we demand whether anything be the same or no, it refers always to something that existed such a time in such a place, which it was certain, at that instant, was the same with itself, and no other.  From whence it follows, that one thing cannot have two beginnings of existence, nor two things one beginning; it being impossible for two things of the same kind to be or exist in the same instant, in the very same place; or one and the same thing in different places.  That, therefore, that had one beginning, is the same thing; and that which had a different beginning in time and place from that, is not the same, but diverse.  That which has made the difficulty about this relation has been the little care and attention used in having precise notions of the things to which it is attributed.

2.  Identity of Substances.

We have the ideas but of three sorts of substances:  1.  God. 2.  Finite
intelligences. 3.  Bodies.

First, god is without beginning, eternal, unalterable, and everywhere, and therefore concerning his identity there can be no doubt.

Secondly, finite spirits having had each its determinated time and place of beginning to exist, the relation to that time and place will always determine to each of them its identity, as long as it exists.

Thirdly, The same will hold of every particle of matter, to which no addition or subtraction of matter being made, it is the same.  For, though these three sorts of substances, as we term them, do not exclude one another out of the same place, yet we cannot conceive but that they must necessarily each of them exclude any of the same kind out of the same place:  or else the notions and names of identity and diversity would be in vain, and there could be no such distinctions of substances, or anything else one from another.  For example:  could two bodies be in the same place at the same time; then those two parcels of matter must be one and the same, take them great or little; nay, all bodies must be one and the same.  For, by the same reason that two particles of matter may be in one place, all bodies may be in one place:  which, when it can be supposed, takes away the distinction of identity and diversity of one and more, and renders it ridiculous.  But it being a contradiction that two or more should be one, identity and diversity are relations and ways of comparing well founded, and of use to the understanding.

3.  Identity of modes and relations.

All other things being but modes or relations ultimately terminated in substances, the identity and diversity of each particular existence of them too will be by the same way determined:  only as to things whose existence is in succession, such as are the actions of finite beings, v. g.  Motion and thought, both which consist in a continued train of succession, concerning their diversity there can be no question:  because each perishing the moment it begins, they cannot exist in different times, or in different places, as permanent beings can at different times exist in distant places; and therefore no motion or thought, considered as at different times, can be the same, each part thereof having a different beginning of existence.