Causation, Information and Specificity

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which ones do we select in our causal judgements? These are facts about either token or type causal relations, and (I st
Causation, Information and Specificity Brad Weslake NYU Shanghai http://bweslake.org/

Philosophy of Science Association Atlanta, 4 November 2016

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Introduction

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Aim

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Recent work on causal importance in biology has involved an oscillation between conceptual claims and empirical claims. This is a talk on the conceptual side. I aim to diagnose a confusion in theories of causal importance. In particular, I claim that many theories of causal importance confuse the actual frequencies that provide evidence for causal importance, with the facts that ground causal importance.

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Plan

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Causal importance. Sober on causal responsibility. Waters on actual difference making. Griffiths et al on specificity. Alternative theories of causal importance. Conclusion.

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Causal Importance

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A Simple Example ▶

A radio with an on/off switch and volume dial (Woodward and Hitchcock 2003).

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Three Questions about Causation Important to keep three questions distinct: ▶

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Actual Causation. Of the various things that might have caused some particular effect, which were the actual causes? These are facts about token causal relations, and (I suggest) they do not depend on our interests. Causal Selection. Of the various actual causes of an effect, which ones do we select in our causal judgements? These are facts about either token or type causal relations, and (I stipulate that, by definition) they do depend on our interests. Causal Importance. Of the various causes of an effect, which ones are more important? These are facts about either token or type causal relations, and (I stipulate that, by definition) they do not depend on our interests.

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Three Varieties of Causal Importance

I will discuss three varieties of causal importance: ▶ ▶

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Causal Responsibility. Which causes were more responsible for the effect, and which less? Actual Difference Making. Which causes actually made a difference to the effect, and which merely potentially made a difference? Causal Specificity. Which causes were more specific for the effect, and which were less specific?

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Sober on Causal Responsibility

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Contribution and Difference Making

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Sober (1988) distinguishes two varieties of responsibility: ▶ ▶

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The contribution a cause makes to an effect The difference a cause makes to an effect

Sober proposes theories of what it is for a cause to make a contribution/difference to an effect to a greater/lesser degree. Note: Does not entail there are two concepts of causation.

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Degree of Responsibility

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Causal contribution identical in Population I and II. Meaningless to ask which made the greatest contribution. Meaningful to ask which made the greatest difference: ▶ ▶ ▶

This is grounded in bare counterfactuals. Bare counterfactuals grounded in actual variation. It therefore varies by population: is non-local. ..

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Three Mistakes

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Defining degree of difference in terms of bare counterfactuals. Defining bare counterfactuals in terms of an expectation. The Confusion Taking actual frequencies to ground difference-making facts rather than constituting evidence for difference-making facts. ▶

The same thought experiment Sober (1988, 308–9) uses to argue that contribution is local can be used to argue that difference-making is local.

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Waters on Actual Difference Making

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Actual and Potential Difference Making

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Waters (2007) distinguishes between two population relative varieties of difference making: ▶

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The potential difference makers. These are all the actual causes of the values of the effect in the population. The actual difference makers. These are all the actual causes of the values of the effect in the population that actually vary, such that were this variation eliminated, variation in the effect would be changed.

This distinction is not intrinsically scientifically interesting. It amounts to the difference between populations that do and do not include individuals that actually vary—a difference that might be accidental (Weber 2016b).

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Specific Actual Difference Making

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Waters (2007) extends these notions by adding a notion of causal specificity in the sense of Woodward (2010), roughly: ▶

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INF. A cause is specific for an effect to the extent that the counterfactual structure between values of the cause and effect variables approaches a bijective function.

Conjoining this with the notion of an actual difference maker yields the notion of a specific actual difference maker.

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A Dilemma ▶

Waters (2007, 579): If biologists were […] limited to considering the causal synthesis of a single polypeptide molecule, they would have no basis for saying that the polypeptide’s linear sequence was determined by DNA, and not by RNA polymerase. […] The causal distinctiveness of DNA is in the population.

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Either specific actual difference making is a concept that applies to populations, in which case it is not intrinsically scientifically interesting; or it is a population-relative concept that applies to individuals, in which case it suffers from The Confusion.

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Griffiths et al on Specificity

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Preamble

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I will argue that the account of specificity defended by Griffiths et al. (2015) also suffers from The Confusion. If I am right then there is an irony here, since Griffiths and Stotz (2013, 188–99) have themselves criticised Waters for his claim that biologists are only interested in actual variation.

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An Informational Measure of Specificity ▶

The Griffiths et al. (2015) proposal for measuring specificity: ˆ = H(E) − H(E|C) ˆ I(E; C) ▶ ▶ ▶

H(E) is the entropy of E. ˆ is the conditional entropy of E on C. ˆ H(E|C) ˆ ˆ I(E; C) is the mutual information between E and C.

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Since entropy is a function of a probability distribution, we need probability distributions over both cause and effect for these quantities to be well defined.

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Griffiths et al. (2015) propose to use the maximum entropy distribution, which assigns equal probability to all variable values. Call the resulting measure SPEC.

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A Problem

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As Griffiths et al. (2015) note, SPEC entails that in the natural causal model used to represent the simple radio example, the dial is not more specific than the switch. The response by Griffiths et al. (2015) is puzzling: ▶

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They note their measure does provide a nice quantitative generalisation of Waters (2007), if we replace the maximum entropy distribution with the actual frequency distribution. They then claim that SPEC is a precisification of INF. But it cannot be, as the simple radio example shows!

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Probability and Modality

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Pocheville, Griffiths, and Stotz (forthcoming): Our measure of specificity […] depends on what probability distribution we choose to impose on the the causal variable C, as well as on the mapping from C to E. In our earlier paper we showed that this is very much a feature and not a bug of our measure.

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It’s a bug! ▶

…or at least, it’s a bug if the aim to is provide a precisification of INF. For to think that SPEC measures INF is to succumb to a version of The Confusion.

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Four Unsuccessful Measures of Specificity

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More generally, none of the following probability distributions can serve as a precisification of INF: ▶

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SPEC (Griffiths et al. 2015) The maximum entropy distribution. SAD (Waters 2007) The actual frequency distribution. REL (Weber 2016a) The biologically normal distribution. MAXSPEC (Korb, Hope, and Nyberg 2009) ˆ The distribution that maximises I(E; C).

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Alternative Theories of Causal Importance

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Some Alternative Measures of Specificity ▶

A strategy for defining a token precisification of INF: ▶

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For the state of the model that reveals that the cause is an actual cause, take the measure of the mutual information between cause and effect as given by SPEC.

Two strategies for defining a type precisification of INF: ▶

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For all possible states of the other variables in the model, take the measure of the mutual information between cause and effect as given by SPEC. This gives us a set of measures. Two ways to produce a single measure from this set: ▶ ▶

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Aggregate the measures. Take the maximum of these measures.

These measures come apart in simple examples.

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Conclusion

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The Actual and the Possible

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I have argued that we should not be tempted to construct theories on which actual frequencies ground causal importance, at least at the level of individuals. Actual frequencies provide evidence for facts concerning causal importance but do not ground those facts. This doesn’t mean that informational measures of causal importance must fail—but care must be taken to ensure that the modal nature of causal importance is captured.

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References I Griffiths, Paul E., and Karola Stotz. 2013. Genetics and Philosophy: An Introduction. Cambridge: Cambridge University Press. http://dx.doi.org/10.1017/CBO9780511744082. Griffiths, Paul E., Arnaud Pocheville, Brett Calcott, Karola Stotz, Hyunju Kim, and Rob Knight. 2015. “Measuring Causal Specificity.” Philosophy of Science 82 (4): 529–55. http://dx.doi.org/10.1086/682914. Korb, Kevin B., Lucas R. Hope, and Erik P. Nyberg. 2009. “Information-Theoretic Causal Power.” In Information Theory and Statistical Learning, edited by Frank Emmert-Streib and Matthias Dehmer, 231–65. Boston MA: Springer. http://dx.doi.org/10.1007/978-0-387-84816-7_10. Pocheville, Arnaud, Paul E. Griffiths, and Karola Stotz. forthcoming. “Comparing Causes: An Information-Theoretic Approach to Specificity, Proportionality and Stability.” In ..

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References II Proceedings of the 15th Congress of Logic, Methodology and Philosophy of Science, edited by Hannes Leitgeb, Ilkka Niiniluoto, Elliott Sober, and Päivi Seppälä. London: College Publications. Sober, Elliott. 1988. “Apportioning Causal Responsibility.” The Journal of Philosophy 85 (6): 303–18. http://dx.doi.org/10.2307/2026721. Waters, C. Kenneth. 2007. “Causes That Make a Difference.” Journal of Philosophy 104 (11): 551–79. http://dx.doi.org/10.5840/jphil2007104111. Weber, Marcel. 2016a. “Causal Selection Versus Causal Parity in Biology: Relevant Counterfactuals and Biologically Normal Interventions.” In Philosophical Perspectives on Causal Reasoning in Biology, edited by C. Kenneth Waters, Michael Travisano, and James Woodward. Minnesota Studies in the Philosophy of Science. Minneapolis: University of Minnesota Press. ..

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References III

———. 2016b. “Which Kind of Causal Specificity Matters Biologically?” Philosophy of Science. Woodward, James. 2010. “Causation in Biology: Stability, Specificity, and the Choice of Levels of Explanation.” Biology and Philosophy 25 (3): 287–318. http://dx.doi.org/10.1007/s10539-010-9200-z. Woodward, James, and Christopher Hitchcock. 2003. “Explanatory Generalizations, Part I: A Counterfactual Account.” Noûs 37 (1): 1–24. http://dx.doi.org/10.1111/1468-0068.00426.

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