Cats have claws and teeth and fur. They do not have implications. No physical thing has implications. The _term_ "cat" has implications. How can this difference be explained? On the ground that we cannot use the "cat" object inferred from given indications in such a way as will test the inference and make it fruitful, helpful, unless we can detach it from its existential dependence upon the particular things which suggest it. We need to know what a cat would be _if_ it were there; what other things would also be indicated if the cat is really indicated. We therefore create a _new_ object: we take something to stand for the cat-in-its-status-as-inferred in contrast with the cat as a live thing. A sound or a visible mark is the ordinary mechanism for producing such a new object. Whatever the physical means employed, we now have a new object; a term, a meaning, a notion, an essence, a form or species, according to the terminology which may be in vogue. It is as much a specific existence as any sound or mark is. But it is a mark which notes, concentrates, and records an outcome of an inference which is not yet accepted and affirmed. That is to say, it designates an object which is _not yet_ to be reacted to as one reacts to the given stimulus, but which is an object of further examination and inquiry, a medium of a postponed conclusion and of investigation continued till better grounds for affirming an object (making a definite, unified response) are given. _A term is an object so far as that object is undergoing shaping in a directed act of inquiry._ It may be called a possible object or a hypothetical object. Such objects do not walk or bite or scratch, but they are nevertheless actually present as the vital agencies of reflection. If we but forget where they live and operate--within the event of controlled inference--we have on our hands all the mysteries of the double world of existence and essence, particular and universal, thing and idea, ordinary life and science. For the world of science, especially of mathematical science, is the world of considerations which have approved themselves to be effectively regulative of the operations of inference. It is easier to wash with ordinary water than with H{2}O, and there is a marked difference between falling off a building and 1/2_gt_^{2}. But H{2}O and 1/2_gt_^{2} are as potent for the distinctive act of inference--as genuine and distinctive an act as washing the hands or rolling down hill--as ordinary water and falling are impotent.