The Ontology of Emergence
by Adam Reed
Emergent properties, like quantum mechanics, are more often talked about than understood. That is because emergent properties, like quantum mechanics, have been used as a metaphor to justify all manner of supernatural and mystical bullshit. Magnetism was commonly used in a very similar way in the nineteenth century, until Einstein's Theory of Relativity provided an explanation of magnetism—as a relativistic correction to the strength of the electric field—that was simple enough for a college sophomore to understand. Thanks to Ayn Rand's Objectivist Epistemology (Rand 1966), it is now possible—see below—to explicate emergent properties with the same simplicity. If you were able to follow the derivation of magnetism as a relativistic correction to the operation of Coulomb's Law in college physics, you ought to be able to follow this discussion of emergence.
According to Rand (1966), a concept is a grouping of existents that share a set of attributes, so that each of those attributes has a specific, but possibly different (in different individual instances) measurement, or value, for each instance.
An existent's identity consists of the measurements of its attributes.
A property is a proposition about an existent whose truth is a consequence of the identity of that existent—that is, a consequence of the measurements, or values, of that existent's attributes. Thus, a strut has the attribute of load-bearing strength, defined as the weight of the heaviest load that it can support. A strut may have the property of being able to support a 100-kilogram load by virtue of (the value, or measurement, of) its load-bearing strength.
An existent that is composed of several other existents (called components) is called a system. Most systems have attributes whose measurements can be computed from the measurements of the attributes of their components. For example, the strength of a system of two struts can be computed from the measurements of the attributes of the two struts that compose the system. A system attribute is said to be reductive if it can be "reduced to," or computed from, the measurements of the attributes of the components composing the system. A property of a system is reductive if it is a consequence of the measurements of that system's reductive attributes. For example, the system of two struts may have the property of being able to bear a load of 150 kilograms as a consequence of its load-bearing strength, which in turn is the combination—that is, a function—of the individual load-bearing strengths of the two struts that compose the system. This makes it a reductive property.
An emergent property is a non-reductive property—that is, a property that cannot be "reduced to" (computed or deduced from) the measurements of the attributes of the separate components that compose the system. Because a property is a proposition about an existent whose truth is a consequence of the identity of that existent—that is, a consequence of the measurements, or values, of that existent's attributes—emergent properties require emergent attributes, that is, system attributes whose measurements cannot be reduced to the measurements of the attributes of the system's components. Do such attributes exist?
The position that emergent attributes do not exist—that is, that all attributes and properties of systems can be reduced to the measurements of the attributes of their separate components—is called reductionism. Demonstrating the existence of emergent attributes disproves reductionism. A disconfirmation of reductionism does not disconfirm the universality of causation—it only disconfirms the idea that all the properties of a system have causes inherent in its separate components. A plausible alternative is that relations—in this case, relations among the components that constitute the system—have causal efficacy in addition to the causal efficacy of the causes inherent in the separate components.
It turns out that it is not at all difficult to demonstrate the existence of emergent attributes and properties.
Consider a basic component of information processing circuits, a NAND ("not and") gate. The NAND gate is a component with two inputs and one output. The relevant attribute (usually voltage or current) of each input or output has two recognizable values, corresponding to "true" (Boolean 1) or "false" (Boolean 0). If input A and input B are both true (both 1) then (A AND B) is true, (NOT(A AND B)) is false, and the output is 0. If either input is 0 then the output of the NAND gate is 1.
The NAND gate operates with a fixed physical delay. Its output always reflects the state of its inputs at a specific moment, a fixed number of picoseconds in the past. The state of its output carries no information about anything that may have happened at any other time in the more remote past. In other words, it is independent of any other time in the past, and does not have any attributes that would measure the storage of information across time.
Now consider a system of two NAND gates, interconnected so that the output of each feeds into one of the inputs of the other, like this:
This system of two cross-connected NAND gates is called a "flip-flop." We know from the specification of a NAND gate that if the remaining input to one of the NAND gates is 0, then the output of that gate is 1. If the other input to the flip-flop is 1, then the second gate's two inputs are 1-1, and its output is 0. Therefore if the inputs to the flip-flop are 0-1, the outputs are 1-0. If the inputs are 1-0, the outputs are 0-1.
Now change the input that was in state 0 to state 1. The other input to the same gate comes from the output of the other gate, both of whose inputs are 1. Therefore the other input is 0, and the output of the gate remains 1. Therefore if the inputs change from 0-1 to 1-1, the outputs remain 1-0. If the inputs change from 1-0 to 1-1, the outputs remain 0-1. In either case, the output of the flip-flop is no longer uniquely determined by what its inputs were a fixed number of picoseconds in the past. In either case those inputs are (or n picoseconds ago, were) 1-1, but now the outputs tell us which input more recently had a value of 0, at some more remote time in the past.
By itself, neither NAND gate stores information across time. Therefore neither NAND gate has an attribute measuring the amount of information that "it could store, if it could store information." But the flip-flop has such an attribute; its measurement is one bit. It belongs to the concept of information storage devices, which consists of existents having such an attribute. This attribute is not reducible to the attributes of the separate NAND gates that make up the flip-flop. Its cause is the crossed interconnection between the outputs and inputs of the two NAND gates. It is an emergent attribute. The property of being able to store information across time is an emergent property, caused by the relation of the two NAND gates to each other in the flip-flop, and not by anything inherent in either or both of the separate NAND gates.
The fact that relations can cause attributes means that relations are "out there" in reality, independent of consciousness. Relations are ontological. [Correction: I originally wrote "and not—as Rand believed—only epistemological." As I was prompted by the discussion thread to learn, I misinterpreted Rand in this regard; Rand identified relations as a special kind of ontological existent.]
My operating conjecture in the study of information processing, of consciousness, and of mind, is that they all are emergent, and more specifically, relation-dependent, aspects of information-processing entities. I suspect that the latter two are emergent aspects only of one specific type of information-processing system, a living organism—and that so is life itself. But that is a conjecture open to research.
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