<P> Thus, our understanding does not exist independent of our ability to perceive and determine relationships anchored in experience itself . Not only what we think in the abstract, but also our very perceptions are completely intellectual and subjectively determined via extraction, new formation, and modified formulation . Already we have the philosophical grounds for Nietzsche's perspectivism, though given in different language: representation (Vorstellung). One may also translate "Vorstellung" as the English word "idea"--indeed, Schopenhauer himself provides this translation from Kant's similar use of "Vorstellungen ." However, this "idea" is semantically distinct both from the Platonic Idea (which Schopenhauer insists be expressed with the German "Ideen") and from Berkeley's use of "idea ." </P> <P> Schopenhauer's central proposition is the main idea of his entire philosophy, he states simply as "The world is my representation ." The rest of his work is an elaborate analysis and explanation of this sentence, which begins with his Kantian epistemology, but finds thorough elaboration within his version of the principle of sufficient reason . This is responsible for providing adequate explanations for any' thing,' or object that occurs in relation to a subject of knowing; of any representation possible there is always a possible question of' why?' that one can address to it . It amounts to what Schopenhauer has done, in his view, to extend and complete what Kant began in his Critique of Pure Reason . </P> <P> Four classes of explanation fall under the principle's rubric . Hence, four classes of objects occur always and already only in relation to a known subject, according to a correlative capacity within the subject . These classes are summarized as follows: </P> <Ul> <Li> Becoming: Only with the combination of time and space does perceptual actuality become possible for a subject, allowing for ideas of interpretation, and this provides the ground of becoming judgment . This is the law of causality, which is, when considered subjectively, intellectual and a priori - linked understanding . All possible judgments that are inferences of a cause from an effect--a physical state any subject infers as caused by another physical state or vice versa--presumes this as primary ground for the expected potentials of such judgments . The natural sciences operate within this aspect of expanding principles . Schopenhauer proposed a proof of the a priori of causality (i.e. that the universe indeed operates, at least in general, as causal instead of just being perceived so a posteriori, due to the repeatability of sequences) that remains different from Kantian Theory . Proof relies on the intellectuality of perceived things (representations)--these are produced by "projecting causality backwards in time," from physical excitations of cells and nerves (this is the afferent role of the intellect, or brain)--and is apparently influenced by the medieval philosopher Witelo and his work on optics and the psychology of seeing . </Li> <Li> Knowing: This class of objects subsumes all judgments, or abstract concepts, which a subject knows through conceptual, discursive reason rooted in the ground of knowing . The other three classes of objects are immediate representations, while this class is always and already composed of fixed representations of representations . Therefore, the truth - value of concepts abstracted from any of the other three classes of objects is grounded in referring to something outside the concept . Concepts are abstract judgments grounded in intuitions of time and space, ideas of perception (causality apparent in the outer world), or acts of direct will (causality experienced from within). That conceptions are easier to deal with then representations; they are, in fact, to these almost as the formula of higher arithmetic to the mental operations which give rise to them and which they represent, or as logaritm to its number (please researching scientific creativity for more understanding, i.e Simonton's "chance configuration theory / 1988", Simontons random permutations have a strong relations with him in this class). This class makes language (in the form of abstract judgments that are then communicable) possible, and as a consequence, all the sciences become possible . </Li> <Li> Being: Time and space comprise separate grounds of being . These a priori (prior to experience) forms respectively allow for an "inner," temporal sense and an "outer," spatial sense for the subject; subjectively, these are the forms of pure sensibility--they make sensations possible for a subject . The first makes arithmetic possible, and is presupposed for all other forms of the principle of sufficient reason; the other makes geometry possible . Time is one dimensional and purely successive; each moment determines the following moment; in space, any position is determined only in its relations to all other positions (fixed baselines) in a finite, hence, closed system . Thus, intuitions of time and space provide the grounds of being that make arithmetical and geometrical judgments possible, which are also valid for experience . </Li> <Li> Willing: It is possible for a subject of knowing to know himself directly as' will .' A subject knows his acts of will (efferent actions) only after the fact, in time . Action then, finds its root in the law of motivation, the ground of acting, which is causality, but seen from the inside (afferent perception). In other words, not only does a subject know his body as an object of outer sense (efferently), in space, but also in an inner sense (afferently), in time alone; a subject has self - consciousness in addition to knowing his body as an idea of perception (afferent - efferent processes / a priori - a posteriori correlations). </Li> </Ul>

The fourfold root of the principle of sufficient reason