The topic of metaphysics, in my meaning, is concrete existence, whether those concretes are entities, attributes, actions, or relations, whether actual or potential. This conception of metaphysics is consistent with Rand’s views that all existents have particular and specific identities (AS 1016, 1035–37; IOE 6, 240), that “everything that man perceives is particular, concrete” (IOE 1, 199), and that “‘things as they are’ are things as perceived by your mind” (AS 1036).
To fully comprehend the concrete, we require the abstract. To fully comprehend the actual and the potential, we require the possible.
Rand conceived of logic as “the art of non-contradictory identification,” and she held that “logic rests on the axiom that existence exists” (AS 1016). Recall that Rand’s first axiom for metaphysics is the affirmation that existence exists. Two further axioms are manifest to one in the act of grasping the statement “existence exists.” These are that something exists which one perceives and that one exists and possesses consciousness of existing things (AS 1015). We have the following:
(E) Existence exists.
(E1) Something exists which one perceives.
(E2) One exists and possesses consciousness of existing things.
I concur with the preceding, and to Rand’s E-axioms I would add a related supposition, which I call my epsilon-premise:
(epsilon) There is nothing in existence whose existence cannot be asserted.
If something exists, its existence can be asserted. Then because (E1) and (E2) are implicit in the act of grasping the assertion that any particular thing exists, there is nothing in existence that is not potentially the subject of acts of consciousness.**
Rand also takes as axiomatic that “to exist is to be something, as distinguished from the nothing of nonexistence, it is to be an entity of a specific nature made of specific attributes” (AS 1016). A thing is itself, it is what it is. An object is of one sort or another, it possesses certain attributes and not others, and its actions are certain ones and not others. In three words,
(I) Existence is identity.
Every existent is with identity. If something exists, then it is not without identity.
The identities of existents exist with them. Adding (epsilon), we may conclude (iota): all identities of existents can be asserted. Any identity of an existent that is so can be asserted to be so. Implicit in the act of grasping the statement that a certain identity is so, of a certain existent, is the fact that some identity holds which one perceives and that one exists as a consciousness of identities.
Concerning consciousness, taken as the act of perceiving that which exists, Rand poses the further axiom:
(C ) Consciousness is identification.
The art of noncontradictory identification is logic, in Rand’s conception of it, and “logic rests on the axiom that existence exists” (AS 1016). Then it is not a logical possibility that nothing exists.
Rand presents (E) expressly as an axiom. She does not present (I) and (C ) expressly as axioms, though she strongly suggests that they are axioms. They are introduced as completing the traditional law of identity, the principle that a thing is itself, or A is A (AS 1016). Rand takes (I) and (C ) to state primary facts and to be immediate and most important elucidations of the three concepts she takes to be axiomatic expressly: existence, identity, and consciousness (IOE 55–56).
Our standard modern logic has come to be called classical logic. This logic expanded and revised the logic of Aristotle as it had been developed up to the time of Kant. Classical logic, as taught in texts such as R. L. Simpson’s Essentials of Symbolic Logic and W. V. O. Quine’s Methods of Logic, is the culmination of innovations by Boole, De Morgan, Jevons, Peirce, and above all, Frege (1879).
Standard modern logic is called classical to distinguish it from extensions of it in modal logics and from rivals of it, such as intuitionist logic, many-valued logics, paraconsistent logics, fuzzy logics, quantum logics, and relevance logics. This last and modal logic, as well as the ways in which classical logic improves on Aristotelian logic (e.g., existential fallacy), stand out as promising productive integration with Rand’s metaphysics and conception of logic.
Predications are conceptual identifications. Edward Zalta takes the discipline of logic to be “the study of the forms and consequences of predication” (2004, 433).*** That conception of logic fits well with Rand’s conception of logic as “the art of non-contradictory identification.” The ramifications of Rand’s idea that “logic rests on the axiom that existence exists,” combined with her E-, I-, and C-axioms, need to be charted through the terrain of classical logic, modal logic, and relevance logic.
Within the course of discussion appending this post, we can tackle the topic of the kinds and degrees of necessity and impossibility (cf. ##88, 488, 490 in the Analytic-Synthetic thread), the kinds and nature of membership relations, and the various types of logical consequence. This new thread is also a good setting within which to tackle the character of mathematical existence.
~~~~~~
*That does not mean the sciences traditionally not counted among the physical sciences should be thought of as subdivisions of the physical sciences.
**There are things no longer in existence which were not subjects of consciousness during their existence and which are now no longer potential subjects of consciousness.
*** “In Defense of the Law of Non-Contradiction” in The Law of Non-Contradiction, Priest, Beall, and Armour-Garb, editors (Oxford). Two beginning works have addressed how predication can be taken under Rand’s thesis “existence is identity.” These are the final section (IX) of my 1991 Objectivity essay “Induction on Identity” (V1N3) and David Kelley’s paper “Concepts and Propositions” read at the 1996 summer seminar of the Institute of Objectivist Studies.
This post has been edited by Stephen Boydstun: 29 June 2007 - 07:53 AM

Help
















