Existence, Relation, and Measurability

Existence, Relation, and Measurability
by Luke J. Morris

I often hear people, including New Agers, evangelicals, and other touchy-feely types, claim that universal concepts such as love "cannot be measured." For several millennia, religious groups have been applying this idea to God—the great divine spirit, whoever He may be, is infinite, and thus ipso facto immeasurable. But in her Introduction to Objectivist Epistemology, Ayn Rand offers a clever little refutation of the possibility of the existence of an immeasurable[1] entity. While it is hard to do her position justice outside the context of the entire work, one paragraph sums up the challenge nicely:

     Measurement is the identification of a relationship in numerical terms—and the complexity of
     the science of measurement indicates the complexity of the relationships which exist in the
     universe and which man has barely begun to investigate. They exist, even if the appropriate
     standards and methods of measurement are not always as easily apparent nor the degree of
     achievable precision as great as in the case of measuring the basic, perceptually given
     attributes of matter. If anything were actually “immeasurable,” it would bear no relationship
     of any kind to the rest of the universe, it would not affect nor be affected by anything else in
     any manner whatever, it would enact no causes and bear no consequences—in short, it
     would not exist. (39)

This argument is subtle, and needs fleshing out to show how it works. This is how I read it:

1. Everything that exists, exists in relation to something (or everything) else.
2. The identification (and quantification) of particular relationships is measurement.
3. Every existent bears some such relation or relations that can be measured (from 1 and 2).
     The measurable relationships exist even if the particular methods and standards of
     measurement in given cases have not yet been discovered, and even if exacting precision
     in measurement cannot be achieved. (This applies to relational concepts such as love, as
     well as to perceptually given concretes.)
4. Therefore, to be actually ‘immeasurable’ would be to bear no relation to anything else (from
     3).
5. A thing that bears no relation to anything does not exist (from 1).
6. Therefore, an immeasurable thing cannot exist (from 4 and 5).

This argument applies to anything described as "infinite" as well as "immeasurable" since, if a thing were actually infinite, it could not be relationally quantified to anything finite, and thus could not be measurable.[2] The argument disproves the possibility of a God of the Christian type—an omniscient, omnipotent, infinite being—but of course this does not prove the impossibility of any type of divinity. A finite deity, who fell within standards of possible measurability, is not ruled out here. That, however, is beside the point.

The point is that whatever exists is measurable in some way. Naturally, this necessity can be sidestepped if one wishes to deny (1), but then the challenger faces the burden of proof in showing how something could exist bearing no relation to anything else. And even proving this would seem to entail a contradiction, since to prove the existence of a non-relational thing would be to stand in some relation to it. A challenge may be levied at (3), if one holds that it does not follow from (2); that is, if we argue that the fact that some particular relationships can be measured does not entail that all relationships are measurable. But here the challenger again faces the burden of proof in showing how one thing can stand in relation to another without there being some possible method and standard by which to measure that relationship. The burden does not lie on Rand to show that every relationship must be measurable; if there is a relationship at all, it seems to entail a difference and a similarity of some sort, in some degree, which entails comparability by some similar standard, which entails measurability. If one wants to show that this entailment does not hold, he will have to show how a counterexample is possible. And that he cannot do, I argue, without falling into contradiction.

[1] "Measurability" could be interchanged with "quantifiability" here, for semantic purposes. Thus, the argument might set to prove that everything that exists can (in principle) be quantified; hence, no infinite/immeasurable/unquantifiable thing could exist. Allowing for quantification without measurement per se lets us sidestep empirically-based objections that one might draw from Heisenberg’s Uncertainty Principle and the like.
[2] Of course, Rand already makes an argument for this conclusion in a much simpler form (without relying on relations), from the axiom of Identity—that is, everything that exists has some identity, and therefore must exist in some quantity. The argument she offers here merely offers another, more logically complex angle to the same end.

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