Causation and Context
Dr Rani Lill Anjum
University of Tromsø / University of Nottingham
[email protected]
Introduction
Causation is often claimed to contain necessity. That C causes E with necessity. But is
necessity a necessary aspect of causation, and if it is, in what way can we say that causation
involves necessity? I want to argue that causation is essentially context-dependent, which
means that necessity in this connection can at least not mean that C causes E independently of
everything else. I will do this by focusing on how conditionals are always true or false
according to a certain set of background conditions, and if we change these background
conditions, true conditionals can become false and vice versa. This should be relevant for how
we understand causation, as hypotheses typically have a conditional form: ‘If C then E’.
1. Conditionals and hypotheses
The truth functional interpretation of ‘If A then B’ defines conditionals as being nothing but a
certain combination of truth-values assigned to ‘A’ and ‘B’:
A
T
T
F
F
B A⊃ B
T
T
F
F
T
T
F
T
But this seems to dissolve the very conditional relation that ‘if’ is supposed to express.
Consider the following valid inferences for the material conditional, none of which are valid
for ‘If A then B’:
1.
2.
3.
4.
(A & B) ⇒ ((A ⊃ B) & (B ⊃ A))
(¬A & ¬B) ⇒ ((A ⊃ B) & (B ⊃ A))
B ⇒ ((A ⊃ B) & (¬A ⊃ B))
¬A ⇒ ((A ⊃ B) & (A ⊃ ¬B)
A correct understanding of conditional is important for understanding causation, as the
conditional form is used to express hypotheses: ‘If C then E’.
With a material conditional understanding of ‘if’ we get that:
All hypotheses that are not tested will come out as true.
This is the so-called problem of counterfactuals, where conditionals with false antecedents are
defined as true: ¬A ⊃ (A ⊃ B).
The most commonly proposed solution is to treat conditionals with false antecedents as
special cases.
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2. Counterfactuals or subjunctives?
The very problem of counterfactuals stems from a confusion. One typically expects the
distinction between indicatives and counterfactuals to be indicated by the grammatical mood
of the statement, as in the following pair of conditionals:
1. If Oswald didn’t kill Kennedy, then someone else did it.
2. If Oswald hadn’t killed Kennedy, someone else would have.
The fact that we would accept (1) in the indicative mood but not necessarily (2) in the
subjunctive mood, is used as an argument for a separate logical treatment of
counterfactuals/subjunctives. But this is a mistake, because:
i)
ii)
The subjunctive form does not indicate counterfactuality, but hypotheticality.
The change of truth conditions for (1) and (2) is due to a change in background
conditions, not the change of grammatical mood from indicative to subjunctive.
For all conditionals, the change of grammatical mood from indicative and subjunctive will not
change the truth conditions of the conditional, as long as the background conditions remain
the same:
a. If my head gets chopped off, I will die.
b. If my head got chopped off, I would die.
c. If my head had gotten chopped off, I would have died.
(a), (b), and (c) have the same set of truth conditions. This is because they all refer to the same
conditional relation and to the same set of background conditions. Hence they all have a
subjunctive, hypothetical relation, or what is often (mis)taken for the counterfactual aspect of
conditionals.
3. Indicatives and subjunctives
David K. Johnston notice that most conditionals with an apparent indicative form originally
had an explicit subjunctive grammatical marking in Old English. We can recognise these
originally subjunctive conditionals in that a change in the mood from indicative to subjunctive
does not change the conditional’s truth conditions, like in (a), (b), and (c) above. Thus
according to Johnston’s analysis, these conditionals are all essentially subjunctive.
But not all conditionals behave like this, which is why we get the divergence in truth
conditions for the pair of conditionals (1) If Oswald didn’t kill Kennedy, then someone else
did it, and (2) If Oswald hadn’t killed Kennedy, someone else would have. The reason for the
divergence in truth conditions is the divergence in background conditions:
In (1) it is assumed that Kennedy is killed and that someone killed him. It is an open question
whether Oswald did it, but if he didn’t do it, then someone else did. Accordingly (1) seems to
follow logically from the background conditions that someone killed Kennedy. For every x, if
x didn’t kill Kennedy, then someone else did it. But this is not a subjunctive relation like the
one in (2).
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In (2), however, we are asked to disregard the fact that Kennedy is killed, and predict what
would have happened if Oswald hadn’t killed him. It is assumed that Oswald was the one who
actually killed Kennedy, and that more people were prepared to kill him if Oswald didn’t.
Johnston calls conditionals of the type (1) non-subjunctive because they don’t have a
corresponding subjunctive conditional with the same set of truth conditions. Other nonsubjunctive conditionals are:
a. If the butler didn’t do it, then the maid did it.
b. If Jane bet on heads, she won.
c. If John took that plane, he is dead.
What seems to be common for the non-subjunctive conditionals is that they seem to follow
from a set of de facto background conditions. In (a) we seem to know that something has been
done and that only the butler or the maid could have done it. In (b) we seem to know that the
coin landed heads, and in (c) we seem to know that everyone on that plane died. Hence these
conditionals are different that the ones where we would be in a situation of not knowing what
will actually happen, but predicting that if the butler will not do it, then the maid will, or that
if Jane bets on head, she will win, or even worse, that if John takes that plane, he will die.
Those would all be subjunctive conditionals, involving prediction and hypotheticality.
4. Preliminary conclusion: Conditionals are essentially subjunctive
Johnston’s findings indicate that a conditional is essentially subjunctive, and that so-called
counterfactuals are paradigmatic examples of conditionals, not special cases that should be
treated separately from other conditionals. Assuming that conditionals have their logical
properties according to factuality or counterfactuality, one misses the point that it is the
relation − not the relata − that is in focus. And this relation is essentially subjunctive.
But what is the subjunctive aspect? I will say that this is the hypothetical and causative aspect
of the conditional: We hypothetically assume the antecedent and predict what will or would
follow from it.
It is the essence of a hypothesis, scientific or other, that it is hypothetical, causative and
subjunctive.
5. Causation versus regularities
Hume demonstrates that we cannot directly observe a causal relation between some A and B.
We can observe that:
i. A and B
ii. A before B
iii. some sort of contact between A and B
But we cannot observe that:
iv. B because A
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Hume’s analysis of causation shows us how we can never infer a causal relation between two
particulars only from their joint occurrence, or even constant conjunction. Now this is exactly
what is done in the material conditional, where every conditional ‘If A then B’ is taken as true
unless A is true and B is false. In other words, every hypothesis that is not directly falsified is
considered verified.
Focusing solely on the truth-values of the statements ‘A’ and ‘B’, the material conditional is
bound to miss out on the conditional relation expressed between them in a conditional ‘If A
then B’. But this is not a flaw only of truth functionality and the material conditional. All
approaches to causal relations that can only deal with the occurrence or non-occurrence of
some particular A and B are bound to end up in some sort of logical atomism where causal
matters simply are reduced to the joint occurrence of A and B.
If Hume is right in his analysis of causation, we are unable to distinguish between
regularities, where B always (at least up to this point) follows A, and causation, where B
happens because of A.
So why should this be a problem? If we always had full control on what B would follow what
A, then do we really need an additional relation of causation between them? Isn’t regularities
enough?
No, we do need causation to:
a) account for hypothetical cases, and mere potentialities
b) explain how a causal relation sometimes is prevented by contextual factors.
6. Causation: Categorical or conditional?
When we say that ‘All Fs are Gs’ this can be taken as a categorical or conditional statement.
This makes a logical difference:
Interpreted as a categorical, ‘All Fs are Gs’ is taken to express that the class of Fs is contained
in the class of Gs. Examples of claims that are naturally interpreted as categorical are:
a) All men are mortal.
b) All even numbers are divisible on 2.
The categorical is understood as stating a logical relation, where one will not allow or expect
counterexamples. The finding of an x that is F but not G would necessarily be taken as a
genuine counter-example to the general statement. The finding of a black swan made the
classification of all swans as white invalid (sic!). Hence one single counter-example would
force us to reject our original claim and revise our classification.
In this way, the categorical interpretation does not open for context-sensitivity in the same
respect as conditionals, as no background conditions are thought to make an even number not
divisible on 2 or make a man not mortal. Fs are classified as Gs. Hence there is no
hypotheticality, induction, ceteris paribus conditions or prediction involved in this
interpretation.
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Conditionals
Interpreted conditionally, ‘All Fs are Gs’ is taken to express that for any x, if Fx then Gx.
Examples of claims that are naturally interpreted as conditional are:
a) If I drop this pen, it will fall.
b) If a dog doesn’t get water for three days, it will die.
The conditional is understood to state a hypothetical, causal, empirical relation, where we
predict that F will cause G. Still we get a problem of induction, since there is always a chance
of some interfering factor that may interfere and prevent the relation. Hence we also need to
add a ceteris paribus clause to conditionals, saying that ‘If F then G, all background
conditions being equal’.
The logical form of causation must be the conditional, rather than the categorical. Just like the
conditional, a causal relation is always sensitive to a change of background conditions. But
the conditional aspects of such causal relations are not first of all found in whether or not they
are expressible as a conditional ‘If some triggering factor, then this manifestation’. Such an
understanding of the conditionality of causation is too simple. This is evident when we
consider how causal relations, no matter how necessary, might be prevented from manifesting
themselves given certain background conditions of interfering factors.
This is why in our reasoning about causal relations we need a ceteris paribus clause as an
added premise in order to ensure that ‘If C then E’, while no such clause is needed for a
classification. Since causal relations can always be prevented by an external factor, the
problem of induction is indeed a genuine problem for causation.
This also points to the important role of background conditions in relation to explanations of
causal relations. Just like the background conditions are what can prevent a causal relation it
is also what’s making the ground for a causal relation: A causal relation must always be
found, justified and explained outside the immediate context of some C and E.
An example:
Lack of fuel causes a car to stop, − but only if it is a fuel-driven car! This is so obvious to us
that it feels stupid to even mention it. But let’s say that we wanted to find out if there was a
causal relation between lack of fuel and the car stopping, only by looking to A and B as such:
the lack of fuel and the car stopping. That wouldn’t help us at all. We have to check out the
motor of the car to see how it works. We can say that the motor of a car, together with all the
other pieces, is one part of the background conditions that we need to understand causal
relations in the car. If it’s an electric car, then it couldn’t have been the lack of fuel that
caused the car to stop. And we know that because we know something about how cars work.
Thus we would need a ceteris paribus clause for conditionals and any causal relation, in the
sense that no F alone will ever be enough to cause G. A conditional ‘If F then G’ is only true
according to a certain set of background conditions. This means that the ceteris paribus clause
will only play the role of fixing the set of background conditions: ‘If F then G, all things
being equal, meaning; given no change in this particular set of background conditions that
makes the causal relation true.’
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7. Some claims about causation and necessity
If we want to understand causation, we need to focus on the relation, not the relata. This is the
same with conditionals: A conditional statement ‘If A then B’ cannot be reduced to two
particulars A, B and some relation R. To avoid that ‘If A then B’ just points to a regularity,
where A is in general followed by B, we seem to think that we need an additional clause of
necessity to get causation from regularities. But what should necessity mean in this
connection? − Surely not a strict conditional, where A ⇒ B in the sense that A ⊃ B is a
tautology?
Sometimes the necessity involved in causation seems to be mistaken for some sort of logical
necessity, where something is regarded as completely independent of contextual elements.
But then ‘C causes E’ would have to mean something like ‘E follows C independently of
everything else’. But it is actually an essential part of causation that it is not so.
Just like a conditional is true only relative to a certain context, a causal relation is necessary
only according to a certain set of background conditions. This necessity is empirical and a
posteriori, not logical and a priori. But it follows with empirical necessity that E follows from
C, given this particular set of background conditions. If we got the background conditions
wrong, or there was some element we didn’t know of, then we must revise our theory.
But this doesn’t mean that the adding a ceteris paribus clause to a causal relation means ‘If C
then E, unless not’. The ceteris paribus clause points to the relevant background conditions.
But how do we know what these relevant background conditions of a causal relation are?
Well, that is our job to us to find out if we want to understand a phenomenon.
8. Understanding causation by way of failure
Only when we understand how a causal relation can be prevented, will we understand what
the causal relation is, or what the phenomenon is. In this way, understanding causation must
happen by way of understanding the apparent counter-examples. − Not by trying to confirm
and generalise the hypothesis to see if C is always followed by E with logical necessity.
Furthermore, because the generality that is part of causation cannot be one of logical
necessity, but must be an empirical, context-sensitive necessity, we cannot fight the problem
of induction. But as with the ceteris paribus clause, induction is not something to fight to
guarantee that there actually is a causal relation between C and E. Instead, the fact that a
relation is vulnerable to induction only points to the empirical and informative part of
causation.
If causation was a relation of logical necessity and complete context-independence, we would
have to ask for its usefulness in science and our everyday lives. Then causation would be
nothing but a logical, analytic, tautological, and self-evident matter. And who needs that?
9. Some conclusive remarks about causation
What I have argued in this paper is that the logical form of causal statements must be
conditional rather than categorical or material. I have also tried to say something about the
nature of conditionals and what kind of generality that must be involved in statements about
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causal matters. My main aim has been to show that when we state that ‘C causes E’, then this
should be understood as a genuinely conditional claim, saying that ‘If C then E’.
If correct, my analysis of conditionals should be informative for how we understand
causation. But because causal relations are in the world while conditional statements are in
language, the one will never be reducible to the other. Also, causal relations can also be
expressed in other ways than in the conditional form. The point is that an insight into
conditionals also represents an insight into causation. The following characteristic of
conditionals should therefore also tell us something essential about causation.
Conditionals are:
subjunctive in essence, involving prediction
hypothetical, not factual or counterfactual
context-dependent, not independent of everything else
a posteriori, not a priori or logically true
more or less general, not universal
involving induction, allowing counter-examples without rejecting the general
hypothesis
− in need of a ceteris paribus clause, fixing the set of background conditions
− irreducible, not reducible to some C, E and additional relation R.
−
−
−
−
−
−
To compare, causal relations are:
−
−
−
−
−
−
−
−
approached by way of prediction
a matter of potentiality
context-dependent; no F will ever alone be sufficient to cause G
empirical
a matter of more or less generality, not necessity
subject to the problem of induction, as it can be prevented by external factors
in need of a ceteris paribus clause, fixing the set of background conditions
always found, justified and explained outside the immediate context of some
C, E and additional type of necessity
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