Published on December 9, 2024 8:24 AM GMT
In a recent essay, Euan McLean suggested that a cluster of thought experiments “viscerally capture” part of the argument against computational functionalism. Without presenting an opinion about the underlying claim about consciousness, I will explain why these arguments fail as a matter of computational complexity. Which, parenthetically, is something that philosophers should care about.
To explain the question, McLean summarizes part of Brian Tomasik’s essay "How to Interpret a Physical System as a Mind." There, Tomasik discusses the challenge of attributing consciousness to physical systems, drawing on Hilary Putnam's "Putnam's Rock" thought experiment. Putnam suggests that any physical system, such as a rock, can be interpreted as implementing any computation. This is meant to challenge the idea that computation alone defines consciousness. It challenges computational functionalism by implying that if computation alone defines consciousness, then even a rock could be considered conscious.
Tomasik refers to Paul Almond’s (attempted) refutation of the idea, which says that a single electron could be said to implement arbitrary computation in the same way. Tomasik dismisses this as , but I think a related argument succeeds. That is, a finite list of consecutive integers can be used to 'implement' any Turing machine using the same logic as Putnam’s rock. Each step N of the machine's execution corresponds directly to integer N in the list. But this mapping is trivial, doing no more than listing the steps of the computation.
It might seem that the above proves too much. Perhaps every mapping requires doing the computation to construct? This is untrue, as the notion of a reduction in computational complexity makes clear. That is, we can build a ”simple” mapping, relative to the complexity of the Turing machine itself, and this succeeds in showing that the system is actually performing arbitrary computations - both the system performing computations and the one being mapped from. Rocks and integers cannot, since any mapping must be as complex as the original Turing machine.
Does the mapping to rocks or integers do anything at all? No. Crucially, the mappings to rocks or integers require the computation to be performed elsewhere to generate the mapping. Without the computation occurring externally, the mapping cannot be constructed, and thus, it is misleading to claim that the computation happens 'in' the rock or the integers. Further, Crucially, the mappings to rocks or integers require the computation to be performed elsewhere to generate the mapping. Without the computation occurring externally, the mapping cannot be constructed, and thus, it is misleading to claim that the computation happens 'in' the rock or the integers.
The ability to 'map' Turing machine states to integers implies that we have solved the halting problem — a logical impossibility. But even if we can guarantee the machine halts, the core issue remains: constructing the mapping requires external computation, refuting the idea that the computation occurs in the rock.
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