Ceteris Paribus Hedges:
Causal Voodoo That Works
The Cognitive Uses of Causal Order
Lecture III
The World Is Complex
High-Level Regularities Are
Fine-Grained
Ravens are black
☛ But not bleached ravens
Printing money to pay government debts
causes inflation
☛ But not if debts are domestic and the
new money is kept in mattresses
Why So Fine-Grained,
So Complex?
The causal mechanisms that cause regularities
are complicated and temperamental
1. Require various enabling conditions
2. Are vulnerable to interference
3. Can have their effects reversed
From Complexity,
Problems for Science
A Principle
A statement of a high-level law should entail its
corresponding Humean generalization
Ravens are black should entail the actual
pattern of blackness in ravens
A Consequence
A statement of a high-level law should entail its
corresponding Humean generalization
This world’s Humean generalizations are
super-complicated
So, true high-level law statements must be
super-complicated
Two Problems
1. High-level sciences cannot formulate law
statements that have any chance of being
correct
2. Even if all serious possibilities are
formulated, too hard to figure out which law
statements are true
Four Solutions
1. Law statements describe ideal system, not
reality
2. Law statements need not entail
corresponding Humean regularities
3. Corresponding regularities need not be
“exact”
4. Magical incantations
The Ceteris Paribus
Hedge Solution
Ceteris Paribus Voodoo
Saying ceteris paribus adds to a law statement
the content necessary to imply the supercomplicated regularity: correct enabling
conditions, correct non-interference conditions,
correct non-reversal rider
Three Magical Things
1. Two words add super-complicated content
2. They add the correct super-complicated
content
3. They add content that is opaque – unknown
to the formulator of the statement
My Claim
There is a simple, plausible way to understand
a certain class of law statements – the causal
generalizations – on which ceteris paribus can
do all of this
Causal Generalizations
A Causal Generalization Is…
A generalization intended to describe a
pattern of events that is a consequence of a
certain kind of causal mechanism
Examples
Genes assort independently
Paranoid schizophrenics hear voices
Ravens are black
Hunter-gatherers share large food items
Cepheids’ period increases with their absolute
magnitude
Restriction
Directed generalizations where the antecedent
is part of a mechanism bringing about the
consequent
Truth Conditions for
Causal Generalizations
Canonical Form of a Causal
Generalization
In conditions Z, Fs are G
Round One
In conditions Z, Fs are G means
☛ There exists a causal mechanism that
has as its only enabling conditions or
components Z and F, and that brings
about G
Round Two
In conditions Z, Fs are G means
☛ There exists a causal mechanism that
has among its enabling conditions and
components Z and F, and that brings
about G
Round Three
In conditions Z, Fs are G means
☛ The contextually determined target
mechanism M has among its enabling
conditions and components Z and F,
and brings about G
☛ By way of the target mechanism, Z and
F bring about G
Questions
1. How are target mechanisms picked out?
2. What if scientists are on the wrong track?
3. What if scientists have no particular
mechanism in mind?
Approaches to Ceteris
Paribus Hedges
Three Strategies
1. Softening
2. Narrowing
3. Annotating
Which Strategies Add
Complex Content?
1. Annotating: no
2. Softening: no
3. Narrowing: can do
What Ceteris
Paribus Means
Truth Conditions for Hedged
Generalizations
Ceteris paribus, in conditions Z, Fs are G
means
☛ When conditions O hold, then by way
of the target mechanism M, conditions Z
and the property F bring about G
where O is the set of conditions required for
the successful operation of M.
Comparison
Unhedged: By way of the target mechanism, Z
and F bring about G
Hedged: When conditions O hold, then by
way of the target mechanism, conditions Z and
the property F bring about G
O = conditions for successful operation of
target mechanism
Conditions for Successful
Operation
1. All enabling conditions hold
2. No interference
3. No reversal
Effect of Ceteris Paribus Hedge
1. Add super-complicated content
2. Add correct content
3. Opacity
Hedged Generalizations Are
Not Trivially True
Ceteris paribus, ravens are green
Ceteris paribus, hunter-gatherers share large
food items only with their maternal uncles
Ceteris paribus, Cepheids’ absolute magnitude
decreases with their period
Three Questions
1. Why opacity?
2. Is there opacity?
3. How to determine mechanisms when
ignorant?
Case Study:
Cepheid Variable Stars
Cepheid Variable Stars
A variable star changes in brightness over time
In Cepheid variables, the variability is regular:
they have a fixed period
Luminosity varies proportionally with period:
the brighter the Cepheid, the longer the period
Cepheid Variable Stars
Causal generalization:
Cepheids conform to following period/
luminosity relation: M = –2.81 log(P) – 1.43
Because apparent luminosity varies (roughly)
with distance, can use period to determine
distance
The Discovery of
Cepheid Behavior
Proportional relation between luminosity and
period first observed in: 25 stars in the Small
Magellanic Cloud (Henrietta Leavitt)
Projected to: other stars in the Milky Way with
similar spectra, dynamics
M = –2.81 log(P) – 1.43
Three Questions
1. Why opacity?
2. Is there opacity?
3. How to determine mechanisms when
ignorant?
Why Opacity?
If your hypothesis concerns the consequences
of a particular mechanism…
…it ought only to make predictions about what
happens when the mechanism operates
successfully
Leavitt’s Hypothesis (Now Law)
The hypothesis describes the consequences of
whatever mechanism causes the variability of
the Magellanic Cloud stars in the study.
Not just those variable stars, but all stars with
same mechanism – and no others
Is There Opacity?
Star comes along that does not fit formula
It later turns out to have a variability
mechanism that differs from the SMC 25
Was it a counter-instance, a falsifier?
No, because no claim was made about that
mechanism
Cepheid Mechanism
Determination
Hypothesis restricted to mechanism causing the
variability of the stars in the study
1. Baptismal group
2. Criterion for “same mechanism as”
3. Sameness of mechanism in baptismal group
Case Study:
Biological Kinds
Ravens Are Black
Intended to make a claim about the natural
color of ravens
That is, the color produced by the natural
coloration mechanism
Irrelevant ravens: painted ravens, bleached
ravens, plucked and dyed ravens…
A Case of Opacity
Suppose that ravens require copper to
manufacture their black pigment – but science
doesn’t know this
Discovery: A population of ravens in a copperpoor environment that are gray not black
Do these ravens refute the raven hypothesis
Ravens are black?
Gray Refuters?
No; they are irrelevant for the same reasons
that the bleached ravens are irrelevant
Not produced by natural mechanism, so not
counterexamples to a claim about the effects of
the natural mechanism
Gray Refuters?
It makes no difference whether we already
know about the importance of copper in
coloration
Whether we know it or not, they are not
naturally colored so not counterexamples
Picking Out the Mechanism
We have a way of referring directly to the
mechanism: the “natural mechanism”
Picking Out
Mechanisms:
Further Remarks
Biological Mechanisms
Need Not Be Natural
Paranoid schizophrenics hear voices
Not a small baptismal group but a large group
symptomatically defined
Otherwise like the Cepheids
Mechanism Determination Can
Fail
And often does
Failure can be total or partial
☛ Diabetes causes hypoglycemia
☛ Hysteria causes insomnia
Picking Out
Mechanisms:
Individuation
Proposal
The G-ness of one system is produced by the
same mechanism as the G-ness of another just
in case they have the same causal explanation
Sameness of causal explanation is observerindependent
How Explanation Determines
Operation Conditions
A causal explanation takes the form of a
causal model: a representation of a causal
process successfully running to completion
without reversal
To satisfy the operation conditions is to satisfy
the model. No need to specify the many ways
the model might not be satisfied.
How Explanation Gives You a
Non-Interference Condition
An explanation of G that attributes it to
mechanism M cannot be correct if something
interfered with the operation of M
The correctness conditions for explanation
therefore contain an implicit specification of
what would count as an absence of interferers
Hedge and Method
Methodological Convenience
of Opacity
Can state causal hypotheses that have some
chance of being correct
Actually, a really good chance (since ceteris
paribus automatically adds the correct
conditions of application)
Methodological Inconveniences
of Opacity
Content of theory is held hostage to unknown
facts
Predictions are unclear
What counts as evidence depends on unknown
facts
Causal Inquiry
Inquiry into reality on a mechanism-bymechanism basis
Causal Inquiry
Is it relevant? means Was it produced by the
mechanism in question?
Like it or not, the answer may be out of our
grasp
We’ve built this standard of relevance into
causal hypotheses themselves
One More Thing
Need Explicit Hedges?
No; the truth conditions for hedged causal
hypotheses are the truth conditions for all
causal hypotheses
Michael Strevens
Philosophy Department
New York University
www.strevens.org
[email protected]