As we saw in Part 1, the supervenience formula works to capture the meaning of supervenience in philosophy of mind. We began to see how it can be applied to kinds of changes in mathematics, elementary physics, and quantum mechanics. To illustrate the variety of ways in which the supervenience formula can be used, we now consider cases from disparate areas of inquiry: Computing and AI, learning and foolishness, public policy, and organizational change.
The main point of these examples is to show that what we really need is to develop a logic of change. Supervenience then turns out to be just one type of logical relationship among pairs of changes. No wonder that the concept of supervenience finds such wide application in philosophy; for unless one is an extreme monist, one's philosophy has to deal with change.
5. Computing and AI
In a standard algorithm in which randomness does not figure, the output O supervenes on the input I. It is impossible for there to be a change in the output and there not be a change in the input:
¬◊(ΔO · ¬ΔI) (1)
The converse does not hold. For example, every time we enter 5 + 2 in a calculator and then press = we get 7. However, we can get 7 as an output after an indefinite number of operations. So, the input does not supervene on the output:
◊(ΔI · ¬ΔO) (2)
We can, as before, use the strict conditional to describe the relationship between change in output and change in input in an algorithm that does not include randomness. The output strictly implies the input, i.e., there is a change in the output only if there is a change in the input, which we write ΔO ⇁ ΔI, but not conversely.
Even a passing acquaintance with generative AI shows us that in those algorithms, i.e., neural nets that include randomness, it is possible for there to be a change in the output and there not be a change in the input. In these kinds of algorithms, the output does not supervene on the input:
◊(ΔO · ¬ΔI) (3)
In generative AI that creates text output, it's not so clear whether it is possible to have a change in the input but no change in the output. The main reason for this is that even with the same input it is extremely improbable that one will get exactly the same output.
Foolishness and Learning
Frequently, people repeat the tired refrain that it is the definition of “insanity” (let's just call it foolishness) to continue doing the same thing and expect different results. It is foolish to believe, we could now say, that the results R do not supervene on what we are doing D:
◊(ΔR · ¬ΔD) (4)
6. Foolishness is failing to recognize that the results supervene on what we are doing.
However, the tired refrain is insensitive to the Drano effect. When the drain is slow and I apply clog remover, there is no noticeable change in the rate at which the water drains. However, if I repeat the application of the clog remover several times, the rate at which the water drains improves significantly. If we let R be the rate at which the water drains and D what we are doing, i.e., applying the same amount of drain remover, then:
◊(ΔR · ¬ΔD) (5)
Naturally, we do not believe in general that for any physical process change accumulates from nothing. The key is simply that we did not notice the “microscopic” changes taking place in R, which eventually accumulate to a noticeable change.
Now suppose I am trying to learn a skill, such as how to juggle a soccer ball or how to play a song on the piano. The old adage that “practice makes perfect” has recently been updated to “practice makes permanent”. To work toward perfection, common wisdom dictates, we don't just practice, i.e., repeat the same thing over and over. We engage in intentional and reflective practice making small changes in light of a careful analysis of what leads to improved outcomes. If O is our desired outcome and P is the set of practice behaviors, the “new” wisdom about practicing is that O supervenes on P:
¬◊(ΔO · ¬ΔP) (6)
This relationship between practice and outcomes is not new at all, of course. It is, for example, the centerpiece of Dewey's view of learning as much as it is of Popper's “trial and modification” view of scientific knowledge. Arguably, it goes much further back in philosophy at least to the time of Aristotle and his conception of a moral virtuous circle the ascent through which leads to a better character. We'll discuss this separately later.
6. Public Policy
Suppose someone wanted to defend the claim that we cannot change the rate of gun violence G without changing gun legislation L. They would be arguing that gun violence supervenes on gun legislation. Using the supervenience formula, we could write:
¬◊(ΔG · ¬ΔL) (7)
Interpreting “only if” as indicating strict implication, such a person is claiming that there is a change in rates of gun violence only if there is a change in legislation. This supports the inference that if there is no change in gun legislation, there will be no change in the rate of gun violence.
A proponent of changes to gun legislation will recognize, nevertheless, even if we change gun legislation, it may happen that there is no change in gun violence: a change in gun legislation does not supervene on changes in gun violence, i.e.,
◊(ΔL · ¬ΔG) (8)
While rates of gun violence supervene on gun legislation, the converse may only hold ceteris paribus. Exactly what counts as all other things being equal in this case is specific to this case. However, this is just a special case of types of changes in which a supervenience relationship holds in one direction but the converse holds only ceteris paribus
7. Organizational Change
A business wishes to change how it delivers a service S to its clients. Employees are convinced that such a change will be accompanied by a change (specifically an increase) to their workload W. The firm claims that it is possible to change how the service is delivered and not change work load. The employees claim that a change in service supervenes on their work load:
¬◊(ΔS · ¬ΔW) (9)
Management denies this claim and maintains that the change in service does not supervene on working conditions:
◊(ΔS · ¬ΔW) (9)
Supervenience Simplified
In six of the seven examples we have explored talk of supervenience seems philosophically heavy-handed. Yet, it can be a compact way of expressing the relationship between how changes in one thing are related to changes in another thing. For us, the supervenience formula is particularly helpful because it clearly articulates the relationship among the changes in pairs of things without importing associations with the word supervenience, for example with the concept of emergence, which would in many contexts be out of place.