Ned Hall (left) and L. A. Paul (right) on causation.

Suzy throws a rock which causes a window to break. That is token causation: a particular event c causes another particular event e. According to a simple counterfactual account of token causation, c is a cause of e exactly if e wouldn’t have occurred if c hadn’t occurred. In this episode, Hall and Paul discuss why the pursuit of a counterfactual account is attractive, and consider problems for such an account raised by preemptive causes, preventive causes, the transitivity of causation, and overdetermination.

Related works

by Hall:

“Rescued from the Rubbish Bin: Lewis on Causation” (2004)

“Causation and the Price of Transitivity” (2000)

by Paul:

“The Counterfactual Analysis of Causation” (2010)

“Constitutive Overdetermination” (2007)

Collaborations:

Collins, Hall, and Paul (eds.), Causation and Counterfactuals (2004)

Hall and Paul, “Causation and Preemption” (2003)

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Have you considered cases, as in the physical sciences, where causal relationships are expressed in terms of functional relations between variables? Seeing things

in terms of variables (they need not always be quantitative) allows one to view

perspicuously all the potential cases that may or may not be causes and all the possible effects and non effects that would be related by the functional relation.

Variables are based on sets such that no member of the set may be assigned to

the symbol denoting the variable at any given time.

I like to think of it in terms of

attributes and objects, and how objects come bearing attributes as a kind of

“metaphysical” foundation. But attributes come grouped into distinct sets.

Within any variable set one and only one attribute-member may be assigned

to an object at any given time. They are mutually exclusive in their assignments

to objects. Wittgenstein noted that the proposition ” X is 111 mm long” is

not logically independent of the “atomic propositions” “X is 112 mm long”,

“X is 109 mm long”, “X is 110 mm long” etc. etc. If the first is true, the others

are necessarily false. ditto for any one of the others being true.

Distinct variables are distinct sets such that a member from each set may

be assigned simultaneously to the same object. So, “X is 111 mm long

and weighs 225 mg”. But X cannot be both 225 mg heavy and 220 mg

heavy. This is so fundamental, most people don’t think of the implications

philosophically for this. It’s there staring you in the face and you don’t

notice it.

Now, a functional relation is a relation between two sets, a first set, the

domain of the function, and a second set, the range of the function, such

that for any member of the first set it may be mapped to one and only one

member of the second set.

But two members of the first set could be mapped to the same member

of the second set. Only no object would have those two members at the

same time.

The variable and functional relationship concepts organize our thinking

so that we can view things perspicuously. We now see that if a certain

functional relation occurs between two variables, we have a set-up for

discussing things counterfactually. Whereas at a certain time X1 may

map to Y3 and be observed to do so, we may also consider counterfactually

what would be the outcome if X2 had occurred instead, it might map to

a different value of the effect variable. In fact we have a full set of

potential counterfactual cases to consider by considering all values of

X other than X1 and how they are mapped to Y. So, the functional

relationship between variables concepts is a marvelous synthesis of

many elements to be considered in causality. We just have to have

the right functional relation to do this correctly.

But it doesn’t stop there. I work in the field of quantitative psychology with

specializations in linear causal modeling with structural equations. We

can put variables together in complex networks of interrelations, and this

introduces possibilities for more ways of considering actual and counterfactual

cases. It’s a higher level of synthesis when we consider syntheses of variables

rather than syntheses of attributes into variables. But with variables we

can consider that on one variable, we observe a certain value, and then

consider possibile outcomes if other variables have counterfactually other

values than what we observe. We can even consider counterfactually,

say, “Suppose we had a different network with some other variables,

what would we be able to say then?”

Some of these ideas appear in a chapter titled “Causation” in my book

Mulaik, S. A. (2009). Linear Causal Modeling with Structural Equations.

Boca Raton, FL: Chapman & Hall/CRC of Taylor and Francis Group.

Anyway, I enjoyed your discussion, although I winced at your considering

only binary cases like “Suzie threw the rock at the window”, “Suzie did

not throw the rock at the window.” And “The Window broke”, “The Window

did not break”. It’s hard to see it, but you can find variables here, in

e.g. the case of Suzie moving her arms in different ways: maybe she

threw a slider or a curve ball. Or she threw side arm or underhand as in

softball. Or she threw with a certain velocity, etc.. And you can talk

counterfactually about each of these cases. And you might consider that

the effect on the window can be described in multiple, mutually exclusive

ways. The window was displaced 3 mm (but not enough to break).

The window was displaced 2 mm. The window was pushed in 1 mm, etc. etc.

Bringing in Billy brings in another causal variable, and you are constructing

in your minds a causal network among variables.

Any enjoyed your presentation. Someone notified us on SEMNET which

is the Structural Equation Modeling Net work Listserv about your presentation,

and that’s how I found you.

Stanley Mulaik, Ph.D.

Professor Emeritus of Psychology

Georgia Institute of Technology

Atlanta, Georgia

191 Vistawood Lane

Marietta, GA 30066