10:06 Theory of causal explanation, not causation. Something in our - PowerPoint PPT Presentation

10:06 Theory of causal explanation, not causation. Something in our heads, not in the world. James Woodward’s Manipulability Theory of Causal Explanation The Scientific Revolution, Experimentation, and Causation HILR—Fall, 2017 1

10:08 = Before stripping: - Not go into math Acceleration of block on inclined plane • Angle of plane - Use your intuitions • Color of block • Strength of gravity • Mass of block = Next: Woodward’s theory concerns causal explanation • Roughness of surfaces • Material of block

10:13 = At end of stripping: Causal Explanation A causal explanation proceeds by showing > Why “not logically or conceptually”? how an outcome depends > Why that instead of “physically”? (not logically or conceptually) on other variables or factors, > Also: substitute event for: thus furnishing information relevant to - outcome ? manipulation and control. - other variables or factors ? = Next 3 slides are basic concepts we need [correlation]

10:18 = First concept concerns relation of causation to correlation Correlation vs Causation > Reading and weather are correlated Barometer reading > Reading is not a cause of the weather (or vice versa) Atmospheric pressure > The reason for correlation is the common cause: atmospheric pressure > Hypothesis: all “true” correlations are result of deep causal connections Weather > Prediction and control - Correlation is good enough for prediction - But causation is needed for control > Classical and operant conditioning > Understanding and action = Second basic concept is distinction between type and token

10:24 = What is the distinction? Type-level vs. token (actual) causal explanations TAP • Examples > smoking; dinosaurs • Precedence in reality TAP talk • Precedence in thought TAP talk, - so must understand type first - everything will be about type-level until near the end = Third concept is directed graph

10:27 = We are interested in X as a possible cause of Y TAP A directed graph > Arrow represents a direct causes (to be defined) A > Letter represents an event X > So there can be prior causes of our candidate cause B C D TAP Y > There can be events between our cause and the e ff ect TAP > There can be more than one path from cause to e ff ect TAP > And there can be other causes of the e ff ect = Candidate definition of cause

10:30 = At end of stripping slide > Wiggle wobble Candidate Definition of Cause > Two problems: X is a cause of Y if and only if - Meaning of intervention; possible there is a possible intervention on X - Definition is inadequate that will change Y or the probability distribution of Y > Approach in some background circumstances. - Intervention - Then why inadequate, and what to do about it - In process, explain “some background circumstances” - Will get to “possible” at very end, but for now, obviously: Has to be very broad Events in past Astronomical events = So, what’s an intervention?

10:33 = Will read quickly then walk through example Intervention then walk through this definition again I is an intervention on X with respect to Y if and only if: 1. I causes X 2. I acts as a switch for all the other variables that cause X 3. Any directed path from I to Y goes through X 4. I is (statistically) independent of any variable that causes Y and that is on a directed path that does not go through X .

10:35 = Read prototype A prototypical intervention TAP The prototypical intervention is the randomized, blind, controlled experiment, as for a possible drug. > Explain all causal factors random assignment = Intervention A = access ; attitude TAP 1. I causes X X = medicine > Intervention is randomized determination of who gets the medicine administration placebo = B C = germs D = immune system by shotgun TAP = health Y 2. Intervention switches o ff other causes of X: > A does not cause X 3. No path from I to Y except through X > Consider the potential placebo e ff ect: - There isn’t really a causal arrow from the medicine itself to the e ff ect - It’s from the belief that you are taking the medicine TAP > So have to blind subjects to which group they are in > To avoid creating a path from the I to Y that doesn’t go through X > To pick a more extreme example, TAP > Administering drug by shotgun would create path not through X 4. I cannot be correlated with causes of Y not on path through X > OK for e ff ect on germs to be correlated with I, since it’s on the path. > For example - Don’t want I correlated with D, the immune system - which is not on the path from X to Y - so need large enough sample to assure decorrelation = So let’s walk back through the definition with example in mind

10:45 = Strip and talk Intervention = Now that we completely understand what an intervention is, I is an intervention on X with respect to Y if and only if: 1. I causes X let’s return to the candidate definition of a cause random assignment 2. I acts as a switch for all the other variables that cause X access and attitude 3. Any directed path from I to Y goes through X placebo shotgun 4. I is (statistically) independent of any variable that causes Y and that is on a directed path that does not go through X . germs immune system

10:49 =Makes sense =But there’s a problem Candidate Definition of Cause—Again X is a cause of Y if and only if there is a possible intervention on X that will change Y or the probability distribution of Y in some background circumstances.

10:51 = Explain relationships Pill > At end: - Pill doesn’t meet candidate definition of cause Thrombosis - But in fact the pill is a cause of thrombosis Pregnancy - Have to modify definition > What we want is the idea of a contributing cause > To get there, we need the idea of a direct cause = Direct cause

10:53 = Do slide Direct Cause > So, it’s really very simple: A necessary and su ffi cient condition for X to be a (type-level) direct cause of Y - hold everything else constant with respect to some variable set V - wiggle X is that there be a possible intervention I on X that will change Y (or the probability distribution of Y ) - if Y wobbles, X is a direct cause of Y when all other variables in V besides X and Y are held fixed at some value by additional interventions that are independent of I . = Back to example of thrombosis

10:56 = Here’s how: > The only variable except X (pill) and Y (thrombosis) is pregnancy > So we have women either take or not take the pill (intervention 1) Intervention 1 Pill > While holding pregnancy fixed at some value (intervention 2) Thrombosis - Yes: they are already pregnant Intervention 2 Pregnancy - No: they can’t get pregnant > And we find the pill is a direct cause of thrombosis > Notice that whether X is direct cause of Y depends on choice of other variables for analysis = Another example

10:59 = Do slide Gas pedal > First, Injector - There is some value of Gears (engaged) Cylinders . . . - and some value of Brakes (not engaged) Acceleration Gears - for which intervening on Gas Pedal will change Acceleration Brakes > But, - if we fix the value of any variable intervening btw Gas and Accel - intervening on Gas doesn’t change Accel. > So Gas is not a direct cause of Acceleration > Rather, it is a contributing cause = So what is a contribution cause?

11:03 Break?

11:13 = Do slide Contributing Cause A necessary and su ffi cient condition > Define directed path for X to be a (type ‐ level) contributing cause of Y > Some values for variables not on path: not all values with respect to variable set V is that (i) there be a directed path from X to Y and that - Gear (ii) there be some intervention on X that will change Y when all variables in V that are not on this path - Brake are fixed at some value . > Some intervention on X: not all interventiions - Lightswitch - Sound system = Now ready to define cause

11:16 = Do slide Definition of cause > In fact, direct is special case of contributing, so just contributing A necessary and su ffi cient condition for X to be a (type-level) cause of Y is for X to be = At end: either a direct cause of Y > Thus endeth the explication of type-level causes or a contributing cause of Y . > Next, consider token causes, in actual situations > To do this, think about the French Foreign Legion example > [next slide]

11:18 = But eliminate the sand man: just poison and hole Poison in water Hole in canteen > Who did it? Poison in body Dehydration = Actual causation defined Death

11:26 = Do slide Actual Causation Based on a type-level graph of dependency relationships, > Key is actual values of other direct causes of Y X = x is an actual cause of Y = y if and only if: > Rather than just any value that makes Y depend on X 1. The actual value of X = x and the actual value of Y = y . 2. There is at least one route from X to Y for which an intervention on X will change the value of Y, = Back to example given that other direct causes of Y that are not on this route have been fixed at their actual values.

11:30 = What happens if we hold the other direct cause of Y at its actual value and wiggle the hole in the canteen? Poison in water Hole in canteen Poison in body Dehydration > Discussion = No > Woodward: - If, by some intervention, we assured he didn’t have poison in his body, Death - Then if, by some intervention, there was no hole in his canteen, - Then he would not have died. = The 3-murderer example is tougher