PHILOSOPHY PATHWAYS Issue 162

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

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.

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 assertion:

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 falsehood.

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.

II. 'PARFIT, LEWIS AND THE LOGICAL WEDGE: FUSION-FISSION'S CHALLENGE TO COEXTENSION' BY OLIVER GILL

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.

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:

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.

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 persons'[10].

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 procedure.

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' disappears.

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)
                  |                  |
                  |                  |
                  |                  |
                  |                  |
                        FISSION
                            |
                            |
                            |
             ---------------------------- t2
                            |
                            |
                            |
                         FUSION
                  |                  |
                  |                  |
                  |                  |
                  |                  |
             ---------------------------- 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.

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.

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 states.

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

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

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 context.

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, pp.211-225.

Lewis, D. (1983), 'Survival and Identity', in Martin, R. & Barresi, J. (eds.) (2003), Personal Identity, Oxford: Blackwell, pp.144-167.

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.

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

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 causality.

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 are.

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.

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

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