(_a_) The _existence_ of a part may be connected by a natural or causal necessity with the existence of the other parts of its whole; and further what is a part of a whole and what has ceased to be such a part, although differing intrinsically from one another, may be called by one and the same name. Thus, to take a typical example, if an arm be cut off from the human body, we still call it an arm. Yet an arm, when it is a part of the body, undoubtedly differs from a dead arm: and hence we may easily be led to say ‘The arm which is a part of the body would not be what it is, if it were not such a part,’ and to think that the contradiction thus expressed is in reality a characteristic of things. But, in fact, the dead arm never was a part of the body; it is only _partially_ identical with the living arm. Those parts of it which are identical with parts of the living arm are exactly the same, whether they belong to the body or not; and in them we have an undeniable instance of one and the same thing at one time forming a part, and at another not forming a part of the presumed ‘organic whole.’ On the other hand those properties which _are_ possessed by the living, and _not_ by the dead, arm, do not exist in a changed form in the latter: they simply do not exist there _at all_. By a causal necessity their existence depends on their having that relation to the other parts of the body which we express by saying that they form part of it. Yet, most certainly, _if_ they ever did not form part of the body, they _would_ be exactly what they are when they do. That they differ intrinsically from the properties of the dead arm and that they form part of the body are propositions not analytically related to one another. There is no contradiction in supposing them to retain such intrinsic differences and yet not to form part of the body.