Amazing variety of uses of the word 'concept', and corresponding diversity of roles that the notion has been taken to play (Rey 1983, Laurence & Margolis 1999, Prinz 2002, Glock 2010).
Each philosopher has his own enumeration of the roles of concepts; what one philosopher regards as central (e.g. that concepts are meanings of general words, Glock 2011) may be seen as peripheral at best by another philosopher (Prinz 2002). Some take such a variety at face value: concepts are all these things, they do play all these different roles.
Hence, a decent theory of concepts ought to accomodate them all:
characterize a single class of entities whose elements can play all the envisaged roles.
2 E.g., Prinz (Furnishing the Mind, 2002):
1. Concepts should be characterized in such a way that it makes sense to say that there are concepts of all sorts of different things, e.g. of pain, of number, of democracy, etc.;
2. Concepts must be such that they stand for, or are about things other than themselves (they have reference);
3. Nevertheless, a concept's content should not be exhausted by its reference (concepts have cognitive content);
4. At least some concepts must be such that they can be acquired; if some concepts are taken to be innate, the theory ought to explain how they can have evolved;
5. Concepts underlie categorization (including both recognition and inference); 6. Concepts are ingredients of thoughts;
7. Concepts are shared by different individuals, and by one individual at different times.
All these requirements correspond to features that have been attributed to concepts.
However, it doesn’t follow that there has to be a uniformly characterizable class of entities whose elements share all such features.
E.g. (re requirement 1.) it might turn out that there is no concept of democracy in the same sense in which there is a concept of red, i.e. that any entity that is a plausible candidate to being the concept of red has features that any plausible candidate to being the concept of democracy must lack.
Or it may turn out that if concepts are ingredients of thoughts (6.) then they cannot be recognitional abilities or recognitional procedures (5.) (Glock 2011).
It may be that the bits of theory (both philosophical and naive) that have been phrased using the word 'concept' are incoherent with one another, unless 'concept' is equivocal. In principle, there is no reason why our use of the word 'concept'
4 Ultimately, I will claim that there is indeed no such coherent theory: there is no
single notion of concept, i.e. there is no well characterized class of entities whose
elements simultaneously possess all the features that have been attributed to concepts.
However, there are apparent difficulties that arise along the path towards a theory of concepts that I regard as superficial.
The word 'concept' occurs in contexts that carry incompatible sortal restrictions. Examples:
- many have claimed that the meanings of (some) words are concepts (Fodor, Horwich 1998, etc.);
- but we say that concepts are instantiated by objects;
- however, meanings are not the sort of entities that are instantiated by objects.
(We say that Socrates instantiates the concept being brave, but we don't say that he instantiates the meaning of ‘brave‘, Glock 2010).
Or again:
- some (Geach, Kenny) say that concepts are abilities, but:
- we say that concepts are defined, yet the definition of a concept is not the definition of an ability;
- we don't say of abilities that they are instantiated by objects; - we don't say that an ability has an extension;
- concepts are taken to be ingredients of propositions, abilities are not. As a description of our use of ‘concept’, this is unobjectionable. Does it follow that
- either there are many different notions of concept,
- or any univocal characterization of concepts that intends to be coherent should be strongly revisionary with respect to usage (both ordinary and philosophical)?
6 Consider other cases of polysemy:
'occupation‘:
(1) the process of taking possession of a territory ("Japanese occupation of the Philippines required about one month");
(2) the state resulting from such a process ("Japanese occupation of the Philippines lasted about 3 years");
(3) any activity that takes a portion of a person's time and resources ("Learning to read is the major occupation of a 6-year-old");
(4) (particularly) a trade or employment ("Plumbing is Mary's occupation"). - no process is a state;
- nothing is both a process of occupying and a state of being occupied.
Nevertheless, we hesitate to conclude that there are three (or more) different
concepts of occupation. There appears to be a common conceptual core that is
Mary's time and resources are appropriated by plumbing, the Philippines were appropriated by the Japanese,
and it took them about one month to achieve the result.
(there are various distinctions to be made: we may say that the sense of 'occupation' in which plumbing occupies Mary's time is a metaphorical extension of the sense in which the Japanese occupied the Philippines).
BUT we don't want to say that no state of occupation2 can result from a process of occupation1: on the contrary, occupations2 are exactly the outcome of occupations1.
Similarly with some uses of ‘concept’:
- we don't say that Socrates instantiates the meaning of 'courageous',
-but we do say that Socrates instantiates the concept expressed by 'courageous'. - necessarily, if x is the meaning of a (predicate) word w, then there is exactly one
8 Similarly,
- a concept's definition (man = rational animal) may not look like the definition of an ability,
- but it can be read as establishing that possession of the ability to categorize an object as a human being amounts to possession of both the ability to categorize something as an animal and the ability to categorize something as rational.
Or,
- we don't say of an ability that it has an extension,
- but we do say that the ability to categorize apples singles out objects belonging to the extension of apple.
We choose to use the same word for both the ability to pick out members of the class of apples and the principle or rule that fixes the membership of that class.
Depending on how we decide to count notions,
- we may decide e.g. that there is a notion of occupation for the process of taking possession of a territory, and another, different though homonymous notion for the state resulting from such a process;
- or we may decide that there is one basic notion, taking different forms depending on whether we are considering the result of the process or the process itself.
Nothing of philosophical significance hinges on such a decision.
(Even if we make the former decision [two notions], we should not fail to realize that there is a well defined, biunique relation between being a process of occupying and being a state of occupation: every occupation1 results in exactly one occupation2, and every occupation2 is the result of exactly one occupation1.)
10 When two notions are so related I will say that they are in harmony with each other:
N1, N2 are in harmony with each other iff their extensions are necessarily isomorphic, i.e. iff there is a 1-1 function f such that Nec(x)(N1x N2(fx)). Two notions that are in harmony with each other are not the same notion:
husband and wife, though in harmony with each other (in monogamic systems), are not the same notion,
yet they may be regarded as specifications or “variants” of one basic notion (spouse).
Many problems with the notion of concept are of this kind.
One should not try to solve them by looking for entities that (e.g.) can be both abilities and things of which we would naturally say that they have an extension: there are no such entities.
Nevertheless, restricted to certain abilities (e.g. the ability to single out things that look yellow) and certain extension-determining functions (e.g. the fcn that picks up things that look yellow), there is a biunique function between the abilities and the functions. With such restrictions, the notion of concept as an ability and the notion of concept as an extension-determining function are in harmony.
Once the connection has been made clear, the polysemy of ‘concept’ is harmless.
12
Focus on a particular conflict involving two notions of concept: the
cognitive notion and the metaphysical notion.
Both notions, and both uses of ‘concept’, are central to philosophical
discourse on concepts (one is psychologically important as well), so that
neither is easily renounced; neither use appears to be reducible to the
other; moreover, as I will claim, they are not in harmony with each other.
THE COGNITIVE NOTION
We say that concepts are possessed by human beings: it is thanks to possession of the concept potato that they recognize potatoes, tell potatoes from kiwis, follow advice concerning potatoes ("Don't plant potatoes when it's too cold!"), and more. [cognitive]concepts are features of a human being's cognitive system:
- many of us can recognize potatoes and tell them from kiwis; how exactly we manage to do so is an empirical question, but it is uncontroversial that this and other similar abilities can be characterized as "cognitive" if anything can;
- it is likewise uncontroversial that the exercise of such abilities interacts with the motor system and the perceptual system;
- their exercise activates relatively well defined brain areas, and they can be lost because of brain damage.
14 THE METAPHYSICAL NOTION
We also say that something falls under the concept of P if and only if it is a P; for example, something falls under the concept of potato iff it is a potato.
The [metaphysical] concept of P is whatever determines the class whose only members are the Ps (all the Ps, and nothing but Ps).
To fall under the concept of P is to be a member of the class determined by the concept of P. The concept itself is not the class, but an entity that fixes the class: it may be conceived [Frege] as a function whose value is the True if the argument is a P, and the False otherwise. The extension of the concept = the class of the arguments for which the value of the function is the True.
This notion of concept applies to functions, rules, or principles that determine membership in a class in accordance with some metaphysical property such as
Claim: not that the cognitive and the metaphysical notion of concept are different
because nothing can be both a cognitive ability and an abstract entity.
(as long as the relevant notions are in harmony with each other, differences of this kind may be regarded as superficial)
For example, it might be that for every metaphysical concept there has to be one and only one cognitive concept that picks out exactly the metaphysical concept's extension, and viceversa.
Suppose that necessarily, the cognitive ability to recognize potatoes singled out exactly the objects that are potatoes; suppose further that this were the case for all cognitive concepts, and that for every metaphysical concept there were a cognitive ability that picks out exactly the metaphysical concept's extension. In that case, the cognitive and the metaphysical notion of concept would be in harmony with each other
16 Distinctions similar to the cognitive vs. metaphysical distinction:
- possession conditions vs. semantic value (Peacocke 1992); - nominal content vs. real content (Prinz 2002);
- “subjective” vs. “objective” dimension of concepts (Glock 2009, 2010). Closest: epistemological vs. metaphysical function of concepts (Rey 1983).
However: for Rey, a concept’s epistemological function = "the means by which an agent categorizes things, decides whether or not something is of a certain kind“.
This lumps together different kinds of categorization (see Malt & Sloman 2007).1 It is one thing for a subject to recognize a cat, and quite a different thing for a scientist to decide, after painstaking research, that a certain entity is a virus.
Cognitive vs. epistemological categorization:
EC (of something as a virus) is based on formal scientific knowledge & structured practices, both observational and experimental. CC (of something as a cat) is not so based;
EC takes time, CC is immediate;
EC requires some kind of formal training, CC doesn’t (even if the ability to recognize cats is regarded as acquired, it is not formed through formal training). Both underlying abilities can be seen as dispositions, but in EC's case, the list of conditions on which recognition is effected is going to be indefinitely long and complex.
18 We need a further distinction, between a cognitive and a properly epistemological function of concepts:
- Cognitively understood, concepts underlie ordinary, unreflective categorization, such as recognition of something as a P given some perceptual input;
- Epistemologically understood, they underlie reflective categorization, based on explicit knowledge and skills in addition to perceptual inputs.
(Claim) Neither the cognitive, nor the epistemological notion of concept is in harmony with the metaphysical notion.
However, my discussion will be limited to the cognitive notion and its opposition
A quick argument to show that the cognitive and the metaphysical notion of concept are not in harmony:
Some concepts are not observational: we do not recognize democracies just by looking (pace Prinz), nor tautologies (pace Wittgenstein), nor doubts.
Democracies, tautologies, or doubts are not unreflectively categorized given some perceptual input.
So, there are no cognitive concepts of democracy, doubt, or tautology, whereas there are metaphysical concepts of all such things.
Hence, there is no isomorphism between the set of cognitive concepts and the set of metaphysical concepts.
Consequently, by definition, the two notions, the cognitive and the metaphyisical, are not in harmony.
20 A more interesting argument (Part One).
(1) Consider observational concepts such as water or cat. Recognition of something x as a cat by a subject S is based on S's cognitive resources: no features of x that are inaccessible to S's cognitive system can play a role in S's recognition of x as a cat.
(2) However, features of x that are criterial for being a cat may or may not be cognitively accessible to S.
It may be that although x shares with the cats every feature that is accessible to S's cognitive system (i.e., it looks, sounds, and smells exactly like a cat), it also has features that rule out that it is a cat, though such features are cognitively inaccessible to S. Or it may be that x doesn't look (sound, smell, etc.) at all like a cat, so it is not recognizable as a cat, yet it is a cat, for it has cognitively inaccessible features that determine it to be a cat. (Putnam, etc.)
(Argument, Part One)
Call "cat's application class" the class of things that a subject is disposed to recognize as cats.
Then cat's application class may not coincide with the extension of the metaphysical concept cat. Indeed, given common sense knowledge about both human beings and their environment, in most cases a concept P's application class
will not coincide with its metaphysical extension.
Thus, there is no one-one mapping of the cognitive concept’s application class onto (or even into) the extension of the metaphysical concept.
22
Argument, Part Two
What would a reasonable isomorphism be between the set of cognitive
concepts and the set of metaphysical concepts? I.e., what connection
between cognitive and metaphysical concepts would make it plausible for
us to regard them as variants on a single notion of concept?
A plausible candidate:
if C
1is a cognitive concept and A
1is its application class, then there is
exactly one metaphysical concept C
2such that E
2is its extension and A
1=
E
2(and conversely).
I.e., the only reasonable way to set a correspondence between cognitive
and metaphysical concepts is by way of coincidence of their application
classes and metaphysical extensions.
(Argument, Part Two)
But we saw that there is no such isomorphism: in general, a cognitive
concept's application class does not coincide with the extension of any
non-trivially defined metaphysical concept.
[The proviso is due to the possibility of considering the metaphysical
concept (e.g.) thing that is recognized by S as a cat].
So, again, the cognitive and the metaphysical notion of concept are not in
harmony with each other. They are “deeply” different notions.
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Objections:
1) The scientific reply - All this just shows that the cognitive notion is not a
serious candidate to being a genuine notion of concept. First, it is too limited in scope (observational concepts are relatively few). Secondly, as cognitive "concepts" are supposed to be part of the cognitive endowment of individuals, they are both hard to pin down and liable to be inadequate for all sorts of reasons (such as individual idiosyncracies, variability even over short periods of time, etc.). The serious candidate to being a counterpart of the metaphysical notion is the
epistemological notion: scientific concepts are categorization devices whose
application class coincides with metaphysical extension. The epistemological notion can thus be shown to be in harmony with the metaphysical notion.
Answer:
If the objection were sound, it would make science unrevisable.
If the scientific concept water (say, being H2O) were guaranteed to have an
application class coinciding with the extension of being water, that would mean that present-day science has captured once for all the nature of water, so that every change in the scientific conception of water would amount to an error.
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2) The externalist reply - The lack of fit between the cognitive and the
metaphysical notion is due to a misconception of the cognitive notion. Mental mechanisms, like all mental entities, should be individuated externalistically: the concept cat is individuated by its relation to cats, i.e. to things that are cats. If it is conceived as a "detection mechanism" (e.g. Prinz 2002), then it should be seen as the mechanism that detects cats and only cats. Hence, harmony of the cognitive and the metaphysical notion is not at issue: it is built into the very notion of concept as a mental mechanism. A cognitive mechanism so conceived may of course malfunction for all sorts of reasons; in principle, however, its application class is bound to coincide with metaphysical extension.
This account does solve the harmony problem, as it builds harmony into the
cognitive notion by projecting metaphysical concepts into the mind. However, it
must face at least three problems: (a) generality,
(b) finiteness,
(a) generality - If cognitive concepts (as unreflective mental detection mechanisms) are individuated by objective relations to things in the world, how comes we have no such concepts for democracy, or tautology, or doubt? After all, we do stand in objective relations to democracies, tautologies, and cases of doubt, yet we possess no ability to tell democracies from non-democracies on the basis of perceptual input.
(b) finiteness - If our cognitive concepts' application class coincides with metaphysical extension, then the application class of addition (as a cognitive concept) coincides with the extension of the addition function. But, as Kripke (1981) pointed out, our disposition to apply addition does not encompass triples of very large numbers that are, however, members of the extension of the addition function.
28
(c) cognitive limitation - No matter how they are individuated, cognitive
concepts are mechanisms based on our cognitive resources - ultimately,
on our neural resources. Hence, cognitive concepts as detection
mechanisms are insensitive to differences or similarities that are
inaccessible to perception. Their application class is restricted
accordingly: the application class determined by our disposition to apply
the concept cat is not sensitive to the metaphysical property being a cat or
to whatever grounds that property. Indeed, it is not even sensitive to
whatever grounds (what we take to be) the biological property being a
cat: we do not recognize cats by analyzing their DNA - our naked
perceptual system is inadequate to the task. So, independently of
individuation, application class and metaphysical extension do not
coincide, not because of occasional malfunctioning but because of
systematic inadequacy.
If all the externalist wants to say is that our cognitive concepts are,
somehow, anchored (causally, teleologically, or otherwise) in things that
belong to certain metaphysical classes, that's fine. This may be enough to
individuate a certain detection mechanism as the concept red or the
concept cat. But it does not entail -not even in principle- that the concept's
application class coincides with the metaphysical concept's extension.
Even if a cognitive mechanism is individuated as the concept cat because
it is mostly activated by cats, or because it was selected thanks to its
capacity to tell most cats from most non-cats, etc., it remains that the
mechanism is not sensitive to the metaphysical property being a cat or to
whatever grounds that property.
The magnetic reply – If concepts as cognitive structures grouped objects into all
sorts of bizarre, gerrymandered classes, it would be hard to explain why we have
concepts at all. Concepts are a useful cognitive device –one that it makes sense
for evolution to have produced- only if they group together objects that belong together, i.e. only if they "carve nature at its joints". Hence, a cognitive concept's extension should be identified not with the concept's application class, but (e.g.) with the natural class that the application class best approximates.
Answers:
(a) Cognitive concepts = perceptually based detection mechanisms (insensitive to "deep" properties unless they correlate with perceptually accessible properties). Suppose we have a concept that picks out certain smallish, red, blue, or purple fruits typically growing on bushes; call it the concept berry.
Suppose it is later discovered that the blue berry-producing bushes are biologically very close to another berry-producing plant that looks quite different (grows on the ground, its berries, though also blue, are much larger, etc.)
A new concept is formed -call it BIO- covering both the bush-growing and the ground-growing fruits.
- the layman may or may not keep categorizing the bush-growing ones as "berries”
- the expert will categorize them together with the ground-growing fruits.
34
But in any case, the original concept berry did not cover the ground-growing fruits,
in spite of their sharing a joint-carving property with the bush-growing ones.
How could it? Perceptually, the ground-growing fruits were quite different, while the shared joint-carving property was perceptually inaccessible. It would be
implausible to insist that even the original concept did extend to the natural class of the Bios and did not extend to other berries.
(b) The concept that is most useful to have is not necessarily the one that best
carves nature at its joints.
Suppose most fruits picked out by the perceptually based concept were nutricious; suppose further that most of them –some nutricious, some not- shared some "deeper", perceptually inaccessible biological property.
Though the deep biological property is more joint-carving than the property of being nutricious, it is not plausible to suppose that we developed the concept berry because of the deep biological property, not because of the property of being nutricious.
(As far as words are concerned, we are free to say that 'berry' refers to fruits sharing the deep biological property: we may want reference to go with nature's joints rather than with macroscopic features of human environment. But as far as concepts as detection mechanisms are concerned, functionality to human interests (e.g., survival value) is crucial.)
An Objection (E.Lalumera, personal communication)
It is indeed possible to show that the cognitive notion and the metaphysical notion are in harmony with each other: the required isomorphism is provided by the relation of grasping.
Every cognitive concept is a grasping of some metaphysical concept, and every metaphysical concept is grasped by some mind by way of a cognitive concept. (The grasping of a metaphysical concept is going to be partial in many cases: the extension of the cognitive concept only approximates the metaphysical extension)
Reply 1: If approximation is allowed, we are bound to run into problems.
E.g.: necessarily, almost all successors of 0 are successors of 5. Hence, the
cognitive concept "successor of 5" is a (partial) grasping of the metaphysical
concept "successor of 0" (as well as of the metaphysical concepts "successor of 1", "successor of 2", etc.).
But then, the relation of grasping is not an isomorphism, as a single cognitive concept counts as a grasping of several different metaphysical concepts, and the same metaphysical concept, "successor of 0", is grasped by way of several different cognitive concepts.
Reply 2: If cognitive concepts are seen as "detection mechanisms" (as above), the
suggested harmony won't be there, for there are many concepts (in the metaphysical sense) to which no cognitive concept corresponds (democracy, tautology, etc.).
Therefore, Lalumera insists that cognitive concepts should not be so limited: "Reflective property production, lexical understanding, deductive and inductive inference and imagination are generally taken to be conceptual tasks by psychologists – tasks in which concepts are involved".
So, concepts in the cognitive sense must be "far richer than procedures for unreflective categorization. At least, as rich as licensing inferences."
- If she means that while cognitive concepts are more than detection mechanisms, being a detection mechanism is anyway necessary for being a cognitive concept, the reply stands.
-If, on the other hand, being an inference-licensing device is sufficient for being a cognitive concept, then we have a cognitive concept of whatever we have a theory of, including phlogiston, unicorns and ghosts.
It follows that for every such (cognitive-inferential) concept there necessarily is a metaphysical concept, i.e. an extension-determining function whose extension is at least approximated by the cognitive concept.
One wonders what that amounts to in the case of phlogiston, or unicorn, or ghost, or the many other theoretical constructs that are the object of false, though inferentially structured theories.
- no such metaphysical concepts?
40 We need (and have) two distinct notions of concept. One for mental mechanisms of categorization, another for whatever determines membership in a class.
Other parallel cases of duality between a cognitive and a logical or metaphysical notion:
reasoning vs. inference,
content of semantic competence vs. what determines a word's reference.
Since Frege, for a long time analytic philosophy worked on the presupposition of a sharp distinction between psychological notions and semantic, and, later, metaphysical notions;
In the cognitive 80s, some philosophers (Block, McGinn, Lycan, etc.) suggested that semantic content had two aspects, one psychological, the other not;
In the naturalistic 90s, some people (Prinz, Peacocke, Millikan) tried to show that a single notion could do both jobs. This is still the received view.
I propose a reactionary turn. But with an interest in the naturalistic notions that the classics didn’t share.
