1. Causal relations, constitutive relations, and interlevel experiments
Bert Leuridan
Centre for Logic and Philosophy of Science
Ghent University
MaCitS 2009
Canterbury

2. Craver C.F. (2007), Explaining the Brain.
Mechanisms and the Mosaic Unity of
Neuroscience.
Oxford: Clarendon Press.
CLAIM 1:
Mutual manipulability is not a
sufficient condition for constitutive relevance
CLAIM 2:
This gives rise to further inferential challenges
for (interlevel/intralevel) experimental practice
(problem of underdetermination)

3. Outline
1. Mechanisms 2. Intralevel causal relations 3. Interlevel constitutive relations 4. Mutual manipulability not sufficient for constitutive relevance 4.1. parthood as spatial containment: virus and general 4.2. causal feedback in biology 4.3. measuring synchronicity 4.4. causal-constitutive propagation

4. 1. Mechanisms

5. Mechanisms A mechanism is
a set of entities and activities organized such that they exhibit the phenomenon to be explained. (Craver 2007, 5)
More precisely
Entities are the components or parts in mechanisms. They have properties that allow them to engage in a variety of activities. [...] Activities are the causal components in mechanisms. [...] Finally, the entities and activities in mechanisms are organized together spatially, temporally, causally, and hierarchically [...] The behavior of the mechanism as a whole requires the organization of its components [...]. (Craver 2007, 5-6)
(Carl Craver (2007) Explaining the Brain. Mechanisms and the Mosaic Unity of Neuroscience. Oxford: Clarendon Press.)

6. Mechanisms S-ing X22-ing X11-ing X44-ing X33-ing
A phenomenon (top) and its mechanism (bottom) (from Craver 2007, p. 7)

7. 2. Intralevel causal relations

8. Mechanisms Question: How should activities be characterized?
Answer: Woodward’s manipulationist theory of causation
(Craver 2007, chapter 3)

9. Intralevel causation Manipulationism:
The central idea is that causal relationships are distinctive in that they are potentially exploitable for the purposes of manipulation and control.
More specifically, variable X is causally relevant to variable Y in conditions W if some ideal intervention of X in conditions W changes the value of Y (or the probability distribution over possible values of Y). (Craver 2007, 94)

10. Ideal (etiological) interventionsU
(Craver 2007, p. 97) X S Y I C

11. Ideal (etiological) interventions
An ideal intervention I on X with respect to Y is a change in the value of X that changes Y, if at all, only via the change in X. More specifically, this requirement implies that: (I1) I does not change Y directly; (I2) I does not change the value of some causal intermediate S between X and Y except by changing the value of X; (I3) I is not correlated with some other variable M that is a cause of Y; and (I4) I acts as a ‘switch’ that controls the value of X irrespective of X’s other causes, U. (Craver 2007, 96; adapted from Woodward and Hitchcock 2003a)

12. Mechanisms S-ing X22-ing X11-ing X44-ing X33-ing
A phenomenon (top) and its mechanism (bottom) (from Craver 2007, p. 7)

13. 3. Interlevel constitutive relations

14. Interlevel constitutive relations
Question: how should constitutive relations be characterized?
Answer:
Negative: constitutive relations are not causal!
Positive: constitutive relevance as mutual manipulability
Craver (2007, chapter 4)
Craver & Bechtel (2007) “Top-down causation without top-down causes,” Biology and Philosophy 22:

15. Constitutive relations
Constitutive relations are not causal:
Symmetry: All constitutive relations are symmetric; (most) causal relations are asymmetric
Synchronicity: All constitutive relations are synchronic; if causes must precede their effects, causal relations are diachronic
Logic: mechanisms and their components are not distinct; causal relations ought to involve distict relata

16. Mutual manipulability
Question:
When is a part of S a component in the mechanism of S’s - ing? (Craver 2007, 140)
When is a part constitutively relevant?
Not all parts are components!
Craver: Working Account (sufficient condition)
[A] component is relevant to the behavior of a mechanism as a whole when one can wiggle the behavior of the whole by wiggling the behavior of the component and one can wiggle the behavior of the component by wiggling the behavior as a whole. The two are related as part to whole and they are mutually manipulable. (Craver 2007, 153)

17. Mutual manipulability
X is a component of the mechanism for S’s -ing if:
(i) X is part of S;
(ii) in the conditions relevant to the request for explanation there is some change to X’s -ing that changes S’s -ing; and
(iii) in the conditions relevant to the request for explanation there is some change to S’s -ing that changes X’s -ing.
(Craver 2007, 153)

18. Mutual manipulability
(CR1) When  is set to the value 1 in an ideal intervention, then  takes on the value f(1). (Craver 2007, 155)
[Moreover] there should be an ideal intervention on X's -ing that changes the value of S's -ing under the conditions (CR1a) that the intervention, I, leaves all of the other dependency relations in S’s -ing unchanged and (CR1b) that other interventions have removed the contributions of other redundant components. (Craver 2007, )
(CR2) [I]f  is set to the value 1 in an ideal intervention, then  takes on the value f(1). (Craver 2007, 159)

19. Ideal (interlevel) interventions
An ideal intervention I on  with respect to  is a change in the value of  that changes , if at all, only via the change in . This implies that:
(I1c) the intervention I does not change  directly;
(I2c) I does not change the value of some other variable * that changes the value of  except via the change introduced into ;
(I3c) that I is not correlated with some other variable M that is causally independent of I and also a cause of ; and
(I4c) that I fixes the value of  in such a way as to screen off the contribution of ’s other causes to the value of .
(Craver 2007, 154)

20. Ideal (interlevel) interventions
S-ing I
X22-ing
X11-ing
X44-ing
X33-ing

21. Ideal (interlevel) interventions
S-ing I
(I4C)
X22-ing
X11-ing
X44-ing
X33-ing

22. Ideal (interlevel) interventions
S-ing M
(I3C) I
(I4C)
X22-ing
X11-ing
X44-ing
X33-ing

23. Ideal (interlevel) interventions
S-ing M
(I3C) I
(I2C)
(I4C)
X22-ing
X11-ing
X44-ing
X33-ing

24. Ideal (interlevel) interventions
S-ing M
(I3C)
(I1C) I
(I2C)
(I4C)
X22-ing
X11-ing
X44-ing
X33-ing

25. 4. Mutual Manipulability not sufficient

26. Constitutive relevance (recap)
X is a component of the mechanism for S’s -ing if:
(i) X is part of S;
(ii) in the conditions relevant to the request for explanation there is some ideal intervention to X’s -ing that changes S’s -ing; and
(iii) in the conditions relevant to the request for explanation there is some ideal intervention to S’s -ing that changes X’s -ing.
Claim: is this not a sufficient condition for componency
start: when is X part of S?

27. Parthood as spatio-temporal containment?
Question: when is X part of S? (NOT “when is X a component of S?” Suggestion: when X is spatio-temporally contained in S

28. Parthood as spatio-temporal containment?
The virus and the general:
When a virus kills a general, this seems to be an interlevel causal interaction. [...] However, the general and the virus are not at different mechanistic levels. The virus is not a component in any of the myriad mechanisms composing the general. This is simply a case where things of different sizes interact. (Craver and Bechtel 2007, 556)
In practice: virus seems constitutively relevant
token virus spatially contained in token general
virus’s presence/absence and general’s presence/absence are mutually manipulable
virus  general : evident
general  virus : cf. the mass extinction of stock to suppress epidemics in agriculture

29. More than a toy-example
Virus & General: toy-example
However:
examples of causal feedback are legion in the biological, including neuroscience, and the social sciences: mutual manipulability
causal feedback is even considered one of the motors generating biological complexity and higher level phenomena – the very phenomena Carl Craver wants to explain (Mitchell forthcoming, 34-44).
(Note: causal feedback in figure 1.1, Craver 2007, 7)

30. Tree of problems
IF X part of S AND X and S mutually manipulable, THEN X component of S
Parthood as spatial containment
Virus a component of the general?
Solution 1:
virus and general distinct
Solution 2:
Distinct notion of parthood
Solution 3:
Relation is diachronic
Measuring synchronicity
Begs the question
Which?
Causal-constitutive propagation

31. Measuring synchronicity
Causal,
Time-lag
Causal,
Time-lag
Causal,
Time-lag
Causal,
Time-lag
Craver (2007, 146)
Even if constitutive relations are synchronic,
they may look like diachronic relations in practice

32. Causal-constitutive propagation
Even if constitutive relations are synchronic, they may look like diachronic relations in practice
Bottom up:
do(i=i*)  =’: constitutive, synchronic
do(i=i*)  j =g(i*): causal, diachronic
j=g(i*)   =’’: constitutive, synchronic
Top down: analogously
This is not a case of redundancy/recovery! And it is not ruled out by CR1a and CR1b

33. Causal-constitutive propagation
S-ing
=f(’1, ’2, ’3)
X11-ing
1=’1
X22-ing
2=’2
X33-ing
3=’3

34. Causal-constitutive propagation
S-ing
=f(1*, ’2, ’3)
X11-ing
do(1=1*)
X22-ing
2=’2
X33-ing
3=’3 t

35. Causal-constitutive propagation
S-ing
=f(1*, g(*1), ’3)
X11-ing
do(1=1*)
X22-ing
2=g(1*)
X33-ing
3=’3 t

36. Causal-constitutive propagation
S-ing
=f(1*, g(*1), g’(g(1*)))
X11-ing
do(1=1*)
X22-ing
2=g(1*)
X33-ing
3=g’(g(1*)) t

37. Causal-constitutive propagation
An intervention on Xi’s i-ing induces, diachronically, a change in S’s -ing
An intervention on S’s -ing induces, diachronically, a change in Xi’s i-ing
Xi is spatially contained in S
Is Xi a component of S?
Or are Xi and S mutually causally related?

38. Conclusion
Mechanisms involve intralevel causal relations and interlevel constitutive relations
Both are characterized by means of ideal interventions
Claim 1: mutual manipulability (+ parthood) not sufficient for constitutive relevance
Claim 2: problem of underdetermination in experimental practice: suppose that
X is spatially contained in S
X and S are mutually manipulable
Question:
is X a component of S?
or are X and S mutually causally related

39. References
Craver (2007), Explaining the Brain : Mechanisms and the Mosaic Unity of Neuroscience. Oxford: Clarendon Press.
Craver and Bechtel (2007), “Top-down causation without top-down causes,” Biology and Philosophy 22:
Mitchell (forthcoming), Unsimple Truths: Science, Complexity and Policy. Chicago: University of Chicago Press.
Woodward (2003), Making Things Happen. A Theory of Causal Explanation. Oxford: Oxford University Press.
Woodward and Hitchcock (2003), “Explanatory Generalizations, Part I: a Counterfactual Account,” Nous, 37: 1-24.

40. Argument from symmetry
I endorse the claim that all constitutive relations are symmetric
But some Woodward-causal relations are symmetric :
Ideal gas law
Causal feedback in biological/social sciences
Therefore:
Argument from symmetry shows a distinction at the conceptual level
But provides no way to distinguish between symmetric causal relations and constitutive relations

41. Argument from synchronicity
I endorse the claim that all constitutive relations are synchronic
But some Woodward-causal relations are synchronic :
ideal gas law?
pendulum?
Problems:
Problem of measuring synchronicity
Problem of causal-constitutive propagation
Therefore:
Argument from synchronicity shows a distinction at the conceptual level
But provides no way to distinguish between synchronic causal relations and constitutive relations

42. Argument from non-distinction
I endorse the claim that all causal relations must involve distinct relata
Therefore:
The argument provides a way to distinguish between causal relations and constitutive relations: if X and Y are related as part and whole, none is a cause of the other
Problem: how do we know that X is part of Y?

43. A note on etiological invariance
If invariance under interventions is to count as a sufficient condition for causal relevance (Woodward)
Then it should be complemented with the addendum that the relata are not related as part and whole (not currently in Woodward)
Otherwise: constitutive relevance implies causal relevance