Notions like "lemon", "religion", "school", "table" , "story" , and "fascism" are cluster concepts.
To be a lemon, there are a number of conditions (defining attributes). The conditions:

may not be essential (a lemon has a waxy skin) and
are meetable to some degree (a lemon is yellow) or only as has/doesn't have (a lemon has internal seeds).

If we know the conditions (defining attributes) in the cluster and we are fairly well agreed on their relative importance, we are ready to communicate.

More, thanks to Norman Swartz

Let's try to work out our own case to see what sort of thing Wittgenstein's metaphor amounts to. I propose we try to define the term "lemon" [Note 27]. We begin by listing some of the characteristics lemons typically exhibit. Lemons typically:

1.	are yellow	10.	are internally segmented
2.	are sour	11.	are pulpy
3.	are ovoid	12.	have a pocked surface
4.	grow on trees	13.	are green prior to maturation
5.	are as big as a ten-year old's fist	14.	grow in a semitropical climate
6.	are juicy	15.	have a waxy skin
7.	have internal seeds	16.	contain vitamin C
8.	have a peculiar (lemony [Note 28]) aroma	17.	are edible
9.	have a thick skin	18.	other ... ?

With this rather long list before us, can we proceed to construct a definition of "lemon" that satisfies the classical theory?

     First we ask whether there is any item on the list which is a necessary condition for calling a thing a "lemon". Is being yellow? Suppose we find something which in all other respects except its color, which happens to be pink, is just like all the lemons we have ever encountered. Would we call it a "lemon"? More than likely. But if so, being yellow is not a necessary condition for a thing's being called a "lemon". Similarly for virtually any other item in the list. If a thing resembled lemons as we now know them save it were sweet instead of sour, we probably would still call it a "lemon". And so on and so on. The upshot of the argument is that few, if any, items on the list are necessary conditions. Virtually any one could be abandoned and we might still call the object which exemplified all the rest a "lemon". Perhaps we might even let some pairs of items be deleted, or maybe even some threesomes. (Even so, obviously some items are more important than others.)

     Clearly if an object exemplifies every item on the list it properly can be called a "lemon": the entire list is jointly sufficient. But the list is overdetermined; something less than the entirety might also be jointly sufficient.

     In summary, few, if any, items in our list are necessary and something less than the entirety is jointly sufficient.

     It would seem, then, that what it is to be properly called a "lemon" is to score fairly well in most of the various categories.

     But if this is so, how are we to construct a precise (more exactly, an intensional) definition? How are we going to capture in our definitions the vague notions of "score fairly well" and "most"? The classical theory did not allow the intrusion of these vague qualifying terms; yet they seem to be unavoidable in the present case.

     The answer favored by many (perhaps most) philosophers nowadays is that we cannot construct a classical definition for "lemon". The term, "lemon", is a so-called 'cluster-concept' [Note 29] – it is made up of a number of conditions which generally are not singly necessary and are jointly oversufficient.

     There is no doubt that all of us are able successfully to use the word "lemon" and we could 'go on' classifying various things as lemons or not. But because all the lemons we have ever seen have been yellow, we have never had to ask ourselves whether something which is orange could properly be called a "lemon". We have not had to ask whether being yellow is a strictly necessary condition for a thing's being called a "lemon". Thus in one sense we do not know the definition of "lemon": that is, we cannot give a classical intensional definition for it. Yet it would be absurd to say that we do not know what "lemon" means. Of course we do. The concept, lemon, is a cluster concept, and we know the conditions in the cluster and we are fairly well agreed on their relative importance.

     It should be clear that classical definitions are possible for only a relatively minute number of terms. Virtually all the sophisticated classificatory terms that we use mark out 'clusters' of characteristics and not hard-and-fast lists of characteristics. Typically we know very well what "lemon" means, what "religion" means, what "school" means, what "table" means, what "story" means, etc. But any attempt to define "lemon", "religion", "school", "table", or "story" by means of a specification of necessary and sufficient conditions will do violence to the accepted extension. If we attempt to specify a single list of necessary and sufficient conditions for the application of the definiendum, we will be faced with this dilemma: Either (1) the list of conditions will be too long (the intension will be too narrow) and consequently will eliminate from the extension various members which properly belong in the extension but which fail to exemplify every necessary condition mentioned, or (2) the list of conditions will be too short (the intension will be too broad) and thus will admit into the extension various things which properly belong outside of it but which do succeed in satisfying the set of jointly sufficient conditions specified. There is little prospect of specifying a single set of individually necessary and jointly sufficient conditions which marks out the same extension as a cluster-concept constructed from those same conditions.

     In short, very often we know the extension of a term very well, we can even 'go on' reasonably well, yet we are unable to specify the intension, and moreover ought on many occasions to resist the demand that we try to give an intensional definition for the term.
[ Return to Table of Contents ]