Synthesized answer
The world as idea is subject to the principle of sufficient reason [1]. This principle explains the connections of phenomena [4]. The form of the object, which is the world as idea, is the principle of sufficient reason in its various forms [5]. Time, for example, is described as nothing more than that form of the principle of sufficient reason [1].
The principle of sufficient reason governs each class of ideas absolutely, such that knowing its special form reveals the nature of the whole class, as the class itself is no more than this form [5]. However, the passages also state that the principle of sufficient reason explains the connections of phenomena but not the phenomena themselves [4]. We cannot arrive at the real nature of things from the idea under the guidance of the laws that merely combine objects, ideas, among themselves, which are the forms of the principle of sufficient reason [3]. Therefore, the passages do not fully explain how Schopenhauer's "Idea" relates to the "Principle of Sufficient Reason," beyond stating that the idea is subject to this principle and that the principle is the form of the object.
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
becoming, but never being; in Spinoza as the doctrine of the mere accidents of the one substance which is and endures. Kant opposes what is thus known as the mere phenomenon to the thing in itself. Lastly, the ancient wisdom of the Indian philosophers declares, “It is Mâyâ, the veil of deception, which blinds the eyes of mortals, and makes them behold a world of which they cannot say either that it is or that it is not: for it is like a dream; it is like the sunshine on the sand which the traveller takes from afar for water, or the stray piece of rope he mistakes for a snake.” (These…
e; and therefore the subject remains always outside the province in which the principle of sufficient reason is valid. The controversy as to the reality of the outer world rests upon this false extension of the validity of the principle of sufficient reason to the subject also, and starting with this mistake it can never understand itself. On the one side realistic dogmatism, looking upon the idea as the effect of the object, desires to separate these two, idea and object, which are really one, and to assume a cause quite different from the idea, an object in itself, independent of…
t they are connected according to certain laws, the general expression of which is the principle of sufficient reason. We wish to know the significance of these ideas; we ask whether this world is merely idea; in which case it would pass by us like an empty dream or a baseless vision, not worth our notice; or whether it is also something else, something more than idea, and if so, what. Thus much is certain, that this something we seek for must be completely and in its whole nature different from the idea; that the forms and laws of the idea must therefore be completely foreign to…
therefore it is not possible to construct, as Spinoza wished, a philosophy which demonstrates _ex firmis principiis_. Philosophy is the most general rational knowledge, the first principles of which cannot therefore be derived from another principle still more general. The principle of contradiction establishes merely the agreement of concepts, but does not itself produce concepts. The principle of sufficient reason explains the connections of phenomena, but not the phenomena themselves; therefore philosophy cannot proceed upon these principles to seek a _causa efficiens_ or a _causa…
ts from the object; it begins by assuming what it proposes to deduce, the necessary correlative of its starting-point. The method of our own system is _toto genere_ distinct from these two opposite misconceptions, for we start neither from the object nor from the subject, but from the _idea_, as the first fact of consciousness. Its first essential, fundamental form is the antithesis of subject and object. The form of the object again is the principle of sufficient reason in its various forms. Each of these reigns so absolutely in its own class of ideas that, as we have seen, when the…