The Journals of Ayn Rand (134 page)

This will be the issue of “teaching the world my particular kind of epistemology” (which I took to be self-evident and known). This is also why I always thought of philosophy as a static, “finite” base, like logic, i.e., as a closed discipline which has to be learned in order then to proceed to live, with “life” beginning above this base. This, probably, is the root of what Leonard [Peikoff] had in mind when he called the present state of the world “the age of pre-reason.” It will help me to think of my job as
“Philosophy for Hank Rearden.
”

[Most of the remaining notes for the book deal with AR’s theory of concepts, which she later published in
Introduction to Objectivist Epistemology.]

A unit is a concrete entity
considered apart from the other entities which are subsumed under the
same abstraction.

Thus, an
inch is
a concrete entity of the abstraction
“length
” and is a
unit of measurement
for any other length which is conceptualized by means of its relationships to the chosen unit; thus a yard is so many inches, a mile is so many yards, etc.

Number is the abstraction of the process of abstraction.
It stands for the relationship of an entity to other entities, all of which have to be absolute and immutable
in their defining characteristic,
in that which permits them to be regarded as
units
subsumed under
a single concept.
Number is the concept that identifies the transition from
“entity
to
”unit,
“ the mental transformation of a
concrete, perceptual entity
into the material to be integrated by a
concept.
Mathematics is the pattern (the blue print) of the conceptual level of man’s consciousness—the abstract pattern of the process of concept-formation, in the sense that it isolates and identifies the process which man’s mind has to perform in regard to every abstraction, every concept it reaches, regardless of the concretes involved—that is: the abstraction of ”number“ stands for
any
concrete entities regarded as ”units“ to be integrated into a concept which then becomes a new,
single unit.
(The concept ”ten“ is a single unit denoting a certain number of ”ones“; the abstraction ”man“ is a single unit denoting
”n
number“ of concrete men, that is: denoting a mathematical series to be extended into infinity, to subsume
any
number of men.)

(Next step:
The relationship of every concept to the “open-ended” mathematical series.)

“Measurement”
is the establishment of a
relationship
—the relationship between a concrete unit, which serves as the standard of measure, and other concretes belonging to the same abstraction (length, weight, etc.). A
“concept”
is also the establishment of a
relationship
—the relationship between a concrete unit and other concretes belonging to the same abstraction; the standard of measure here is the defining characteristic.

“Stolen Concept” (connected with “irreducible primaries”).

“Context-dropping.”

“Reification of the Zero.”

“Stepping into Limbo.”

“Non-differentiation between Existence and Consciousness.”

(A
“unit”
is the concept of
identity.
If you take “a group” as a start and proceed to define a “unit” by breaking up the group—you have committed the fallacy of the “stolen concept”: you have already accepted the group as a
unit.)

Regarding
“context-dropping ”:
a variant or corollary fallacy is the idea that considering a thing
in context
is a
“relativistic
” premise, thus: if values are selected by man, they are “relative” to man. This is an example of the “whose whim” fallacy: either values are
intrinsic
(arbitrarily set by the whim of God or nature)—or they are
subjective
(“relative” to or set by the whim of man); the concept of objectivism (of an immutable
nature
of things) is missing. The reasoning behind it goes like this: if a thing has to be considered in a context, then it is not an absolute, then anything goes. The error is: the substitution of infinity for a given,
known
context. Example: [a philosophy professor] claiming that the airplane invalidates the absolutism of the law of gravitation.

 

 

The basic and most universal concepts in the functioning of a human consciousness are: existence—identity—entity—unit.

The first two pertain to metaphysics, the second two to epistemology.

To grasp existence is to grasp that existence is identity—that a thing is what it is.

To grasp that is to grasp the concept of entity—a
thing.

To continue the process of consciousness is to transform the concept of entity into the concept of a unit, thus: a
“unit”
is an entity which is independent of any other entity of its own kind—or, a unit is any part of an entity
considered
independently of the rest of its own kind, such as an inch of string considered as an independent length of string while it is part of a ten-inch string.
This
is the start of the process of
measurement.

All measurement is integration, by means of a basic unit, that is: the bringing of a vast or complex whole into conceptual form by relating it
mathematically
to a basic unit. Example: a
mile
is so many
feet.

All abstractions (all concepts) are the identifications of a basic unit of measurement, with the specific measurements of the particular concretes omitted. For example,
length
is the abstraction of spatial extension, which omits the specific spatial extension of any given entity, but defines the kind of unit by means of which this entity is to be measured in regard to its attribute of spatial extension.

The unit of measurement for all concepts pertaining to consciousness is their
content.
Since consciousness is a “representation” or “reflection” (a more exact term is here needed) of existence, the concepts pertaining to consciousness are ultimately reducible to the
existents
which they “reflect” or “represent.” Examples: a “thought” is differentiated from another thought by means of its subject (of what the thought is about); an “emotion” is differentiated from another emotion by means of the value judgment it represents, and a value judgment is a thought (a thought dealing with the realm of action in existence).

In establishing a unit of measurement one has to observe two rules: the unit has to be a tool of both division and integration, it must give one the conceptual possibility of breaking an entity into such units and of integrating it back again, as well as integrating it with other entities of the same kind into groups or sums. Example: if an “inch” is taken as the unit to measure
length,
one must be able to break up a longer string into inches, then add them up to get a concept of the string in terms of an
integrated sum of inches.
(This requires a great deal more careful thinking and more precise definitions. But this is a lead to the process of forming concepts or abstractions.) [...]

My hypothesis is that all consciousness is a mathematical process (or, rather, the
function
of any consciousness is a mathematical process). To prove this I would have to identify the basic principles common to perception and mathematics. (By perception I mean here the total process of human awareness, from sensations to perceptions to conceptions.) I would have to identify the wider abstractions underlying the processes of concept-formation and of mathematics. And I would have to integrate them with neurology on the one hand (with the physiological part of the integration of sensations into perceptions)—and with metaphysics on the other.

If my hypothesis is true, then algebra might give me the clue to the
objective
rules of induction—to a kind of “Organon of Induction.”
[Aristotle’s works on logic are called the “Organon, ” Greekfor “instrument. ”]

 

 

Arithmetical numbers are
taken
as entities in any arithmetical calculation, which means: an arithmetical calculation is an action by which the relationship of certain entities leads to the discovery of a final entity, which is the goal
and the stop
of the action. A series of arithmetical equations involving action is incomplete until it has reached the stopping point of a specific arithmetical entity, e.g., a
number.

But the numbers themselves are composites. The only
primary
entity here is the
unit
—the concept of
one (1).
Every other number is an abstraction which replaces a certain repetition of ones by a single concept meant to stand for that repetition
(111
1 means
4).

This is the epistemological method of the first level of abstractions—that is, the abstractions (or conceptions) derived directly from perceptions and constituting “ostensive definitions,” e.g., the abstractions of immediately perceived objects, such as: chair, table, man, red, green, color, living being, etc. (Note the mixture of levels, such as “red” and “color.”) [AR
seems to be correcting herself here
—
“color” and “living being” are not

“first-level” abstractions.]
(Perceptions here mean that which a human consciousness
automatically
integrates out of sensations.) The next (and
voli
tional) level are the abstractions from abstractions—which is the epistemological method of algebra (the discovery of unknown quantities by means of their relationship to the known quantities).

Re:
fallacies.
The two most important fallacies which I must define thoroughly are, in effect,
extensions
of two of the fallacies defined by Aristotle:
“context-dropping”
is really the wider (and more modem) name for Aristotle’s “ignoratio elenchi”; and
“the stolen concept”
is the other side, the reverse, of “petitio principii.” If this last is “begging the question” or “assuming that which you are attempting to prove,” then “the stolen concept” is “begging the answer” or “assuming that which you are attempting to disprove.” (Many instances of “the stolen concept” are, in fact, instances of “petitio principii,” such as [Bertrand] Russell’s attempt to derive the concept “unit” from [the concept] “group,” which, throughout the whole reasoning, presupposes knowledge of the concept “unit.” But such instances are merely fraudulent attempts to
prove
something; the most important part of “the stolen concept” is its application to the fraudulent attempts to
disprove
something, particularly to disprove basic axioms. This is the worst of the fallacies in modern philosophy.)

[The notes for
Objectivism: A Philosophy for Living on Earth
end here.]