In praise of mechanisms

Ned Hall

Introduction

There is an attractive idea found in some recent work on causation – work that emphasizes the connection between causation and intervention. We’ll put it in the mouth of an imagined Justly Celebrated philosopher.* JC says:

A successful philosophical account of causation need not include an account of

causal mechanisms.

I shall endeavor to disagree. Or at least, to pretend to.

*Minor inside joke: JC is eerily similar to John Campbell.

What do we expect from an account of causation?

“I think conceptual analysis is required to reveal what it is that all the actual and possible varieties of causation have in common.”

One good answer: A contribution to empirical psychology.

Yet another good answer: A conception of causal structure of interest to the sciences.

• one aim: illuminate the structure of scientific inquiry

A still different, influential—but not so obviously good—answer:

• a second aim: improve scientific inquiry (e.g., by cleaning up the foundations of statistical inference)

“Scientific inquiry aims to discover and describe the causal structure of the world.” What conception of ‘causal structure’ will make this a true and illuminating thing to say?

Another good answer: A contribution to the law.

The proper role of intuitions about cases“When common sense delivers a firm and uncontroversial answer about a not-too-far-fetched case, theory had better agree. If an analysis of causation does not deliver the common-sense answer, that is bad trouble. But when common sense falls into indecision or controversy, or when it is reasonable to suspect that far-fetched cases are being judged by false analogy to commonplace ones, then theory may safely say what it likes.”

Lewis view: Intuitions are data; if the data are good enough, they are non-negotiable.

Rival view: Intuitions are defeasible guides to where a potentially useful concept or concepts might be found.

A spectrum of positions…

…on this question: If our aim is to illuminate the structure of scientific inquiry, to what extent should we take seriously the commitments of our ordinary conception of causation?

not at all

very little

somewhat somewhat+ quite a lot

fully

Russell John NortonJC me

LewisDavid Armstrong?

Sample commitments to reject:• primitivism about causation

• transitivity of causation

• causes typically make a difference to their effects• causal information is crucial for decision-making and explanation

• the possibility of action at a temporal distanceSample commitments to accept:

Unclear:

Woodward’s two conceptions of causation

The first approach … involves what I will call a geometrical/mechanical conception of causation. This way of thinking about causation focuses on cases in which there is a physical process connecting cause and effect and, more broadly, on phenomena that are mediated by contact-mechanical forces and in which spatio-temporal or geometrical relationships play an important role. Causal interactions themselves are conceptualized in terms of contact forces and energy/momentum exchange. This contrasts with a second way of thinking about causation involving a difference-making conception. This second conception focuses on causal judgments that are sensitive to contingency or difference-making information (roughly, information that compares what happens to the effect in presence versus the absence of its putative cause). Such judgments may not be guided, at least in any direct way, by spatio-temporal or contact-mechanical information. …there are deep conceptual differences between geometrical/mechanical and difference-making approaches to causation and these lead, in certain cases, to strikingly different causal judgments. Notoriously, these conceptual differences have made it difficult for philosophers to combine the two approaches into a single, integrated account of causation.

The geometrical/mechanical conception

Observe how hard it is not to see the following little movie as having a very specific causal structure:

The attractive idea, reformulatedConsider this intuition about causation: Causes are connected to their effects via (or by the mediation of) causal mechanisms.

Very attractive claim: This intuition flows from the geometrical/mechanical conception of causation.

BUT:

• That conception is overly inflexible.

• It is rooted in a comparatively primitive (though no doubt highly adaptive) part of our overall cognitive economy.

THEREFORE:• We need not heed the intuition, given our aims in constructing an account of causation.

• We can give an attractive explanation for why the intuition is so compelling and difficult to give up. (Compare the living/non-living distinction.)

A Grand Metaphysical Picture

1. Reality consists of

• a spacetime, filled with a succession of complete physical states;• fundamental laws governing how earlier states generate later states.

3. It is the job of fundamental physics—and fundamental physics alone—to discover and describe the fundamental laws.

4. All other structure reduces to this structure.

So: any structure that the other sciences aim to discern reduces to this structure.

2. These fundamental laws dictate not merely what does happen, but what would have happened, given alternative (but nomologically possible) initial conditions.

Laws and counterfactual structure

The red ball does not move…

Laws and counterfactual structure

…but, if the white ball’s direction of motion had been slightly different, the red ball would have moved:

Laws and counterfactual structure

The fundamental laws endow the world with a local counterfactual structure.

time

space

tweaking the state of the world at this time and place…

would lead to corresponding changes at this later time:

Causal structure as localized dependence structure

Looking at the world just through the lens of fundamental physics, we won’t see the need for any interesting concept of causation.

But the need for such a concept of causation comes into view as soon as we reflect on our actual human predicament:

• We have a basic need to control our world.

• We have a basic need to understand our world. • We can only build up to a grasp of our world’s fundamental nomic structure by way of piecemeal approximations.

The scientific value of causal concepts is precisely that they facilitate control, understanding, and piecemeal approximation. For the basic function of any causal concept is to record — with varying degrees of precision and informativeness — facts about how localized aspects of the world at one time counterfactually depend on localized aspects at earlier times.

Connection to Lewis on causation as “influence”

Event C influences later event E to the extent that variations in the manner of occurrence of C would have been followed by corresponding variations in the manner of occurrence of E:“Think of influence this way. First, you come upon a complicated machine, and you want to find out which bits are connected to which others. So you wiggle first one bit and then another, and each time you see what else wiggles. Next, you come upon a complicated arrangement of events in space and time. You can't wiggle an event: it is where it is in space and time, there's nothing you can do about that. But if you had an oracle to tell you which counterfactuals were true, you could in a sense 'wiggle' the events; it's just that you have different counterfactual situations rather than different successive actual locations. But again, seeing what else 'wiggles' when you 'wiggle' one or another event tells you which ones are causally connected to which.”

Attractive idea: Scientific inquiry begins with causation, so understood. But as it matures, it expands its focus to include the structure of the patterns of influence themselves. (Lewisian singular causal relations can still matter, for explanation.)

… that flows naturally from this attractive idea:

A proposal about special science taxonomies…

A taxonomic scheme will

• provide a method for distinguishing the parts of some complex situation;

• specify a range of possible states for these parts;

Such schemes will prove their explanatory worth to the extent that they allow for interesting, widely instantiated generalizations about localized counterfactual structure.

• specify a similarity metric over these possible states.

Three quick benefits: thinking about science in these terms helps clarify what “structural equations” are, what is at stake in debates about reduction, and how utterly silly certain debates about ‘causal exclusion’ are.

JC: “For the case of smoking, consider how you would react to a spokesman for the tobacco industry who argued that smoking is not a cause of cancer; that smoking and cancer are both merely epiphenomenal upon an underlying microphysical reality at which the true causal relations are to be found. The natural point to make in reply is that smoking is a control variable for cancer; interventions on smoking have large, specific and systematic correlations with cancer. That is the case for saying that the causal relations between smoking and cancer are to be found at the macrophysical level.”

Problem #1: Late pre-emption(base case)

A E

“Neuron” A fires, sending a signal to E, which fires as a result.

No problem: Any reasonable account of causation can get the structure of this case right.

Problem #1: Late pre-emption(trouble case)

A E

B

A fires. B fires. The signal from A stimulates E to fire. E then goes “dormant”. So when the signal from B reaches it, nothing happens:

Getting this case right has caused, in the literature, much wailing and gnashing of teeth.

Problem #1: Late pre-emption(trouble case)

A E

B

A Popular Approach: The B-signal never reaches a non-dormant E. Holding this fact fixed, it is true that:

• had A not fired, E would not have fired;

• had B not fired, E would still have fired.

Problem #1: Late pre-emption(variant on the trouble case)

A E

B

A fires. B fires. The signal from A stimulates E to fire. E then resets. So when the signal from B reaches it, it fires again:

Observe that the Popular Approach does not work, in this case. (And it doesn’t work, in the other case, anyway.)

Problem #2: Isomorphic dependence structures

A E

C

B

F

A and C jointly cause E:

Problem #2: Isomorphic dependence structures

A E

C

B

F

G D

A and C still jointly cause E:

Problem #2: Isomorphic dependence structures

A E

C

F

C prevents E:

D

Problem #2: Isomorphic dependence structures

A E

C

B

F

D

A causes E, but C does not:

Problem #2: Isomorphic dependence structures

A E

C

B

F

D

A causes E, but C still does not:

G

Problem #2: Isomorphic dependence structuresSame models, but different causes:

A

BC

F

E

DG

A

BC

F

E

DG E = A and F*

F* = D* or B

D* = G* and not-C

B = C

E = A and F

F = D or B

D = G and not-C

B = CF* = not-FD* = not-DG* = not-G

E = A and not-F

F = D and not-B

D = G or C

B = C

Problem #3: causal and explanatory discrimination

Not everything in the past (or in the past light-cone) of some localized phenomenon counts as a cause of, or as explanatorily relevant to, that phenomenon.

Problem #3: causal and explanatory discrimination

Not everything in the past (or in the past light-cone) of some localized phenomenon counts as a cause of, or as explanatorily relevant to, that phenomenon.

Problem #4: the “laws” of the special sciences

The so-called “laws” of the special sciences almost invariably come with a “no-interference” clause. For example:

A metal bar will expand when heated, in proportion to its change in temperature…

…provided nothing interferes.

Problem #4: the “laws” of the special sciences

We can distinguish three difficulties.

1. How do we distinguish genuine from ersatz counter-instances? (Common worry: without a means to do so, these laws will be either vacuous or non-testable.)

2. How do we distinguish genuine from ersatz instances?

3. How do we distinguish disjunctive from non-disjunctive laws?

Candidate law: Whenever conditions of type C obtain at time t, conditions of type E will follow at time t’, provided nothing interferes.

Problem #5: not-not counterfactuals

Suzy throws a rock at the window.

Suzywindowrock

If Suzy had not thrown the rock, the window would not have broken. Right?

Weird answer: “Who knows? She might have thrown a brick, or a pumpkin, or her ipod, or…”

If Suzy had not thrown the rock, the window would not have broken. Right?

Problem #5: not-not counterfactuals

Moral: That the weird answer is mistaken suggests that, when we evaluate this not-not counterfactual, we have a reasonably definite idea of what Suzy is doing instead (namely, nothing).

Contrast: Suzy is 5’8” tall. If she had not been that tall, then her height would have been…?

A distinction between “nothing happening” – or default – states, and deviations therefrom, will be crucial in what follows. It is a GLARING OPEN QUESTION how, in general, to analyze this distinction!

More on the “default”/“deviant” distinction

Sometimes, we can model events as deviations from some default state.

A useful heuristic test: When considering a counterfactual “if event C had not occurred, then…”, do we have a reasonably clear conception of what would have happened instead? Something we can reasonably describe as an inactive, or nothing-happening, state?

We said: A taxonomic scheme will

• provide a method for distinguishing the parts of some complex situation;

Now we add that it may also

• specify a range of possible states for these parts;

• single out certain states as default, or “nothing happening” states.

• specify a similarity metric over these possible states.

How an appeal to “mechanisms” could help

Late preemption: What distinguishes the genuine cause from the idle backup is the fact that a causal mechanism (of the right type) connects it to the effect.

Focus on late preemption, and the troubles with special science laws.

Pretend that we can get away with taking the notion of “causal mechanism” as primitive.

Special science laws: These should be taken to assert the existence of some causal mechanism such that in a suitably wide range of circumstances, C-conditions are connected to E-conditions via this mechanism.

Some terminology

Let event E occur at some time t1, and let {C1, C2, …} contain those of its causes occurring at earlier time t0.

The process leading from the C’s to E is just the (sum of) the C’s, together with all other intermediate (t0 to t1) causes of E.

Mechanisms are certain process-types (equivalently: properties of processes; equivalently: sets of possible processes).

Assume that each process instantiates a unique mechanism.

How “mechanism” might be analyzed

Collect together a set of such “reference processes”, unified by their intrinsic and causal similarity to one another.

Focus on canonical easy cases: cases in which a process unfolds in circumstances sufficiently neutral that an analysis of causation can get the causal structure of the process right. “Sufficiently neutral” means, roughly, that when the process begins, nothing else is happening. (This is where the default/deviant distinction comes in.)

Given such a set S, say that an (arbitrary) structure of events matches S iff it is intrinsically similar to the processes in S in those respects in which they are similar to one another.

Then the mechanism associated with S will simply be the set of all and only those event-structures that match S.

Example: the classic Billy/Suzy case• Begin by focusing on the case where all that happens at time t is that Suzy throws a rock at the window (which breaks, as a result). Imagine ringing changes on this “canonical easy case” by changing the intrinsic characteristics of the event-structure S that consists of the shattering, together with all of its causes back to the time of Suzy’s throw. Require that we stay within the realm of nomological possibility, and leave causal structure invariant.

• Then these are changes in the intrinsic characteristics of S that make no difference to its causal structure.

• Collect the results into a set of alternatives to S. Its members will be intrinsically similar to one another, except in those respects that do not matter to their (shared) causal structure.

• So: they will be intrinsically similar to one another in every respect that does matter to their causal structure.

• So: some event structure S’ that is similar to S in those respect in which S and its associated variants are similar to one another thereby instantiates the same causal mechanism as S.

We assume, here, that we have an account of causation that succeeds in identifying all the causes of the shattering, in these “nothing else happening” cases.

Gory details, part 1: A regularity-style analysis

Consider an event E, and some time t earlier than the time at which E occurs. Let the set S consist of events occurring at t.

S is sufficient for E if and only if E would still have occurred, had only the events in S occurred at t.

S is minimally sufficient for E if and only if it is sufficient for E, but no proper subset of it is.

If (note: not “if and only if”) S is the unique set of t-events minimally sufficient for E, then the events in S are all the causes of E occurring at t.*

*Doesn’t quite work—but it’s close enough.

Note the implicit appeal to a default/deviant distinction here.

Gory details, part 2: reference processes

Start with a canonical easy case:

• at later time t’, event E occurs;

Our analysis counts the C-events as all (and, obviously, only) the t-causes of E.

• some events—call them the C-events—occur at time t;

• no other events occur at t;

• the C-events are minimally sufficient for E.

Suppose it also accurately maps the intermediate causes of E.*

Then: Call the structure consisting of E, together with all of its causes back to time t, a reference process.

*Full disclosure: this is non-trivial.

A more careful analysis will leave this out.

Gory details, part 3: mechanisms as process-types

For a given event E, there will typically be many nomologically possible reference processes.

These variants will divide into classes unified by the close intrinsic and causal similarity of their members.

Call any such class a blueprint for E.

Some structure of events will match a given blueprint iff it is similar to the processes belonging to that blueprint in those respects in which they are similar to one another.

Some of them will be variants on others.

For a given blueprint B, the mechanism picked out by B is just the set containing all and only those event-structures that match B.

Late pre-emption revisited

Suzy and Billy both throw rocks at a window; Suzy’s gets there first. We would like to say:

Suzy’s throw counts as a cause of the window’s breaking because it belongs to a structure of events that is relevantly similar to what would have happened, had Suzy alone thrown. Billy’s throw belongs to no such structure.

This now becomes:

Suzy’s throw, and the window’s breaking, belong to a structure of events that instantiates a causal mechanism. Billy’s throw, and the window’s breaking, do not.

Special science “laws” revisited

Candidate law: Whenever conditions of type C obtain at time t, conditions of type E will follow at time t’, provided nothing interferes.

For each way that the C-conditions can obtain, there will be a possible situation (a “canonical easy case”) in which

• the C-conditions obtain in that way at some time t;• nothing else happens at time t.

So: Nothing happens that could interfere with the C-conditions.

The law will be true iff, in every such case, the appropriate E-conditions obtain at the appropriate time t’.

Special science “laws” revisited

We might demand more: The law should be underwritten by a unique causal mechanism. That is what it is for the law to be non-disjunctive: The reference processes exhibited in the canonical instances of the law are unified by the close intrinsic and causal similarity of their members.

If so, then ersatz counter-instances and ersatz instances are alike in the following respect: The underwriting causal mechanism is not instantiated.

Observe, finally that this approach can easily answer the common charges of vacuity and non-testability: For we are often well placed to judge, in a given situation in which C-conditions obtain at some time t, that what unfolds from them is closely similar to what would have unfolded had nothing else occurred at time t. (Suitable controlled experiments, for example, will give us such reason.)

Rich vs. impoverished causal structure

Consider a cellular automaton in which each cell can have, at each moment, one of four different colors: red, blue, green, and yellow:

A deterministic rule fixes the state of each cell at time t+1 as a function of the state of it and its eight neighbors at time t. This rule, furthermore, fails to distinguish any of these states as in any sense a “nothing happening” state.

Rich vs. impoverished causal structure

Consider a cellular automaton in which each cell can have, at each moment, one of four different colors: red, blue, green, and yellow:

A deterministic rule fixes the state of each cell at time t+1 as a function of the state of it and its eight neighbors at time t. This rule, furthermore, fails to distinguish any of these states as in any sense a “nothing happening” state.

Rich vs. impoverished causal structure

Consider a cellular automaton in which each cell can have, at each moment, one of four different colors: red, blue, green, and yellow:

A deterministic rule fixes the state of each cell at time t+1 as a function of the state of it and its eight neighbors at time t. This rule, furthermore, fails to distinguish any of these states as in any sense a “nothing happening” state.

Rich vs. impoverished causal structure

Consider a cellular automaton in which each cell can have, at each moment, one of four different colors: red, blue, green, and yellow:

A deterministic rule fixes the state of each cell at time t+1 as a function of the state of it and its eight neighbors at time t. This rule, furthermore, fails to distinguish any of these states as in any sense a “nothing happening” state.

Rich vs. impoverished causal structure

Consider a cellular automaton in which each cell can have, at each moment, one of four different colors: red, blue, green, and yellow:

A deterministic rule fixes the state of each cell at time t+1 as a function of the state of it and its eight neighbors at time t. This rule, furthermore, fails to distinguish any of these states as in any sense a “nothing happening” state.

Rich vs. impoverished causal structure

Consider a cellular automaton in which each cell can have, at each moment, one of four different colors: red, blue, green, and yellow:

A deterministic rule fixes the state of each cell at time t+1 as a function of the state of it and its eight neighbors at time t. This rule, furthermore, fails to distinguish any of these states as in any sense a “nothing happening” state.

Rich vs. impoverished causal structure

Consider a cellular automaton in which each cell can have, at each moment, one of four different colors: red, blue, green, and yellow:

A deterministic rule fixes the state of each cell at time t+1 as a function of the state of it and its eight neighbors at time t. This rule, furthermore, fails to distinguish any of these states as in any sense a “nothing happening” state.

Let event C consist in a particular cell’s being yellow, at a particular time t. Ask: “What would have happened, had C not occurred?”

The only available answer: What would have happened is exactly what the cell-dynamics entail, regardless of which of the three alternative states we choose.

Ask: “What would have happened, had C alone occurred?”

The only available answer: The question makes no sense!

One upshot: rich vs. impoverished causal structure

Our rainbow-cellular-automaton world has very little in the way of articulated causal structure.

For example: There is nothing that could count as “pre-emption” (late or otherwise), in this world.

And again: There is nothing that could count as a non-trivial special-science law (of the sort we have been considering); for there is no way to give content to the claim that “nothing interferes”.

Upshot: This world is, of course, intelligible—but not in the rich and multi-layered way that our own world is.Provocative speculation: Perhaps parts of our world are like the r-c-a world. Perhaps, for example, aspects of human psychology are like this.*

*Special thanks to JC for the example!

Minor methodological moral

Philosophers who pursue an analysis of causation—especially, one that stresses the importance of ordinary intuitions—face a challenge: Why should anyone (except perhaps those interested in the semantics of the English word “cause”) care whether they succeed? The challenge can be met, if the analysis yields a concept that has important and interesting connections to other things we care about. The connections between causation, causal mechanism, and the laws and taxonomic schemes of the special sciences—if they are as I have suggested!—provide a case in point.