When do parts form wholes? Integrated information as the restriction on mereological composition.

The composition question asks under what conditions material objects form a whole. Existing answers are either vague or face counterexamples, leading many philosophers to accept that composition either never occurs or always occurs. This paper introduces integrated information theory (IIT), a theory of consciousness, and argues that it provides a precise, non-trivial answer: composition occurs when integrated information is maximized. The IIT restriction avoids the problems of vagueness and counterexamples that plague other proposals. An appendix explains how to calculate parts and wholes using a simple system.

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Abstract

Under what conditions are material objects, such as particles, parts of a whole object? This is the composition question and is a longstanding open question in philosophy. Existing attempts to specify a non-trivial restriction on composition tend to be vague and face serious counterexamples. Consequently, two extreme answers have become mainstream: composition (the forming of a whole by its parts) happens under no or all conditions. In this paper, we provide a self-contained introduction to the integrated information theory (IIT) of consciousness. We show that IIT specifies a non-trivial restriction on composition: composition happens when integrated information is maximized. We compare the IIT restriction to existing proposals and argue that the IIT restriction has significant advantages, especially in response to the problems of vagueness and counterexamples. An appendix provides an introduction to calculating parts and wholes with a simple system.