Abstract
Neuron diagrams are heavily employed in academic discussions of causation. Stephen Mumford and Rani Lill Anjum, however, offer an alternative approach employing vector diagrams, which this paper attempts to develop further. I identify three ways in which dispositionalists have taken the activities of powers to be related: stimulation, mutual manifestation, and contribution combination. While Mumford and Anjum do provide resources for representing contribution combination, which might be sufficient for their particular brand of dispositionalism, I argue that those resources are not flexible enough to further accommodate either stimulation or mutual manifestation. Representational tools are provided to address these limitations, improving the general value of the vector model for dispositionalist approaches to causation.
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Notes
M&A treat the terms “power” and “disposition” as equivalent, which I will do as well.
Again, this will not require adopting their pessimistic view of neuron diagrams but, rather, require appreciating M&A’s underlying goal of securing a dispositionalist friendly model, which we will pursue within the vector approach.
As M&A (2011a, ch. 4) acknowledge, vector addition cannot handle genuine cases of non-linear composition. Vector addition, as an additive mode of composition, requires that the output of a system be proportional to the input: f(x + y) = f(x) + f(y). But there are arguably real world systems that violate this principle, such as the weather with the butterfly effect. For M&A’s handling of this issue, see their (2011a, ch. 4).
Moreover, vector addition in general seems to presume a degree of objective precision regarding the magnitude and direction of a power, which one might question as well (e.g., Elina Pechlivanidi and Stathis Psillos, unpublished). Fragility, for instance, is determined by the degree of pressure it takes an object to break relative to a certain context (e.g., the typical handling conditions of a vase) or the degree of pressure it takes an object to break relative to another object (e.g., a crystal vase vs. a copper vase). Indeed, such points might be pressed to challenge the very idea of modeling powers as vectors.
Another basic concern with the vector approach is that it cannot represent inactive or dormant powers (e.g., Jennifer McKitrick and Anna Marmodoro in McKitrick et al. 2013). As M&A explicitly state, “vectors represent only the powers that are exercising or operating” (2011a, p. 38). But a key feature of dispositionalism, which takes powers to be more than mere potentialities, is that powers can exist without manifesting or even being active at all—they can exist “ready to go.” Therefore, interacting powers should be able to yield results that involve inactive powers, which the vector model would be unable to represent. For M&A’s response to this apparent weakness of the vector model, see McKitrick et al. (2013).
A responding power could itself be a stimulating power as well. This would be the case for fragility, were the breaking of the vase to involve the activation of a further power (e.g., a disposition of the delicate display table to scratch).
One might be tempted here to put vector addition aside and, instead, appeal to the centered vertical line in order to connect the two powers. However, that line represents merely our starting point in the quality space. Moreover, the stimulation relation is asymmetrical, yet the vertical line suggests no such directionality between the powers represented by vectors a and b.
Christopher Austin (2015) is also sensitive to the difficulty M&A’s vector model faces in trying to represent mutual manifestations. However, Austin does not take this to be a problem, since he does not think that mutual manifestations need to be included in a dispositionalist approach to causation. The primary aim of this paper, though, is not to settle such debates among alternative dispositionalist ontologies but, rather, to help provide a general model for representing those various approaches to causation. In which case, the inability of vector addition to represent mutual manifestations remains a concern for us, as we are interested in the value of the vector model from a broader, methodological perspective.
Matthew Tugby (2010) highlights the heavy favoring of a diachronic approach. He also challenges it, arguing in favor of a synchronic account of stimulation. One might expect, then, that Tugby would be content with the suggestion on offer. It seems to me, however, that Tugby is not really after stimulation but, instead, promoting a mutual manifestation ontology (see especially pp. 333–334). So, Tugby would probably prefer employing my strategy for representing mutual manifestations, which will be proposed in the next section.
It is tempting here to try to gauge the intensity of a stimulating power using the intensity of the stimulated power. Remember, however, that the two powers aim at different manifestations, which makes it difficult to see how such a connection is assured between their respective intensities. Notice as well that such an approach would be rendered problematic were the intensity of a power allowed to be greater than that which is necessary for it to stimulate another power (e.g., a bridge’s disposition to collapse under 6 tons of weight being stimulated by a 7-ton vehicle).
The ability to employ time-indexing would also prove useful here, as Heil’s causes appear to precede their resulting causings. In the example involving two cards remaining upright upon a table, for instance, the cause (carefully placing the cards upon the table) precedes the resulting causing (reciprocal powers of the cards and the table mutually supporting the cards’ remaining upright).
Feel free to assume that the original shared vector of interest involves more than two powers, so that the second diagram will not involve a non-shared vector. Notice, though, that the suggestion on offer would then involve a multi-track approach towards those dispositions remaining in the second diagram, since they will be represented by a shared vector involving a different set of reciprocal dispositions for a different kind of mutual manifestation.
References
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Heil, J. (2012). The universe as we find it. Oxford: Oxford University Press.
Hitchcock, C. (2007). What’s wrong with neuron diagrams. In J. K. Campbell, M. O’Rourke, & H. Silverstein (Eds.), Causation and explanation (pp. 69–92). Cambridge, MA: MIT Press.
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Mumford, S., & Anjum, R. L. (2011a). Getting causes from powers. Oxford: Oxford University Press.
Mumford, S., & Anjum, R. L. (2011b). Spoils to the vector. The Monist, 94(1), 54–80.
Pechlivanidi, E. & Psillos, S. (unpublished) What powers are not. http://philsci-archive.pitt.edu/12080/.
Tugby, M. (2010). Simultaneity in dispositional interaction? Ratio, 23(3), 322–338.
Acknowledgements
I am grateful to Jacob Caton, Neil Williams, Jessica Wilson, audience members who heard conference versions of this paper, and four anonymous referees for their helpful feedback. I also owe a special thanks to Adam Podlaskowski, who read several drafts, provided a ton of useful comments, and engaged me in fruitful discussions regarding a variety of ideas in this paper.
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Baltimore, J.A. Expanding the vector model for dispositionalist approaches to causation. Synthese 196, 5083–5098 (2019). https://doi.org/10.1007/s11229-018-1695-x
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DOI: https://doi.org/10.1007/s11229-018-1695-x