Synthesized answer
In Book II, the "Objectification of the Will" refers to the body. The body is described as the objectivity of the will, meaning the will has become idea and is perceived [1, 2]. Every true act of will is immediately a visible act of the body, and the action of the body is nothing but the act of the will objectified, or passed into perception [3]. The entire body is considered objectified will, or will become idea [3].
The passages explain that the world has two aspects: it is entirely idea, and in another aspect, it is entirely will [5]. The body is presented as the immediate object when viewed from the perspective of the idea [1]. Thus, the body is the objectivity of will, and the will is the knowledge _a priori_ of the body, while the body is the knowledge _a posteriori_ of the will [1].
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
follow upon mere stimuli, and, indeed, that the whole body is nothing but objectified will, _i.e._, will become idea. All this will be proved and made quite clear in the course of this work. In one respect, therefore, I shall call the body the _objectivity of will_; as in the previous book, and in the essay on the principle of sufficient reason, in accordance with the one-sided point of view intentionally adopted there (that of the idea), I called it _the immediate object_. Thus in a certain sense we may also say that will is the knowledge _a priori_ of the body, and the body is the…
an idea of perception, the body, has to that which is not an idea at all, but something _toto genere_ different, will. I should like therefore to distinguish this from all other truth, and call it κατ᾽ εξοχην _philosophical truth_. We can turn the expression of this truth in different ways and say: My body and my will are one;—or, What as an idea of perception I call my body, I call my will, so far as I am conscious of it in an entirely different way which cannot be compared to any other;—or, My body is the _objectivity_ of my will;—or, My body considered apart from the fact that it…
n two entirely different ways to the subject of knowledge, who becomes an individual only through his identity with it. It is given as an idea in intelligent perception, as an object among objects and subject to the laws of objects. And it is also given in quite a different way as that which is immediately known to every one, and is signified by the word _will_. Every true act of his will is also at once and without exception a movement of his body. The act of will and the movement of the body are not two different things objectively known, which the bond of causality unites; they do…
ost meaning of the question, which it failed to find, is this:—What is this world of perception besides being my idea? Is that of which I am conscious only as idea, exactly like my own body, of which I am doubly conscious, in one aspect as _idea_, in another aspect as _will_? The fuller explanation of this question and its answer in the affirmative, will form the content of the second book, and its consequences will occupy the remaining portion of this work. § 6. For the present, however, in this first book we consider everything merely as idea, as object for the subject. And our own…
adopted in consequence of some arbitrary abstraction. And yet it is a conception from which he can never free himself. The defectiveness of this view will be corrected in the next book by means of a truth which is not so immediately certain as that from which we start here; a truth at which we can arrive only by deeper research and more severe abstraction, by the separation of what is different and the union of what is identical. This truth, which must be very serious and impressive if not awful to every one, is that a man can also say and must say, “the world is my will.” In this…