In his 2007 book I Am a Strange Loop, Douglas Hofstadter uses an analogy based on a domino computer.
For definiteness, let’s imagine a “domino computer” able of determining whether an integer (entered in binary) is prime or not. The result is read on the last domino. If the latter falls, the number is prime. If it remains standing, the number is not prime.
Now, assume we enter the number 7 as input in the algorithm. The last domino falls.
How can we answer the following:
Why did the last domino fall?
Answer 1: Because the penultimate domino made it fall.
Answer 2: Because the number 7 is prime.
The first answer focuses on the physical character of the device. Each physical event is taken in a causal sequence of events and therefore has a complete causal explanation.
The second answer provides an explanation based on a mathematical property, ignoring the physical implementation of the algorithm in order to refer only to its function.
Hofstadter uses this analogy in order to address the notion of functionalism.
My puzzle is the following:
Although Answer 2 sounds very intuitive, it seems to imply a causal influence of an abstract mathematical property (being prime) of an abstract mathematical concept (the number 7) on a material object (the last domino).
How can we think of such a causal influence of an abstract property on the physical world?
Is anyone aware of references addressing this issue?