Hi everybody! Sorry for the late post!
On the notion of cause
In this paper Russell discusses the notion of cause as used
in science and philosophy. He states that his three aims as the following,
1. To discuss the flaws in the use of the term ‘cause’ in a scientific context
2. Suggest a more appropriate alternative to the ‘law of causality’
3. Explore some of the problems in theology and determinism that result from the improper use of ‘cause’
This first post will discuss the first of these points as
the others depend on the assumption of the first.
The cause of an event is often
considered to be a crucial part of scientific inquiry, with the likes of Ward
suggesting that causes are indeed the very ‘business of science’. In this piece
Russell contends that not only are ‘causes’ not the subject of advanced sciences
but that in reality there is no such thing. He first questions the
appropriateness of the word cause by using the then
available definitions of the word, taken from Baldwin’s dictionary. These are
as follows,
(1)
CAUSALITY
- The necessary connection of events in the time-series
(2)
CAUSE (notion of) - Whatever may be included in
the thought or perception of a process as taking place in consequence of
another process
(3)
CAUSE AND EFFECT - Cause and effect are
correlative terms denoting any two distinguishable things, phases, or aspects
of reality, which are so related to each other, that whenever the first ceases
to exist, the second comes into existence immediately after, and whenever the
second comes into existence, the first has ceased to exist immediately before
Russell discusses the appropriateness of each of these in
turn (and at length) so let us begin with the first.
Causality:
From the statement it is clear that the meaning of causality is
dependent on the meaning of necessary. Hence to fully understand the
implications of cause it is first required that we determine the meaning of
necessary. Necessary is defined as follows,
NECESSARY - That is necessary which not only is true, but
would be true under all circumstances. Some-thing more than brute compulsion
is, therefore, involved in the conception; there is a general law under which
the thing, takes place
Russell points out several problems with this statement. To
understand Russell’s critique it is required that we first understand his ideas
of a proposition and a propositional functions.
Proposition – A statement which is either true or false, no
other considerations can apply
Propositional Function – A statement containing a variable,
which is called the argument. Assigning a value to the variable creates a
proposition (the statement must then be either true or false).
[I’m curious as to
whether these were well established concepts or are they of Russell’s own
creation. This would seem to have a significant impact on the validity of his
argument, given that it relies on Baldwin making an informed inclusion of the
terms in his definition.]
With these definitions in mind let us re-examine the
definition of necessary. According to Baldwin for something to be necessary it
must be ‘true in all circumstances’. This implies that the subject must
therefore be a propositional function rather than a proposition. The example
given is that ‘if x is a man, then x is mortal’. As all men are mortal any
value for x which satisfies the first parameter must therefore satisfy the
second. Russell suggests an alternative definition for necessary on this basis,
NECESSARY – “is a predicate of a propositional function,
meaning that it is true for all possible values of its argument or arguments.”
However Baldwin’s definition states that for something to be
necessary it must also be true. This is impossible to rectify with Russell’s
ideas of propositions and propositional functions (which are mutually
exclusive) as the definition requires that a statement be both at the same time
(impossible because whilst a statement can become a proposition from a
propositional function it could not under Russell’s definition be both at the
same time).
[My personal thoughts
on this are that Russell is being ‘unnecessarily’ literal with Baldwin’s
definition. Whilst I accept the point that there is a conflict, it would appear
more obvious (and convenient!) to dismiss Baldwin’s double use of true as mere
emphasis. Dismissing the either, allows the definitions of causality and
necessary to fit.]
Russell resolves this conflict by requiring the argument of
the function to be identified within the statement. He therefore arrives at the
following definition which satisfies the implied meaning of causality,
NECESSARY - A proposition is necessary with respect to a
given constituent if it remains true when that constituent is altered in any
way compatible with the proposition remaining significant.
Armed with this definition Russell gives what he interprets
to be the universal law of causality (whilst making 100% sure he is not tied to
its authenticity!)
Cause
(Notion of):
Russell doesn't really spend much time discussion the 2nd
definition as it does not really concern the meaning of cause which is of
interest to him (so I won’t either).
Cause and
Effect:
Definition 3 appears to be the closet to what is
traditionally meant by causality in my opinion (or at least when it is used in
reference to science). The problem with the statement according to Russell is
the implied temporal contiguity. Treating the current and prior states as
distinct entities introduces the requirement for causal relations between the
two.
[The implications of this get a bit wordy but I’ll do my
best to simplify what I think Russell is trying to say.]
The definition seems to describe cause and effect as having
an associated finite time (not really instantaneous). Hence within the duration of the cause there can be said
to be earlier and later parts. If this is taken to be true then only the later
stages of the cause, those immediately preceding the effect, can be truly relevant
to the effect. The earlier parts of the cause are not contiguous to the effect
and so could therefore be altered without changing the effect. Really you’re
supposed to think that the effect is only dependent on a certain final part of
the cause.
This is clearly a bit ridiculous, and does not fit what
cause is supposed to be (at least in my opinion). Russell agrees and says it is
hardly acceptable that the effect should just spring from a cause at some
point. Cause and effect cannot therefore be contiguous in time. Russell then
introduces the time-interval to solve this.
I reckon this is enough for a first blog as it covers
Russell’s critique of Baldwin’s definitions. I shall put a second post up
tomorrow which will discuss the proposed solution to the 3rd
definition.
Hey Will, thanks for posting! You've made everything clear :)
ReplyDeleteI would wait for the next part of your post to ask you a question but since my question is pretty broad I suppose it doesn't matter - things do get a bit tricky towards the end with regards to cause and effect. I'm not even sure what to make of what we call "cause and effect" - are we just trying to arrange our experiences in such a way that they provide patterns for us to recognize for future inferences? If not, does the solution to the 3rd definition satisfy you?
Hi Emma, I totally agree with you that it does get a bit muddling towards the end. To me this arises because of the way Russell wants to define cause and effect. I think he wants us to see cause as what brings about a transition between two states, Whilst the transition itself is the effect. This allows him to treat both cause and effect as discrete events which happen over a finite period of time. So every change in a circumstance (transition) must be comprised of something which leads to it happening (the cause) and something which then happens (the effect). This interpretation suits Russell as it is very easy to break down and doesn't really stand up to much scrutiny. Whether this is a fair way of describing cause and effect, I don't know!
DeleteHi, thanks Will,
ReplyDeleteI did not understand the first step in Russell's argument against the contiguity of cause and effect (on page 5):
That cause and effect are contiguous means that both are events over a time interval and the cause finishes at some moment and the effect starts exactly the moment after.
(1) There are no contiguous moments, because for every two moments there exists a moment in between (is that what is meant by "the time series is compact"?). But that seems enaugh to claim that cause and effect are not contiguous, since between the end of the cause and the beginning of the effect, however close they are, there is always a moment in between (I guess "contiguous" means that they do not overlap).
(2) I think I haven't understood the meaning of "endure for a finite time". Does that mean that since there cannot be a moment between cause and effect that is neither, this moment between cause and effect must be part of either the cause or part of the effect. Thus, cause or effect must be more than a single moment (at least two moments, but the same problem arises again), it endures a finite amount of time. But then there is no real moment where one starts or the other ends.
(3) Where does this enter into the rest of the argument? The rest seems to assume that it is the cause that consists of more than one moment, which is what Russell claims is intended by the formulation. So here the possibility of the effect enduring a finite amount of time and the cause just for one moment is not considered.
Anyway, I might have misunderstood the whole idea, that first part of the paragraph was pretty confusing.
I think Russell means something along the lines of this when he says compact: http://en.wikipedia.org/wiki/Compact_space .
DeleteWhen Russell says `No two instants are contiguous, since the time-series is compact' I think he means by `instant' a point in time with no extension (eg exactly 3s after the start of the universe). Two such instants cannot be contiguous since, owing to the compactness of the time-line, either they are the same instant, or there are other instants between them. This is the same as saying something like `there is no ``next'' real number'. This isn't sufficient to establish that causes and effects cannot be contiguous however, as causes and effects could be extended in time.
DeleteIn such a case both the cause and effect would occur during intervals in time (eg between 3s and 5s after the start of the universe), if the end-point of the cause's interval was the same as the start-point of the effect's interval they would indeed be contiguous.
The third part of the argument is is then that for any cause occurring during an interval in time only the final instant (in the earlier sense of durationless point in time) of the interval can be contiguous to the effect's interval. Hence one can reduce the duration of the (`finite' ie occuring over an interval of time) cause indefinitely and there will always remain a part of it which isn't contiguous to the effect.
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DeleteI think Russell's argument can be summarised as follows:
Deletecause and effect are either contiguous or separated by a finite time interval. If they are contiguous, they happen either on two instances of time or two intervals of time. They cannot happen on two instances of time because two points of compact time can never be contiguous. So they have to happen during two intervals which are contiguous (time compactness allows contiguity of intervals). Here there are also two alternatives: either cause is static or it changes during its time interval. it cannot be static because "suddenly explod(ing) into the effect, when it might just as well have done so at any earlier time, or have gone on unchanged without producing its effect" seems very strange. So if cause and effect want to be contiguous, cause should change during its time interval. Russell says this last option is still problematic, because if cause changes, "only the later parts can be relevant to the effect, since the earlier parts are not contiguous to the effect." Again using the compactness of time one can infer no matter how much one diminishes the size of cause's time interval, she won't get to that part of interval which is contiguous to the effect and deserves to be called cause according to the third definition. Considering all these exhaustive options, Russell infers there is no way to maintain contiguity of cause and effect. So they should be separated by a finite time interval.
I don't like the way Russell rejects the idea of cause being static during its time interval. He says it is strange! But he doesn't elaborate on his point and so it remains unclear why we should care about strangeness of this situation!
DeleteI believe, the inconsistency of the idea of cause and effect happening during two contiguous time intervals with Baldwin's third definition of causality can be shown in a simpler way:
It seems Baldwin demands that cause and effect never exist simultaneously. He says: "whenever the [cause] ceases to exist, the [effect] comes into existence immediately after". If cause and effect exist during two contiguous time intervals, it means they both exist at the instance which is the border between two intervals, which means there is an instance which cause and effect exist simultaneously and this is inconsistent with Baldwin's definition.
I also think that there may be a way to rescue Baldwin's definition and that is by reinterpreting the term "immediately". It is Russell's interpretation that this term means cause and effect are contiguous, but Baldwin, in response, can easily claim that what he meant by this term is that the time interval which separated cause from effect is rather short.
Thank you Will for the summary. I think that I agree with you that Russell treats Baldwin's definition of necessity too literally by saying that Baldwin is demanding a proposition to be both true and true in all circumstances.
ReplyDeleteHi all,
ReplyDeleteI think you’ve together done a good job of analysing Russell’s argument against the contiguity of cause and effect. Jon is presumably right that, by “compact”, Russell means *something along the lines of* ‘compact’ in the current topological sense, but ‘compact’ doesn’t seem to be quite the right word. I think what he wants to say is that the time-series is complete or continuous or closed in the sense that it contains all its own limit points. A compact point set in Euclidean space must have this property and also be bounded, but presumably Russell did not really think that time itself is bounded, and he doesn’t need that property to make his point. In fact, he doesn’t need completeness either; all he really needs to claim is that the time-series is dense, i.e., between any two moments there is a third moment.
I want to clarify another point here. Assuming time has the structure of the real number line, two enduring events *can* be contiguous without charing a point. Event A might for example occupy the interval from 10,000,000 seconds after the birth of the universe to 10,000,100 seconds after, including the last moment of that span (i.e., it’s a closed interval), while event B occupies all times after that last moment, up to, say, 10,000,200 seconds after the birth of the universe. In that case, B has no first moment; it occupies an open interval (or at least, open on the left). On the other hand, A could occupy an open interval while B occupies a closed one. In either case they are temporally contiguous. (But Russell then argues that cause and effect cannot be contiguous in this way.)
Thank you Matt for your comment. I think your last point shows that my suggested proof for showing the inconsistency of the idea of cause and effect happening during two contiguous time intervals with Baldwin's third definition of causality, is wrong. Am I right?
Delete