all more complex logical relations must really rest.
The Nature of Inference.
The question, What is Inference? is involved, even to the present day, in as much uncertainty as that ancient question, What is Truth? I shall in more than one part of this work endeavour to show that inference never does more than explicate, unfold, or develop the information contained in certain premises or facts. Neither in deductive nor inductive reasoning can we add a tittle to our implicit knowledge, which is like that contained in an unread book or a sealed letter. Sir W. Hamilton has well said, “Reasoning is the showing out explicitly that a proposition not granted or supposed, is implicitly contained in something different, which is granted or supposed.”12
Professor Bowen has explained13 with much clearness that the conclusion of an argument states explicitly what is virtually or implicitly thought. “The process of reasoning is not so much a mode of evolving a new truth, as it is of establishing or proving an old one, by showing how much was admitted in the concession of the two premises taken together.” It is true that the whole meaning of these statements rests upon that of such words as “explicit,” “implicit,” “virtual.” That is implicit which is wrapped up, and we render it explicit when we unfold it. Just as the conception of a circle involves a hundred important geometrical properties, all following from what we know, if we have acuteness to unfold the results, so every fact and statement involves more meaning than seems at first sight. Reasoning explicates or brings to conscious possession what was before unconscious. It does not create, nor does it destroy, but it transmutes and throws the same matter into a new form.
The difficult question still remains, Where does novelty of form begin? Is it a case of inference when we pass from “Sincerity is the parent of truth” to “The parent of truth is sincerity?” The old logicians would have called this change conversion, one case of immediate inference. But as all identity is necessarily reciprocal, and the very meaning of such a proposition is that the two terms are identical in their signification, I fail to see any difference between the statements whatever. As well might we say that x = y and y = x are different equations.
Another point of difficulty is to decide when a change is merely grammatical and when it involves a real logical transformation. Between a table of wood and a wooden table there is no logical difference (p. 31), the