Biology Reference
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Q
¼ α þ β
P
ð
3
:
15
Þ
P
¼ δ þ γ
Q
:
ð
3
:
16
Þ
Solving (
3.15
) and (
3.16
) yields
¼
α þ βδ
1
Q
βγ
;
ð
3
:
17
Þ
¼
δ þ αγ
1
P
βγ
:
ð
3
:
18
Þ
Both variables are determined by the same set of parameters. It would be
impossible, therefore, that we alter the value of one of them without also altering
the value of the other. We might, then, regard the two variables as having a two-way
or mutual causal relationship. But should we really call variables that have no
causal relationships distinguishable from one another as standing in a causal
relationship with each other? It would be more to the point to say that, causally
speaking, there is no difference between them.
The issue arises not only in simultaneous systems of equations. Consider instead
the following system:
A
¼ α;
ð
:
Þ
3
19
B
¼ β
A
;
ð
:
Þ
3
20
C
¼ β
A
:
ð
:
Þ
3
21
On Simon's criterion,
A
clearly causes both
B
and
C
, but what is the causal
relationship between
B
and
C
? It might appear to be mutual, since there is no
intervention on either variable that does not alter the other. But this seems counter-
intuitive, because the connection is through the parameter
rather than through the
variables; yet our presumption is that causal relationships are mediated only
through variables. If we imagine the variable
B
and Eq. (
3.20
) eliminated, nothing
would change for
C
.
We see, then, that some systems with or without mutual or simultaneous
causation are problematic, but there is no reason to believe that problematic cases
arise inevitably in simultaneous systems. We need a way of characterizing prob-
lematic and unproblematic systems. This suggests that we characterize causal
identity and causal distinctiveness:
β
Causal Identity
: Two variables are
causally identical
if aside from their mutual
relationship, they have all the same causes and effects.
Causal Distinctiveness
: Variables that are not causally identical are
causally
distinct.
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