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Counterfactuals vs Generic Conditionals: Causation and

Dispositions

Peter Menzies

Macquarie University

Peter.Menzies@mq.edu.au

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1. Introduction

Philosophers have often thought that counterfactuals can be used to analyse/clarify the concepts of causation and dispositions.

This is a mistake. The crucial clarificatory conditional is not the counterfactual, but the generic conditional.

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1. IntroductionWhat I propose to do is:• describe some of the problems faced by counterfactual analyses of the concepts of causation and dispositions;•argue that counterfactuals are subject to a rule of actuality that makes them unsuitable for analysing these concepts;•introduce generic conditionals and explain how they are better suited to fulfil the clarificatory role.

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2. Problems for Counterfactual Theories of Causation

Here’s a simplified version of Lewis’s 1973 theory:

Event e counterfactually depends on event c iff

(i) c occurs e occurs

(ii) c doesn’t occur e doesn’t occur.

Event c caused event e iff (i) c and e are distinct events and (ii) e counterfactually depends on c.

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2. Counterfactual Theories of Causation

One recalcitrant problem for this theory concerns late preemption:

c1

c2

e

e does not counterfactually depend on either c1 or c2

.

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2. Counterfactual Theories of Causation

Simplified revised Lewis 2000 analysis:

If c and e are distinct actual events, c influences e iff there is a substantial range c1, c2,… of not-too-distant alterations of c and there is a range of e1, e2,… of alterations of e such that if c1 had occurred, e1 would have occurred, and if c2 had occurred, e2 would have occurred, and so on.

c caused e iff (i) c and e are distinct events; (ii) c influences e.

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2. Counterfactual Theories of Causation

This analysis is supposed to solve the late pre-emption problem: Sheila’s throw influences the bottle shattering and Bruce’s does not.

Problems for this analysis:

Bruce’s throw has some degree of influence on the shattering of the bottle. For if Bruce had thrown his rock earlier (so that it preceded Suzy's throw) and in a different manner, the bottle would have shattered earlier and in a different manner.

Influence is not the same as causation. Rain in December delays a forest fire; if there had been no December rain, the forest would have caught fire in January rather than when it actually did in February. The rain influences the fire with respect to its timing, location, rapidity, and so forth. But commonsense is more discriminating about causes.

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3. Counterfactual Theories of Dispositions

Simple Analysis: An object is disposed to M when C iff it would M if it were the case that C.

Problem 1: Finkish Dispositions (C.B. Martin)A wire, although live, is connected to a device which reliably senses when the wire is about to be touched by a conductor and makes the wire dead in every such circumstance.

Sophisticated Analysis (Lewis) overcomes this problem: An object is disposed to M when C iff it has an intrinsic property B such that if it were retain B in the circumstances C, then the object would M.

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3. Counterfactual Theories of Dispositions

Problem 2: Masked Dispositions/Antidotes (Johnston/Bird):

• A fragile vase is disposed to shatter when dropped but because it is carefully protected by packing material it does not shatter when dropped.

• A poison is disposed to kill when ingested but because a person takes an antidote beforehand, she does not die when she ingests a poison.

Sophisticated analysis 2 (Mumford):An object is disposed to M when C iff if the object were subjected to test condition C in ideal circumstances, it would M.

What are the ‘ideal circumstances’? If they are just the circumstances in which the object would M in test conditions C, then the analysis is trivial.

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3. Counterfactual Theories of DispositionsCounterfactuals are unsuitable to analyse dispositions because they conform to the Rule of Actuality. In the standard semantics for counterfactuals this rule is expressed by the requirement that the system of spheres of similarity be centred on the actual world.

Strong centring: no world is as similar to the actual world as it is to itself. P & Q, therefore P QWeak centring: no world is more similar to the actual world than it is to itself. P, P Q, therefore Q.

@

P

Q

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3. Counterfactual Theories of Dispositions

These inference rules fail for dispositions:

The vase is dropped and does not shatter. P & ~Q

The vase is disposed to shatter when dropped. [P Q]

The vase is disposed to shatter when dropped. [P Q]

The vase is dropped. P

The vas does not shatter. ~Q

The failure of these rules for dispositions suggest that the dispositional concept cannot be analysed in terms of counterfactuals that conform to a Rule of Actuality.

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4. The Common Problem

The common problem for counterfactual theories of causation and dispositions is that the presence of objects extraneous to the relevant systems mask the true relation between cause and effect or between conditions of manifestation and the manifestation of a disposition.

This is an recalitrant problem for counterfactual theories because counterfactuals conform to the Rule of Actuality. The counterfactuals must, therefore, hold fixed the presence of the extraneous object which masks the true relations.

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5. Generic Conditionals

Generic conditionals are related to generic sentences:

Tigers are striped.

Ducks lay eggs.

Some generics are about particular objects (habituals):

The cat eats when he’s hungry.

Jones smokes when he gets home from work.

These generics are paraphrasable thus:

Normally, if something is a tiger, it is striped.

Normally, if the cat is hungry, he eats.

Normally, if Jones gets home from work, he smokes.

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5. Generic Conditionals

I suggest that we should think of the system of spheres for generic conditionals as being centred, not on the actual world, but on a set of worlds that hold fixed what we regard as normal, or to-be-expected, or natural.

I call these the default worlds because they represent assumptions that constitute reasonable starting points for our investigations, assumptions we relinquish only when we are forced to do so.

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5. Generic Conditionals

R P

@

Q

Normally, if this vase is dropped, it breaks. P QThe vase is dropped. PIt does not break. ~Q

Normally, if this vase is dropped, it breaks. P Q Normally, if this vase is wrapped and dropped, P & R ~Q It does not break.

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5. A SE Model of Generic Conditionals

I want to explicate generic conditionals in the Structural Equations framework developed by Pearl (2000) and others.

The first thing to note is that this framework relativises the truth conditions of causal claims to a kind of system (or model), represented by an ordered triple <U, V, E>:•U is a set of exogenous variables whose values are determined by factors outside the system. •V is a set of endogenous variables whose values are determined by factors within the system.•E is a set of structural equations that express the value of each endogenous variable as a function of the values of the variables in U and V.

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5. SE Model of Generic ConditionalsLate pre-emption example:

SP = 1 if Sheila and her rock are present, 0 if not.

BP= 1 if Bruce and his rock are present, 0 if not.

ST =1 if Sheila throws a rock, 0 if not.

BT=1 if Bruce throws a rock, 0 if not.

SH=1 if Sheila’s rock hits the intact bottle, 0 if not.

BH=1 if Bruce’s rock hits the intact bottle, 0 if not.

S=1 if the bottle shatters, 0 if not.

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There is a structural equation for each endogenous variable, representing an ‘independent causal mechanism’ by which its values are determined.

ST=SPBT=BPSH =STBH = BT & ~SHBS = SH v BH

Informally, a structural equation encodes a series of generic conditionals. E.g the third equation asserts that if Suzy throws her rock, the rock hits the bottle; if she doesn’t throw her rock, it doesn’t hit the bottle.

.

5 Continued

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5. Continued

Some conditions: (i) the structural equation for a variable X must include as arguments all and only the variables of the system on which X depends, given the values of the other variables; (ii) the structural equations must be invariant in the sense that they continue to hold even when values of variables are fixed by interventions.

The causal graph for this system:SP ST SH

S

BP BT BH An edge is drawn from X to Y iff X appears on the RHS of the structural equation for Y. (Then X is a parent of Y.)

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5. Continued

Some more concepts:

•Def 1: The actual setting (of the exogenous variables U) for a system <U, V, E> sets the values of these variables at their actual values. •Def 2: The default setting (of the exogenous variables U*) for a system <U, V, E> sets the values of these variables at their default (normal, natural, to-be-expected) values rather than their actual values.

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5. ContinuedSuppose the default values are SP=1 and BP=0:

ST=1

BT=0

SH=1

BH=0

S=1

I will call this the default world for the system.

SP=1

BP=0

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5. Continued

The following are defeasible rules for assigning default values to exogenous variables and for selecting default worlds:

Rule 1: When the actual sequence of events involves some system with an extraneous presence, the default worlds preserve the system with its intrinsic properties but not the extraneous presence.

Rule 2: When the actual sequence of events is less than ideal (from a design, functional, moral point of view), the default worlds consist of a more ideal sequence of events.

Rule 3: When the actual sequence of events involves omissions or absences, the default worlds involve a generative process of some kind.

Rule 4: When the actual sequence of events involves choices or decisions of a free agent, the default worlds omit (or vary) these choices or decisions.

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6. Conditionals in SE Framework

Within the SE framework, the truth-conditions for counterfactuals and generic conditionals can be stated as follows:

X=x Y=y is true iff replacing the structural equation for X with X=x in the actual setting of the exogeneous variables results in Y=y.

X=x Y=y is true iff replacing the structural equation for X with X=x in the default setting of the exogeneous variables results in Y=y.

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6. Generic Conditionals in SE Framewwork

Counterfactuals:

ST= 1

BT=1

SH= 1

BH=0

S= 1

ST= 1 S= 1 ST=0 S= 1

BT=1 S= 1 BT=0 S= 1

SP=1

BP=1

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6. Generic Conditionals in the SE Framework

Generic Conditionals

ST= 1 S= 1 ST=0 S= 0BT=1 S= 1 BT=0 S= 1

ST= 1

BT=0

SH= 1

BH=0

S= 1

SP=1

BP=0

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6. Generic Conditionals in SE Framework

Within this framework, one can distinguish two kinds of generic conditionals. Consider the difference between the following contrast situations.

Counterfactual antecedent

Actual antecedent

Counterfactual antecedent

Actual world as deviant

Actual world as default

Actual antecedent

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6. Causation

I propose that the truth conditions of token causal claims should be understood in terms of generic conditionals:

The claim that “X=x caused Y=y” is true relative to the default model <U*,V,E> only if

(i) X = x Y= y; and (ii) X= x’ Y=y’, where x’ and y’ are the default values of X and Y.

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6. CausationThis is only a necessary condition for actual causation. It tells us only what normally happens in the given kind of situation, and not what happens in the actual situation.In the late-pre-emption case we have at least shown that the actual cause meets this necessary condition:

ST= 1 S= 1 ST=0 S= 0

Haven’t we also shown that

BT= 1 S= 1 BT=0 S= 1?

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7. Dispositions

I propose as the truth-conditions for the dispositional claims:

An object is disposed to display M=m when subject to test conditions C=c relative the default model (U*,V,E) iff the object has intrinsic properties P=p such that the following generic conditional is true:

‘The object has P=p and retains it when it is in condition C=c M=m’.

It is easy to see that the generic conditional will be true in the case of finish dispositions.

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7. Dispositions

More importantly, these truth conditions solve the cases of masked dispositions/antidotes. Consider the example of protected vase. M =1 if vase has molecular property X, 0

otherwise; D = 1 if vase is dropped, 0 otherwise, 0 otherwise;W = 1 if vase has protective wrapping, 0

otherwiseS = 1 if vase shatters, 0 otherwise.

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7. Dispositions

In the natural model, the structural equations,the default settings of the exogenous variables, and causal graph are:

S = M & ~W & D

M=1

W=0

D=0

S=0

The vase is disposed to shatter when dropped andthe following generic conditional is true:M=1 & D=1 S=1 is true.

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8. Insensitive Causation

I want to connect the account of generic conditionals that I’m proposing with some interesting observations made by Jim Woodward (2006).Like Lewis, he defines counterfactual dependence between events in terms of these counterfactuals:

(a) c occurs e occurs(b) c doesn’t occur e doesn’t

occur.

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8. Insensitive Causation

He says, however, for the causal claim “c caused e” to be true, the counterfactual (a) has to be insensitive: ie there is broad range of background conditions Bi that are not “too improbable or far-fetched” such that the following counterfactual is true:

c occurs in circumstances Bi different from the actual circumstances e occurs.

Example of insensitive causation: shooting a person at close range with a large calibre bullet caused his death.

(a) If you were to shoot the victim at close range, he would die.

Example of sensitive causation: Lewis’s writing a letter of recommendation for X caused N’s death.

(a) If Lewis were to write a letter for X, N would die.

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8. Insensitive Causation

I suggest that the phenomenon Woodward describes is naturally explained in terms of generic conditionals.

• The (a) counterfactuals are trivially true. But the corresponding generic conditionals are not.

• For the (a) counterfactual to be insensitive, the counterfactual must hold invariantly through the admissible variations in background conditions. The set of default worlds for the corresponding generic conditional represent these admissible variations in background conditions.

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8. Insensitive Causation

The insensitivity of the (a) counterfactual in Lewis’s shooting example reflects the fact that there are natural structural equations and natural default settings such that the corresponding generic conditional is true.

Structural equation: Victim dies = You shoot & ~Interference

The generic conditional is true: You shoot Victim dies.

Woodward’s claim that the variation in which an interference is too ‘improbable or far-fetched’ reflects the fact that the default value of Interference is 0.

You Shoot =0

Interference=0

Victim dies=0

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8. Insensitive Causation

The sensitivity of the (a) counterfactual in Lewis’s letter writing example reflects the fact that there are no natural structural equations and default settings such that the corresponding generic conditional is true.

L’s letter for X

Y displaced to city C

Y meets his wifeY is born

Y’s wife is born

N’s father is born

N’s father meets mother

N isborn N diesN’s mother

is born

N’s heart attack

Even with this simplified model there is no natural assignment of default values to the variables such that the conditional “Lewis writes letter N dies” is true.

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8. Insensitive Causation

Woodward uses the notion of insensitivity to explain many different features of causal concepts. Consider what he has to be say about genetic causation.

Jencks’ example: female genotype causes long hair length

Contrast example: APSM gene causes microcephaly which causes low IQ

Woodward’s explanation: the following differ in sensitivity

(a) If X were to have the female genoype, X would have long hair.

(a) If X were to have the APSM gene, X would have a low IQ.

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8. Insensitive Causation

The phenomena are better explained in terms of generic

conditionals with their characteristic default settings: If X has female genotype, X has long hair.

If X has APSM gene, X has low IQ.

F sexual =1features

F genotype=1

Societalconventions=0

Social expectations =0for long hair

Long hair=0

APSM =1 gene

Small cortex = 1 Low IQ=1

Internal=1 factor Internal=1

factor

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8. Insensitive Causation

The fact that causation requires a non-trivial (a) conditional as well as a (b) conditional explains the distinction between causes and background conditions.

My not being hit by a meteor is a condition, but not a cause of my writing this paper.

Conditions satisfy the (b) conditional but not the (a) conditional.(a) Normally, if I am not struck by a meteor, I write this paper. (b) Normally, if I am struck by a meteor, I do not write this paper.

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8. Insensitive Causation

The (a) conditional is not true in the most salient model.

Hit =0 by meteor

Write = 0 this paper

Invited = 0 to write paper

Accept=0invitation to write paper

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9. A Counterexample Parried

Some have thought that the following type of example is a counterexample to this account of causation:

X prevents an explosion by disconnecting a bomb fuse.X’s disconnecting the bomb fuse caused the explosion not to occur.

(a) Normally, if X disconnects the bomb fuse, the explosion doesn’t occur. True(b) Normally, if X doesn’t disconnect the bomb fuse, the explosion does occur. False?

But in fact the default worlds need not preserve the normal (=common) occurrences. The rules for selecting default worlds entail that the default worlds will preserve the positive generative processes eg the terrorist has lit the fuse, the connection between fuse and bomb is intact etc.

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9. Conclusion

I have argued for the following claims:

• The traditional counterfactual theories of causation and dispositions encounter difficulties because counterfactuals obey a Rule of Actuality.

• Generic conditionals are better suited than counterfactuals to clarify causation and dispositions because they are centred on a set of default worlds rather the actual world.

• There are a set of specific rules that guide the selection of default worlds for a given system.

• Suggested truth conditions for dispositional claims in terms of generic conditionals solve the problems of finkish dispositions and masked dispositions.

• A suggested necessary condition for causal claims in terms of generic conditionals present a partial solution to the problem of pre-emption.

• This suggested necessary condition provides an alternative basis for Woodward’s insights about insensitive causation.