Actual Causation: Looking Backward and Looking Forward Christopher - PowerPoint PPT Presentation

Actual Causation: Looking Backward and Looking Forward Christopher Hitchcock California Institute of Technology

Overview • I’m going to talk about attempts to understand the relation of ‘actual causation’ • Set up the problem in a familiar framework • Some standard problems • Approaches that seem promising, but don’t quite work

Overview • Offer a suggestion for a way forward • Think about why have such a concept • What is distinctive about it • Solicit suggestions

Actual Causation • By ‘actual causation’, I mean the kind of relationship that is described by statements like: 1. A meteor strike in the Yucatan caused the extinction of the dinosaurs 2. Sparks cast by a locomotive caused the fire that destroyed Jacob Anderson’s house 3. The emission of X-rays from a charged vacuum tube in Roentgen’s lab caused an image to appear on a screen

Actual Causation • Actual causation has been of interest to philosophers, and also legal theorists, because it is involved in the concepts of moral and legal responsibility • It is also involved in the explanation of particular events (such as the extinction of the dinosaurs)

Actual Causation • A standard view among philosophers is that what is distinctive about relations of actual causation is that they involve particular events • A particular meteor struck at a particular location at a particular time, etc. • Particular sparks cast by a particular locomotive caused a particular fire, etc.

Actual Causation • This is contrasted with causal generalizations , which relate types of events • Large meteor impacts cause extinctions • Sparks cause fires • Etc.

Actual Causation • I will suggest that another characteristic feature of actual causation is that it is backward- looking as opposed to forward-looking • Questions of actual causation tend to arise when some event has occurred, and we retrospectively ask why it occurred

Counterfactual theory • A well-known approach to causation is the counterfactual theory • Developed in detail by the American philosopher David Lewis

Counterfactual • To a first approximation • C is a cause of E just in case the following counterfactual is true: If C hadn’t occurred, E wouldn’t have occurred • If the meteor had not struck the Yucatan (or anywhere else on earth) the dinosaurs would not have gone extinct (when they did)

Preemption and Overdetermination • The counterfactual definition has problems with cases of preemption and overdetermination • E.g., suppose Billy and Suzy are standing by with rocks in their hands • Suzy throws her rock at a window and it shatters

Preemption and Overdetermination Picasso: Girl throwing rock

Preemption and Overdetermination • If Suzy hadn’t thrown her rock, Billy would have thrown his rock at the window and it would have shattered anyway • Suzy preempted Billy • Here we want to say that Suzy’s throw caused the rock to shatter • But the corresponding counterfactual is not true • If Suzy hadn’t thrown, the window still would have shattered

Structural Equation Models • We can represent the causal structure of a case like this… • …including the relevant counterfactuals… • …using structural equations models

Structural Equation Models • We represent events in the story by variables • E.g., we will have variable Suzy throws , which takes the value 1 if Suzy throws, and 0 if she doesn’t • We represent the pattern of dependence among the variables by equations

Tools for Representing Causation Window SR= 1 Shatters BR = 1 ST = SR Billy Throws BT = min {BR, 1 – ST} Suzy Throws WS = max {ST, BT} Billy Ready Suzy Ready

Tools for Representing Causation • To represent counter- SR= 1 factuals, we replace BR = 1 the original equation ST = SR with a new one specifying the value of BT = min {BR, 1 – ST} the variable WS = max {ST, BT}

Tools for Representing Causation • To represent the SR= 1 counterfactual ‘If BR = 1 Suzy had not ST = SR thrown…’, replace the third equation BT = min {BR, 1 – ST} WS = max {ST, BT}

Tools for Representing Causation Window SR= 1 Shatters BR = 1 ST = SR Billy Throws BT = min {BR, 1 – ST} Suzy Throws WS = max {ST, BT} Billy Ready Suzy Ready

Tools for Representing Causation Window SR= 1 Shatters BR = 1 ST = 0 Billy Throws BT = min {BR, 1 – ST} Suzy Throws WS = max {ST, BT} Billy Ready Suzy Ready

A Promising Approach • There is a promising approach to defining actual causation, developed by me, and Joe Halpern and Judea Pearl • Look for path-specific effects

A Promising Approach Window • We want to isolate the Shatters influence along a single path Billy • We ‘clamp’ the other Throws path, by fixing the Suzy value of the variable Throws Billy Ready Suzy Ready

A Promising Approach • We set ST to 0, while SR= 1 also setting BT to 0 BR = 1 ST = SR BT = min {BR, 1 – ST} WS = max {ST, BT}

A Promising Approach • We set ST to 0, while SR= 1 also setting BT to 0 BR = 1 • Now we get WS = 0, ST = 0 the window doesn’t shatter BT = 0 WS = max {ST, BT}

A Promising Approach • However, this approach ends up being too liberal • There are path-specific effects that do not correspond to relations of actual causation

A Promising Approach • Question: • Why do we have a conceptual tool for identifying path-specific effects? • Perhaps an answer to this question will help us restrict the class of path-specific effects that underwrite relations of actual causation

A Hunch • When we identify actual causes, we are identifying ‘handles’ in the world • Identifying targets of intervention for producing desirable outcomes • But this idea needs to be refined

A Hunch • In decision theory , we evaluate potential actions • We consider what would happen (with what probability), if we were to perform various actions • This is similar to considering a counterfactual (except that it is future tensed, rather than past) • But in decision theory, we are not interested in path-specific effects

A Hunch • E.g., suppose that Suzy wants, above all else, for the window to shatter • Should she throw the rock? • If she throws, the window will shatter • If she doesn’t, Billy will throw, and the window will shatter • Decision theory tells us that Suzy should be indifferent between throwing and not throwing

A Hunch • Decision theory considers only the counterfactuals ‘If Suzy throws…’, ‘If Suzy doesn’t throw…’ • But not: ‘If Suzy doesn’t throw, and neither does Billy…’

A Hunch • Decision theory involves ‘cause-forward’ reasoning • Consider a range of actions, and evaluate them according to their consequences

A Hunch • But consider a different kind of practical reasoning problem • I have some goal that I want to reach • I reason backward from that goal, arrive at a series of steps I will follow • A plan • ‘Effect-backward’ reasoning

A Hunch • Now, when I consider which action to perform at the beginning, I don’t think of the future as fully ‘open’, to be determined by my present action • Rather, I must consider which action will work best in conjunction with future actions that are part of the plan

Illustration • We are members of a city council • We want to make our city bicycle friendly • We want to encourage people to ride bicycles, and we want bicycle riders to be safe • We are considering a mandatory helmet law • Our goal is to decrease the proportion of accidents that result in serious head injuries

Illustration • But we want to do this without increasing the number of accidents, or discouraging people from riding • Consider the effect of a helmet law on a typical rider

CCC Wear helmet Head injury Helmet Ride law Accident Bicycle Other lanes riders

Illustration • There are multiple causal paths whereby a helmet law influences the chance of a head injury

CCC Wear helmet Head injury Helmet Ride law Accident Bicycle Other lanes riders

Illustration • But we don’t have to just implement the helmet law and let the chips fall where they may • We can separately intervene to undo the undesired consequences of the law

CCC Wear helmet Head injury Helmet Ride law Accident Bicycle Other lanes riders

Illustration • We are left with the causal path in which the helmet law encourages the rider to wear a helmet, and wearing a helmet protects her head in case of an accident

Illustration • If this path-specific effect is not present… • either because the law would have no effect on whether people wear helmets… • or because helmets don’t provide adequate head protection… • then the helmet law is completely pointless

Illustration • Suppose a particular cyclist gets in an accident, bangs his head on the ground, but does not suffer a serious head injury • My conjecture is that it is the very same causal path that would be relevant to determining whether enacting the helmet law was an actual cause of the the cyclist suffering only minor injuries