IOE, Chapter Six
Axiomatic Concepts
by Thomas Ryan Stone
Date: 10 May 1995
Forum: Moderated Discussion of Objectivist Philosophy
Copyright: Thomas Ryan Stone
Ayn Rand indicates the importance of axiomatic concepts in the first paragraph of the chapter: "The base of man's knowledge - of all other concepts, all axioms, propositions, and thought - consists of axiomatic concepts"(p55). She does so again at the end of the chapter as she states: "Do you want to assess the rationality of a person, a theory or a philosophical system? Do not inquire about his stand on the validity of reason. Look for the stand on axiomatic concepts. It will tell the whole story."(p61) In properly treating any topic, it is necessary to have a guiding principle or set of such principles. Regarding axiomatic concepts, I see four main questions that I will use as my guide in this essay: What are they?, How are they formed?, What are their functions?, and Why do we need them?
I. WHAT ARE AXIOMATIC CONCEPTS?
Ayn Rand notes that *axioms* are typically considered to be propositions identifying self-evident truths. As such they are not "primaries". This is because mental "primaries" are in the form of concepts, from which propositions are later built. The concepts that produce *axioms* when put into propositional form are the *axiomatic concepts*.
Ayn Rand defines *axiomatic concept* as an "identification of a primary fact of reality, which cannot be analyzed, i.e. reduced to other facts or broken into component parts"(p55), and are
1. implicit in all facts
2. implicit in (alternately, the "base of") all knowledge
3. the fundamentally given
4. the directly perceived or experienced
5. that which requires no proof or explanation
6. that upon which all proofs and explanation rest
7. the base of all other concepts, axioms, propositions, thought
Axiomatic concepts are those and only those concepts that fit the definition given above with all of its aspects. She states that the first and primary axiomatic concepts are "existence", "identity" (called a corollary of "existence"), and "consciousness". She then proceeds to discuss in what way these three examples are "axiomatic" and in what way they are "concepts". They are axiomatic because they display the above listed properties. An interesting question arises, however, when we ask "In what sense are they *concepts*?" Miss Rand's answer is that they are concepts because they require identification in conceptual form. This seems clear: take an animal who is not above the conceptual threshold, and consider whether it could explicitly grasp existence qua existence, identity qua identity, or consciousness qua consciousness. They are perceived or experienced directly, but grasped conceptually.
Questions:
1. The genus of axiomatic concept should be the same as that given for concept, shouldn't it? That was given as "mental integration" (p13), but no where is it found in our definition of "axiomatic concept". If axiomatic concepts are *concepts*, which they are, then they should have the same genus. We need to formulate the definition of the concept so as to include the genus.
2. Is Ayn Rand being redundant when she says "first and primary axiomatic concepts"? How are these words different from "fundamental", which she also uses?
3. What exactly is meant by "implicit" in "implicit in every state of awareness"?
4. What exactly is meant by "corollary" in "[identity] is a corollary of existence"?
5. After admitting that they can't be "proven", can't we make a stronger claim than attribute 5, replacing "requires no" with something stronger?
6. An on-going project: after making sure that the list of attributes given above is complete (is it?), it would be interesting to detail other concepts that fail to be axiomatic concepts, even while they are "identifications of a primary fact of reality, which cannot be analyzed". It would be interesting to see a conceptual web develop that would detail which attributes are missing from these near-axiomatic concepts. Some possible candidates include perceptual and introspective-experiential concepts (e.g. desire, urge, anxiety, pleasure/pain), time, space/place, volition, direction, entity, unit, life, motion, change, being, substance, quantity, quality, shape, relation, faculty, function, event, action, phenomenon, cause/effect, equal, matter, intention, awareness, state, position, modality, similarity/ difference, ...
II. HOW ARE AXIOMATIC CONCEPTS FORMED?
Ayn Rand notes that these concepts involve an abstraction of a very special sort: "...not the abstraction of an attribute from a group of existents, but of a basic fact from all facts. Existence and identity are *not attributes* of existents, they *are* the existents. Consciousness is an attribute of certain living entities, but it is not an attribute of a given state of awareness, it *is* that state"(p56). The units for these concepts are every entity, attribute, action, event or phenomenon that exists (for "existence" and "identity") and every state or process of awareness that one experiences, has ever experienced or will ever experience.
There *is* a process of measurement omission: that which is omitted from axiomatic concepts "are all the measurements of all the existents they subsume; what is retained metaphysically is only a fundamental fact, epistemologically only one category of measurement, omitting its particulars: *time*, i.e. the fundamental fact is retained independent of any particular moment of awareness."(p56)
Questions:
1. Ayn Rand's position seems to be that existence (and identity) is not an attribute of an object. This is a common question amongst philosophers and is usually raised as "Is existence a predicate?". Why then does she say "The units of the concepts "existence" are every entity, ..., *that exists*..."? This seems to be acknowledging existence as an attribute of entities. This raises a favorite topic of mine: modes of existence. This doesn't just apply to questions of ontological categories (e.g., in what way do relations "exist"), but also questions concerning "fictional existence" (i.e. is it reasonable to have such a concept).
2. Regarding the measurement-omission: What is left when we omit "all the measurements"? Miss Rand's answer is "a fundamental fact"; but what does this mean? What is the fundamental fact that remains? Regarding the one category of measurements that remains, that of *time*: why isn't this considered a part of "all the measurements"? Did she mean "all...except its temporal measurement"? Later she mentions "implicit psychological time measurements"(p56-7): is this what she means here? If so, this seems to be the answer, for it isn't an attribute of the object but rather of the awareness of the object. I found this section (on p56-7) to be very confusing.
III. WHAT ARE THE FUNCTIONS OF AXIOMATIC CONCEPTS?
Miss Rand states that axiomatic concepts are the *constants* of man's consciousness. They are the *cognitive integrators* that identify and thus serve to protect its continuity. She relates this back to the fact stated earlier that axiomatic concepts have as their omitted measurement the implicit psychological time measurements (p56-7).
Axiomatic concepts have a second function: they "identify the precondition of knowledge: the distinction between existence and consciousness, between reality and the awareness of reality, between the object and the subject of cognition. Axiomatic concepts are the foundation of *objectivity*."(p57) Later they are described as the "foundation of reason" (p.60) [NOTE: perhaps it is more accurate to say that *man* identifies the precondition of knowledge..., *by way* of axiomatic concepts].
A third function of axiomatic concepts is the underscoring of primary facts of reality: that something *exists*, that *something* exists, and that I am conscious.
Questions:
1. Wouldn't it be great to see an essay entitled "Axiomatic Concepts as the Foundations of Objectivity"? Yet another example of why this treatise is only an "Introduction".
2. See Question #2 in section II.
3. Can somebody explain to me in what way the axiomatic concepts are constants of man's consciousness? As concepts they must be open-ended, right? Are they only "constants" in an attenuated sense? If so, in what context and what is meant by that description?
IV. WHY DOES MAN NEED AXIOMATIC CONCEPTS?
Axiomatic concepts each designate a fundamental fact. While this is so, Miss Rand states that "axiomatic concepts are the products of an *epistemological* need - the need of a volitional, conceptual consciousness which is capable of error and doubt."(p.58) For this reason man's consciousness needs axiomatic concepts to embrace and delimit the entire field of its awareness - to delimit it from the void of unreality to which conceptual errors can lead. They are epistemological guidelines that sum up the essence of all human cognition: "something *exists* of which I am *conscious*; I must discover its *identity*.(p.58-9)
Questions:
1. Wouldn't it be interesting to hear discussion on the topic of "Axiomatic concepts as necessary conditions of human survival", one that would take an evolutionary biology slant (tying in the discussion of Miss Rand's assertion concerning animals, pg. 58)?
Additional comments:
This chapter had its share of unsupported assertions. Many involve assertions about "animals", which is typical of Ayn Rand. I almost always agree with the essence of her points, but I would like to see empirical evidence so we know how to chop up the animal kingdom, i.e. is it really man and non-man? Others involve "logical positivists", "logical atomists", "modern philosophy", "modern philosophers", "the works of Kant and Hegel", and various existentialists (judging by her tone, these folks often seem to be the aforementioned "animals"!). All of these assertions, while simply assertions as found in the chapter, would make for very interesting essays/articles indeed! So get cracking everyone!
Please bring up any other questions you have about this chapter; don't feel restricted to the many I have raised.
Note: all citations are from the 2nd edition.
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