Measurement and Computational Skepticism

Matthews, Robert J.; Dresner, Eli

doi:10.1111/nous.12142

Cited by 10 publications

(7 citation statements)

References 22 publications

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“…Blackmon (2013) also emphasizes the relativity of implementation. For connections between the applicability of mathematics and computational implementation see(Matthews and Dresner 2017) and(Schweizer 2019a).20 At least, up to any indeterminacy in the properties cited by the specific scheme. Although this is itself a serious issue, I will not pursue it here.21 To be clear, I do not claim that a system's computational identity is determined by the total set of computations it implements (as inMilkowski 2013).…”

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confidence: 99%

The determinacy of computation

Curtis-Trudel

2022

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A skeptical worry known as 'the indeterminacy of computation' animates much recent philosophical reflection on the computational identity of physical systems.On the one hand, computational explanation seems to require that physical computing systems fall under a single, unique computational description at a time. On the other, if a physical system falls under any computational description, it seems to fall under many simultaneously. Absent some principled reason to take just one of these descriptions in particular as relevant for computational explanation, widespread failure of computational explanation would appear to follow. This paper advances a new solution to the indeterminacy of computation. Very roughly, I argue that the computational identity of a physical system is determinate relative to a contextually specified way of regarding that system computationally ---known as a labelling scheme. When a system simultaneously implements multiple computations, it does so relative to different labelling schemes. But relative to a fixed labelling scheme, a physical system has a unique computational identity. I argue that this relativistic conception of computational identity vindicates computational explanation and comports well with computational practice.

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confidence: 99%

The determinacy of computation

Curtis-Trudel

2022

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“…by demonstrating that they are infeasible to compute relative to a hybrid model of computation which operates on (say) both strings and numbers or propositional formulas simultaneously. See (Matthews and Dresner 2017) for a recent articulation of a similar point contra related skeptical concerns about the interpretation of physical implementations of computers of the sort originally introduced by Putnam (1988) and ?.…”

Section: Problems and Mathematical Difficultymentioning

confidence: 99%

Computational Complexity Theory and the Philosophy of Mathematics†

Dean

2019

Philosophia Mathematica

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Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} \neq \mathbf{NP}$ problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof.

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“…Fresco and Miłkowski (2019) agree with Piccinini that computation is context-dependent, but offer a different account of the nature of the system-environment interaction. Pragmatists suggest that the feature that singles out the relevant computation depends on the explanatory aims of the scientists (Egan 2012, Rescorla 2014, Matthews and Dresner 2017. Proponents of the semantic account suggest that the missing ingredient is the content of the physical states (e.g., Sprevak 2010).…”

Section: Input 1 Input 2 Outputmentioning

confidence: 99%

On Two Different Kinds of Computational Indeterminacy

2022

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It is often indeterminate what function a given computational system computes. This phenomenon has been referred to as “computational indeterminacy” or “multiplicity of computations.” In this paper, we argue that what has typically been considered and referred to as the (unique) challenge of computational indeterminacy in fact subsumes two distinct phenomena, which are typically bundled together and should be teased apart. One kind of indeterminacy concerns a functional (or formal) characterization of the system’s relevant behavior (briefly: how its physical states are grouped together and corresponded to abstract states). Another kind concerns the manner in which the abstract (or computational) states are interpreted (briefly: what function the system computes). We discuss the similarities and differences between the two kinds of computational indeterminacy, their implications for certain accounts of “computational individuation” in the literature, and their relevance to different levels of description within the computational system. We also examine the inter-relationships between our proposed accounts of the two kinds of indeterminacy and the main accounts of “computational implementation.”

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Measurement and Computational Skepticism

Cited by 10 publications

References 22 publications

The determinacy of computation

The determinacy of computation

Computational Complexity Theory and the Philosophy of Mathematics†

On Two Different Kinds of Computational Indeterminacy

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