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作者：Anonymous 在 罕见奇谈 发贴, 来自 http://www.hjclub.org
Logic and Metaphysics
CAUSATION
DAVID PAPINEAU
SEMESTER 1 2000-2001 Mondays 11 am 2B08 Strand Bldg KCL
The Regularity Theory
Hume
Our idea of causation is not just of spatio-temporal continguity. It
involves an element of necessitation. Whence this idea? We form it when we
find two kinds of events, A and B, constantly conjoined. (This still doesn't
account for the idea of necessitation, since constant conjunction is just A
and B happening to go together, repeatedly. Hume gave a psychological
explanation for our idea of necessitation; causation in the objects is
nothing more than constant conjunction.)
Laws and Accidents
Most modern philosophers have focused on the idea of constant conjunction,
and forgotten about any extra 'necessitation'. But there are constant
conjunctions (true universal gens) where A and B are intuitively quite
unconnected causally. We want to distinguish the lawful regularities from
the accidents. There are two general strategies for dealing with this
problem:
(i) Humeans stick to the idea that laws just state constant conjunction, and
try to explain why some such statements are better than others (they fit
into theory, are inductively supportable);
(ii) Non-humeans (Armstrong) say that laws state relationships of
necessitation, which claim more than constant conjunction.
Mackie and INUS Conditions
What shape of regularity is required for A to cause B? We don't seem to want
A sufficient (by law) for B -- short circuits aren't always followed by
fires. But nor do we want A necessary for B -- we can get fires without
short circuits. (Don't confuse A necessitates B, with A is necessary for B
(the latter just means (x)(-Ax -> -Bx)).)
Mackie said that A is a cause of B just in case A is an INUS condition of B:
A is an Insufficient but Necessary part of a set of conditions which are
together Unnecessary but Sufficient.
The idea is that A&M&N, say, Suffice for B; but A alone doesn't -- it's
Insufficient; and M&N alone don't suffice either -- so A is Necessary for
them to suffice; moreover, other conjunctions which don't include A, such as
P&Q, say, also suffice for B -- so the A-M-N set is Unnecessary.
Symbolically (x)({Ax&Mx&Nx OR Px&Qx} -> Bx). (Note that we now have a third
sense of "necessary" -- A ia necessary-for-A&M&N-to-be-sufficient.)
Singular Causation
Hume's Second (Counterfactual) Definition
What is it for a particular instance of A to cause a particular instance of
B? (It's clearly not enough just that A is an INUS condit of B, and A and B
occur, since the other factors required for A to suffice for B may be
absent.)
Hume's 2nd def: "If the first object had not been, the second never had
existed".
This is a counterfactual conditional (if not-p, then not-q, where p actually
occurred).
Can't we still explain this counterfactual, and hence causation, i.t.o. INUS
conditions? I.E: if the actual circumstances contain an US condition for B,
and A is a IN part of that US condition. Then the actual circumstances
suffice for B, but wouldn't if A were absent.
But there's a problem: the idea is裷emove A from the actual circs, hold
everything else fixed, and see what follows by law. However, why doesn't
this allow, "If there hadn't been the short-circuit, there wouldn't have
been the frayed insulation" (because laws tell us that in the circs frayed
insulation implies short circuit)? We are in danger of concluding that
effects cause their causes. And similarly, "If the barometer hadn't fallen,
there wouldn't have been a storm" (because laws tell us that in the circs no
barometer fall implies no pressure fall implies no storm). We are in danger
of concluding that mere symptoms cause effects.
(NB it's counterfactual/subjective conditionals, not indicative
conditionals, that are at issue here: compare "If Oswald didn't kill
Kennedy, somebody else did" (certainly TRUE) with "If Oswald hadn't killed
Kennedy, somebody else would have" (FALSE補ssuming the Warren Commission is
right and there was no conspiracy). Similarly "If there hadn't been the
short-circuit, there wouldn't have been the frayed insulation" is FALSE,
even though in the same circumstances "If there wasn't a short-circuit, the
insulation didn't fray" could be TRUE. If we want to analyse causation i.t.o
conditionals, we want "If no short-circuit, then no frayed insulation" to be
FALSE, and so must focus on counterfactual conditionals, not indicative
ones.)
Lewis's Account of Counterfactuals and Causation
Lewis thinks the difficulty of getting counterfactual conditionals right is
fatal to a regularity theory of causation. He wants to stick with the
connection between singular causes and counterfactuals, but analyses the
latter directly, and not in terms of lawful regularities.
He explains counterfactuals in terms of possible worlds: "If A had been,
then B" is true iff (roughly) the nearest A-world is also a B-world.
Lewis also points out that the connection between countefactuals and
causation is a bit more complex than Hume's second definition sugests. Hume
said in effect that particular A causes particular B iff If not-A, then
not-B. But, while the rhs implies the lhs, we can have cases where A causes
B, yet B would still have occurred without A -- namely where A preempts an
alternative cause C which would have caused B if A hadn't. (Imagine that
overheating causes a valve to open A and thereby stops the pressure increase
B. But if the valve had failed to open then the power would have cut out C
and caused B anyway.)
Lewis explains why A still causes B here, even though B doesn't
counterfactually depend on A, by saying that a chain of events between A and
B, each of which counteractually depends on its predecessor, suffices for
causation of B by A. In our example he would thus postulate a D, the release
of steam, say, which wouldn't have been there if the valve hadn't opened,
and without which the pressure wouldn't have fallen.
But why is it true that without D the pressure wouldn't have fallen? Why
can't we argue that without D, the release of steam, there wouldn't have
been A, the valve opening, and so C, the power switch, would have been
triggered, and B, the pressure would have stopped, anyway. Lewis blocks this
by saying that it's false that without D, the release of steam, there
wouldn't have been A, the valve opening. But why so?
More generally, why does Lewis assume that effects depend counterfactually
on their (direct) causes, but that causes don't depend counterfactually on
their direct effects? If the nearest not-C world is a not-E world (If not-C,
then not-E), why isn't the nearest not-E world a not-C world? This was the
point that made him reject regularity theories, but it is not clear he is
any better.
Lewis's Asymmetry of Overdetermination
Lewis recognizes the problem and has an interesting answer.
Consider first this case. "If Nixon had pushed the button (P), there would
have been nuclear war (N)". True. But a P and not-N world is surely much
closer to actuality that a P and N world (it doesn't have all that mess).
Lewis suggests not. For a P-world will have lots of other effects apart from
N, and they will have lots of effects, . . . So even a P and not-N world
will be very far from actuality, and in addition will require a little
miracle, to stop N. So, all in all, it will be further than a P and N world.
You might regard this as ad hoc. But it does lock onto something real, which
does distinguish causes from effects non-question-beggingly. The basis of
the asymmetry here is a de facto feature of the world, namely, the asymmetry
of overdetermination: overdetermination of effects by causes is very rare,
but massive overdetermination of causes by effects is absolutely normal.
This means that it's relatively "easy" to "remove" an effect by "removing"
its cause裻here's nothing else left to fix the effect裝ut "difficult" to
"remove" a cause just by "removing" one effect裺ince all the other effects
will still be there to fix the cause.
This is a good explanation of causal asymmetry, but it can be detached from
Lewis's possible worlds account of counterfactuals. Lewis's argument against
the regularity account of single-case causation was in effect that it had no
grip on causal direction (that's why it has problems with epiphenomena and
pre-emption). But he has now offered a way in which regularity theorists can
get a grip on causal direction. This means that they can explain
counterfactuals and hence singular causation, by saying "Remove C from the
actual world, but hold fixed everything that's caually prior to or
independent of C, and then see what follows by law . . ."
Why couldn't regularity theorists just use time here? Hold fixed things
before and including time of A. But this is unattractive. We don't want to
take it for granted that the causal arrow lines up with the termporal one,
and so rule out "backwards causation" (time travel, precognition) a priori.
The Direction of Causation
Hume's Temporal Analysis
Problems: (i) can't there be simultaneous causes and effects [inconclusive];
(ii) isn't backwards causation conceivable? [inconclusive] (iii) mightn't we
want to explain the direction of time in terms of the direction of
causation?
Different Arrows in Time
Assume that time is a dimension. The idea that there is an arrow of time,
which goes from earlier events to later ones, is a further idea (NB there
are no spatial arrows). The arrow of causation is another arrow which can be
imposed on this dimension.
Some philosophers want to explain the earlier-later arrow in terms of the
movement of the present from past to future. But this idea seems incoherent
(McTaggart, Mellor Real Time). The past-future difference isn't an
objectively moving point, but an indexical contrast available from every
point in time. But if time doesn't move, we need another way to explain the
contrast.
Why not in terms of the causal arrow? Consider: could there be a world in
which causes always come later than their effects? But what would it be like
to live in such a world? We'd remember the "future" and make plans to affect
the "past". But that would be just like the actual world. Turning round the
causal arrow will turn round the temporal arrow.
But now we'd like another arrow to explain causal direction (given that
analyses of causation have trouble making it asymmetric).
Lewis's Arrow of Overdetermination
Take any event. In one direction in time there will be lots of events of the
kinds it is generally associated with; in the other direction there will be
only one such event. This fixes another arrow. Lewis explains the causal
arrow in terms of this arrow. he thinks that if this arrow turned around in
time, then so would the causal arrow (and the temporal one).
Another way to explain the direction of time is in terms of probabilistic
asymmetry. First, by way of introduction to this, let me say something about
Probabilistic Causation
We'd like to allow causes that aren't constantly conjoined with their effect
(where not-E wouldn't have been certain given not-C). Hempel suggested that
it be enough that C make E highly probable. But smoking doesn't make cancer
highly probable. Bettter (Salmon): C should make E more probable than not-C
does: Prob(E/C) > Prob(E/-C). Taken as a generalization, this is just the
requirement that C and E be correlated, which allows "spurious" causation.
So need to add that there be no common cause D which screens off the
correlation: no D such that Prob(E/C&D)=Prob(E/D) and
Prob(E/C&-D)=Prob(E/-D). Question: can these probabilities merely be
reflections of our ignorance, or do they need to reflect to genuine
indeterminism?
A Probabilistic Arrow
Lewis's arrow can be put in probabilistic terms (whether or not the
probabilities reflect our ignorance, or genuine indeterminism). The
different effects of a joint cause are correlated: Prob(A&B) >
Prob(A)Prob(B), but the different causes of a joint effect aren't.
It's a bit tricky to translate this into an explicit analysis of causal
direction. But Dan Hausman has an elegant formulation. Take two correlated
events A and B. Both A and B will be correlated with lots of other events.
If all the events correlated with A are also correlated with B then A must
cause B. Conversely, if some events correlated with B are not correlated
with A, then again A must cause B.
NB this only works nicely (the last two sentences don't give conflicting
answers) if, for every cause-effect pair, there is another cause of the
effect that is uncorrelated with the first cause. Question: couldn't there
be a world in which there was only one cause and one effect? Hausman: no.
The Relata of Causation
Which kinds of entities are related by single-case causation: events,
property-instantiations, facts, or what?
Events
Davidson takes causation to relate events, construed as particulars. Such
events can be picked out by many different properties. So the following can
all report the same causal truth, for Davidson: The hurricane caused mass
destruction; the event decribed on page 3 of the Times caused mass
destruction; the most frightening thing I've ever seen caused mass
destruction.
Davidson thinks causation requires laws. But there need only be some
description under which the cause-event and effect-event are related by a
law; given that, the events can be picked out by other descriptions.
Facts
For Mellor the relata of causation are facts. So for Mellor the basic causal
truth is: Much was destroyed because there was a hurricane. By contrast,
it's not true that: Much was destroyed because an event was described on
page 3 of the Times. The facts in question need to be counterfactually
dependent/related by law.
A complication. Kim says that causation relates "events", but that (contra
Davidson) events are instantiations of properties. This is actually a
version of Mellor's view, not Davidson's. For a particular possessing a
property is one kind of fact. But -- for Mellor, and against Kim -- these
are not the only facts, and other kinds (existential facts, conjunctive
facts, . . .) seem able to enter into causal relationships. (NB. The
fact-theory does not require a non-Humean view of laws. There is a
connection. Both require properties. But you can have properties, and still
be a Humean about laws.)
Causal Explanation versus Causation
Davidsonians need to explain why "The hurricane caused mass destruction"
seems "more causal" than "The event decribed on page 3 of the Times caused
mass destruction". They say the former, unlike the latter, is a causal
explanation, in that it presents the events via descriptions that enter into
laws.
Mellorians need to explain why "The event decribed on page 3 of the Times
caused mass destruction" is true. They say that "Event c caused event e"
follows from "An event of kind E occurred because an event of kind C
occurred". And they agree that in this construction we can refer to the
events by other descriptions. But these particular-event causal truths are
derivative from the causal relationships between facts.
The Slingshot
So far a stand-off. But the issue matters to other philosophical topics (esp
in phil of mind). You might prefer Mellor because it keeps causation closer
to laws/dependence. But Davidson has the notorious "slingshot argument" as a
reductio of the idea that "E because C" names facts on either side of the
"because" relation. If it did, he says, then we ought to be able to
substitute salva veritate the logically equivalent sentence "{x: x=x & C} =
{x: x=x}" for "C", thus getting "E because {x: x=x & C} = {x: x=x}". And
then, given any sentence "T" equivalent in truth value to "C" we ought to be
able to substitute salva veritate the co-referring "{x: x=x & T}" for {x:
x=x & C}", thus getting "E because {x: x=x & T} = {x: x=x}". And then,
substituting logical evivalents again, we should be able to get "E because
T". But it's absurd that "E because T" should be true (or false) whenever "E
because C" is and "T" and "C" have the same truth value.
If you want to block this, you need to deny either that the logical
equivalent sentences, or co-referring descriptions of sets, can be
substitued salva veritate in "E because C".
作者：Anonymous 在 罕见奇谈 发贴, 来自 http://www.hjclub.org |
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