Why computational complexity may set impenetrable barriers for epistemic reductionism

According to physicalism, everything is physical or metaphysically connected to the physical. If physicalism were true, it seems that we should - in principle - be able to reduce the descriptions and explanations of special sciences to physical ones, for example, explaining biological regularities, via chemistry, by the laws of particle physics. The multiple realization of the property types of the special sciences is often seen to be an obstacle to such epistemic reductions. Here, we introduce another, new argument against epistemic reduction. Based on mathematical complexity, we show that, under certain conditions, there can be "complexity barriers" that make epistemic reduction - in principle - unachievable even if physicalism were true.

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Michael Herzog, Christian Sachse, Adrien Christophe Doerig
2023
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https://infoscience.epfl.ch/record/308025?ln=en

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Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.

Complexity class

In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory) requirements.

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