valid objection to the soundness of our principle of interpretation, but a necessary consequence of the infinity of Reality.[92] Any consistent attempt to exhibit an infinite whole as an orderly system of terms _must_ lead to the indefinite regress. Now it strikes one at once that Professor Royce’s conclusion is in danger of proving too much. You certainly do not show a method of dealing with facts to be sound by showing that it leads to the indefinite regress. It is a common experience that the liar who tells his first lie must tell a second to back it, and a third to support the second, and so on indefinitely. And you cannot put a quart of liquor into a pint pot without first putting half the quart into half the space, and so forth _ad indefinitum_. Yet these considerations do not prove that lying or putting quarts of liquor into pint pots is a consistent way of dealing with reality. A purpose may lead in execution to the indefinite regress because it is self-contradictory and therefore self-defeating, as these familiar illustrations suggest. And this raises the question whether the purpose to arrange an infinite whole in an ordered system of terms may not lead to the indefinite regress for the same reason, namely, that the treatment of a true whole as a sequence of terms is incompatible with its real nature. It is at least worth while to ask whether Professor Royce’s own treatment of the subject does not contain indications that this is actually the case.[93] To begin with, we may note one point of some importance in reference to which Prof. Royce’s language is at least ambiguous. He speaks of the indefinite succession of infinite series which arise from the single purpose of “representing” the series of natural integers adequately by a selection out of itself as if they could be actually constructed in pursuance of this purpose. But this is clearly not the case. All that you can actually do is to construct the various series _implicitly_ by giving a rule for their formation. The actual construction of the series would be a typical instance of a self-defeating and therefore internally contradictory purpose, inasmuch as it would involve the actual completion of an unending process. Hence we seem forced to make a distinction which Prof. Royce has perhaps unduly neglected. If your purpose of ordering the number series on a definite plan means no more than the formulation of a rule for obtaining any required number of terms of the successive series, it can be executed, but does not involve the indefinite regress; if it means the actual completion of the process of formation of the series, it does involve the indefinite regress, but is therefore self-contradictory and cannot be realised in act. Similarly, we may say of the scheme of qualities in relation, that if it is taken for no more than a rule for the systematic arrangement and organisation of a finite material, it does not involve the completion of