The subsequent explanations can be made easier to follow by a small piece of symbolism: Let _aEb_ mean that "_b_ is part of _a_." We need not decide whether we are talking of time-parts or space-parts, but whichever choice is supposed to be made must be conceived as adhered to throughout any connected discussion. The symbol _E_ may be considered as the initial letter of "encloses," so we read "_aEb_" as "_a_ encloses _b_." Again the "field of _E_" is the set of things which either enclose or are enclosed, _i. e._ everything "_a_," which is such that _x_ can be found so that either _aEx_ or _xEa_. A member of the field of _E_ is called "an enclosure-object." Now, we assume that this relation of whole-to-part, which in the future we will call "enclosure," always satisfies the conditions in that the relation _E_ is (1) transitive, (2) asymmetrical, and (3) with its domain including its converse domain. These four conditions deserve some slight consideration; only the first two of them embody hypotheses which enter vitally into the reasoning. Condition (1) may be stated as the condition that _aEb_ and _bEc_ always implies _aEc_. The fact that an entity _b_ can be found such that _aEb_ and _bEc_ may be conceived as a relation between _a_ and _c_. It is natural to write _E_^2 for this relation. Thus the condition is now written: If _aE_^2_c_, then _aEc_. This can be still otherwise expressed by saying that the relation _E_^2 implies, whenever it holds, that the relation _E_ also holds. Condition (2) is partly a mere question of trivial definition, and partly a substantial assumption. The asymmetrical relation (_E_) is such that _aEb_ and _bEa_ can never hold simultaneously. This property splits up into two parts: (1) that no instance of _aEb_ and _bEa_ and "_a_ diverse from _b_," can occur, and (2) that _aEa_ cannot occur. The first part is a substantial assumption, the second part (so far as we are concerned) reduces to the trivial convention that we shall not consider an object as part of itself, but will confine attention to "proper parts." Condition (3) means that _aEb_ always implies that _c_ can be found such that _bEc_. This condition, taken in conjunction with the fact that we are only considering proper parts, is the assertion of the principle of the indefinite divisibility of extended objects, both in space and in time. An indivisible part will lack duration in time, and extension in space, and is thus an entity of essentially a different character to a divisible part. If we admit such indivisibles as the only true sense-objects, our subsequent procedure is an unnecessary elaboration.