A NOTE ABOUT THE METAPHYSICS: The structure which I have presented here is in fact the same structure presented by Dr. Leonard Peikoff in "OBJECTIVISM: The State of the Art," but for three qualifications.

First, in the taped lecture series, he verbally focuses on the linear order of the concepts and principles which constitute the metaphysics (note: to recover the order, simply read the elements from left to right, and then down, like you are reading an ordinary text), i.e., on the order in which they must be at least implicitly grasped, which he identifies with the logical order, and although he mentions columns, he does not state explicitly that there are two (although, I would argue, the structure which I have presented is the only structure which makes sense of the order).

Second, he states some reservation regarding the question of whether entity precedes action. I myself do not regard this issue as a serious one: to be an action is to be the action of an entity. One may perceive entities which are not acting, but one may not perceive an action without the entity which is acting. I doubt that Dr. Peikoff presently regards this as issue.

Third, I added the two parenthetical elements in the "principles" column, although, in my view, they do not significantly advance the logic of the structure.

The norms of reduction are those epistemic norms which govern the method by which man keeps his ideas connected to the perceptual level of awareness, the level of awareness upon which all knowledge is radically-dependent. Among the central norms of reduction, only two are specifically concerned with the problem of identification: the cardinal norms of reduction. The rest are boundary norms, concerned with the problem of differentiating identification and cognition from other processes, and recognizing the fact that logically, identification and cognition come first.

The primacy of perception is the epistemic norm through which we recognize that if cognition is to be a form of awareness, it must conform to perceptual awareness, that is, to our metaphysically-given awareness of existence. Conceptual awareness is the volitional level of man's awareness, thus by reference to the principle of the metaphysical vs. the man-made, we recognize the fact that if conceptual awareness is to be awareness qua awareness, it must conform to that which it is radically-dependent on: the metaphysical level of man's awareness-- perception.

In order to properly understand the role of the norm of linear reasoning in the theory of Dual Foundationalism, it is helpful if we first recognize the fact that there exists a reciprocal relationship between knowledge and cognition: knowledge makes possible (further) cognition, and cognition makes possible (further) knowledge. Given this formal relationship between knowledge and cognition, we are able to view the process either in terms of knowledge being the cause of cognition (which corresponds to the model in which we begin logically with axioms-- the metaphysical foundation), or cognition being the cause of knowledge (which corresponds to the model in which we chronologically begin with the perceptually-given-- the empirical foundation). However, it is possible to view the process simply in terms of knowledge: thus some knowledge makes possible further knowledge. From this perspective, some knowledge is the cause, later knowledge is the effect. As such there exists an order to knowledge. The recognition of this fact gives rise to the norm of linear reasoning, recognized in the logical structure of any proper argument. Importantly, the norm of linear reasoning omits the nature of the cause-effect relationship which exists between the preceeding element(s) of knowledge (the premises) and the succeeding one (the conclusion): it may be due to either the inductive transmission of justification (as when we move from the empirical foundation to the metaphysical foundation, observing the chronological order of cognition and knowledge) or the deductive transmission of justification (as when we move from the metaphysical foundation to the empirical foundation, observing the logical order of knowledge and cognition).

The primacy of identification is the first of the three central boundary norms. As such, it does not guide the actual process of identification itself, but distinguishes the process of identification from other processes (primarily from the process of evaluation) and recognizes that, logically, identification comes first. Given the fact that it does not guide the process of identification, all of the cardinal norms of integration are properly regarded as preceding it. Nevertheless, it is a norm of reduction, and as such, its essential function is to act as part of the means by which we recognize that the ultimate source of justification lies in the two foundations of knowledge, that is, that evaluation does not have some separate foundation (e.g., in either "apriori knowledge" or "divine revelation").

The primacy of cognition is the second of the three central boundary norms. Its primary purpose is to distinguish the process of cognition (which includes evaluation) from the process of emotion, and underscore our recognition of the fact that cognition is the cause of emotions, and as such, emotions cannot serve as the source of knowledge.

The norm of intellectual independence is the third and last of the three central boundary norms. Its primary purpose is to distinguish between the individual's means of awareness and the extention of this awareness which is made possible through the existence of others, and to underscore the fact that, logically, the individual's awareness (e.g., cognition) comes first (e.g., prior to communication). As such, the norm of intellectual independence is the primary epistemic norm through which we recognize various forms of appeal to authority as fallacious.

More broadly, the norm of linear reasoning, the primacy of identification, the primacy of cognition, and the norm of intellectual independence together with the norm of context-keeping (which is one of the norms of integration) form the basis for what is normally called informal logic through which we recognize the informal fallacies of circular reasoning, ad hominem, appeal to emotion, appeal to authority, and false alternative, etc. as fallacious forms of reasoning.

Normally, Objectivists do not differentiate between the law of identity and the norm of coherence. However, I believe, in logic, they must. The law of identity is a metaphysical law. As such, it cannot be violated. The norm of coherence, by contrast, is an epistemic norm which should, but does not necessarily guide human cognition: people can violate it. One refers to existence qua existence, the other refers to voltional awareness of existence, and not simply to what it is, but what it should be.

Now in the full sense of the term "law of identity," objectivists ultimately mean a great many things, for they take it to be synonomous with "existence is identity." This is taken to include such things as "To be is to be something in particular, possessing specific attributes in specific degrees," etc.. However, by the law of identity, one may simply mean either "A is A" (which is the standard meaning) or "a thing cannot be both A and not A at the same time and in the same way" (which is what will often be refered to separately by the name "the law of non-contradiction").

Which then, is the actual meaning of the principle through which we identify the law? The answer to this problem is that, while the law itself remains the same, our knowledge of the law grows with the context of our knowledge. Our first awareness of the law arises when we recognize that one thing is different from another (see Dr. Leonard Peikoff's "OBJECTIVISM: The State of the Art"). However, at this point, the nature of the difference has not yet been specified: it could be qualitative, and yet it could merely be quantitative. To get beyond this elemental state of cognition, concept-formation must take place, but such concept-formation takes place in accordance with the rule of simplicity, through which we recognize our need for unit-economy.

The norm of coherence, in its prohibitive function, corresponds to the law of non-contradiction. In its obligatory function, corresponds to the metaphysical law "A is A." It is the norm in accordance with which the process of deduction takes place. The rule of simplicity is the norm in accordance with which induction takes place. Induction (through which generalizations are formed) must precede deduction (through which generalizations fulfill their role as explanatory principles), however, deduction is discovered first. Induction is originally discovered only by means of its contrast with deduction-- in the case of induction, the conclusion does not necessarily follow from the premises.