The "With-Measurement" Program
by Stephen Boydstun
In our family, the young people have taught us the proper way to read your fortune cookie when we go for Chinese dinner. Each person is required to read their fortune aloud, followed by the words “in bed.” The added phrase puts the fortune in a whole new light. To the fortune “You will soon be sitting on top of the world,” you must add the words “in bed.” See how it goes next time you go for Chinese.
My program for the development of Ayn Rand’s theoretical philosophy has a serious parallel to the “in bed” shift of perspective. To every topic in metaphysics or epistemology, my program requires I add the phrase “with measurement.” Here are some topics: The Ontology of Universals; The Theory of Predication; The Nature of Entity; Existence is Identity; Causality and Natural Law; The Synthetic-Analytic Distinction; and The Computational Mind and Perception. To each such area of philosophical investigation, my task is to add “with Measurement.” Then, really do it. Each topic is being recast in the forge of modern logic, set theory, and mathematics as well.
Why? Because Rand’s measurement-omission analysis of concepts implies a distinctive magnitude structure for metaphysics. The argument supporting that claim was given in the sixth paragraph of my essay “Universals and Measurement” (The Journal of Ayn Rand Studies 5(2): 271–305). What is that argument? It is simple: All concretes can be placed under concepts. All concretes can be placed within some concept-class or another. For all concretes, some of those concept-classes will be of the Randian measurement-omission form. Then all concretes must stand in some magnitude relations such that the Randian form of conceptual rendition is applicable to them.
The preceding argument does not rely on a supposition that all one’s concepts are formed by a process of measurement omission. The argument says only that any concept you give me can be reformed into a measurement-omission form, or if not, at least this much is true: all the concretes falling under your concept fall under some concept(s) or other for which we can discover its measurement-omission form. That last, modest premise is all I need to conclude that Rand’s measurement-omission form of concepts implies that all concretes must stand in certain minimal magnitude relations.
Rand’s concept theory—not her formation theory, but her analysis theory—implies a specific, meager (but nontrivial) magnitude structure for all concretes, which is to say, a distinctive magnitude structure for metaphysics. In my “Universals and Measurement,” I uncovered that minimal structure and characterized it in three ways: by its automorphisms, by its mathematical category, and by the types of measurement it affords.
What is meant by a magnitude structure? That means an ordered relational structure. These structures are not only abstractions. They can be concretely realized relations. The most accessible example is geometry. Not analytic geometry (with coordinate systems, calculus, and all that), but the plain old synthetic geometry such as one learns to weave in a high school geometry course. The various geometries are all ordered relational structures, but some have all the structure of others plus more. Here are some geometries in their cumulative hierarchy of structure:
{Euclidean [Affine (Ordered) Absolute] Euclidean}
{Euclidean [Absolute (Ordered) Absolute] Hyperbolic}
{[Elliptic (Projective) Affine] Euclidean}
These layers of ordered relational structure are an objective matter. They have been discovered, not arbitrarily constructed.
The minimal magnitude structure implied (by measurement-omission concept analysis) for all concretes is metaphysical structure. It is structure beyond logical structure; it is constraint on possibility beyond logical constraint. Yet it is structure ranging as widely as logical structure through all the sciences and common experience.
Well, fields are ripe, and harvest waiting. I should get back to executing the program. I am very slow due to physical impairments, but I am persistent. So I hope to bear further sheaves to the publishers.
If I have not already worn out my welcome on this tableau, I’d like to say a word on what the “with-Measurement” program is not. In “Universals and Measurement,” which was the first accomplishment in the program, I sought and found the specific minimal magnitude structure the world must have such that Randian conceptual rendition of the world is possible.
To ask for such structure conditions for the possibility of conceptual rendition sounds suspiciously similar to Kant’s quest for the conditions of possible experience or his quest for the conditions of possible cognition (CPR B138). There is a great difference between what I was seeking in “Universals and Measurement” and what Kant was seeking in his famous questions. The magnitude structure I captured is not something that our cognitive system (specifically, our conceptual faculty) prescribes for the knowable world. Rather, however pervasively that structure is in the world, it is there independently of our cognitions.
Ours is not a Kantian program. We do not say that because our conceptual faculty works necessarily in such-and-such way we must find the world everywhere conforming to that way. We do not say that our concepts must all necessarily be susceptible to being cast in measurement-omission form, and that therefore we must find the world affording that form. Rather, we leave open to trial whether we shall find the world everywhere congenial to the measurement-omission form of concepts.
We take as our thesis that the world is that way, and we run with it (if only I could run!). We run it to all the traditional and current topics of epistemology, philosophy of mind, metaphysics, and philosophy of science, and we run it fully concordant with modern science and mathematics.
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