Abstract

A single physical process may often be described equally well as computing several different mathematical functions—none of which is explanatorily privileged. How, then, should the computational identity of a physical system be determined? Some computational mechanists hold that computation is individuated only by either narrow physical or functional properties. Even if some individuative role is attributed to environmental factors, it is rather limited. The computational semanticist holds that computation is individuated, at least in part, by semantic properties. She claims that the mechanistic account lacks the resources to individuate the computations performed by some systems, thereby leaving interesting cases of computational indeterminacy unaddressed. This article examines some of these views, and claims that more cases of computational indeterminacy can be addressed, if the system-environment interaction plays a greater role in individuating computations. A new, long-arm functional strategy for individuating computation is advanced.

Highlights

  • Computational explanations are typical in the cognitive sciences

  • In response to the task argument, he claims that “a functional individuation of computational states is sufficient to determine which task is being performed by a mechanism, and which computation is explanatory in a context” (Piccinini, 2015, p. 43)

  • Sometimes even “the system plus its immediate causal environment are not [...] sufficient for fixing the actual computations performed by the system”. (Piccinini’s short-arm strategy is insufficient in such cases.) the computational semanticist concludes that the computational individuation of, at least some, physical systems requires semantic constraints

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Summary

Introduction

Computational explanations are typical in the cognitive sciences. The identification of the mathematical function being computed by a physical system—be that a brain circuit, or a single neurone—may be complicated by the fact that some such functions have other “isomorphic copies”—a term that will shortly be clarified using a simple example. If the voltage range 1–3 V represents False and 4–6 V represents True, Table 1 turns out to be the standard truth-table for Boolean conjunction. If the voltage range 1–3 V represents True and 4–6 V represents False, G computes an isomorphic copy of conjunction, namely: inclusive disjunction (or is an OR-gate). Whether a given account of computation is able to settle the indeterminacy of computation when it arises has been deemed a litmus test for the adequacy of that account. What those properties are is an open question.

1–3 V 4–6 V 1–3 V 4–6 V
Mechanistic individuation of computation
Semantic individuation of computation
1–2 V 2–3 V 2–3 V 2–3 V 2–3 V 2–3 V 2–3 V 2–3 V 4–6 V
A new strategy: long‐arm functional individuation of computation
Long‐arm individuative strategy
The long‐arm strategy need not be semantic
Shagrir’s indeterminacy challenge revisited
Conclusion
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