The expression ‘we may well be asked’ as used in the passage means

  If our thoughts is to be clear and we are to succeed in communicating it to other people, we must have some method of fixing the meaning of the words we use. When we use a word whose meaning is not certain, we may well be asked to define it. There is a usual traditional device for doing this by indicating the class to which whatever is indicated by the term belongs and also other particular property which distinguishes it from all other members of the same class. Thus we may define a whale as a ‘marine animal that spouts’. ‘Marine animals’ in this definition indicates the general class to which the whale belongs and ‘spouts’ indicates the particular property that distinguishes whales from other such marine animals as fishes, seals, jellyfish and lobsters. In the same way, we can define an even number as a finite integer divisible by two or a democracy as a system of government in which the people themselves rule.

  there are other ways, of course of indicating the meaning of words. We may for example, find it hard to make a suitable definition of the word ‘animal’, as we say that an animal is such a thing as a rabbit, dog fish or goat. Similarly, we may say that religion is such a system as Christianity, Islam, Judaism and Buddhism. This way of indicating the meaning of a term by enumerating examples of what it includes is obviously of limited usefulness. If we indicate our use of the word ‘animal’ as above, our hearers might for example be doubtful whether a sea-anemone or a slug was to be included in the class of animals. It is however, a useful way of supplementing a definition if the definition itself id definite without being easily understandable. Failure of an attempt at definition to serve its purpose may result from giving as distinguishing mark one which either does not belong to all the things the definition id intended to include, or does belong to some members of the same general class which the definition is intended to exclude.