According to the homeostatic property cluster family of accounts, one of the main conditions for groups of properties to count as natural is that these properties be frequently co-instantiated. I argue that this condition is, in fact, not necessary for natural-kindness. Furthermore, even when it is present, the focus on co-occurrence distorts the role natural kinds play in science. Co-occurrence corresponds to what information theorists call redundancy: observing the presence of some of the properties in a frequently co-occurrent cluster makes observations of other members of the cluster comparatively uninformative. Yet, scientific practice often, and increasingly often, singles out as natural groups of properties that are not redundant, but synergic: instantiations of properties in synergic clusters are not necessarily informative about instantiations of other properties in the cluster; rather, it is their joint instantiation that plays the explanatory role for which the natural kind is recruited.
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Not always. See Bird (2015) for discussion.
Inductive inference takes widely different forms, of course, and go far beyond this somewhat caricaturesque example. It is possible that some of the shortcomings of the homeostatic property cluster account I identify in this paper could be traced back to relying on this kind of simple induction as a guiding example. As we will see, much of the inductive inference science engages in is significantly more complex.
In current philosophy of biology, essentialism about species has taken a historical turn (Godman 2015; Griffiths 1999; Millikan 1999; Okasha 2002) whereby essences are no longer taken to be intrinsic, but rather historical properties of lineages of populations. In what follows I will be defending a conservative modification of the homeostatic property cluster theory of natural kinds, and in particular one that is compatible with the postulation of historical essences for species.
While throughout this paper I often talk of causal structure, the models I will describe in subsequent sections are causally agnostic, and focus on probabilistic (informational) connections. In any case, whenever these connections are grounded on causal facts my discussion applies to them as well. See also footnote 6.
Note that I have not given a causal gloss on the role of essences. This is because causal facts cannot be read off probability distributions. This causal agnosticism is, I submit, an advantage of the model: it allows it to apply to the HPC account proper, with its reliance on causal connections, and to other, related accounts such as Slater (2015)’s stable property clusters, that substitute causal connections with a modal stability constraint. This kind of constraints, arguably, are precisely what probability distributions inform us of. I discuss Slater’s account in the following subsection.
More formally, two properties \(P_i\) and \(P_j\) provide redundant information about the world iff the mutual information between the joint random variable, \(W\), of all random variables in the world, and the joint random variable (\(P_i, P_j\)) is less than the sum of the mutual informations of W and each individual random variable: \(I(W; P_1) + I(W; P_2) > I(W; P_1, P_2)\). The definition of redundancy for more than two random variables is an open theoretical problem.
More formally, two properties \(P_i\) and \(P_j\) provide synergic information about the world iff the mutual information between the joint random variable, \(W\), of all random variables in the world, and the joint random variable (\(P_i, P_j\)) is more than the sum of the mutual informations of W and each individual random variable: \(I(W; P_1) + I(W; P_2) < I(W; P_1, P_2)\). The definition of synergy for more than two random variables is also an open theoretical problem.
The answer to this question might have to do, for example, with whether Ken has an individual essence, and whether such essence is independent of his sex. Adherents to Kripkean essentiality of origin theses (Kripke 1980) will answer this question affirmatively if triplewart seadevil sex is fixed after conception, but there might be other reasonable positions. The worry I am sketching here, and is developed more fully by Magnus in his (2011), is that Boyd’s approach makes polymorphism hostage to these comparatively arcane metaphsical considerations.
This discussion is indebted to an anonymous referee.
I would like to thank an anonymous referee for helping me distinguish these two sorts of examples.
That is, graphs in which individual nodes have a small average number of connections to other nodes, yet the average distance between two arbitrary nodes in the graph is also small. See Watts and Strogatz (1998).
Suppose, that is, that cortical minicolumns are the atomic functional units in a mammalian cerebral cortex. See Sporns et al. (2005), p. 247, for discussion.
Although the precise way in which information should be separated into its synergic and redundant components is an open theoretical problem, and one which is the focus of much recent research. See Williams and Beer (2010), Griffith et al. (2014), Bertschinger et al. (2013), Griffith and Koch (2014).
No analogue of the Homeostasis condition is needed: the presence of informational dependence already presupposes that probabilistic connections are not a matter of chancy coinstantiations.
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Financial support for this work was provided by the Research Foundation—Flanders, Research Grant FWO G0C7416N. I would like to thank two anonymous referees, audiences in Barcelona and Paris, and my colleagues at the Centre for Philosophical Psychology, University of Antwerp, for comments and suggestions on earlier drafts.
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Martínez, M. Synergic kinds. Synthese 197, 1931–1946 (2020). https://doi.org/10.1007/s11229-017-1480-2
- Homeostatic property clusters
- Information theory
- Natural kinds
- Richard Boyd