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 NECESSITY. 291 knowledge of what we are talking about will often lead us to see that what we had thought true of it is false. But the order of discovery is generally just the reverse of this. We must have judged correctly that certain collections of objects were three in number many times over, before we could know exactly what three was. And so here I must examine the cases in which things are said to be necessary, before I can discover what necessity is. Now it would appear there are three classes of entity which are commonly called necessary- We may call a connexion necessary, or we may call a thing necessary, or we may call a proposition necessary. And there is at least one property which may be common to all these three. All three of them may be forced upon the mind. We may have the feeling of compulsion with regard to them. We may feel compelled to believe that two objects have a certain relation, or that a certain thing exists, or that a certain proposition is true. But this feeling of compulsion, though it may probably have been the origin of all our ideas of necessity, has certain pro- perties which prevent us from identifying it with them. For it accompanies different beliefs at different times and in different persons. If we were to say that a necessary truth is one, belief in which is accompanied by a feeling of com- pulsion, we should have to admit that the same truth was necessary at one time and unnecessary at another, and even that the same truth might be simultaneously both necessary and unnecessary. But it is certain that necessary is often used in a sense which would exclude this possibility. Neces- sary truths, it would be said, are truths which are always necessary : and whether there are any such or not, we certainly mean by them something different from truths, belief in which is sometimes accompanied by a feeling of compulsion. Nor can it be said we only mean such truths as are generally accompanied by such a feeling. For the truths which are most commonly regarded as necessary do not now generally excite any such feeling when we believe in them. A belief in the truths of arithmetic, for example, has now become so habitual, that we obtain it with the greatest ease. And, if it be said that these beliefs are nevertheless all of such a nature that they would generally excite the feeling of compulsion, if we tried to believe the opposite, it HIM be admitted that this is true. Probably in most cases we should find it difficult to believe the opposite of those truths which we call necessary. They would force themselves upon us in spite of our efforts. But there is no reason to believe that any truths have this property universally. It