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P H I L O S O P H Y   P A T H W A Y S                   ISSN 2043-0728

Issue number 162
5th May 2011


I. 'Are there uncontroversial error theories?' by Terence Edward

II. 'Parfit, Lewis and the Logical Wedge: Fusion-Fission's Challenge
to Coextension' by Oliver Gill

III. 'Towards a Spatial Theory of Causation' by Esteban Céspedes



We are now getting increased attention from young academic
philosophers. In this issue, we have three papers by graduate
students/ researchers from the analytic tradition, which exemplify
the high standards required for work at this level. Anyone
contemplating a graduate course in philosophy should study these
papers closely.

Terence Edward is a teaching assistant in the School of Social
Studies, Manchester University. His article concerns a
'meta-philosophical' claim concerning the nature of error theories in
general. Error theories in philosophy typically take the form of
denying the truth of things we unreflectively believe -- for example,
the belief that the colours we see are somehow 'in' the objects
themselves. But is this really an 'error' that we make, or is it the
philosopher who misinterprets our everyday beliefs? One issue that
needs to be clarified is what counts as a legitimate objection
to such error theories. Terence Edward argues persuasively that a
plausible defence of error theories against philosophical objections
doesn't work in the way it was meant to.

Oliver Gill gained his MA in Philosophy from the Open University in
2010. His article tackles one of my favourite topics, the science
fiction scenarios which raise doubts about our unreflective notion of
'personal identity' (as in the film 'The Sixth Day' starring Arnold
Schwarzenegger, 2000). How do you describe a case when a person is
put into a fission machine and two persons emerge? or if you could
put two people into a fusion machine? Gill's target is a claim --
which I have always found rather plausible -- that you can save the
logic of identity in cases of fission by retrospectively deeming the
person who went into the machine as 'having been' two persons all
along. Arguably, a similar defence can be given in the case of
fusion. But as Gill cleverly shows, this strategy doesn't work when
we combine fusion and fission.

Esteban Céspedes is a PhD student at Goethe University Frankfurt. The
purpose of his rather difficult article on causation can be best
illustrated if we consider the question how one defines the direction
of time. Imagine a universe just like ours where time goes backwards.
What's the difference? According to the physicists' view that the
world is just a four-dimensional block of spacetime, there is none.
Time has no real direction. But couldn't you define the direction of
time in terms of causation? For example, dropping a stone at a window
causes it to break. But that only works if you can define causation
without including in your definition the idea of priority in time --
otherwise your account of the direction of time is patently circular.
That's what Céspedes sets out to do. In the theory he defends,
causation is more like a relation between vertical slices taken out
of the 'cake' of spacetime -- if you can bend your mind to that idea.

Geoffrey Klempner




This paper evaluates an argument for the meta-philosophical
conclusion that in order to produce a viable objection to a
particular error theory, the objection must not be applicable to all
error theories. The reason given for this conclusion is that error
theories about some discourses are uncontroversial. But the examples
given of uncontroversial error theories are not good ones, nor do
there appear to be other examples available.


There are various theories which are classified as error theories.
Some of these theories have been subject to much discussion. One
example is the theory that any judgement which ascribes a colour
property to a material object is false. Another example is the theory
that any judgement which asserts or implies that there are objective
moral standards is false. These theories have their supporters and
their opponents. The purpose of this paper is not to discuss any
particular error theory, however. Rather its purpose is to evaluate
an argument that it makes sense to describe as meta-philosophical,
because the argument concerns how philosophical work on error
theories should be pursued. The argument is concerned, more
specifically, with what a philosopher who is assessing a particular
error theory should not do. Its conclusion is that the philosopher
should not produce an objection which can be applied to any error
theory whatsoever. My aim below is to show that the argument that has
been made for this conclusion does not succeed.

The argument to be considered comes from a paper entitled 'In defence
of error theory'. The authors of this paper, David Liggins and Chris
Daly, seem to regard the argument as patently sound, since they do
not consider any objections to it. Here is their articulation of it:

     The following constraint holds on viable objections to
     error theory. Philosophers need to take care that their
     chosen objection to a given error theory does not prove too
     much by yielding a more general objection that applies to
     any error theory. This is because error theories about
     certain discourses are compelling: we should be error
     theorists about, for example, astrology, palmistry and
     numerology. This places an important constraint on
     objections to error theory. An objection to a
     philosophically controversial error theory should not
     provide an objection to a philosophically uncontroversial
     error theory. (2010: 211, their emphasis)
Liggins and Daly accept the following premise: if there are
philosophically uncontroversial error theories, then one should not
make an objection to a philosophically controversial error theory
that applies to any error theory. They also accept the premise that
there are philosophically uncontroversial error theories. From these
two premises, they derive their conclusion: one should not make an
objection to a philosophically controversial error theory that
applies to any error theory.

If Liggins and Daly's argument is sound, it seems that any
philosopher writing about a particular error theory or about error
theories in general ought to be aware of it. This impression fits
with how they present their argument. According to them, error
theories are rated poorly by a number of philosophers (2010: 210).
Their paper seeks to dispute the reasons given for this rating of
them. However, the reasons they consider in detail are always reasons
for rating a subset of error theories poorly, not any error theory
whatsoever. They present the argument above before considering these
reasons, in a section entitled 'How not to object to error theories'.
What they convey is that an objection which violates their constraint
goes wrong in an elementary way. Nevertheless, they do find two
philosophers guilty of producing such objections, namely Hilary
Putnam and Susan Hurley (2010: 211-212). Since their argument, if
sound, identifies an important constraint and since some philosophers
have been charged with violating the constraint, it seems that any
philosopher who writes on error theory ought to be familiar with the
argument, on the condition that it is sound. But is the argument
sound? Below I shall contest their premise that there are
philosophically uncontroversial error theories.

Liggins and Daly provide us with three examples of discourses which
it is uncontroversial to regard as consisting of erroneous claims:
astrology, palmistry and numerology. But they do not say why we
should be error theorists about these discourses. It is natural to
interpret anyone who gives these three discourses as examples,
without saying where the error in them lies, as believing that the
knowledge that science has provided us with conflicts with the
understanding of reality that these discourses involve. If Liggins
and Daly are opposed to this interpretation, presumably they would
have said so. But to accept that we have the relevant scientific
knowledge, one must suppose that radical forms of scepticism are
false. Radical forms of scepticism, on the understanding employed
here, are sceptical doctrines that deny us knowledge of the external
world. For instance, there is the doctrine that one has no external
world knowledge because one cannot rule out the hypothesis that one's
whole life has been a dream (Hanna 1992: 382-383). If this form of
scepticism is true, then we cannot be confident that astrology,
palmistry and numerology consist of erroneous claims. Unless one can
rule out the dream-life hypothesis, one is not in a position to know
how these discourses stand in relation to the external world. But
Liggins and Daly do not attempt to rule out this hypothesis, nor do
they dispute the purported consequence of not being able to rule it
out. Instead they assume the falsehood of radical forms of scepticism.

Much philosophical work assumes that radical forms of scepticism are
false. Perhaps we are entitled to argue on the basis of this
assumption in most contexts. Philosophy would lose much of its value,
one might think, if philosophers with proposals that are opposed to
scepticism should always refute the sceptic. Surely then, there is
nothing of interest in the observation that Liggins and Daly assume
the falsity of radical scepticism. This is an understandable
response. However, they are not entitled to the assumption in the
context in which they are working.

Radical forms of scepticism are error theories as well. We will come
to the issue of when a theory counts as an error theory later. For
now, we need only observe that these forms of scepticism conclude
that each claim which attributes external world knowledge to us is
false. Not only are these forms of scepticism error theories; on any
plausible explanation of what it is to be philosophically
controversial, they are also philosophically controversial ones. (Any
appropriate object of philosophical debate is philosophically
controversial.) Thus in arguing for a requirement on how we should
evaluate philosophically controversial error theories, Liggins and
Daly are already assuming that some of the theories to be evaluated
are false. Given what they are arguing for, they are not entitled to
the assumption. One should not offer an argument for a constraint on
how we should evaluate theories of type X which already assumes that
one theory of type X is false. Since the premise that there are
uncontroversial error theories is not somehow self-evident and since
it has been supported in a way that depends on such an assumption,
the premise has not yet been justified.

In order to grasp the problem which has been identified, it is useful
to imagine that we are about to evaluate a radical form of scepticism,
with the aim of determining whether it is true. Since the object of
evaluation is a philosophically controversial error theory, it is
important for us to first be aware of what we should and should not
do when evaluating a theory of this type, plus the arguments for
these constraints. Thus if it is the case that one should not produce
an objection that can be applied to any error theory, it is important
that we are aware of this constraint and the argument for it. But we
can only accept the argument provided by Liggins and Daly by already
assuming that the theory we are about to evaluate is false, before we
have even begun evaluating. Note that this assumption does not cast
the commonsense view that we have external world knowledge as the
default position: something that we should regard as true in the
absence of overriding considerations. If that was what it did, then
we could evaluate the arguments of the radical sceptic to see whether
they provide us with a compelling reason for abandoning this position.
But Liggins and Daly aim to establish a constraint, not a mere
guideline, that is to say, something by which we must always abide.
They are therefore assuming that radical forms of scepticism are
false in a way that leaves no room for overriding considerations.

My response to Liggins and Daly relies on the claim that radical
forms of scepticism are error theories. But so far no criterion has
been introduced in order to determine what is and is not an error
theory. Liggins and Daly open their paper with the following

     To be an error theorist of a discourse is to claim that
     none of its sentences are true. (2010: 209)

They later say that this definition is a simplification (2010: 209).
The complication that they then introduce is one which they ignore,
for the sake of simplicity (2010: 210). It will not be introduced
here, because we too do not need to concern ourselves with it. The
question is whether Liggins and Daly must treat radical forms of
scepticism as error theories. They write as if each error theory
targets a discourse, but they do not define what they mean by
'discourse'. Nevertheless, from what they write, our knowledge claims
about the external world would constitute a discourse for them.
Discourses are not limited to what we can loosely refer to as
disciplines, such as astrology, astronomy and physics. Liggins and
Daly also write of moral discourse (2010: 209) and colour discourse
(2010: 214). The former consists of sentences which ascribe moral
properties to the world, while the latter consists of sentences which
ascribe colour properties to the world. (If we define these discourses
by the sentences that the relevant error theorists target, both
characterizations actually seem too broad. Moral error theorists
typically do not object to sentences ascribing moral permissibility
to actions, while colour error theorists typically do not object to
the ascription of colour properties to 'inner items', such as mental
images.) Radical forms of scepticism also target sentences each of
which ascribes a type of property to something. These forms of
scepticism target sentences which ascribe the property of having
external-world knowledge to persons. There is no reason then for
Liggins and Daly to deny that radical forms of scepticism are error
theories about a discourse.

Although radical forms of scepticism are error theories, there is a
temptation to overlook them. The temptation arises because the
sceptic about a particular set of beliefs does not say that those
beliefs are false, rather that we do not know whether they are true
or false. Consequently, the sceptic does not appear to be an error
theorist at all. But this appearance is misleading. Since the radical
sceptic is a sceptic about our external world beliefs, they do not say
that we are in error about the external world. But they do say that we
are in error if we ever claim to know about how the external world is.
Every claim that attributes external world knowledge to us is
erroneous, according to this kind of sceptic. Thus it is not our
external world discourse which this sceptic targets, as an error
theorist, rather our discourse of external world knowledge.

Liggins and Daly refer to astrology, palmistry and numerology to make
their argument. Can the argument be rescued by replacing reference to
these things with other examples? If the objection I am making was
that there are true sentences from these discourses or that these
discourses are too vague to be scientifically tested (Popper 1972:
37), then it would be promising to pursue this defence. But the
objection above is quite different. It begins with the inference that
Liggins and Daly are relying on our supposed external world knowledge
to justify error theories about astrology, palmistry and numerology.
If the replacement examples are also discourses that we should be
error theorists about because of what we know about the external
world, then their argument will be open to the same objection. The
replacement that they need is a discourse that we can reject without
assuming such knowledge to justify the rejection. An error theory
about it must also be philosophically uncontroversial. But it is
doubtful that there is any discourse which meets these criteria. Note
that an attempt to dispel this doubt must not just uncover a discourse
consisting of sentences that are clearly not true. There must also be
no philosophical reasons to regard these sentences as meaningless,
instead of false, otherwise it will still be controversial to be an
error theorist about this discourse (Magidor 2010: 554-555).

One might wonder whether it is possible to define a particular
discourse so that, because of the definition itself, an error theory
about this discourse is uncontroversial. For instance, we could say
that the discourse of falsehood is a discourse consisting of all
false sentences, without specifying which sentences are false. We
could then say that an error theory about this discourse is
uncontroversial. But it is not clear that what is being called the
discourse of falsehood is genuinely a discourse. Intuitively, the
sentences of a discourse have a common subject matter, which is
reflected in the label for that discourse. But we have not been told
of any common subject matter running through the discourse of

It may be said that we should not take the word 'discourse' too
seriously. But if we allow for error theories that are
uncontroversial by definition, there is another point to be made
against this attempted defence of the argument. When Liggins and Daly
write of an important constraint on objections to error theory, they
are intending to present a requirement that cannot be met merely by
meeting the general requirement to be consistent. But if there are
error theories that are uncontroversial by definition, then any
consistent objection to a particular error theory cannot be applied
to all error theories. For if an objection also applies to an error
theory of this kind, then when we think through the consequences of
the objection, we will find that we cannot endorse it without lapsing
into inconsistency. Endorsing it would require rejecting an error
theory that we ought to accept because of the very way in which the
target discourse is defined. Furthermore, if the only philosophically
uncontroversial error theories are uncontroversial by definition, then
any consistent objection will allow for all of them. A defence of
Liggins and Daly's argument which seeks out error theories that are
uncontroversial by definition may therefore preserve the letter of
the argument, but it will have done so without identifying a
requirement that goes beyond the general requirement to be
consistent. A defence of the argument that preserves its spirit needs
to identify a requirement that is distinct in practice. I cannot see
how this can be achieved.


Daly, C. and Liggins, D. 2010. 'In defence of error theory'.
Philosophical Studies 149: 209-230.

Hanna, R. 1992. 'Descartes and Dream Scepticism Revisited'.
Journal of the History of Philosophy 30: 377-398.

Magidor, O. 2010. 'Category mistakes are meaningful'. Linguistics
and Philosophy 32, 553-581.

Popper, K. 1972 (fourth ed.). Conjectures and Refutations: The
Growth of Scientific Knowledge. London: Routledge and Kegan Paul.

(c) Terence Edward 2011

E-mail: T.R.Edward@manchester.ac.uk



 1 Introduction

The thesis that the R-relation, as opposed to personal identity, is
'what matters' in terms of survival lies at the core of Derek
Parfit's Reasons and Persons (1987). As one might expect, in
building the case for this thesis, one of Parfit's primary tasks is
to establish that there is, in fact, a distinction to be made between
the R-relation and identity. In terms of this, it is Parfit's
contention that, whilst personal identity can largely be equated with
the R-relation, this equivalence only holds in cases where the latter
relation does not branch. However, David Lewis (1983) has
challenged this distinction on the basis that it fails to compare
'like with like'. To explain, Lewis argues that the proper correlate
of the R-relation is not identity (which relates to persons), but the
I-relation (which relates to person stages). Furthermore, Lewis
contends that the I-relation is 'coextensive' with the R-relation and
that, as such, the distinction that Parfit requires is not here
present. The purpose of this paper is to demonstrate that, even when
we reframe the debate in Lewis's terms, the case of
Fusion-Fission demonstrates that a relevant distinction can
still be drawn. First, however, it is necessary to consider the
metaphysical foundations of this debate and it is to this matter that
the paper now turns.

The Reductionist position in relation to the question of personal
identity is encapsulated in the assertion that we are not 'separately
existing entities'[1] and that, as such, there is no 'further fact' in
which personal identity consists. Otherwise expressed, Reductionists
hold that one's identity is reducible to certain of the more
particular facts that comprise one's being at any given time. In
Reasons and Persons, Parfit adopts just such an approach, with
his key argument for the Reductionist case being that:

     Our experiences give us no reason to believe in the
     existence of... [separately existing] entities. Unless we
     have other reasons to believe in their existence, we should
     reject this belief.[2]
Moreover, Parfit adopts a psychological criterion of personal
identity, with his contention being that one's identity at any point
in time is reducible in its entirety to one's psychological makeup
(e.g. one's memories, beliefs, desires, intentions etc.) at that
time. In line with this, Parfit argues that, for a person (C1) at one
point in time (t1) to be deemed to be numerically identical with a
person (C2) at a different point in time (t2), the two must be
R-related[3] to one another. However, there is, Parfit argues, a
distinction to be drawn between identity and the R-relation. In terms
of this, it is Parfit's contention that C1's being R-related to C2 is
insufficient for their being determined to be numerically identical;
the further premise that C1 be the exclusive holder of this
relation to C2 (and vice versa) is required. In other words, personal
identity (according to Parfit) is equivalent to the holding of the
R-relation in a non-branching (i.e. one-one) form.

 2 Fission & Fusion

Parfit utilises the imagined case of Fission to demonstrate
how, as a consequence of the aforementioned distinction, the
R-relation can become disentangled from personal identity in certain
scenarios. For the purposes of this paper, we will conceive of
Fission as being a machine-driven process. Thus, let us assume that,
when a human being[4] steps into the Fission Machine, a
process starts, whereby the Machine records the exact physical and
psychological makeup of the being in question at that point in time
and then destroys this being. Furthermore, at the point of destroying
this being, the Machine instantaneously creates two beings on the
basis of the recorded data, with each one being qualitatively
identical (most importantly, in terms of their psychological makeup)
with the original. What are we to say about these two beings?
Clearly, whilst they are not R-related to one another[5], they are
both R-related to the predecessor being, since they are
psychologically continuous with and psychologically connected to this
being in a causally-related manner. The question of identity, however,
is less easily resolved. Parfit argues that there are three possible
answers to this question:

(1) That the predecessor being survives as both of the
successor beings;

(2) That the predecessor being survives as one of the
successor beings; or

(3) That the predecessor being does not survive the process.

The problem with (1) is that, because of the formal properties of the
identity relation, it presents a logical contradiction. To explain,
since identity is both transitive and symmetrical, this answer, in
asserting that the predecessor being is the same person as both of
the successor beings, also implies that the successor beings
themselves are the same person. However, this cannot be so, since a
person cannot exist in two different places at the same time. The
second answer also presents logical difficulties. To explain, there
is no logical reason for choosing either one of the successor beings
as the one in which the predecessor being continues his/ her
existence, since both of these successor beings are exactly similar
at the point of fission. Indeed, without a 'further fact' of personal
identity to refer back to and bearing in mind the parity of
R-relatedness of each of the successor beings to the predecessor
being, it would seem that (2) cannot provide a satisfactory answer to
the question posed. As such, Parfit concludes that the 'best'
answer[6] to the question of identity in cases of fission is (3).
However, if we are to accept that the predecessor being does not
survive the procedure, then clearly we must also acknowledge that
identity is not preserved from one side of this process to the other.
As a consequence, we are left with a situation in which the R-relation
and identity do not correlate with one another: the former holds,
whilst the latter fails to do so. It is precisely for this reason
that Parfit asserts that identity must incorporate a 'no branching'
clause and that, this being the case, there is a logical distinction
to be drawn between this relation and the R-relation. Penelope Maddy
(1979) describes this situation well when she refers to Parfit as
placing a 'logical wedge' between the R-relation and identity.

At this point, it is also worth mentioning another of the thought
experiments that Parfit utilises; this being the case of
Fusion. Straightforwardly speaking, Fusion is simply Fission
in reverse. Again, we can conceive of this as a machine-driven
process. Thus, when two beings step into the Fusion Machine,
the Machine records the psychological and physical makeup of these
beings; destroys them; and then forges one successor being from the
information recorded. For our present purposes, the important point
to note is that (for Parfit), while both of the predecessor beings
are R-related to the successor being (in the form of direct
psychological connections), they are not similarly numerically
identical with him/ her, since neither of them is the
exclusive holder of R-relatedness in this respect. Thus,
Parfit contends, Fusion represents another case in which the 'logical
wedge' between the R-relation and identity is made manifest.

 3 Lewis

In Survival and Identity (1983), David Lewis aims to remove
the 'logical wedge' that Parfit places between personal identity and
the R-relation by showing that it is misplaced. It is important to
note that Lewis does not dispute the formal difference between
personal identity and the R-relation noted by Parfit. Rather, Lewis's
contention is that '[i]t is pointless to compare the formal character
of identity itself with the formal character of the relation R'[7]. To
explain, Lewis asserts that the Parfitian comparison of personal
identity with the R-relation is not a fair one, since these two
relations have different relata: the first being related to
continuant persons (e.g. person C1; person C2 etc.); the second to
person stages (e.g. C1 at t1; C2 at t2 etc.). Accordingly, Lewis
proposes that we compare the R-relation, not with personal identity,
but with the I-relation, where this latter concept is defined
as 'the relation between two person-stages which belong to the same
person'[8]. Otherwise expressed, if C1 at t1 and C2 at t2 are to be
parts of the same continuant person, then they must be I-related to
one another.

Having defined the I-relation, we can now turn to consider Lewis's
purpose in introducing this concept. It is Lewis's contention that if
we can show the I-relation to be akin to the R-relation in terms of
its formal properties (and, thus, that the two relations are
coextensive), we can overcome the 'logical wedge'. Thus, Lewis's
objective is to demonstrate that 'the I-relation is the R-relation in
the sense that they have the same extension'[9]. However, there
remains a key obstacle to the achievement of such, in terms of the
fact that, on the assumption that a particular person stage can only
serve as a compositional element in a single continuant
person, the I-relation will, by implication, still be subject to the
'no branching' requirement that attaches to identity and, as such,
will remain separated from the R-relation by the 'logical wedge'. It
is for precisely this reason that Lewis denies the assumption
just stated, in the form of the assertion that 'it may happen that a
single stage S is a stage of two or more different continuant

This point is best illuminated in the context of Fission. However, it
will be necessary to reconfigure our terminology, in order to take
account of 'person stages'. As such, let us refer to the pre-fission
person stage (at t1) as S and the post-fission person stages (at t2)
as S1 and S2. As was clear from our previous discussion, at t2, we
have two distinct continuant persons. Let us refer to these as C1 and
C2. Lewis's proposal, then, is that both C1 and C2 existed at
t1, in terms of the fact that they shared the person stage S.
Effectively, all that Fission has brought about, from t1 to t2, is
the separation of these two continuant persons: where once
there was one body inhabited by two persons, now there are two
bodies, each inhabited by one of the two original persons. Thus, if
we adopt Lewis's proposal of the potential for 'stage-sharing'
between continuant persons, there is, in effect, 'no branching': the
same number of continuant persons exist before and after the

Moreover, stage-sharing in the above sense enables the I-relation to
be coextensive with the R-relation. Recalling Lewis's definition of
the I-relation, it is clear that, since the continuant person C1
includes both S and S1 as person stages, these person stages must be
I-related to one another. Likewise for the person stages S and S2,
which form part of the continuant person C2. However, because S1 and
S2 do not form part of the same continuant person, they
cannot be I-related to one another. This I-relatedness of S
with S1 and S2 (but non-I-relatedness of S1 and S2 themselves)
mirrors R-relatedness in Fission.[11] As such, Lewis contends that
Parfit's case requires the further premise 'that partial overlap of
continuant persons is impossible'[12]. Without this, the distinction
between the formal properties of the two sides of the 'logical wedge'

 4 Critique of Lewis: Fusion-Fission

Having thus set-out Lewis's argument against Parfit's 'logical
wedge', we can now turn to a critical analysis of this position. This
analysis utilises the Fusion-Fission[13] thought experiment as its
basis, an outline of which is sketched in the figure below:

                 S3                 S4
                  |                  |
             ---------------------------- t3 (later)
                  |                  |
                  |                  |
                  |                  |
                  |                  |
             ---------------------------- t2
                  |                  |
                  |                  |
                  |                  |
                  |                  |
             ---------------------------- t1 (earlier)
                  |                  |
                 S1                 S2
In order to explain the concept of Fusion-Fission, let us say that
two continuant persons (C1 and C2) enter the Fusion Machine at a
given point in time (t1). These persons then become 'fused' and a
successor being steps out of the Machine a few seconds later (t2). As
discussed above, this being will be R-related to both C1 and C2.
Furthermore, assuming Lewis's framework for thinking about such a
case, we must say that, at t1, the continuant persons occupy two
distinct person stages (S1 and S2, respectively). Moreover, Lewis's
contention would be that, at t2, we have a single person stage (S),
which is occupied by both C1 and C2. Proceeding on the basis of this
understanding, let us move onto the other half of the thought
experiment. A couple of weeks after t2, the being that stepped out of
the Fusion Machine returns and asks to be put into the Fission
Machine. This request is duly granted, the being steps into the
Machine and, a few seconds later (t3), two beings exit the machine.
On Lewis's account, what are we to say about these two beings?

To explain the question at issue, clearly, at t3, we have two
distinct person stages (S3 and S4). Furthermore, as discussed above,
these stages will be R-related to S and, by implication, to S1 and S2
(since there will, at a minimum, be psychological continuity and, in
all likelihood, psychological connectedness from S1 and S2 to S3 and
S4). However, there remains a question as to which continuant persons
occupy the person stages S3 and S4. On the face of it, there seems to
be no satisfactory answer to this question. To elaborate, in order
for S3 and S4 to be I-related to S1 and S2 (which they must be if the
I-relation is to be coextensive with the R-relation) both S3
and S4 must contain both C1 and C2, due to the fact that the
I-relation only holds between person stages that contain the same
continuant person. Such a situation is, however, impossible, as it
would violate the one-one nature of the identity relation, since
there would now be two of each of C1 and C2. Indeed, it would seem
that, on Lewis's account, the 'best' description that we could
provide of this situation would be that C1 and C2 are 'redivided' by
the Fission Machine and that, as such, S3 is occupied by C1 and S4 by
C2. However, this would mean that, whilst both S1 and S2 would
be R-related to both S3 and S4, they would only be I-related
in a one-one fashion (i.e. S1 to S3; and S2 to S4). As such, the
I-relation would again be separated from the R-relation and the
'logical wedge' would thus be restored.

Nevertheless, Lewis does have a potential response to the above line
of reasoning. To explain, Lewis could challenge the assumption
(implicit within the above description) that only two continuant
persons enter the Fusion Machine in the first place. If we were to
instead assume that four continuant persons entered the
Machine, then Lewis's account could accommodate
Fusion-Fission. This point requires further exposition. In the
revised scenario, then, at t1, S1 is occupied by two continuant
persons (C1 and C2), as is S2 (C3 and C4). Following this line of
reasoning, S at t2 will be occupied by C1, C2, C3 and C4. Moreover,
at t3, we could argue that S3 is occupied by C1 and C3, whilst S4 is
occupied by C2 and C4. In this manner, both S3 and S4 would be
I-related to both S1 and S2, since each of the person stages at
t1 would share a continuant person in common with each of the person
stages at t3. Furthermore, since the I-relation would now take a
one-many form (and thus be coextensive with the R-relation), it
could, on this account, be argued that the 'logical wedge' is once
more dissolved.

So much for the proposed objection, we might contend. However, the
above line of argument brings to the fore a problematic implication
of Lewis's account that wasn't evident in its initial presentation.
To elaborate, if we are to make the I-relation coextensive with the
R-relation, Fusion must bring about the inextricable 'fusing'
of (at least) two continuant persons. The point is that the
R-relatedness of the beings that entered the Fusion Machine is fused
from that point forward, since any future stages that evolve from S
will be R-related back to both of the predecessor beings.
Thus, in order for the I-relation to mirror the R-relation,
continuant persons from each of the predecessor stages must be
similarly fused[14]. In the context of the above example, then, C1
and C3 are inextricably 'fused' at t2, as are C2 and C4. However,
whilst the inextricable fusing of R-relatedness in this manner is
evidently theoretically acceptable, it is the contention of this
paper that the idea that continuant persons should be
inextricably fused is far more dubious.

To see this, let us focus on the person stage S3 (at t3) in the case
of Fusion-Fission described above. As we saw, if Lewis is to make
sense of this scenario, it must be claimed that S3 is occupied by C1
and C3. Moreover, it must be claimed that the being who exits the
Fission Machine is not a person, per se, but, rather, a person stage
that is occupied by two continuant persons. Furthermore, this being
can never be a person, since C1 and C3 are inextricably
fused and, thus, we must characterise this being's future existence as
a succession of person stages, all occupied by two continuant persons.
Now, in the case of Fission alone, the concept of stage-sharing
seemed at least conceivable, on the grounds that the continuant
persons who initially shared a stage were directly relatable to the
two tangible continuant persons that existed after the process
had been completed. Likewise, stage-sharing in a case of Fusion alone
seems plausible, on the grounds that the continuant persons who share
the post-fission stage correspond with the two tangible
continuant persons that exist prior to the procedure. In
Fusion-Fission, however, there are no such tangible continuant
persons that the continuant persons occupying S3 can be related to
and, indeed, nor can there ever be. To explain, in the example
provided above, C1 and C3 have always occupied stages that
have been occupied by at least one other continuant person.
Furthermore, from t3 onwards, these continuant persons are
inextricably fused with one another. As such, at no
point in their existence (pre- or post- Fusion-Fission) can C1 or C3
ever take the form of a distinct, tangible continuant person.
Consequently, the plausibility that was lent to Lewis's
interpretation of Fission and Fusion (when run as distinct processes)
by the tangibility of the continuant persons involved (at some point
in time) is removed: S3 is a person stage of two continuant persons
who have never truly existed as persons (only as composite parts in a
number of person stages). The direct implication of this is that the
additional, inextricable continuant person that supposedly shares S3
seems like a theoretical posit, placed there by Lewis in order to
sustain his position. 

 5 Conclusion

The problem with the above is that it must surely strike us that
these posited continuant persons are akin, in their nature, to the
'separately existing entities' posited by Non-Reductionists.
Recalling Parfit's argument for Reductionism (which Lewis's argument
gives us no reason to doubt), the problem with these posits (both the
Non-Reductionist's and, by implication, Lewis's) is that we have no
reason to believe in their existence. Thus, without a concrete
reason to believe in the potential for inextricable, non-tangible
continuant persons, it seems that, following Parfit's argument, we
should reject this belief. However, without this, the Lewisian line
of reply to the case of Fusion-Fission collapses. To restate Lewis's
conclusion, Parfit's distinction does not require the further premise
'that partial overlap of continuant persons is impossible'. In fact,
all that is required is the further premise that complete and
inextricable overlap of continuant persons is implausible. As should
be clear from the above, this latter premise should be easy to
accept. Furthermore, once we accept it, the case of Fusion-Fission
clearly demonstrates the failure of the I-relation to be coextensive
with the R-relation. Thus, the 'logical wedge' between identity/ the
I-relation and the R-relation is restored.


1. Such as Cartesian Egos.

2. Parfit 1987: 224.

3. Where the R-relation is defined as 'psychological connectedness
and/ or continuity, with the right kind of cause' and, according to
Parfit, 'the right kind of cause' can be any cause. 

4. This term is deliberately ambiguous in relation to the number of
persons present at each stage, as it is precisely this issue that
represents the crux of the debate upon which this paper hinges.

5. The lack of R-relatedness of the two successor beings is due to
there being no causal link /dependence between their psychological

6. Although it should be noted that Parfit has reservations regarding
this answer as well.

7. Lewis 1983: 148.

8. Measor 1980: 406.

9. Lazaroiu 2007: 214.

10. Lewis 1983: 149.

11. It is worth noting that the same logic can be applied to the case
of Fusion.

12. Lewis 1983: 151.

13. It is noteworthy that Parfit described a similar scenario in his
discussion of an imaginary group of people who reproduce via fusion
and fission, although this scenario was not utilised in the above

14. It is worthwhile to note that the number of 'fusings' will
correspond with the number of future branches.


Belzer, M. (2005), 'Self-Conception and Personal Identity: Revisiting
Parfit and Lewis with an Eye on the Grip of the Unity Reaction',
Social Philosophy and Policy, Vol. 22, No. 2, pp.126-164.

Brueckner, A. (1993), 'Parfit on What Matters in Survival',
Philosophical Studies, Vol. 70, No. 1, pp.1-22.

Ehring, D. (1995), 'Personal Identity and the R-relation:
Reconciliation through Cohabitation?', Australasian Journal of
Philosophy, Vol. 73, No. 3, pp.337-346.

Lazaroiu, A. (2007), 'Multiple Occupancy, Identity, and What
Matters', Philosophical Explorations, Vol. 10, No. 3,

Lewis, D. (1983), 'Survival and Identity', in Martin, R. & Barresi,
J. (eds.) (2003), Personal Identity, Oxford: Blackwell,

Maddy, P. (1979), 'Is the Importance of Identity Derivative?',
Philosophical Studies, Vol. 35, No. 2, pp.151-170.

Measor, N. (1980), 'On What Matters in Survival', Mind, Vol.
89, No. 355, pp.406-411.

Parfit, D. (1987), Reasons and Persons, Oxford: Oxford
University Press.

Roberts, M. (1983), 'Lewis's Theory of Personal Identity',
Australasian Journal of Philosophy, Vol. 61, No. 1, pp.58-67.

(c) Oliver Gill 2011

E-mail: gill_oliver@hotmail.com



Almost every theory of causality is closely connected with time. Some
analyse the causal relation presupposing the existence of temporal
precedence. In that case the definition of causation usually includes
the notion of time when it establishes that the cause must always
precede the effect or that, at least, the effect cannot precede the
cause. The supporter of such analysis must also accept that the
causal relation depends on time and thus, that causality is not as
simple as it seems.

Other theories, on the other hand, base the concept of time on
causal grounds, which is a simplification of the causal relation,
since they do not need the precedence notion in order to define
causation. But those theories, I think, often suffer explanation
loops or describe the notion of time better than the notion of

There is also the issue about whether spacetime precedes
causation or whether they coexist, although I am not sure if there
exists any account that, after introducing the causal relata to work
with, does not already presuppose the notion of space in order
to define causality. Causal theories of time, like the one developed
by Tooley [6], must have primarily the notion of space -- even if
they do not say it explicitly -- to establish that our notion of time
is based on our notion of causality.

The other type of theories cannot take it easier. They must also
presuppose the notion of space if they define causation using
temporal precedence; I do not think that causality based on pure
absolute time could make it any better. Perhaps, it should be asked
whether those theories understand space and time as independent
notions or whether they pose them as a spacetime continuum.
Nevertheless, that would be no longer an analysis of the causal
relation, but of the metaphysics of spacetime. Thus, I am sure that
the causal relation must be analysed in terms of spatial relations.

What is not so clear is whether causation does not need any other
notions in order to be defined and that is precisely my goal here. I
will briefly show a first general basis of how a serious analysis of
causality could be developed by avoiding the previous use of temporal
precedence and by assuming that space is the only fundamental notion
we need to define it. It must be noticed, however, that such
assumptions do not correspond to a merely physical, but to an
ontological notion of causality.


A good place to start at is a mereological theory of
causality, although similar ideas can also be expressed in
topological terms based on a system of betweenness, as the one
established by Grünbaum [1]. Such view is partly compatible with what
follows and the details of that compatibility might be a very
motivating topic.

Nevertheless, I will focus particularly on mereology. The account
proposed by Koons [2] takes facts as causal relata and is
based on the parthood relation to define causation. I would
rather prefer regions as causal relata, instead of facts or
situations, which better suits my time aversion. My proposal has some
differences compared with Koons', but it is ultimately grounded on his
account. It goes like this. Suppose that the world is just a big
region of space and every part of the world is also a region. The
parthood relation is defined in terms of intersection, such
that a is a part of b just in case every region that intersects a
also intersects b. It is also reflexive, i.e. every region can
always be part of itself, but whenever two regions are part of each
other, then both are the same region. This last consequence asserts
that parthood is antisymmetric.

It should also be assumed that effects are not part of their causes
-- considering that they are total sufficient causes, i.e. they
include every factor, even if it is indirect or irrelevant --  and if
the effect of a determined cause has a part, then that part is also an
effect of the same cause. It follows immediately that cause and effect
do not overlap. For some part of the cause would also be part of the
effect. Now that part must also be an effect of the cause under
analysis but it would lead to nonsense, since, as we have
established, effects cannot be part of their causes. This is a very
interesting consequence, because it says that causal relata are not
only regions, but also separated ones, which suggests that
they must be regions of the same kind. However, that is not going to
be a topic here.

Until now I have given only some characteristics of the causal
relation, but we have not defined it yet. A definition of the causal
relation can be based on Mackie's account on causation [4]. A cause,
in the sense Mackie defines it, is a necessary part of an unnecessary
but sufficient condition (INUS). Thus, a necessary cause is understood
as a part of a total sufficient cause and, since for total causal
regions holds that they do not overlap with their effects, that also
holds for INUS causes.

In order to avoid some unwanted consequences shared by many accounts
that use sufficient conditions to define causality, we might
introduce a counterfactual to the analysis. If one tries to
understand how it is possible for the total cause to be sufficient
for the effect, one can notice that it actually is not, unless we
include some regularity or law that permits one to derive the
proposition that describes the effect from the set of sufficient
conditions (i.e. the set of propositions that describe the set of
sufficient causes). Well, that introduces the danger of backward
causation, as Lewis warned [3], because the proposition describing
the cause can also be entailed by the effect, together with the laws
and the remaining part of the conditions. One solution against
backward causation is given, of course, by theories that presuppose
the temporal precedence of the cause, a feature that cannot be
present in a theory of causality based on spatial relations, like the
one I am sketching here.

Counterfactual accounts of causation have been able to manage these
problems nicely, since the counterfactual relation itself is not
symmetric. The common counterfactual definition of causality
establishes that a causes b if and only if the following three
conditions are satisfied: a and b occur; if a were the case, then b
would be the case; and if a had not been the case, then b would not
have been the case. This definition solves the problem of backward
causation, because it is not true that if b were not the case, then a
would not be the case.

Nevertheless, many inconveniences come together with the
counterfactual solution, like preemption problems. But these
situations can show that regularity theories of causation are also in
trouble. A good account of causation must be capable of tackling
preemption problems in a simple way and I am going to show that if
the causal relation is based only on spatial grounds, such a way is
at hand. But let me first describe what these problematic situations


Preemption problems could be defined as follows. There is a rich
distinction between early preemption, late preemption and preemption
with trumping, but I will focus only on a general version, which may
include the first two. There are two possible causes for an effect to
occur and the actual cause interrupts the second, potential cause,
making it impossible for it to produce the effect. Modal notions like
'possible' and 'actual' involved in this definition will be set aside
later; we need them for the moment in order to describe the problem.
Firstly, a problem arises immediately for counterfactual theories of
causality, since it is not true that if the cause were not the case,
then the effect would not be the case. The backup cause is waiting
and would produce the effect after the first cause fails. In other
words, as the definition does not detect the cause, we have too
few causes (none actually).

Secondly, an opposite problem arises for regularity theories of
causality. The definition detects the cause rightly; the cause is a
necessary part of a sufficient total cause of the effect. But what
happens if we replace the first cause with the backup, putting it
among the same set of conditions? In that case the effect should also
follow, meaning that the back up cause is also the cause. In short, we
have too many causes now. Neither of both accounts can solve this
problem in a simple way.

On the one side, regularity accounts must introduce more detailed
propositions into the conditions. On the other side, counterfactual
accounts must either accept fragility, i.e. a higher standard
for the definition of the essence of causal relata, or introduce some
suspicious causality transporting entity --  a moving influx
perhaps -- between the causal relata.

If we accept high standards for essences, i.e. if we think that what
it is to be a state of affairs depends on, say, every millisecond and
every detail, then we have to accept spurious causes in other common
cases, which won't be useful for a more general theory of causality.
Besides, introducing fragility grounds causation on temporal blocks,
which is not the aim here. The other kind of solution for the
counterfactual analysis introduces an influx, an entity that is not
acceptable in more simple theories of causation, since they permit
cause and effect to overlap. The best solution for preemption lies, I
think, in some kind of unification between regularity and
counterfactuals. That seems to be a tendency these days.

Let us see how preemption could look like in an example based only on
regions as causal relata. This is not easy at all. For temporal
notions -- e.g. interruption -- are already present in the preemption
problem. I will first say a few things about regions. Suppose that we
represent the world in a two dimensional manner, with a temporal axis
and a spatial axis and every event is represented, as usually, by a
point in the graphic. If one looks only at the spatial axis, for
every point in it, one can construct a line that is parallel to the
temporal axis and that contains every state of affairs, everything
that occurs, occurred and will occur in that region.

That is the sense of region I consider for the spatial approach of
causality. The only thing to do is to eliminate from the world the
temporal axis and what remains are the regions of the world, charged
with everything that occurs in them. This model of the world, which
is only based on spatial regions, has the form of a Leibnizean
preestablished harmony. Every point, as well as every segment
of the spaceline, is a region, assuming that every point contains a
perpendicular line of intemporal states of affairs, which can also be
divided vertically in many regions of the same sort.

The preemptive problem poses then that there are two regions that
might cause a third. The small region that actually causes the effect
does not overlap with the region of the effect, as we defined earlier.
The potential cause does neither overlap with it, but it would be
necessary in different sets of regions for the production of the same
effect. In this sense of necessitation, the actual cause does not
overlap with the back up, which means that preemptive cases relate
three different non overlapping regions of space.

The problem arises when the notion of cause in consideration is
related to the one of necessary condition. In the regularity account,
the result is that too many causes are pointed out, but that is not
the case if one considers the notion of total sufficient cause. The
small cause is just one member of the set of regions that should be
there in order to produce the effect. Total causes are big regions
and counterfactual causes are small ones.

If the solution of the preemption problem can be met after
understanding the crucial alliance between regularity theories of
causation and counterfactual theories of causation, then it is also a
task -- in the context of a spatial account of causality -- to
understand the affinities between the total cause and the regions
that conform it. If total causation is understood in terms of
production and partial or counterfactual causation in terms of
dependence, as Pearl does [5], then causation is definable in a
manner that builds up the partial region and permits to make it
sufficient for its effect.

Thus, the part of the counterfactual definition for causation we must
focus on to understand the affinity between both accounts is the
second condition, i.e. if the cause were the case, then the effect
would be the case. The difficulty arises when one wants to make that
counterfactual true without first having the actual occurrence of the
causal relata (the first condition).

A hypothesis posed by Koons [2] should give us some light on this
point. Consider that if two regions are total causes of the same
event and none of them causes the other, then there exists a
mereological intersection of both that totally causes the effect.
This is called the no overdetermination hypothesis and, since
preemption is one kind of overdetermination, it could be very helpful
for our purposes. It establishes, in other words, that if one region
is produced by two sufficient causes (i.e. if it is overdetermined),
then these two causes are not really sufficient by themselves, but
only their intersection is. This suggests that total causes are
composed by regions that are smaller than one usually thinks, even
outside overdetermination.

But what might this smaller region be? In many cases it is enough to
think that if the causal region had been different, then the region
of the effect would have also been different. But that is not always
the case. I would say that those small differences come from other,
perhaps more distant regions. After all, as neither temporal
precedence nor temporal vicinity are needed for the ideas I present
here, a cause must not be strictly composed of regions that are in a
relation of connectedness to each other. Some regions across the
whole pure space represent a pattern that meets other bigger regions.
Thus, when a particular cause takes place and produces the effect, its
causal region shares parts with other regions in the whole spaceline.

Those extremely small mereological intersections could give us a hint
about the above mentioned laws of nature. But that is another topic,
though it is analysable under a theory purely based on spatial
relations, a theory that can surely be more elaborated than what I
have explored here.


1. Grünbaum, Adolf. (1970). 'Space, Time and Falsifiability'.
Philosophy of Science, 37: 469–588.

2. Koons, Robert. (1999). 'Situation Mereology and the Logic of
Causation'. Topoi, 18: 167–74.

3. Lewis, David. (1973). 'Causation'. Journal of Philosophy,
70: 556–67.

4. Mackie, John. (1980). The Cement of the Universe. Oxford
University Press.

5. Pearl, Judea. (2000). Causality. Cambridge University

6. Tooley, Michael. (1997). Time, Tense, and Causation.
Oxford University Press.

(c) Esteban Céspedes 2011

E-mail: e.cespedes@stud.uni-frankfurt.de

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