The first and fourth points require our especial attention. 1. Let us particularly mark, then, that it is _as defined_, that the terms are "contradictory." The question, therefore, turns upon the definitions. Undoubtedly the definitions are erroneous; but in order to see wherein, the following general reflections may be made:-- The terms infinite and absolute, as used by philosophers, have two distinct applications: one to Space and Time, and one to God. Such definitions as are suitable to the latter application, and self-consistent, have already been given. Though reluctant to admit into a philosophical treatise a term bearing two distinct meanings, we shall waive for a little our scruples,--though choosing, for ourselves, to use the equivalent rather than the term. Such definitions are needed, then, as that absolute Space and Time shall not be contradictory to infinite Space and Time. Let us first observe Hamilton's theory. According to it, Space, for instance, is either unconditional illimitation, or it is unconditional limitation; in other words, it is illimitable, or it is a limited whole. The first part of the assertion is true. That Space is illimitable, is unquestionably a self-evident truth. Any one who candidly considers the subject will see not only that the mind cannot assign limits to Space, but that the attempt is an absurdity just alike in kind with the attempt to think two and two five. The last part is a psychological blunder, has no pertinence to the question, and is not what Hamilton was groping for. He was searching for the truth, that _there is no absolute unit in Space_. A limited whole has nothing to do with the matter in hand--absoluteness--at all. The illimitability of Space, which has just been established as an axiom, precludes this. What, then, is the opposite pole of thought? We have just declared it. There is no absolute unit of Space; or, in other words, all division is in Space, but Space is indivisible. This, also, is an axiom, is self-evident. We attain, then, two poles of thought, and definitions of the two terms given, which are exhaustive and consistent. "Space is illimitable. Space is indivisible." The one is the infinity of Space, the other is the absoluteness of Space. The fact, then, is, all limitation is _in_ Space, and all division is _in_ Space; but Space is neither limited or divided. One of the logician's extremes is seen, then, to have no foundation in fact; and that which is found to be true is also found to be consistent with, nay, essential to, what should have been the other.