Abstract
Scientific practice involves two kinds of induction. In one, generalizations are drawn about the states of a particular system of variables. In the other, generalizations are drawn across systems in a class. We can discern two questions of correctness about both kinds of induction: (P1) what distinguishes those systems and classes of system that are ‘projectible’ in Goodman’s (Fact, fiction and forecast, 1955) sense from those that are not, and (P2) what are the methods by which we are able to identify kinds that are likely to be projectible? In answer to the first question, numerous theories of ‘natural kinds’ have been advanced, but none has satisfactorily addressed both questions simultaneously. I propose a shift in perspective. Both essentialist and cluster property theories have traditionally characterized kinds directly in terms of the causally salient properties their members possess. Instead, we should focus on ‘dynamical symmetries’, transformations of a system to which the causal structure of that system is indifferent. I suggest that to be a member of natural kind it is necessary and sufficient to possess a particular collection of dynamical symmetries. I show that membership in such a kind is in turn necessary and sufficient for the presence of the sort of causal structure that accounts for success in both kinds of induction, thus demonstrating that (P1) has been answered satisfactorily. More dramatically, I demonstrate that this new theory of ‘dynamical kinds’ provides an answer to (P2) with methodological implications concerning the discovery of projectible kinds.
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Notes
I don’t mean to suggest that this is all which empirical science involves or aims at. Nor do I intend to suggest that this is a complete taxonomy of the kinds of inductive practice. For an example of a more complete taxonomy, see (Earman 1985).
Though Goodman (1955) frames his problem in terms of predicates—linguistic entities—his solution is in terms of the extensions of those predicates. Specifically, what he calls “entrenchment” pertains to a class that may be named by many predicates.
I mean (P1) in a thin sense: the shared feature of a kind may or may not be that in virtue of which it is projectible.
Quine, for instance, restricts the term ‘kind’ to collections defined by similarity relations. Since, in his view, mature sciences have no use for such similarity relations, there are no ‘natural kinds’ in science. I am only interested in notions of natural kind that stand as possible responses to (P1). Most of the views considered here take scientific categories to be paradigm examples of natural kinds.
There is some ambiguity as to whether these mechanisms are taken to be homeostatic with respect to the individual, as described in the text, or with respect to the kind. In the latter case, there is some causal mechanism such that the occurrence of one of the properties in the cluster tends to cause the occurrence of the others, though not necessarily in the same individual. The connection between properties is robustly maintained across many instances by the mechanism, but in any one individual the connection may be fragile over time. Boyd (1999) recognizes both possibilities, but the majority of discussion over HPC assumes that each individual belonging to a kind is a distinct instance of a type of causal mechanism. That is, each member of a kind possesses a cluster of properties maintained by an instance of the same type of homeostatic causal mechanism.
There are complex features common to all members of the class. For instance, energy and momentum are conserved. But what is the ‘causal mechanism’ that maintains the association between the two properties “conserves momentum” and “conserves energy”?
Slater (2014) and others have pointed out that it seems to have trouble with kinds such as chemical elements. But it’s not clear that this is really the sort of induction central to scientific practice.
Slater is also motivated by arguments suggesting that causal mechanisms are neither necessary nor sufficient for the sort of robust counterfactual association of properties required for successful projection.
I am neglecting a great deal of detail in Slater’s account—in particular, his use of Lange’s (2009) notion of ‘non-nomic stability’ to spell out a precise sense of counterfactual robustness. But the rough argument I’ve provided is adaptable to these details.
I won’t worry here about Woodward’s definitions of direct, indirect, or contributing causes. While these are useful concepts, we can get far enough with total causation alone.
Precipitation is the sudden formation of a solid from solution that tends to sink or float as a powder or collection of small crystals.
A ‘simple compound’ is just a compound that is composed of one acid and one base or one metal and one non-metallic element.
More precisely still, Wigner equated each kind of elementary particle with one of the irreducible representations of the Poincaré group (which he calls the inhomogeneous Lorentz group).
To be more accurate, Wigner equated irreducible representations of the Poincaré group with what he called an “elementary system.” In a later paper with Newton, he argued that the category of “elementary particle” is narrower, and carries the additional condition that “...it should not be useful to consider the particle as a union of other particles”(Newton and Wigner 1949, p. 400). The latter condition turns out to be problematic, so I’m sticking with the broader category. This includes such things as hydrogen atoms in their ground state. What’s not an elementary system? For one, any unstable particle (Wigner and Newton cite the \(\pi \)-meson) that exhibits a change in state that is not relativistically invariant.
I am using “dynamical” in its broad sense of “active” or “potent”, not in the narrow sense of involving forces.
For finite sets of transformations, the composition function is equivalent to a multiplication table. But for infinite sets, we cannot write an explicit multiplication table.
If the variables are casually complete in the sense that there are no latent causal influences on the variables, then the identity transformation is a symmetry of the system for every choice of variable and index. Therefore, the system possesses a symmetry structure. To show that it is not trivial, suppose that \(X\) is a total cause of \(Y\). By definition, this means that there are some values \(x_0\) and \(x_1\), such that an intervention taking \(X\) from \(x_0\) to \(x_1\) induces the value of \(Y\) to change. In general, the dependence of \(Y\) on \(X\) can be described by a function, \(f(x, y_0)\), where \(y_0\) is the value of \(Y\) when \(X = x_0\), i.e., \(f(x_0, y_0)=y_0\). Since the change in \(X\) induces a change in \(Y\), we know that \(f(x_1, y_0) \ne y_0\). Consider a transformation, \(\sigma (y)=y_0\). Applying \(\sigma \) and then changing \(X\) takes us from a state \((x_0,y_0)\) to \(f(x_1,\sigma (y_0))=f(x_1,y_0)\). Changing \(X\) and then applying \(\sigma \) takes us from a state \((x_0,y_0)\) to \(\sigma (f(x_1,y_0)) = y_0 \ne f(x_1,y_0)\). Thus, \(\sigma \) fails to be a symmetry, and so the symmetry structure cannot be trivial.
Incidentally, the category of first-order chemical reactions mentioned earlier is a dynamical kind characterized by an analogous family of scaling transformations.
In particular, there is ample discussion of the use of symmetry arguments in solving physical problems, and of ’Curie’s Principle’—the claim that asymmetries in an effect must be present in the cause (Ismael 1997; Rosen 1995; Fraassen 1990). These are rich topics, but well beyond the scope of this essay.
Unfortunately, Wigner calls these “dynamic principles of invariance,” and, as with virtually every term associated with symmetry, similar phrases have been used throughout the literature to refer to a variety of distinct notions. Obviously, I am not helping the situation with my choice of terminology. However, the phrase ‘dynamical symmetry’ seems best to express what I have in mind and, in many of it’s previous uses, is not so far off from the concept presented here. I beg the reader’s indulgence for further overloading the term.
This story is recounted in Pais (1986).
See (Neuenschwander 2011) for a thorough discussion.
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Acknowledgments
I would like to thank the participants of the 2013 Ontology & Methodology conference at Virginia Tech, Anjan Chakravartty, and Richard Burian for helpful discussion of the ideas presented here. I am especially grateful to Kelly Trogdon and two anonymous referees for comments on earlier drafts.
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Jantzen, B.C. Projection, symmetry, and natural kinds. Synthese 192, 3617–3646 (2015). https://doi.org/10.1007/s11229-014-0637-5
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DOI: https://doi.org/10.1007/s11229-014-0637-5