to either of these words as applied to the totality of Space, and therefore no exclusion of two antagonist states of consciousness by one another. Both alternatives being unthinkable, the proposition should be put thus: Space is either        or is        ; neither of which can be conceived, but one of which must be true. In this, as in some other cases, Sir William Hamilton continues to work out the forms of thought when they no longer contain any substance; and, of course, reaches nothing more than verbal conclusions. Ending here these comments on doctrines of Sir William {193} Hamilton, which Mr. Mill rejects on grounds that will be generally recognized as valid, let me now pass to a doctrine, partly held by Sir William Hamilton, and held by others in ways variously qualified and variously extended—a doctrine which, I think, may be successfully defended against Mr. Mill’s attack. * * * * * In the fourth and fifth editions of his _Logic_, Mr. Mill treats, at considerable length, the question—Is inconceivability an evidence of untruth?—replying to criticisms previously made on his reasons for asserting that it is not. The chief answers which he there makes to these criticisms, turn upon the interpretation of the word _inconceivable_. This word he considers is used as the equivalent of the word _unbelievable_; and, translating it thus, readily disposes of sundry arguments brought against him. Whether any others who have used these words in philosophical discussion, have made them synonymous, I do not know; but that they are so used in those reasonings of my own which Mr. Mill combats, I was not conscious, and was surprised to find alleged. It is now manifest that I had not adequately guarded myself against the misconstruction which is liable to arise from the double meaning of the word _belief_—a word which, we have seen, is used for the most coherent and the least coherent connexions in consciousness, because they have the common character that no reason is assignable for them. Throughout the argument to which Mr. Mill replies, the word is used by me only in the first of these senses. The “invariably existent beliefs,” the “indestructible beliefs,” are the indissoluble connexions in consciousness—never the dissoluble ones. But _unbelievable_ implies the dissoluble ones. By association with the other and more general meaning of the word _belief_, the word _unbelievable_ suggests cases in which the proposition admits of being represented in thought, though it may be with difficulty; and in which, consequently, the counter-proposition admits of being {194} decomposed. To be quite sure of our ground, let us define and illustrate the meanings of _inconceivable_ and _unbelievable._ An inconceivable proposition is one of which the terms cannot, by any effort, be brought before consciousness in that relation which the proposition asserts between them—a proposition of which the subject and the predicate offer