Saturday, February 12, 2011

Induction of Objectivity (Ayn Rand)

[Previous post in the series: "Reduction of Objectivity (Ayn Rand)"]

The reduction of Rand’s idea of “objectivity” complete, we can now work through how she induced her redefinition of objectivity as involving both facts about the world and facts about human consciousness.

The induction will take two series of steps:

The first, basic series:

1. Assuming Aristotle’s knowledge, discover that knowledge has an order.
2. Discover that knowledge involves integration.
3. Find out that measurement is the essential means of moving beyond percepts.
4. Discover that consciousness has identity.

The second series:

1. From Aristotle’s discoveries and the above four, reach Ayn Rand’s theory of concept-formation.
2. Integrate her theory of concepts with Aristotle’s view of objectivity, and note the amendments that this involves, which include a reformulation of what it means to “follow logic,” and what it means to “be objective.” Two elements of knowledge that Aristotle only implicitly recognized, that knowledge is formed in a context and it exists in a hierarchy, will be explicitly included in logic, as it was in Rand’s view. This is the way that we’ll know how to adhere to reality by following a certain method, because we’ll be explicating that very method further than it was explained before by Aristotle.

Knowledge has a Definite Order

The first induction we’d have to reach is that “knowledge has an exact, definite order.” In an informal lecture on the art of nonfiction writing, Ayn Rand stated the principle as: "Knowledge is acquired in steps." (Ayn Rand, "The Art of Nonfiction," transcribed and edited by Robert Mayhew.)

Aristotle knew many facets of this view, and so he’s the precondition of Rand for this. He knew that reasoning starts with observations, and that we then arrange our premises in a successive manner until we ultimately reach the conclusion we want to prove. Further, he knew that we form gradually broader concepts, leading to a hierarchy of concepts with each level supported by the preceding level. Rand had two advantages over Aristotle on this point though. One was that she lived in the 20th century, with all of the discoveries of science, and the clear-cut order of learning in our educational systems. Another advantage was her level and sheer amount of self-awareness and introspection, which she practiced her whole life. Her self-awareness that’s relevant here is that she knew that whenever she learned something, it made new routes available to learn other things, and to learn something from those, etc. She knew the generalization that we construct knowledge on top of earlier knowledge in a definite order, and it wasn’t hard for her to learn this due to the advanced scientific context she grew up in. She didn’t need her “theory of concepts” to reach this point; actually, this principle is a precondition for that theory, just as scientific progress is the precondition for the generalization that knowledge follows a definite order.

Knowledge Involves Integration

The second induction is that knowledge involves putting things together, integration. At first, we grasp that knowledge can be broken up into a series of independent pieces, which is like “analysis,” but later on, we grasp the importance of putting these pieces together, the synthesis. Long before her theory of concepts, Rand knew that all knowledge is interrelated, and that you have to put all cognitive items into a particular sum.

Aristotle knew the importance of integrating propositions, and he knew that he should integrate problems with their philosophical, scientific solutions into a total system (like his answer to “what is soul?” in On the Soul), but he never reached the principle that all knowledge as such should be integrated together.

It might have been Georg W. F. Hegel who first expressed this principle: “The truth is the whole.” (Preface to Phenomenology of Mind.) Not that I know a lot about Hegel, but his philosophy is obsessed with integration, that integration is the key to knowledge, to truth (he accepts a form of the coherence theory of truth) and to self-realization. Rand didn’t seem to use Hegel as a start-off point for this idea, though.

What she used to understand integration was her own mental exercises. Since she was 12, she would recognize relations that people never even dreamed of looking for. The kinds of relations that we take for granted now: between trade and justice, epistemology and capitalism, logic and morality, etc. She would discover contradictions in people’s thinking, and they wouldn’t have even suspected that the elements of their thinking contradict in any way.

(One example is: “[Mill’s principle] ‘The greatest good for the greatest number’ is one of the most vicious slogans ever foisted on humanity.” Most people who know Mill wouldn’t agree with this, because they see Mill as a defender of capitalism, individual rights, and liberty, but Rand could trace logical consequences of that principle that they wouldn’t notice, and which she was thoroughly against. Rand noticed that this could justify the most horrendous practices committed by the majority according to what they believe is good, like the German populace in the 1930s and 40s who largely supported the prosecution and extermination of the Jews. It wouldn’t surprise Rand at all that in Mill’s work On Liberty, you can find statements like, “[t]he spirit of improvement is not always a spirit of liberty, for it may aim at forcing improvement on an unwilling people.” She would explain the tension between liberty and “the greatest good for the greatest number” in Mill’s philosophy as caused by the fact that, “’the good’ is not determined by counting numbers and is not achieved by the sacrifice of anyone to anyone.”

For some more examples of how Mill isn’t the champion of liberty and rights that he’s largely regarded to be, consult Laura Snyder’s Reforming Philosophy: A Victorian Debate on Science and Society, chapters 4-5.)

Rand also had contempt for compartmentalizing, that is, refusing to apply the knowledge you have to other areas of knowledge or other subjects beside your specialty, like a biologist refusing to connect his views to its implications in psychology or political science. In addition to that, she hated the “concrete-bound” mentality: the kind of person who deliberately does not relate cognitive items together, but focuses only on specific issues without any connection to abstract principles and context. An example we could see her using is: communism not working in Russia, communism not working in Cuba, and then someone asking, “what would this have to do with communism in Venezuela?” The person will not relate his knowledge and reach the abstract conclusion that communism does not work as a viable political-economic system, no matter in what country it is applied. (Of course, that conclusion rests of some understanding of the system of communism and why it fails, but that's the general pattern of the "concrete bound" mentality.) These examples of non-integration were amazing to her because her normal mental functioning was connecting things, and this may have something to do with her (implicit) allegiance to induction; it’s because of this allegiance that she was constantly looking for the broader principles that could be inferred from concretes, and reaching even broader principles from her earlier ones. The result is that she would constantly surprise people when she presented these connections. (For a good example of Rand’s ability to do this, consult Peikoff’s essay, “My Thirty Years with Ayn Rand,” where she surprises him with several principles he hadn’t even thought of before.)

It wasn’t very difficult for her to induce the principle that knowledge involves integration. The principle became so important to her that it was even mentioned in the summary of Objectivism given in Galt’s speech from Atlas Shrugged: in one sentence, Galt speaks of integrating every item, without contradiction, into the sum of one’s knowledge.

(Here are the relevant sentences in Galt’s speech:
All thinking is a process of identification and integration. […] No concept man forms is valid unless he integrates it without contradiction into the total sum of his knowledge.)
And once she knew that all knowledge is a sum that is arrived at by integration, she could later integrate that with the first principle: that this sum, at each stage, made possible the next stage.

Measurement is the Essential Means of Transcending Percepts

The third induction revolves around something that Rand had to know about math before she could think to explain integration in concept-formation using mathematical terms. She needed to know basic things about math, such as that measurement requires a unit of measurement (foot, pound, gram, etc.), that the unit varies according to the subject matter (the unit for measuring radiation is different from the unit for measuring distance, etc.), and that what measurement does is relate the entity or attribute to the proper unit. Of course, she didn’t originate any of these points, but whoever discovered it had to use a range of examples, and then reach an inductive generalization: “there must always be a unit; that this unit varies depending on the subject-matter; and what the essence of measurement is.”

Rand needed to know the conclusion that measurement expands the range of our consciousness beyond the level of percepts, a conclusion which she didn’t originate, either. Take an example: let’s say that the average car weighs 2 tons. It isn’t possible to grasp how much 2 tons is by the sensations of touch and pressure, and you can’t explain the object’s heaviness to an animal, but it is possible to grasp it by relating the non-perceivable to the perceivable. You can relate it by saying that a car weighs 2 tons; a ton is 2000 pounds; and a pound is this. This principle about mathematics is an easy inductive conclusion, known well before Ayn Rand, and later she would connect this to her knowledge that concepts transcend the perceivable, as well.

Consciousness has Identity

Rand might have reached the idea that consciousness has identity before reaching her theory of concepts (at least, this is what Peikoff speculates). What the principle means is that you observe the functions of consciousness, noticing that it operates in certain, definite ways and does so in a fixed manner, and you observe that it can’t grasp things or do other cognitive feats without carrying out these processes. The principle isn’t a mere deduction from the law of identity, like “X is X,” because that wouldn’t give consciousness content. Rather, ideas such as the first three principles are cases of this principle: human consciousness gains knowledge in a definite order, its knowledge is gained by a process of integration, and conceptual knowledge is capable of transcending percepts—all of that is part of its identity. When you connect that with the law of identity, you reach something profound and metaphysical, “consciousness has identity,” and this leads to not only further specifying the law of identity axiom, but also you’ve gained more knowledge by identifying the processes of consciousness as something that consciousness has by its nature, that its identity consists (in part) of those processes. So, “consciousness has identity,” isn’t self-evident, but is rather grasped through a study of advanced issues concerning consciousness.

There were a few other paths for Rand to reach this conclusion about consciousness:

(1) The Sophist’s (and modern philosophers, like David Hume’s) attacks on the senses: a stick appearing bent in water, an object appearing smaller or larger depending on distance, when in fact the size doesn’t change, etc. Rand could see past all these attacks and recognize the common problem: if you perceive in a certain way or through certain means, all the critics seemed to say, then you don’t perceive at all.

(2) Her encounter with the ideas of Immanuel Kant. For instance, in the Critique of Pure Reason, Kant says this:
For we can understand only that which brings with it, in intuition, something corresponding to our words. If by the complaints - that we have no insight whatsoever into the inner (nature) of things – it be meant that we cannot conceive by pure understanding what the things which appear to us may be in themselves, they are entirely illegitimate and unreasonable. For what is demanded is that we should be able to know things, and therefore to intuit them, without senses, and therefore that we should have a faculty of knowledge altogether different from the human and this not only in degree but as regards intuition likewise in kind -- in other words, that we should be not men but beings of whom we are unable to say whether they are even possible, much less how they are constituted. (Critique of Pure Reason, A277/B333, Chapter III. The Ground of the Distinction of all Objects in general into Phenomena and Noumena, “Note to the Amphiboly of the Concepts of Reflection.” Emphasis in original. For a list of Kantian terms like “intuition” and “pure understanding,” see this site)
Kant’s view is that we have certain subjective means of perceiving and conceiving objects (like the forms of intuition, “space,” and “time,” see those terms in the glossary website above), and that these are our human means of representing reality, that is, they structure or organize reality in relation to consciousness; the result of this thinking is that the noumenal world is composed of things insofar as they are outside of any relation to any consciousness, they are things-in-themselves (instead of things “in relation to consciousness”), and thus are unknowable. What Rand took away from this is that Kant is attacking the fact that consciousness has identity:
His [Kant’s] argument, in essence, ran as follows: man is limited to a consciousness of a specific nature, which perceives by specific means and no others, therefore, his consciousness is not valid; man is blind, because he has eyes—deaf, because he has ears—deluded, because he has a mind—and the things he perceives do not exist, because he perceives them.
She had to confront these sorts of criticisms before reaching her theory of concepts. And it should be clear how she had a plethora of examples, both positive and negative, from which she could induce the generalization that “consciousness has identity,” and that this was an important principle.

What constitutes the identity of consciousness is the kind of information that we’ve gone over in this essay thus far, that the senses function in a certain way, that there’s some intimate connection between measurement and gaining conceptual knowledge, etc. Later on, she would use her theory of concept-formation to describe the essence of human consciousness as a conceptual faculty that functions by omitting measurements, and this supplied her with a ton of knowledge as to the ways that “consciousness has identity.”

Concepts are Formed by Measurement-omission
…Historically, it happened this way. Somewhere in the 1940s, so it’s over twenty years ago, I was discussing the issue of concepts with a Jesuit, who philosophically was a Thomist. He was holding to the Aristotelian position that concepts refer to an essence in concretes. And he specifically referred to ‘manness’ in man and ‘roseness’ in roses. I was arguing with him that there is no such thing, and that these names refer merely to an organization of concretes, that this is our way of organizing concretes.

We never really finished the argument. But after this conversation, I was dissatisfied with my own answer. Because I felt, ‘Yes, I have indicated where concepts come from, but I haven’t indicated what is the process by which we organize concretes into different groups—because I certainly don’t agree with the modern nominalists who claim it’s an arbitrary convention or an arbitrary grouping.’

And then I asked myself, ‘What is it that my mind does when I use concepts? To what do I refer, and how do I learn new concepts?’ And within half an hour, I had the answer.

Now it took me longer than that to check it, to apply it to various categories of concepts, and see if there are exceptions. But once I had the answer, by the logic of it, I knew that that’s it. And that’s it. [Ayn Rand, Introduction to Objectivist Epistemology, 2nd Expanded Edition, p. 307]
After reaching Aristotle’s understanding of objectivity, and reaching the four principles we’ve discussed above, she reached her theory of measurement-omission through introspection. By analyzing what her mind does with concepts, she realized that concepts are formed by integrating particulars which share common attributes, and that this process consists in not specifying—omitting—the specific measurements of these shared attributes, thus including all of the relevant measurements and particulars under one conception. Concepts are formed by abstracting and retaining similar characteristics that the particulars share—Rand realized that “similarity” and “abstraction,” when analyzed, both amount to: measurements omitted.

And as she said, she may have reached her idea that “measurement-omission” is the process by which concepts are formed, but regarded it as only a hypothesis: in order to make sure that it was valid, she wanted to consider every kind of concept in a methodical manner. And this investigation is another example of induction: in chapter 2 of Introduction to Objectivist Epistemology, after presenting her definition of concepts as formed by a process of measurement-omission, she applies it to nouns, materials, verbs, adverbs, prepositions, adjectives, pronouns, and conjunctions; in chapter 3, she applies it to forming higher level concepts, whether wider in scope, like “mammal” in comparison to “man,” or more narrow, ‘like “policeman”; chapter 4, concepts of consciousness, like “introspection,” “extrospection,” “thought,” “emotion,” and “love”; chapter 5, the role of definitions, a reduction of the need for the concept of “justice,” and a discussion of the concept “objective”; chapter 6, the basic axiomatic concepts, “existence,” “identity,” and “consciousness”; chapter 7, the concept of “unit-economy,” “Rand’s Razor (like Occam’s Razor, but for concepts),” and the cognitive function of concepts generally.

(Peikoff mentions that he gets the historical credit for Rand applying the theory to concepts of materials, like “water” and “gold.” He asked: “How does it apply to water?” After corresponding back and forth with each other, it ended up being included in chapter 2.)

Peikoff summarizes Rand’s massive scale induction in the sentence: “the similar concretes integrated by a concept differ from one another only quantitatively, only in the measurement of their characteristics.” Also, as reported by Peikoff, Rand said that her theory of concept-formation was purely an inductive conclusion, with no attempt to deduce it from the nature of reason or of the mind or of consciousness; she simply observed what her mind did, used mathematics to assist her in identifying what she observed, and then induced based on the observations.

Finally, her theory was completed when she integrated her view of concepts with her earlier identifications about consciousness, by spiraling back to those principles and reformulating them.

• The principle that knowledge involves a definite order: this was easily incorporated into Rand’s view that concepts are formed in an inherently hierarchical structure, that advanced concepts cannot be formed or understood without forming or understanding the concepts on which they depend. So what started as an observed regularity or generalization, later on becomes a description of the very nature of concepts. In other words, a principle first reached by induction now becomes a corollary of a principle that was also reached by induction—in detailing her theory of concept-formation, Rand not only incorporated the principle that “knowledge involves a definite order,” but explained why this is necessarily the case. (Further, in the taped epistemology discussions transcribed in the second edition of Introduction to Objectivist Epistemology, she discusses the hierarchy of knowledge more generally: that perceptual concretes allow us to form concepts, that we can cognitively hold information sophisticated enough to form propositions in a perceptual form, and that we form propositions by first forming their constituent concepts and then uniting them.)

• The principle that knowledge involves integration: this is connected with Rand’s discovery that a concept, the basic unit of conceptual knowledge, is itself a form of integration, of relating cognitive items. Since a concept is a means of integrating cognitive data, human consciousness is, by nature, an integrating mechanism. The principle that knowledge is a sum, that it involves integration, is then tied to the points that concepts have a certain nature and are formed in a certain context, that concepts are by nature contextual and hierarchical. So these two epistemological principles that Rand initially used to reach her theory are now seen as aspects or tenets of that very theory.

Once she had her theory of concept-formation and integrated it with her earlier ideas about knowledge, she kept expanding the theory with her own growing knowledge about knowledge. In chapter 7, she discusses the “crow epistemology,” the point that the amount of perceptual or conceptual material that a person can hold at any time is limited, and that the power of concepts is to condense a vast amount of information into a few, manageable units. This originally came from a scientist discussing an experiment with crows to Rand, and after hearing how limited crows are in counting objects, someone then exclaimed, “how limited crows are compared to human beings!” But Rand gleamed a much different conclusion: not how different human are from crows or other animals, but how similar we are; Rand readily recognized that our mental capacity to hold information is very limited as well, limited to perhaps 5 or 6 units at most, and that concepts save us by allowing us to integrate cognitive data on an unlimited scale, expanding what we can be conscious of on a scale entirely different from, and unavailable to, other animals. Take her theory’s idea that concepts integrate an unlimited number of perceptual concretes into one unit, and this new knowledge about crows, and it leads to the deductive conclusion that concepts are mental space-savers, constantly expanding the amount of material we can mentally hold at a given time.

Objectivity is a method that Adheres to Facts while Recognizing the Context and Hierarchy of Knowledge

Once Rand reached her theory of concept-formation, how did it lead to her reformulation of Aristotelian “objectivity”?

Though she rejected the realist and nominalist approaches to concept-formation, there were two ideas that she gleamed from her own study:

1. Concepts are based on factual data about the world, and are not arbitrary inventions of the mind.
2. Concepts are human: they are made by a process of measurement-omission, a human process, and this implies that we don’t know how other conceptual beings would form concepts other than humans.

She also knew that concepts relate the (humanly) perceivable to the (humanly) non-perceivable, so they are formed in part from the structure of our cognition to that extent. So concepts are human because they satisfy a human need: more cognitive space. We don’t have any knowledge of alien conceptual consciousnesses and how they would deal with a complexity of data and non-perceivables.

Concepts are tools of our consciousness to handle the issues we face in reality. They don’t pertain to consciousness alone, contra Nominalism, and they don’t pertain to existence alone, contra Realism. Concepts are a specific kind of relationship between the two, consciousness and existence.

Without proper preparation, Rand might have (conceivably) been led to apologize for the fact that concepts have a human dimension or element, or try to minimize this aspect somehow. She would have minimized it, rather than claim that concepts lead to subjectivism, that we don’t conceive of reality in an objective way, which leads to Kant’s critical philosophy. (Kant even went so far as to redefine “objectivity” himself, meaning the forms of consciousness that make experience possible, like the Categories or the schema of imagination. See the glossary again here.) But what happened instead is that she insisted upon the point that concepts have a human element, and remarked that it was only because of this fact that it could give us knowledge about the world. She was counting on the principle that “consciousness has identity,” as this allowed her to move from her theory of concept-formation to affirming the fact about concepts that preserves their ability to confer knowledge and to make knowledge possible. Aristotle held that the mind is like a blank writing tablet, on which anything can be written (and thus that it is potentially everything) as he thinks that this is how he can show that the mind has a common element with everything. (Consult “On the Soul,” book 3.) But if he were right, then how could reality write on the mind? How could it reach us? If the mind had no element of its own, with nothing to add to cognition, then it wouldn’t exist.

The same point can be applied to the nominalists and philosophers like Kant, who thought that if the mind contributes anything of its own, then it is a distortion of reality, some form of subjectivism. Rand held that no such distortion exists: whatever the various methods and kinds of consciousness there are, they are all forms and methods of grasping something, reality. There’s nothing else to be conscious of or to grasp. And this is the relevance of “consciousness has identity.” A human consciousness must grasp in some form by some means, according to its nature, and that of the processes that it performs. To object to the fact that there’s a human element in cognition is to really object to: A is A. Having understood the role of consciousness in concept-formation, she integrated that with the principle that consciousness has identity: she distinguished between the form of cognition from the object, and from then on there was no problem. Later, she would claim that conceptualization involves both consciousness and existence, and proclaim in opposition to the philosophers who preceded her: “identity is the means of knowledge, not the obstacle to it.”

The point that concepts are based on facts really isn’t enough to fully validate “objectivity.” If objectivity were merely based on a kind of correspondence between facts and a tablet or mind with no nature of its own, then someone could say: “Our consciousness is not a ‘nothing.’ It works by definite means, and we can only perceive and conceive as humans do, so there is no real objectivity.” The standard objection to objectivity is that it’s a method based only on facts, and that logic has no relation to the means and identity of our consciousness. Rand had to reach the right theory of concept-formation and the idea that “consciousness has identity,” in order to use both to reformulate objectivity, that logic is based on facts and the requirements of human cognition.

One example of the "requirements of human cognition" is measurement-omission, which is a method even though it doesn’t depend on our knowledge or choice, or even awareness: people have been omitting measurements for as long as we have been forming concepts, just as we knew before Rand that people abstracted to form concepts. (In her book on epistemology, Rand notes:
Concepts of method designate systematic courses of action devised by men for the purpose of achieving certain goals. The course of action may be purely psychological (such as a method of using one’s consciousness).[…]Concepts of method are formed by retaining the distinguishing characteristics of the purposive course of action and of its goal, while omitting the particular measurements of both. (Introduction to Objectivist Epistemology, 2nd edition, pp. 35-36, emphasis added by me.)
With that in mind, the method of measurement-omission consists in regarding certain measurements as existing but not specifying them, with the goal being the formation of a conceptual product (like a concept).

Method is thus a broader term than “logic”: “method” covers more than conscious processes, and it means any process we can engage in that’s divisible into steps that we can pursue, whether consciously or not. It applies to successive steps leading to any goal, not only those of epistemology like knowledge or truth: there’s a method of driving, swimming, of building a house, etc. This is why the final meaning is: “objectivity” is adherence to reality based on certain rules of method, a method based on facts and appropriate to man’s form of cognition.

“Method,” in conscious terms, still means “logic,” so Aristotle is completely right, here. But Rand chooses to use “method,” instead of logic, so that she can include the conscious and subconscious methods of the conceptual level of consciousness. The subconscious level includes what we’ve gone over thus far: omit measurements, knowledge having a definite order, integration, context, hierarchy, abstraction, etc.

The benefits of Rand’s reformulation of “objectivity” is that she can identify the exact relationship between concepts and reality and thus validate them (which previous theories couldn’t do, or gave up trying to do), and we can construct the conscious method of logic much more completely than Aristotle could. We know that human consciousness needs logic due to its capability to form concepts within a context and within a hierarchy, such that anything that is “logical” cannot neglect or drop either of these. Aristotle would say, “don’t commit contradictions,” whereas Rand would say, “yes, and to know that you’re avoiding contradictions, you must keep the full context and hierarchy in connection with every attempt to check propositions against the laws of logic.” Rand’s additional point offers a new window into logic that wasn’t attainable before her.

“Don’t contradict”—we couldn’t really grasp what a noncontradictory identification is, until we learned that the propositions in an argument must take into account the sum of knowledge and not just a compartment or solitary fragment (the issue of context), and that they have to be not only themselves reduced, but that each constituent concept of each proposition must be reduced to sensory data (the issue of hierarchy). What this means is that to show that a conclusion is “objective,” we would have to (1) validate each concept of the argument by showing that it can be reduced back to sensory data, (2) show that the propositional conclusion is itself reducible back to this evidence, and (3) show that it can be integrated with everything else that we know. This is Rand’s contribution to the science of logic insofar as it’s a corollary of “objectivity,” thanks to her theory of concept-formation as measurement-omission.


In the induction of Aristotle’s view of “objectivity,” we contrasted objectivity with subjectivity, the latter being the illogical techniques of people ignorant of or spiteful towards logic, the objective approach. In Rand’s case, there are three schools: the intrinsic, subjective, and objective. Using the genus method, we could have said “knowledge involves some kind of relationship between consciousness and existence.” The three positions we could have derived are “only contributor is consciousness (subjectivist),” “the only contributor is existence (intrinsicist),” and “both contribute and it’s the relationship that’s the most significant (objectivist).” She would discuss many issues and aspects in philosophy and in life in terms of the “intrinsic-subjective-objective” trichotomy, including the theories of universals/concept-formation, the selection of essential characteristics/essences for a concept, approaches to knowledge generally, the status of values, of “the good,” and beauty (and more). We should be able to more fully understand how she reached this idea of “objectivity” with which to contrast subjectivity and intrinsicism.

[Next post in the series: "Reduction of 'the Initiation of Physical Force is Evil.'"

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