This post represents a small philosophical excursion from the measures of robustness research program I am working on. That research program constructs Markov models of systems from data and analyzes them so find the system's tipping points and further uses those points (and other features) to measure robustness-related properties (including sustainability, resistance, recoverability, stability, and being static; as well as their counterparts: susceptibility, vulnerability, fragility, and collapsibility. While working on the formal definitions of those concepts I realized that these are all dispositional properties and dispositional properties are philosophically interesting and troublesome. That connection immediately made me wonder if my mathematical formalism might shed some new light on how to differential dispositional properties form categorical ones; some first thoughts on that are below.

Dispositional properties are philosophically troubling for many reasons mostly stemming from the question of whether their subjunctive conditional status distinguishes them from categorical properties. It may therefore be interesting to consider how to apply my methodology to investigate other dispositional properties such as soluble, malleable, affordable, and differentiate them from other properties with accepted necessary and sufficient conditions. If in addition to the obvious and direct application of this methodology to improve the performance capabilities of systems my research also produces insights into the nature of dispositional properties in general that would be unanticipated but certainly welcome news. Let's look at some details of the problem.

Color properties are known as primary properties and should be excellent candidates of clear-cut categorical properties. Yet the story is not so simple. For example, being red is dispositional in the sense that nothing seems red in the dark or if nobody can see it so something seems red only if viewed by a person in appropriate light. That's a subjunctive conditional description of something seeming red, not of something being red. The redness property supposedly emerges from certain structural properties of the matter making up the red object, regardless of what it may look like to people and how we come to know of the property. That is, here we are interested in the ontological issues rather than the issues of qualia or epistemology. But then fragility seems likely to have a similar micro-structural explanation which again removes the distinction that the types of properties appear to have.

Whether or not redness (or conductive, or triangular, or …) is dispositional in the same way that fragility is is not solved. A big part of the problem is that any property can be given a subjunctive conditional description, but a property would be dispositional iff such a definition is the only possible one. That seems impossible to prove due to the open-endedness of finding alternative descriptions. My mathematical analysis reveals how particular dispositional properties (robustness-related ones) are behavioral in nature and emerge from the microbehavior of the system components. What I hope is that this can be expanded to develop necessary and sufficient conditions for properties to be dispositional in different ways…or at least a step in a helpful direction.

One thing that the robustness measures tell us is the probabilistically defined tendency of a system to stay in functioning configurations. They also identify the aspects of a state that must change in order for the system to leave its functional configuration. A basic version of the results of the vulnerability analysis is that the system would reduce functionality if a particular aspect were to change in a particular way. That certainly sounds dispositional; and since it is a definition it satisfies the necessary and sufficient requirements too. Furthermore, it is a property that a state (or an aspect of a state) has in virtue of the possible behavior of the system in that state.

As the above description makes clear, to evaluate one of these dispositional properties a lot of information about the system's dynamics and the states' aspects needs to be known. But to know whether a state has some aspect (for example if an object in the world at that time is of a particular color) one only needs to know about that state, in fact only about one aspect of that state. So one thing that differentiates these dispositional properties from certain categorical properties is the information requirement; specifically dispositional properties require intertemporal information. But clearly some categorical properties (e.g. falling and other kinds of moving) are also intertemporal. Actually, I could only think of ones that involve moving and I think it's quite kosher to doubt these are really categorical properties of things – they are descriptions and I can imagine recording them as property-like aspects in a Markov model, but that doesn't mean we'd include them in our real-world ontology as properties. It can't be that easy, though. So I need to think of some clear categorical properties that we can't ascribe without intertemporal information to keep that going.

I'm not going to do that now, but before I end this I wanted to say something about the question of whether dispositional properties are reducible to categorical properties. That depends on what one counts as part of a valid reduction. No simple collection of micro-descriptions (aspects of states) would ever imply the macro-description (e.g. fragile), but once you add the rules for generating system dynamics at the micro level you will indeed have your macro-property. In the way I use 'reducible', if a macro property supervenes on micro properties then it is reducible to them. Part of establishing supervenience is elucidating the corresponding changes at the micro and macro levels…which is what the robustness analysis does. We must conclude that since robustness and fragility supervene on the aspects of the states these dispositional properties are reducible to the categorical properties and systemic rules that govern their changes. I think a lot of confusion arises over the use of 'reduction' because people don't think the dynamics are included, but supervenience wouldn't imply reducibility if the dynamics aren't included. So maybe I'm using the wrong terms here, and if so I'd sure like to know what the right ones are, but conceptually I think I've made my point clear (and if not I'd sure like to know). Because the commenting thing gets spammed too much you'll have to send me an email if you've got something to tell me: Thanks in advance.