Toward an Algorithmic Metaphysics

Abstract

Abstract. There are writers in both metaphysics and algorithmic information theory (AIT) who seem to think that the latter could provide a formal theory of the former. This paper is intended as a step in that direction. It demonstrates how AIT might be used to define basic metaphysical notions such as object and property for a simple, idealized world. The extent to which these definitions capture intuitions about the metaphysics of the simple world, times the extent to which we think the simple world is analogous to our own, will determine a lower bound for basing a metaphysics for our world on AIT.Keywords: metaphysics, formal metaphysics, computational metaphysics, algorithmic metaphysics, algorithmic information theory, real patterns.Both philosophers and mathematicians have flirted with the idea that algorithmic information theory (AIT) could provide some foundation for basic notions in metaphysics. The main inspiration for this paper is one such hint from the philosophy side: in Daniel Dennett's sketch of a metaphysics based on "real patterns", he explicitly appeals to incompressibility, and offhandedly mentions the work of AIT theorist Gregory Chaitin in this connection.1 Meanwhile AIT theorists since Andrey Kolmogorov frequently speak about, for example, the "information content" of objects generally, rather than of binary strings in particular. (Of course, "the original incentive to develop a theory of algorithmic information content of individual objects was Ray Solomonoff 's invention of a universal a priori probability . . . "2 ) This paper aims to help bridge this gap between metaphysics and AIT. As befits a philosophy paper, it contains little in the way of technical results, but some ruminations aiming to pave the way for technical results to come. And as is typical of work bridging discipline X to discipline Y , X theorists are likely to complain that the treatment of X is far too simplistic and sloppy, and that the treatment of Y engages trivial details-while Y theorists complain conversely.

An Algorithmic Metaphysics of Self-Patterns

“…According to Petersen (2013Petersen ( , 2019 the criterion of being a real pattern (characterized in terms of Kolmogorov complexity) can demarcate what is a genuine composite object from the mere sum of independent objects or patterns. According to 7 Logical depth is defined as "a normalized quantitative index of the execution time required to generate the model of the real pattern in question by a near incompressible universal computer program, that is, one not itself computable as the output of a significantly more concise program" (Ladyman and Ross, 2007, p. 220).…”

“…Between these two extremes, there are moderate varieties; some pluralities (such as atoms of hydrogen and oxygen) constitute a new object (such as a molecule of water) and some other pluralities (such as the compound of the pear tree in my yard and the Taj Mahal) do not constitute a new object 6 . In this context, Petersen is advocating a compositional conception of constitution ( Petersen, 2013 , p. 312). According to this approach, for an object to be constituted / composed by some pluralities, there must exist some degree of “connectedness” or “integrity” between the pluralities ( Simons, 2000 , p. 290).…”

“…I suggest that the criteria of compressibility and simplicity of patterns provide precious insight into the question of extendedness of the self. The proposed criteria are inspired by Steve Petersen’s ( Petersen, 2013 , 2019 ) algorithmic metaphysics of the composition of objects (and more originally, by Dennett’s (1991) theory of real patterns, as well as Ladyman and Ross’s (2007) engagement with the idea of real patterns). Dabbling in algorithmic metaphysics in this fashion, I provide answers to the two abovementioned questions.…”

Real patterns and indispensability

“…In our context, this is a relatively idiosyncratic choice: it is universally understood that the main measure of algorithmic complexity is Kolmogorov complexity (Grünwald and Vitanyi 2008) and this is also the notion used in most other papers in the philosophical literature on real patterns (Dennett 1991;McAllister 2003b;Petersen 2013Petersen , 2018. We will opt for a Kolmogorov-complexity version of L&R's definition of real patterns.…”

“…Genomics (Barrett et al 2013), connectomics (Sporns, Tononi, & Kötter 2005), and astronomy (Feigelson and Babu 2012) are obvious examples, but the trend is quite general. Philosophers of science have been paying increasing attention to patterns, so as to keep up with the trend, but also in the hope that these entities will fruitfully supplement other entities, such as natural kinds, in the metaphysics of science (Andersen 2017;Ladyman and Ross 2007;Martínez 2015, Martínez 2017McAllister 2003bMcAllister , 2003aMcAllister , 2011Petersen 2013).…”