equation: "an infinite number of years = infinity;" but if we reckon from to-morrow we have the equation, " an infinite number of years + one day = infinity." If we subtract the one equation from the other we arrive at the result, "one day = nothing."
But how do we arrive at this absurd conclusion? Simply by assuming, in subtracting one infinite front the other, that infinities must be equal; but such an assumption is opposed to the fundamental definition of infinity, which admits neither of equality nor inequality being predicated of it. This question is altogether distinct from the metaphysical one in reference to our power of conceiving or cogitating the infinite. It may be admitted that human thought is so limited that we cannot picture infinity to our minds. The question is, simply, can we not so define the idea of infinity, that it may be validly employed in any process of reasoning? We have seen that the attempts to prove contradictions in the very conception of infinity, are based on the fallacy of using two distinct and contradictory definitions of the term. The correct definition recognises infinites as incapable of comparison; the erroneous and tacitly-assumed definition involves the idea that infinites must be equal. In metaphysics, as well as mathematics, we shall meet with no antinomies if we use the word "infinity" in a correct and consistent manner. In his a priori argument, Dr Clarke does not think it necessary to prove the non-eternity of matter. He
