Let us take some very humble example. Suppose you look in a time-table and find it there stated that a passenger train leaves King’s Cross for Edinburgh at 10 A.M. What is the meaning of this assertion? I shudder when I think of its complexity. If I were to try to develop the theme adequately, I should be occupied with nothing else till the end of the present volume, and then I should have only touched the fringe of the subject. Take first the social aspect: it is not essential that anybody but the engineer and fireman should travel by the train, though it is essential that others should be _able_ to travel by it if they fulfil certain conditions. It is not essential that the train should reach Edinburgh: the statement remains true if there is an accident or breakdown on the way. But it is essential that the management of the railway should intend it to reach Edinburgh. Take next the physical aspect: it is not essential, or even possible, that the train should start _exactly_ at ten; one might perhaps say that it must not start more than ten seconds before its time or more than fifty seconds after, but these limits cannot be laid down rigidly. In countries where unpunctuality is common they would be much wider. Then we must consider what we mean by “starting”, which no one can define unless he has learnt the infinitesimal calculus. Then we consider the definitions of King’s Cross and Edinburgh, both of which are more or less vague terms. Then we must consider what is meant by a “train”. Here there will be first of all complicated legal questions; what constitutes fulfilment of a railway company’s obligations in the way of running “trains”? Then there are questions as to the constitution of matter, since evidently a train is a piece of matter; also of course there are questions as to methods of estimating Greenwich time at King’s Cross. Most of the above points have to do with the meaning of single words, not with the meaning of the whole sentence. It is obvious that the ordinary mortal does not trouble about such complications when he uses the words: to him a word has a meaning very far from precise, and he does not try to exclude marginal cases. It is the search for precision that introduces complications. We think we attach a meaning to the word “man”, but we don’t know whether to include Pithecanthropus Erectus. To this extent, the meaning of the word is vague. As knowledge increases, words acquire meanings which are more precise and more complex; new words have to be introduced to express the less complex constituents which have been discovered. A word is intended to describe something in the world; at first it does so very badly, but afterwards it gradually improves. Thus single words embody knowledge, although they do not make assertions.