Edouard Machery's Doing Without Concepts made a big splash in 2009, since it argues in all seriousness that concepts do not exist.

But wait. In order to claim that concepts don't exist, doesn't Machery need the concepts of "concept" and "exist"? To clarify what Machery means, I will summarize his book.

Machery argues for the Heterogeneity Hypothesis, which makes five basic claims:

1. The best available evidence suggests that for each category (for each substance, event, and so on), an individual typically has several concepts.
2. Coreferential concepts have very few properties in common. They belong to very heterogeneous kinds of concept.
3. Evidence strongly suggests that prototypes, exemplars, and theories are among these heterogeneous kinds of concept.
4. Prototypes, exemplars, and theories are typically used in distinct cognitive processes.
5. The notion of concept ought to be eliminated from the theoretical vocabulary of psychology.

Concepts in psychology and philosophy

After reviewing the psychological literature on concepts, Machery proposes that by "concept" psychologists usually mean something like this:

A concept of x is a body of knowledge about x that is stored in longterm memory and that is used by default in the processes underlying most, if not all, higher cognitive competences when these processes result in judgments about x.

Philosophers, by contrast, usually means something like this:

Having a concept of x is being able to have propositional attitudes about x as x.

As such, psychologists and philosophers are engaging in different projects when they talk about concepts, and Machery reviews some cases in which this has caused confusion.

Prototypes, exemplars, and theories

Since the death of the classical view of concepts, three paradigms about concepts have emerged in psychology: the prototypes paradigm, the exemplars paradigm, and the theories paradigm. 

In fact, we have pretty good evidence for the existence of all three kinds of concepts. Moreover, we seem to possess distinct processes for learning these kinds of concepts, and also distinct processes for categorizing.

Scientific eliminativism

The first seven chapters provide the evidence for Machery's first four claims. The eight chapter makes his eliminativist argument:

In this section, I introduce in some detail a new type of eliminativist argument. Since this argument does not bear on the elimination of folk notions, but exclusively on the elimination of scientific notions and on their replacement by other theoretical notions, I call this form of eliminativism “scientific eliminativism.” Applied to “concept,” scientific eliminativism goes in substance as follows. In contrast to old-fashioned eliminativist arguments, the scientific eliminativist does not dispute that “concept” picks out a class of entities: there are bodies of knowledge stored in long-term memory and used by default in the processes underlying the higher cognitive competences. Instead of arguing that “concept” does not refer, the scientific eliminativist makes a case that the class of concepts does not possess the properties that characterize the classes that matter for the empirical sciences. Or, to use a slogan, that this class is not a natural kind. If “concept” does not pick out a natural kind, then it is unlikely to be a useful notion in psychology. It is even likely to stand in the way of progress in psychology, by preventing the development of a more adequate classificatory scheme that would identify the relevant natural kinds. If this is the case, the term “concept” ought to be eliminated from the theoretical vocabulary of psychology and replaced with more adequate theoretical terms.

...If psychologists were to say that categorization involves prototypes, exemplars, and theories, rather than saying (as they now do) that it involves concepts, it would be clear that psychologists have to describe what prototypes, exemplars, and theories are, rather than describing what concepts are. It would also be clear that they have to explain how the categorization processes that use prototypes, exemplars, and theories are organized. Bringing these tasks to the fore is the main pragmatic reason that justifies the drastic conceptual change proposed in this book—doing psychology without the theoretical term “concept.”

Whether or not you agree with Machery's scientific eliminativism, the main takeaway from his book is that "concept" is not a very good "natural kind" even if it may remain a useful class of natural kinds.

This has implications for philosophy. If we're trying to describe the "concept" of "ought" or of "good," perhaps instead we ought to be discussing the prototypes, exemplars, or theories of "ought" or "good."

For other discussions of Machery's book, see Fenici, Chen, Glymour, Woodfield, and especially BBS.