There is at least one concept that
cannot be used to discriminate between those things that fall
under it and those that do not, namely the concept of identity
(Knne 2007: 344). It makes no sense to sort things into those
that are and those that are not identical with themselves. One
-
What are Concepts? 29
way of avoiding this problem is to gloss classication not as
sorting, but as recognizing. In so far as identity is a bona de
relation at all, it makes sense to recognize that it is one in which
each thing stands to itself.
A second response is to cast our net more widely. There is
a second basic function standardly and plausibly ascribed to
concepts, namely inference. This obviously accommodates the
concept of identity, which has a distinctive role in inference.
In any event, acknowledging inference as a basic function of
concepts in addition to classication is imperative in order to
account for logical concepts. As we have seen, these defy the
labels `mode of presentation' or `way of thinking about', and by
the same token they should not be lumbered articially with the
function of classifying things. At the same time logical concepts
are obviously at least as amenable to being treated as cognitive
techniques as predicative concepts.
Accordingly, the proposal currently under consideration is this:
a concept is not identical with the capacity to classify or infer,
but only with the technique employed by someone who exercises
the ability to classify or infer. Next, the term `technique' needs
to be made more specic. What matters as far as concepts are
concerned whether they be predicative or logical are the
rules or principles that guide conceptual thought. Concepts, the
proposal now runs, are rules or principles of classication and/or
inference.
Even this modied proposal is threatened by category mismat-
ches. It does not seem that to dene a concept is to dene a
principle or rule. Rather, the principle or rule features in the
denition. On the other hand, perhaps this is just a vagary
of the current use of `denition' in English, without further
conceptual import. There is no linguistic infelicity in maintaining
that to explain a concept is to explain a principle or rule for
performing certain mental or linguistic operations.
7
At the same
7
One might further remonstrate that, strictly speaking, it is terms
rather than concepts that are dened. After all, concepts are suppo-
sed to be located at the level of meaning rather than that of symbols.
-
30 Hans-Johann Glock
time one would at the very least feel queasy about violating or
acting in accordance with a concept. But note that one can do
violence to a concept, by misapplying it or stretching it beyond
breaking-point. Finally, while rules apply to subjects or agents
under their `jurisdiction', concepts apply to objects that satisfy
their dening criteria.
Another qualm would be that principles can be true or false,
whereas concepts cannot. Prima facie, at least, rules escape
this diculty. Even if they are expressed by sentences in the
indicative mood, it is arguable that their `truth' amounts to
nothing other than a particular prescription being actually in
force.
The question remains, however, what form these principles
or rules should take. Here we seem to be facing a dilemma.
One apparent option is that these rules are standards for the
employment of concepts. They might, for instance, take the
form of the rules Bennett extracts from Kant (Bennett 1966: 145):
(IV) You may apply concept F to x i x is . . .
But on this proposal, the concept F itself would not be
identical with the rule after all. It would rather be a predicate
the use of which is governed by the rule.
A second option is that the rule species another activity, e.g.
(V) You may treat x in way W i x is . . . .
In that case the danger is that we are stuck with two un-
palatable options. One is that W is a place-holder for practical
activities which may presuppose concept-possession, but which
someone who has mastered the concept need not be able to
But the matter is not straightforward. While one cannot dene the
meaning of an expression, one can certainly explain it. The crucial
point is that in all three cases terms, concepts, meanings one
ultimately species and demonstrates rules or principles for certain
cognitive or linguistic operations.
-
What are Concepts? 31
engage in; the other is that W is a place-holder for conceptuali-
zation, which would render the account unexplanatory.
Fortunately, this dilemma is more apparent than real. The
second horn can be avoided by noting that the form which
a conceptual rule takes depends on the kind of concept or
conceptual operation at issue. It is at least plausible to hold
that those cognitive operations which are genuinely conceptual
revolve around classication on the one hand, inference on the
other. If one is hard up for a generic label, one can say that
conceptual capacities are those involved in judgement (see also
Glock 2010a). Thirdly, the operations governed by rules of
classication and inference are clearly cognitive rather than
practical in nature, which avoids the rst horn of the dilemma.
This leaves one nal question: is there a substantive common
denominator between classication and inference, one that goes
beyond both being advanced cognitive operations? The answer
may well be negative. It is not even clear that classication and
inference always go together. Admittedly, even formal inference
depending on logical concepts presuppose judgements involving
predicative concepts and hence classication. But it is less clear
that classication requires inference of either the formal or the
material kind. There is at least a case to be made that the
behavioural capacities of some non-linguistic creatures amount
to classication rather than mere discrimination of stimuli, yet
without crossing the threshold of inference (see Newen and
Bartels 2007; Carey 2009; Glock 2010a).
9 The proposition problem
We now need to attend to a problem facing all cognitivist ac-
counts. Concepts are treated as the components from which pro-
positions are built, especially in logic and philosophy. At least
prima facie, however, neither abilities, nor ways of thinking, nor
rules of classication and inference occur in normal propositions;
at best, they occur in those propositions which are, respectively,
about abilities, ways of thinking or rules, i.e. explicitly mention
-
32 Hans-Johann Glock
or refer to them.
There are two ways of responding to this `proposition problem'.
I shall argue that in combination, these responses promise to re-
solve this diculty, which would otherwise seem intractable.
If Strawson (1959: Part II) is to be trusted, a universal such as a
property can enter a proposition not just in the direct sense that
the sentence expressing the proposition contains a word or phrase
referring to the property of being F, but also in the less direct
sense that the sentence contains a word or phrase signifying it. By
a similar token, such a sentence would contain a general term ex-
pressing the concept F, even though it does not refer to it. What
is more, one can extend this courtesy to any otherwise plausible
explanans of `concept'. Sticking to the rule proposal, this would
mean that the predicate in (3) expresses a rule for classiying
substances into those that possess the property of being sweet
and those that don't.
Crucial to this construal is that standard propositions, and by
implication our common or garden thoughts, are not about con-
cepts. That insight goes back at least as far as Aquinas. Ideas
(species) are `not what is thought of (id quod intelligitur) but
that by which thinking takes place (id quo intelligitur)' (Kenny
1980: 71). It is also accepted by Price, who identies concepts
with capacities:
The concept is not before the mind as an object of in-
spection. It is at work in the mind, but not as one in-
spectable content among others . . . It shows itself not as
a detectable item of mental furniture, but rather as a gui-
ding force, determining the direction which the series of
presented particulars [mental images or words] takes . . . '
(Price 1953: 342).
Finally, it is congenial to the Neo-Fregeanism propounded by
Knne. In the spirit of Strawson, Knne distinguishes between
application, connotes and expression: the general term `dog' ap-
plies to all and only dogs, connotes the property of being a dog,
and expresses the concept of being a dog (2005: 254 and fn. 31,
-
What are Concepts? 33
263; see also his 2003: 4).
Some such distinction is prerequisite for capturing the dierent
semantic properties or dimensions of general terms. Nonetheless
the StrawsonKnne solution to the proposition problem imme-
diately faces two challenges.
First, can't the courtesy of being allowed to enter into a proposi-
tion indirectly be extended from ways of thinking to all otherwise
plausible candidates for being concepts, notably abilities or ru-
les? Secondly, why should one accept that any of these candidates
feature in all propositions, however indirectly?
The answer to the rst question is straightforward in so far as we
stick to the relationship between concepts and general terms. It is
perfectly commonplace to speak of words as expressing concepts.
And there is no violent infelicity in speaking of general terms as
expressing ways of thinking. The same goes for rules of classi-
cation and/or inference. Perhaps one of these notions `ways of
thinking' or `rule' comes closer to capturing the ordinary mea-
ning of `concept', yet it is not on account of the possibility of being
expressed by general terms. By contrast, it is at best misleading
to speak of general terms as expressing an ability. Conceptual
abilities are possessed by cognitive subjects, and they are expres-
sed by in the sense of being manifested in the mental activities
notably the judgements and inferences of such subjects. And
we might say that those activities manifest concepts indirectly,
keeping this relation apart from the expression of concepts by
general terms. The notion of a conceptual ability points to the
subject of conceptual thought and to the activity (in a suitably
loose sense of the term) of conceptual thinking. By contrast, it is
out of place when it comes to the content of conceptual thought,
which is precisely what the idea of concepts as components of
propositions points to. What we still need is a way of reconciling
the mental or cognitive dimension of concepts with the objective
dimension suggested by their occurrence in propositions.
-
34 Hans-Johann Glock
10 Propositions and concepts as logical
constructions
This takes us straight to the second challenge. The Strawson
Knne response at best removes an obstacle to claiming that
concepts can be ways of thinking and yet appear in propositions.
But what positive reasons do we have for accepting that ways of
thinking appear in propositions, let alone as components of pro-
positions? The answer, I submit, is that both propositions and
their components are logical constructions out of the practices
and abilities of concept-exercising creatures.
Elsewhere (2010b; 2011) I have tried to substantiate this answer.
In the present context I conne myself to indicating some of the
critical steps that need to be taken. They involve attacking an
orthodoxy in the philosophy of mind and language epitomized by
the ubiquitous label `propositional attitude'. According to this or-
thodoxy, intentional verbs like `believe', `know', `desire', `intend'
signify relations between a subject and a proposition, which is
in turn composed of concepts. More specically, this orthodoxy
involves three distinct elements:
a relational model: an intentional state is a relation bet-
ween a subject and a content, something the intentional
state is directed at;
propositionalism: these contents are propositions
a building-block model: propositions are (abstract) who-
les which have (abstract) parts concepts.
All three elements must be rejected. First, propositionalism is
ab initio unsuitable for intentional states like craving x or inten-
ding to (Glock 2010a: 13-4). Next, even `thatish' intentionalverbs like `believe/know/desire that p' are not standardly direc-
ted at propositions (see White 1972). Thirdly, the relational mo-
del which treats believing or desiring that p as a relation to a
bona de object amounts to a reication. Finally, and related-
ly, the building block model, according to which propositions are
complex abstract entities composed of concepts as their proper
-
What are Concepts? 35
parts, is misguided. It transposes the part/whole relation from
the spatial and temporal sphere to a sphere that of abstract
entities to which, ex hypothesis, neither spatial nor temporal
notions apply. What seems to give sense to talk of parts and
wholes in the case of propositions or thoughts is the fact that
the linguistic expressions of thoughts namely sentences have
components namely words (see Kenny 1989: 1267). What is
said or thought has genuine components to the extent to which
its linguistic expression has components (which may, for instance,
be explained when A is called upon to state and explain what she
believes).
My approach is top-down in one respect and bottom-up in an-
other (for the distinction see Dretske 2000: 80-83). On the one
hand, in the spirit of a moderate contextualism, it regards the
components of sentences and intentional contents as abstractions
from entire sentences or `propositions'. On the other hand, this
semantic top-down approach is favoured, among other things, by
a bottom-up perspective on the nature and genesis of thought and
language. To describe more primitive capacities and communica-
tive practices, we do not need to identify conceptual components
but can start, in a holophrastic or holodoxastic mode with whole
sentences or beliefs, respectively. The imperative for parsing ari-
ses only when we reach a more complex phenomena, in particular
those which need to be described in terms of classication and
inference. Even if these phenomena are not conned to creatures
with language, in describing them we employ the apparatus of
fully articulated sentences and their components.
Although propositions are not themselves linguistic entities, they
are akin to what Prior (1971: ch. 2) called logical constructi-
ons from linguistic phenomena, namely from the that-clauses by
which we report and refer to what subjects say or think. The cri-
teria of identity for propositions make essential reference to lin-
guistic acts (sayings or utterances). There are propositions no one
has ever uttered or thought of. But what distinguishes two such
propositions is evident from the declarative sentences which ex-
press them. Although our criteria of identity for propositions are
-
36 Hans-Johann Glock
not the same as our criteria of identity for sentences, we can only
identify the former because we can identify the latter. Although
there are dierent linguistic expressions for the most important
truth discovered by Newton and the most important truth disco-
vered by Einstein, what distinguishes these two truths is evident
from their expressions `F = ma' and `E = mc
2'.
If the relational model, propositionalism and the building-block
model are jettisoned, cognitivism can oer a satisfactory soluti-
on to the proposition problem. In what sense, then, can rules of
classication and inference occur in propositions? The answer is,
very roughly: in the sense that S can only think that a is F in a
fully conceptual sense if S has the capacity to classify or recognize
objects as being F and draw inferences from this fact. Propositi-
ons are what is or can be said or thought. Concepts are rules or
principles that enable a subject to say or think such things, ways
in which subjects do or could conceive of properties.
To talk of propositions and concepts is not just a faon de parler,
and propositions and concepts are not just `make-believe entities'
(to use what is indeed a currently fashionable faon de parler).
Rather, they are logical constructions in a non-reductive sense. It
may prove impossible to paraphrase concepts away. We may need
to refer to them in order to describe the highly evolved cognitive
and/or linguistic abilities of certain creatures. At the same time,
the nature, individuation and function of concepts ceases to be
mysterious once we attend to the abilities that enable and neces-
sitate the ascription of concepts to a subject. In that respect, at
least, the possession question does indeed enjoy priority over the
others (see Glock 2010c: 315-9).
It is only possible to state what propositions and concepts are in
terms which implicitly refer to what subjects can say or do; and
we identify propositions and concepts by grouping or classifying
actual or potential token-expressions according to what they say
or mean. On this basis we may at least hope to reconcile two
apparently incompatible features of the established use of `con-
-
What are Concepts? 37
cept', the cognitive dimension of concepts and their appearance
in propositions.
8
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I wish to thank David Dolby and Frank Esken for helpful comments.
This material has also proted from discussions in Bielefeld, Olden-
burg, Osnabrck and Stuttgart, for which I am grateful. Finally,
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38 Hans-Johann Glock
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