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)
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