1 Introduction

Braddon-Mitchell and Miller (2020) put forward a strong metaphysical thesis to the effect that the relation of being-the-same-person (hereafter referred to as the “SP-relation”) is not an all-or-nothing relation, but rather one that is gradable—i.e. capable of obtaining to varying degrees. (This thesis will hereafter itself be referred to as the “SP-thesis”.) For example, it could be that in 2019 you, the reader, were one-third who you are now, and two-thirds someone else. To justify this thesis, they propose inter alia a thought experiment in which a hypothetical miner, Freddie, must choose between risking getting lost in a mine and the utility-value of his work. They assume that he can make backups of himself which will capture his entire physical and mental state, and that he can be rebooted or reincarnated from these. He can therefore execute a backup of himself today that will be reincarnated 6 months from now. Intuition suggests that if he were to create such backups every day, he would tend to be more at risk of losing his life at work than if the backups were made, say, once every six months. If he died in an accident at noon one day, he would already be able to be revived that evening, because he would have a backup of himself from the morning of that same day. Hence, the frequency of the backing up will affect his inclination towards risk-taking. If a copy were made once every 6 months, Freddie would no longer be so willing to take risks because he could, as it were, lose up to half a year of his life, given the fact of the backups having been performed so infrequently. Braddon-Mitchell and Miller argue that the best explanation for this risk-taking tendency is to postulate the graded character of the SP-relation. Why? Because Freddie, when he is to be resurrected from a copy already 6 months old, will feel that he is not resurrecting himself in his entirety, but only to some degree.

The present article consists of a part that is critical, in which we reject the model of Braddon-Mitchell and Miller, and then a constructive one, in which we present Lewin’s model of persons and seek to explain in a quite different way the regularities that Braddon-Mitchell and Miller have pointed to. Thus, we both reject the SP-thesis and set out to question the justification given by them. We hope to show that their proposed model of persons (which we shall refer to as the “BMM-model”, after the authors’ abbreviated names) is irrelevant and inadequate, and thus amounts to no more than a caricature of personhood. Its irrelevance, we argue, consists in the fact that the person envisaged in the BMM-model does not have much in common with any actual living persons—something which, at the level of ideas, corresponds to the fact that the contents of our idea of persons, and the notion of a person internal to the BMM-model, diverge (cf. Wójtowicz & Skowron, 2022). Its inadequacy, meanwhile, lies in the fact that the content of the BMM-model is not grounded in any intuitions about personhood. In addition, the model generates unacceptable theoretical consequences and methodological assumptions, which even contradict the theses and intentions proclaimed by its authors themselves. The latter have, moreover, smuggled into it some hidden yet significant ontological assumptions about the mode of existence of persons. We set out to show that the intentional mode of existence of persons represents just such an implicit assumption made within the context of the BMM-model. As a matter of fact, this mode of existence was discerned and explored by Roman Ingarden in his phenomenological ontology. Braddon-Mitchell and Miller, we argue, have in essence assumed that persons exist in a similar way to virtual objects—objects, that is, that because of their intentional mode of existence can be copied and rebooted.

Another example of such hidden assumptions is to be found in the highly simplified and counter-intuitive extensional topological structure of persons that results from the BMM-model. In our paper, we present what we take to be Kurt Lewin’s more realistic descriptive account of this. By juxtaposing the two approaches, what the BMM-model omits and why it represents an extreme simplification—and even a caricature—of the structure of persons are made clear. We also point out that the linear and point-based conception of time adopted in the BMM-model is neither tenable nor suited to modelling processes unfolding in time, including consciousness. In our view, a model of persons that does not describe consciousness correctly can hardly be said to be tenable.

We also argue that some sort of holistic vision of persons, their structure, and that of their environment, is called for. Only in such a context can the actual being-the-same-person relation underlying notions of personal identity be properly explored. Such a vision was presented by Lewin (1936), in the form of his topological-dynamic view of persons. A certain topological structure for persons is assumed in the BMM-model—one which we duly seek to reconstruct. Nevertheless, we point out that this structure is inadequate. In fact, Lewin’s topological model supports our assertion that the BMM-model is irrelevant, and that the explanations furnished in the context of that model are ineffective, to say the least. We ourselves claim that the characterisation of persons in terms of the notion of dimension, which Lewin introduced and studied, provides an adequate—and thus superior—explanation of their structure than does the SP-thesis.

Braddon-Mitchell and Miller, proceeding as they do with some measure of caution, cleverly weaken the SP-thesis by according it the status not of a metaphysical thesis but of being the best explanation for a certain regularity as regards risk-taking. However, taking Lewin’s theory as a basis we ourselves seek to show, on the one hand, that Freddie is more likely to go down the mine when his backups are made more often because Freddie is a multidimensional person—that is, one who, within his dynamic energy system, distinguishes degrees of unreality. Here the thought is that within ever higher dimensions, Freddie himself represents successive copies of himself and compares them with the copy from the first dimension. This comparison with the dimension of the most real may lead him to take more or fewer risks. These are not successive copies of himself that are less and less him, but rather increasingly intentional and fused representations of himself occurring in different dimensions of his personal space. At the same time, on the other hand, we reason that the thesis of the graded nature of the SP-relation follows directly from the defining features of the notion of a backup as deployed in the BMM-model, and that the whole fine-grained “thought experiment” is simply unnecessary. The authors of the BMM-model thus find themselves caught up in a kind of vicious circle of proof, as they only demonstrate something they themselves have assumed.

Many theorists are inclined to assume that particular factors responsible for determining the SP-relation are gradable: for example, they may hold that psychical similarity is gradable, even if the SP-relation itself is not so. However, there have also been authors who accept the gradability of the SP-relation itself: Derek Parfit, referring back to Hume, was already propounding such a thesis, as has Peter Unger.Footnote 1 Nevertheless, Braddon-Mitchell and Miller, wishing to furnish a new argument for it, have proposed a novel model of persons intended to underpin the explanation of the SP-thesis. In refusing to embrace this model, we are also rejecting their new argument for the SP-thesis itself.

In Sect. 2, we present the BMM-model in detail. Then, in Sect. 3, we introduce the basic concepts of Roman Ingarden’s existential ontology, and seek to reconstruct the BMM-model of persons within the terms of the latter. We demonstrate that within that model persons are held to exist intentionally. The BMM-model is, therefore, not ontologically neutral, and even contains—on the contrary—certain robust existential-ontological assumptions. In this section, we also point out what we regard as the methodological weaknesses of the BMM-model. In Sect. 4, we then provide several further arguments for rejecting the BMM-model, appealing to both ontological and empirical considerations as furnishing justifications for these. That section also includes a critical discussion of the so-called “desire-first” views invoked by the authors. Section 5 presents Kurt Lewin’s topological-dynamic model of persons. We show that in respect of both persons and the life space, it is dimension that is responsible for decision-making tendencies that pertain to risk-taking. We also show that the holistic construal of persons present in Lewin’s model captures the totality of a person’s ontological situation, in contrast to the reductive character of the BMM-model.

2 The SP-thesis of Braddon-Mitchell and Miller

Braddon-Mitchell and Miller (2020, p. 3806) argue that “the same person relation (henceforth SP-relation) comes in degrees; so for example Annie at t1 might be the same person as Annie at t7 to some degree other than 0 or 1”. Whether we are the same person or not can be measured on a scale from 0 to 1. The most common answer when asked whether I am the same person I was yesterday is “yes” or “no”. However, these two authors opt to enlarge the set of possible answers: I can respond, for example, by saying that today I am half the same person as yesterday, and half a different one. Being the same person is not an all-or-nothing question: on the contrary, it is gradable—i.e. something that comes in degrees.

Defending the SP-thesis turns out to be no easy task. Hence, Braddon-Mitchell and Miller proceed with considerable caution, introducing many constraints and subtle qualifications with regard to their thesis.Footnote 2 Of these, we shall list those we consider most important. First, the SP-relation does not obtain between persons, but between person-phases: it is not persons that are the relata of the relation, but certain stages of a person at points in time. Hence, the sameness that is supposed to be gradable should hold between some pair of such person-phases. Secondly, they concede that “psychological continuity”, “bodily continuity”, and “similarity of life goals” do themselves occur in degrees, and that these relations have an effect on the SP-relation. Nevertheless, this is not what is novel in their approach: “The novelty in our view is that we argue that the SP-relation inherits the gradedness of the contributory factors more or less directly” (Braddon-Mitchell & Miller, 2020, p. 3807). Thirdly, they regard their proposal as “metaphysically parsimonious”, meaning that they assume a desire-first approach, which is defined in opposition to a metaphysics-first one. Roughly speaking, the idea is that metaphysics-first views assume the existence of facts pertinent to the SP-relation that are primary—albeit in an unspecified sense. These primary facts would determine the SP-relation, which would be reducible to them, also in an unspecified sense. Candidates for such primary facts could be those mentioned above: for instance, “psychological continuity” or “bodily continuity”. Nevertheless, the authors are unwilling to adopt a metaphysics-first view, and instead adopt a desire-first one, which means that “the conative states of person-phases are the best (and only) contender to settle between which person-phases the SP-relation obtains” (p. 3820). These conative states are a set of desires to extend oneself: in particular, to look forward with the hope of preserving one’s identity, and to look back to the past with the hope of possessing one’s origin. And it is these desires that come first in the order of explanation: through them they can explain the SP-relation, and not the other way around.

The principal rationale put forward in support of the SP-thesis is that “it makes sense of the kinds of decisions we might make” (Braddon-Mitchell & Miller, 2020, p. 3807). More specifically, when making decisions involving some reward on the one hand and the risk of losing one’s life on the other, it makes sense—and is even necessary—to talk about the gradability of the SP-relation. However, to furnish us with a concrete example of such a decision-making process, Braddon-Mitchell and Miller put forward a certain thought experiment that, in our view, constitutes the core of their main argument. Let us describe this experiment in the authors’ own words:

Suppose it is possible to ‘backup’ the minds of person-phases. Perhaps backups might work like this: the mind of the person-phase is scanned at some time, and a ‘copy’ of all the person-phase’s mental and physical properties is kept on file: that is, sufficient information is retained to allow a machine to create a qualitative duplicate of those mental states and physical properties. Call this copy a backup. There is no question of the backup itself being conscious in the format in which it is stored. Backups only become conscious when they are activated, and we will suppose that this is only done when a new body is created which is a physical and mental duplicate of the person-phase thus backed up. We call the resulting entity an embodied backup. Embodied backups are only created after the person-phase that was backed up, or some later person-phase that bears the SP-relation to that person phase, has been destroyed. Only once there is bodily death of the person-phase backed up, or of some person-phase that is SP-related to that backed-up person-phase, does an embodied backup go live. We call this process rebooting (Braddon-Mitchell & Miller, 2020, pp. 3808–3809).

What they propose is that we consider a miner, Freddie, who on a daily basis incurs some risk of losing his life when he descends into the mine shaft. Nevertheless, his company backs up his backup every day, so that in the event of his death he can be reborn from that backup. Freddie then willingly takes on the risk associated with working in the mine. If he were to die in an accident in the evening, he would be reborn the same as he was the morning before work, when his backup was made. However, if it turned out that the company, due to budget cuts, only performed a backup once every 6 months, Freddie would no longer be so willing to take such risks. After all, were he to be reborn 6 months after the backup, he would lose that six months of life: his embodied backup would no longer entirely be him. He would, the authors argue, be him, but to a lesser extent: for example, he would be half Freddie and half someone else. Therefore, the significance of the risk involved in going down into the mine depends on how often the backup is performed. The longer the intervals between backups, the smaller the inclination of miners will be to put themselves at risk. This regularity, according to the authors, is best explained by the SP-thesis. At the same time, the fact of its being the best explanation is the decisive element in the authors’ argumentation for that thesis.

Below, we embark on a discussion about whether the SP-thesis really offers the best explanation of the dependence of the willingness to take risks on the regularity of backups, setting out what is, in our opinion, a better and more realistic conception. Nonetheless, it is not simply a matter of explaining some fact(s) or other—rather, it is one of adequately knowing what a person is. Therefore, being ourselves keenly interested in the regularities of human behaviour, we shall, in Sect. 5 below, draw attention to what we consider is the much more plausible explanation of the phenomenon of the propensity for risk-taking contained in Lewin’s topological model of persons. The proposed model of Braddon-Mitchell and Miller is motivated by the thought that any of us would make similar decisions if we were in the same circumstances. Of course, as the authors point out, not everyone will necessarily make the same decisions, but rational agents would probably behave in the way that Freddie does. As they even more emphatically put it, “What we hope is that when you read these cases, you think: yes, I can imagine someone not that unlike me, responding in this way” (Braddon-Mitchell & Miller, 2020, p. 3808). The authors therefore trust that we ourselves would behave like the agents in their model.

It should be noted that the main line of argumentation of Braddon-Mitchell and Miller runs as follows: they put forward an overtly metaphysical thesis—which is just what the SP-thesis is—only to deny its metaphysical character, supposedly finding support for this in the argument that the thesis is no more than a pragmatic inference to the best explanation of the behaviour of agents in the model. At the same time, evidence that, for the authors themselves, this thesis is in fact metaphysical is furnished in the form of the overall consequences of their thesis for how we should conceive of persons, their duration in time, and even their moral responsibility—as invoked in the conclusion of their article. These broad implications lead them to believe that “the graded nature of the SP-relation is in fact central to our experience of personhood” (2020, p. 3831). Thus, it is not just a matter of explanation, but of being a person. It concerns what a person is, what constitutes a person, and what makes a person just that and not something else. In short, what Braddon-Mitchell and Miller are engaged in is a vigorous—albeit unconscious—cultivation of a full-blooded reductionist metaphysics of persons, even as they perversely adhere to a state of apparent metaphysical neutrality.

3 The ontological reconstruction of personhood within the BMM-model

3.1 Viewing the model in ontological and topological terms

At first glance, the BMM-model looks like an impartial and innocent theoretical construct. On the one hand, it is only intended to serve as an entirely non-committal thought experiment, but on the other, its authors seek to establish its relevance to the experience of personhood. Thus, it is not just a fictive supposition or conceptual plaything.Footnote 3 Let us therefore try to reconstruct the image of persons implicit in the BBM-model. Proceeding just like its authors with exaggerated caution, we will try to anticipate any possible criticisms by saying that when we talk about the BMM-model, we have in mind our reconstruction of it: that is, our interpretation and reconstruction of what it implicitly supposes to be the case. We are thus able to forestall accusations to the effect that the authors in fact constructed it differently by simply stipulating various features. Indeed, from our perspective the authors’ own caution in this regard is precisely one of the sources of the shortcomings affecting their model.

While Braddon-Mitchell and Miller point out some consequences of their model, we would nevertheless like to draw attention to certain other significant implications—ones perhaps not always so desirable from the authors’ own point of view. Firstly, Freddie is potentially immortal: he can, after all, save his copy every time he turns 40, and when he turns 80, commit suicide and reincarnate as a 40-year-old. If we abandon the assumption that he can only be reincarnated when the currently living copy dies, he can lead countless parallel lives: he could, for example, generate a copy every day and immediately embody that copy. After n days, there would already be at least \({2}^{n}\) Freddies (more-or-less the same as the initial one). Thirdly, a backup is only possible if one assumes that whatever constitutes the person can be frozen: i.e. fixed on some storage medium, and therefore in a “zero–one” manner. We are thus given the image of an immortal person who can re-generate himself (which is tantamount to a certain version of resurrection), live countless lives in parallel, be fixed on a digital medium, and be embodied at any time. The picture of a person that emerges is, then, somewhat frightening: perhaps none of the traditional metaphysical accounts of the soul could be said to be so rich. Even theories of reincarnation and the migration of souls did not allow for so much arbitrariness. Even the gods were not granted so many predispositions.

How is it that the BMM-model can be so far-reaching and so “rich”? It is because Braddon-Mitchell and Miller, contrary to their intentions, have implicitly smuggled some very strong ontological theses into their model. More precisely, the BMM-model is so “rich” because the persons in it exist in a specific manner: i.e. in an intentional way (in a specific ontological sense, which we will explain in due course). If there were no implicit ontological assumptions, it would not be so “rich”, and Freddie’s life would be much closer to ours or anyone else’s. However, before we define intentional objects, we must introduce some basic concepts of Roman Ingarden’s ontology. (This is something we shall address in Subsection 3.3 below.)

In addition to the intentional mode of existence it presupposes, our aim is to reconstruct the implicit topological-ontological assumptions of the BMM-model. The authors themselves indicate that what comes closest to their own considerations is the position known as exdurantism (cf., e.g., p. 3806). However, they consider their conception ontologically neutral, and thus independent of both exdurantism and perdurantism. What is it like in reality? Let us consider a copy of Freddie at some time t1 (or, as the BMM-model authors call it, a copy of phase p1). The authors point out that this copy, at the moment of execution, is completely—or almost completely—identical to Freddie’s actual person (the phase of his person at time t1). Over time, Freddie experiences a whole series of further life situations, changing him physically and mentally—passing, in other words, through successive phases that are no longer encoded and stored in the “frozen” copy at time t1. Here, two major variants are possible:

  1. (1)

    The copy at time t1 is identical to the whole of Freddie at time t1 (i.e. his phase at t1), and thus contains the same information, including his unconscious or forgotten information concerning his body, as the actual Freddie. We additionally assume that the copy also contains information concerning Freddie’s personality-related psychical structure. One further minor sub-version is also possible in this respect:

  2. (1A)

    The copy at time t1 contains information pertaining to his personality-related and consciousness-related features. Still, it is identical to the whole of Freddie’s life “heritage” also in respect of this psychical part: i.e. it contains encoded information about all previous phases in respect of their mental (psychical) as well as their physical (bodily) parts.

  3. (2)

    The second major variant, meanwhile, refers to the situation where the copy at time t1 in the mental part contains only information about Freddie’s life and personality that he was aware of at time t1, and that defined his sense of personal identity at time t1, but—as above—full information concerning his body. This means that the actual Freddie may have forgotten a whole range of situations—for example, from his childhood—and only those experiences, memories and situations that he remembers or can recall at time t1, and that define his actual sense of his personal identity at that moment, are copied.

The situation corresponding to variant (1) is hinted at by the authors, in that they speak of the copy containing “all the person phases, mental and physical properties”. However, they immediately follow this up by laconically suggesting in their article that the embodiment and rebooting of the copy occurs in some body other than Freddie’s—which, after all, may have been completely destroyed in a mining accident (cf. pp. 3808-9). What remains unexplained is how they come by such a body, whether Freddie would feel sufficiently himself in another body, and whether he would recognise his copy at time t1 as being identical to himself. Another possibility might be to make a copy of the body using some kind of “bodily 3D printer” (why not?), or grow a new one in a laboratory. In this case, it seems that the notion of the “bodily structure” stored in the copy refers to the recording of this structure (genotype, cell distribution, neural structure, body shape, facial features, etc.) in such a way that it can be physically reproduced and, in addition, contains a copy of the conscious experiences related to Freddie’s possession of the body. What remains unexplained is why Freddie is prepared to treat his copy as—to some extent—himself when, after the reboot, we are dealing with two numerically different and unrelated individuals. What Freddie feels after making a copy is, after all, unknown to his rebooted copy, and vice versa. When Freddie hurts in some way, his copy knows nothing about it. No one would recognise this other, completely separate and independent individual as themselves; rather, they would only regard them as some other numerically distinct individual, more or less similar to the initial one but by no means actually being them. Destroying one of the copies belonging to this pair changes nothing in this respect: either we destroy the rebooted copy or we destroy Freddie, and it is not the case that Freddie (or anyone else in their right mind) is all that bothered about what specifically is destroyed.

In the case of sub-variant (1A), and assuming what we have just said about the copy of Freddie’s corporeal part, it must be held that each successive total (i.e. corporeal and mental) copy contains within it each previous total copy, and that Freddie’s personality at any given moment is identical to his entire actual personality (or, as the authors also write, his mind). Moreover, Freddie’s actual personality will contain every significantly less rich previous copy as a proper subset of sorts. Thus, where Freddie’s bodily structure is concerned, each successive copy contains information amounting only to a record of all the properties of his body at the time the previous copy was made, with any changes in bodily structure noted or added, together with a record of those changes. By contrast, in the part relating to his psyche, Freddie’s original personality differs from each successive copy only extensionally, by virtue of new experiences and the influence of the situations experienced on its conscious or unconscious registering of them. (For instance, the authors talk about “memories” contained in person-phases; see p. 3809.) Thus, copies of the bodily part contain one another in that later ones contain earlier ones, while the same holds true for copies of the mental part, as these also contain one another inasmuch as earlier ones are subsets of later ones. Thus, we obtain a discrete topology of the family of proper subsets of a given set, in which there is a first and a last element. This model of what a person is may be considered compatible, indeed, with both perdurantism and exdurantism, although perdurantism seems like a more natural context for it.

In this scenario, for obvious reasons, no copy of Freddie indexed in a linear fashion to this or that point in time will be identical to any earlier copy, by definition, and because each of these copies is identical to Freddie’s actual personality (or mind) and bodily structure at a given moment, they are only to some extent identical to Freddie at a later moment—i.e. to his later phases. No thought experiment concerning financial gratification, as broadly described by the authors of the BMM-model, is necessary to demonstrate the thesis of the gradability of the SP-relation that is supposed to occur between Freddie’s phases (corresponding to his copies) at different moments, as these phases are by definition identical to (or rather “the same as”) Freddie at the moment of making these copies. In the present instance, then, the object we are dealing with can be regarded as the extensional sum, in the sense of set theory, of the phases of the continuum of its successive sections.

Where variant (2) is concerned, we may refer to the copy in question as a “psychical copy” of Freddie. In this case, copies of Freddie’s psyche may intersect extensively in terms of their content or, in an extreme case, even be disjoint—as with, for example, a copy made in infancy and one created in old age. The idea is that the actual Freddie may, at any given moment, have lost some of his experiences (“memories”), forgotten many things, etc. Similarly, it can be assumed that the copy of the bodily part only contains information about Freddie’s current bodily structure, and that it is impossible to reconstruct from this, say, the state of his body as a child. Suppose one identifies—as the authors do—such a copy at time t1 with Freddie’s actual person (or the corresponding phase thereof). In that case, the subsequent copy at time t2 > t1 may, if they are not too far apart in time, intersect as regards content with, or contain, the copy at time t1—and, in the extreme case, they also may be disjoint (or “almost” disjoint). Thus, we again get a certain extensional topological structure of partially ordered sets. As before, each copy is only partially identical to each subsequent copy of Freddie. So, once more, the SP-relation must be graded, given the definition of what a section (copy, backup, phase, etc.) is and the conventional identification of this phase with the real Freddie. Again, the conception in question is compatible with both perdurantism and exdurantism, though this time the more natural context is furnished by exdurantism. So it seems that the latter version is the closest to the intentions of the authors of the BMM-model.

In all three cases, Braddon-Mitchell and Miller tacitly assume that only something that does not change can be identical to itself in a “zero–one” way. Moreover, the aforementioned extensionality of the models is based on the tacit assumption of Russell’s theory of descriptions, which boils down to the fact that a given object (or concept) is a certain bundle (extensionally conceived set) of characteristics or properties, devoid of internal structure. There is no distinction between essential and accidental properties, and no structure or hierarchy of superior and inferior features: instead, each feature is equally important and on a par with others when it comes to contributing to the determination of the object in question. There is also no way of explaining certain—even if only relatively constant—features of the psyche here, such as its possession of knowledge, a certain character, modes of behaviour, and so on. In a word, it is a “personality” without any subject. As above, what is entailed by this as regards the topological structure of persons is quite trivial. After all, such a topological structure can be possessed by infinitely many objects markedly different from a human mind or person.

Where certain objects are concerned, it may be said that the above theory explaining their invariant existence in time somehow works: e.g., as regards summative wholes in Ingarden’s sense (cf. Ingarden, 2016, § 43). Such objects are sets in the extensional sense. They can also be characterised (assuming they can be immersed in a time composed of point-like moments) in such a way that all their cross-sections are identical. For instance, if we deprive a set (but only a finite set) of one element (a feature), it “becomes” another set that is not extensionally identical to “itself” at the starting point. If we already assume that they remain perfectly invariant over time, such objects have precisely all cross-sections at time t0, t1, t2…. identical among themselves, and each such cross-section can be identified with the whole of such an object immersed in time. However, it will be impossible to change any feature of the set in the extensional sense so that it continues to remain itself—or, to put it another way, so that it continues to be identical to itself.

3.2 Some methodological concerns

We shall now raise two methodological issues. Firstly, all conceptions of objectual identity (exdurantism, perdurantism and endurantism) assume a linear conception of time composed of point-like moments. The model for such a structure is the real number line, ordered by the “linearity” relation, with the usual topology. Such a model, however, is not suitable for modelling the phenomena of consciousness, which are mostly—due to the act-like structure of the latter itself—certain temporal objects: i.e. processes. Let us give an example. Suppose we make an exact copy at moment t of a piece of music, such as Beethoven’s Ninth Symphony. Such a copy is not identical to it even with respect to a single note. It is impossible to deduce from this copy any information about the earlier phases of this piece, because the state of the object (i.e. the musical work) at time t does not contain any information about its earlier or later phases. It is therefore necessary to consider a copy of the piece up to moment t—and, therefore, over a certain time interval. It is also possible to entertain a different conception of time itself, in which there are no punctual moments and each part of such a time continuum also has a certain temporal extension (i.e. is also a certain continuum). At the same time, the authors of the BMM-model are silent about the phenomena of protention and retention, which apply to any temporally determined process involving consciousness. Consciousness is a process in time, and no copy of it can be created at time t, because no “cross-section” of it is a process. Therefore, there is no such thing as a copy of that consciousness (that mind) at time t. The BMM-model, by definition, is not suitable for describing the structure of consciousness—or, by extension, of the human personality. We shall not present all of the arguments against the punctual theory of time here; instead, we refer interested readers to the appropriate authoritative historical source (see Husserl et al., 2019).

The second methodological issue we must deal with is the form of the thought experiment in question: namely, whether every fable or improbable story can be considered a legitimate instance of such an experiment. It seems that the assumptions of a thought experiment must meet certain minimal requirements of rationality, as otherwise any thesis could be proved, or at least rendered plausible. What we have in mind here, of course, is not a negation of all the assumptions made in a given theory, but rather just of some of them—as a thought experiment generally attempts, within the framework of some accepted theory or given context, to contradict or challenge only certain theses, while nevertheless still accepting the general assumptions of that context. For example, in accepting the General Theory of Relativity, we are performing a thought experiment in order to investigate the consequences of some counterfactual assumption, or of several assumptions taken together: we might, say, imagine that an observer can move at a speed greater than that of light, and set out to investigate the consequences of this assumption. The BMM-model, meanwhile, without making any additional ontological assumptions such as could be relevant, contradicts, for example, quantum mechanics. If we assume that Freddie’s mind is material, it should be made of elementary particles. According to the widely accepted so-called “standard model”, each particle is either a fermion (i.e. a particle that creates “matter”, such as an electron, proton, or quark) or a boson (i.e. a particle that carries interactions between baryons (i.e. a photon, for example). Fermions have only half-spins and are—in contrast to bosons—subject to the so-called Pauli Exclusion Principle. This principle states that no pair of identical fermions can exist in a given system; therefore, it is impossible to create a copy of even just one such particle. We would therefore have to assume that any copy of Freddie’s mind will be necessarily made up of bosons alone, as no such copy can be created for something composed exclusively of atoms, electrons and protons. We would thus be obliged to embrace the idea that Freddie’s mind, or consciousness, is exclusively “electromagnetic” in nature. Such an assumption, however, engenders multiple further consequences whose absurdity makes them impossible to accept, such as that for every electromagnetic wave there will be a corresponding form of consciousness. Electromagnetic waves (photons) do not interact with each other. Therefore, radio or television waves located in space likewise do not “mix” and do not interfere with each other. It follows that if we have a conglomeration of electromagnetic waves, the resulting combination of them into a single beam will exhibit properties that are the sum of the disconnected properties of the individual waves. We do not, as a result of the formation of such a “bundle” of waves, arrive at any kind of emergence of higher types of property of one sort or another—i.e. properties that cannot be found in any component wave.

On the other hand, if Freddie’s mind is immaterial, and therefore not made up of either fermions or bosons, then the problem arises of how it could be possible to create a purely material and ex definitione copy of it at the time of creation? One would have to assume a strict parallelism between the mind and the material copy, and assume that this copy, placed in a computer, would also be endowed with consciousness. Alternatively, were this not to be so, then it would only constitute a material foundation for actual consciousness, which itself would then have to appear, just like Euripides’ deus ex machina, for unknown reasons. The point here is that a story created in complete isolation from the relevant scientific context is simply a fable. For these reasons, it is even more imperative that we reject all three conceptions of objectual identity, as contradicting further principles of quantum mechanics—e.g., the impossibility of the existence of hidden parameters in the latter.

In short, the authors do not go into the kind of detail that would be needed in order to set their thought experiment in a generally accepted scientific context and make it compatible with the latter. Actual thought experiments, such as those performed by Einstein (cf. the paradox of the twins or Einstein-Podolsky-Rosen (see Einstein et al., 1935), exhibit the characteristic of their assumptions being in agreement with hitherto accepted scientific theories. This is what distinguishes a scientific thought experiment from a mythological construct, a fable, or some sort of mere imagining. And in this methodological sense, the “thought experiments” in the BMM-model are fables that have little to do with science and its methods. In the case of thought experiments in philosophy, it seems necessary to consider the consistency of the assumptions of a given thought experiment with some more general philosophical (ontological, etc.) context. In the case under consideration, the authors of the BMM-model state that their conception is consistent with perdurantism, exdurantism and endurantism, while being—in their view—independent of any ontology. However, as has already become clear from our discussion so far, these three concepts have little to do with conceptions of personal identity. Indeed, it should be noted that exdurantism and endurantism are themselves inconsistent with our best scientific theories because they assume the existence of some hidden parameters (cf. Genovese, 2005).

To summarise, the theory on which the BMM-model is based is suitable for comparing objects such as Freddie’s appearance at time t and his photograph at time t—i.e. it will determine similarity in certain respects (e.g., those of shape, structure, etc.), but not the actual sameness of objects. A given theory usually carries ontological implications, which entail certain ontological and topological assumptions. In the following sections, we must therefore take a closer look at both the ontological structure (and, in particular, the assumed mode of existence) and the topological structure of persons.

3.3 The ontology of Roman Ingarden

Ingarden distinguishes between pure and empirical possibilities, restricting ontological considerations to the former only. He divides general ontology into existential, formal and material domains, as in every object matter, form and mode of existence can be distinguished. An object’s matter is any qualitative aspect of it, its whatness, and the qualitative moments of its properties. It is, for example, the moment of redness in a given red rose’s property of being red. Its form is opposite to its matter, being its non-qualitative, purely structural aspects. Forms include, for example, being a subject of properties, having a two-subject structure, being a property, determining one quality via another or in a relationship obtaining between a determinable and a determinans. The existence of an object, on the other hand, is not an unambiguous concept: it is possible, and necessary, to speak in Ingarden’s ontology of various possible modes of existence.

How do the modes of existence differ? They can be understood as something constituted from simpler aspects, which Ingarden calls existential moments. A moment is an inseparable part. This concrete redness cannot be separable from this red paint. The same goes for the oval shape of my face, and my face. Existential moments are also what distinguish various modes of existence. Ingarden describes many such moments: i.e. (non-)self-sufficiency, (in)dependence, originality/derivativeness, and autonomy/heteronomy. (We give their definitions in the next paragraph, immediately below.) Most important here is that non-contradictory combinations of existential moments constitute possible modes of existence. When it comes to the various types of mode of existence, the largest number of modes of existence—eight—fall into the category termed real,Footnote 4 with others being categorized as absolute, ideal or purely intentional.

Let us briefly describe the principal existential moments. Ingarden defines existential originality thus: an entity is original iff it is something that—if it exists—exists of necessity. Alternatively, it is so iff it is something that—if it exists—cannot be produced by something else.Footnote 5 A (possible!) original object would be God, conceived as in (mono)theistic metaphysics, but Ingarden also treats mathematical and logical objects as original ones. An object is existentially self-sufficient iff it does not intrinsically require any other object with which it would have to coexist within one and the same whole—i.e. coexist to form a whole with that something. An example of a non-self-sufficiency would be a concrete property in relation to the subject of that property and vice versa: these are mutually existentially non-self-sufficient. Within self-sufficient objects, one must further distinguish between existentially independent and dependent ones. A self-sufficient object is existentially independent iff it intrinsically requires another self-sufficient object for its existence. An example here would be the human organism, which is dependent on heat within a certain temperature range, or on oxygen in certain doses. Existential heteronomy, meanwhile, accrues to purely intentional objects:Footnote 6 Hamlet is an example of a purely intentional object. This is because all his determinations (the young prince of Denmark, impulsive yet spirited, wielding a rapier not badly, etc.) are intentionally attributed to him by Shakespeare. He is “in himself” neither young nor a prince, etc., because he, in fact—i.e. in reality—does not exist, and never has existed, in the real mode. On the one hand, a purely intentional object has properties vested in it by virtue of its status, so to speak (e.g., its being invented by Shakespeare, being non-existent, etc.), while on the other hand, it has a certain content. In this content there are, as Ingarden writes, spots of indeterminacy: i.e. existential gaps or holes (Ingarden, 2016, pp. 214–219).

Intentional objects are two-subject structures: on the one hand they are “made-up” and “harmless”, but on the other they are precise in their content—e.g., “a threat to villains” (like so-called “superheroes”), “voracious” (like zombies from movies or games)—although they at the same time have many gaps or holes in the sense that it is not specified whether, for example, Hamlet was 180 cm tall or not. (“And what if I, <<the inventor>> of a given purely intentional object, were to define it under this aspect?”, someone will ask. Even if that were to be the case, all aspects could not be determined. It is simply impossible—even relative to a gigantic-yet-finite series of productive-imaginative acts). Indeed, Ingarden is convinced that the deepest difference separating real entities from purely intentional ones is this: that real entities must be exhaustively determined. Here the idea of tertium non datur applies without limit. Since purely intentional entities have nothing of their own, so to speak, they are entirely dependent on a transcendent source. They cannot “rebel”—that is, they cannot go beyond, as it were, what has been ascribed to them by their author, not even by one iota (Ingarden, 2013, pp. 216–217).Footnote 7

A purely intentional object, in turn, can be fixed: for example, in a comic book in the form of drawings and dialogues “in bubbles” (if it can speak—of course, again in its content aspect) or in an animated film, which in turn is fixed not on paper but, for instance, using digital media (as, by the way, can be comics, too) and so on.

Ingarden (2013, p. 117) distinguishes between originally and derivatively purely intentional objects. The former are direct correlates of acts of, for example, imagining (Hamlet as imagined by Shakespeare), or of speech/writing acts relating to fiction (e.g., the sense of the sentence “Once upon a time, in a certain forest, there lived a girl with a red riding hood”), while the latter are purely intentional objects determined by the former (Hamlet as a character determined by the content of the drama entitled Hamlet, Little Red Riding Hood as a character determined by the content of a certain fairy tale). Let us also note that the fixing in writing of an invented character usually involves a certain impoverishment of that character; Ingarden calls this schematization. Usually, the character in the imagination is given as richer in features, although—like any purely intentional object—it, too, has spots of indeterminacy.

3.4 Persons as intentional objects in the BMM-model

Let us first analyse the possibility of backing up a person. What do we assume about a person for it to be backupable? After all, not all objects can be fully backupable—for example, the highest peak in Australia, Mount Kosciuszko, is not so. Mount Kosciuszko exists in a real way. It is impossible to back it up because it is impossible to render its full being in a digital copy. Mount Kosciuszko weighs no small amount. Its digital copy weighs almost nothing. Mount Kosciuszko enters into causal relations (a plane may crash into this mountain), while the digital backup does not enter into such relations. Mount Kosciuszko is fixed in respect of all its qualities, whereas the digital copy must contain spots of indeterminacy—places where the relevant qualities are missing. (Mount Kosciuszko has no such places: any question about a certain quality can be answered by whether Mount Kosciuszko has it or not, but the Mount Kosciuszko backup will not retain this feature—there will always be qualities not represented in it.) Similarly, when we ask about Freddie, whether he is blond or grey-haired, or whether he is perhaps bald, we cannot answer this question if he is only meant to be a digital backup. Virtual objects, like the characters in a novel, are objects that have spots of indeterminacy. Hence, when Braddon-Mitchell and Miller propose backups of person-phases, they commit themselves to a predetermined idea, which is that these person-phases exist intentionally. Otherwise, it would not be possible to back them up.

Intentional objects, such as computer programs, can be fixed in their being and thus become intersubjective. And because they contain spots of indeterminacy, these objects can be embodied. Indeterminate places can be supplemented arbitrarily, even in ways contrary to the principle of non-contradiction. Fixity in respect of being can take the form of a recording on a data carrier. It can be the fixity of the multi-layered structure of a literary work or some character depicted in that work. Again, Mount Kosciuszko cannot be, so to speak, “re-fixed”. It is as it is. It can be moved or destroyed, but it cannot be fixed anew in respect of being, as a text file is. Nor can it be reified by an act of consciousness, because it has as many qualities in it as it has. Mount Kosciuszko is existentially autonomous; the source of all its qualitative determinations is itself. Being “re-fixed” in respect of being is only possible when we are dealing with an existentially heteronomous object. The same is true of possible gap fillers. Only where there are existential gaps can they be filled. When Braddon-Mitchell and Miller posit the reincarnation of persons—i.e. a kind of “re-fixing”—they are postulating an intentional mode of existence for personhood.

An intentional object differs from an autonomous individual object, then, in that the contents of an intentional object may contain another intentional object with all its properties. A computer program may have the potential to produce another computer program, which again may have the potential to produce another computer program, and so on ad infinitum. Shrek may think Shrek, which may think another Shrek, and so on. All programmes, like all Shreks, are contained, as it were, in the initial object: in the first programme and the original Shrek. It is the same with Freddie: in the BMM-model, he can copy himself and be reborn again infinitely many times, even while having originally been one person. The result is an infinite class of people who either are Freddie or would like to be Freddie as much as possible. A real object, such as a chair, cannot copy itself and generate an infinite number of chairs that would be contained within it. Hence, an implicit assumption of the BMM-model is the existential moment of the person, consisting in the fact that further objects similar to the person are generated, as it were, within the person. This existential moment is a component of precisely the intentional mode of existence.

In assuming that a person can be backed up, we assume that her foundation of being is outside herself. More precisely, we assume that the source of her qualitative determinations is somewhere else and not within herself. Freddie can only reincarnate himself because the totality of his personality is enshrined in the medium on which he has been backed up. This digital medium becomes the source of his determinations: only there can information about Freddie’s attributes can be sought, in the event that the currently reincarnated one should die. This again means that, within the BMM-model, persons exist in an existentially heteronomous way. Existential heteronomy, in turn, is the fundamental existential moment of intentional existence. In the context of the BMM-model, Freddie and all his doubles must therefore exist intentionally.

4 A rejection of the model of Braddon-Mitchell and Miller

4.1 An ontologically motivated rejection

Taking Roman Ingarden’s phenomenological ontology as our starting point, we can therefore conclude, firstly, that persons, within the BMM-model, are required to exist intentionally. This means, among other things, that they will be existentially heteronomous, have spots of indeterminacy, and be able to replicate themselves within themselves. Given that Braddon-Mitchell and Miller repeatedly express the hope that Freddie will count as like anyone else, and the fact that all these others actually have the possibility neither of replicating themselves nor of existing heteronomously, one must straightaway conclude that the BMM-model does not meet its authors’ expectations. On the one hand they would like the BMM-model to be as close as possible to our experience of personhood, but on the other they implicitly propose an ontology of persons that, for fundamental ontological reasons, cannot possibly meet their expectations.

Secondly, all of our personal experience indicates that the implications of the BMM-model for what it means to be a person are implausible. Hence, we are entitled to conclude that the model is not credible. It is implausible that a person could be an intentional object. Let us assume that you, the reader, are such an object. This means that you must have an ontological foundation in something (perhaps, even, in more than one thing) that determines your properties, analogously to the way Hamlet has an ontological foundation directly in the sentences recorded on media (paper and digital) that describe him and that make up Shakespeare’s well-known drama—and indirectly, or ultimately, in the (antecedent) imaginative and creative acts of the Bard himself. Who could make you up? Maybe some “deeper self”—along the lines of a homunculus? Or perhaps some external self? Needless to say, since this homunculus or these external selves are also persons, according to the assumption in play they would also be purely intentional, which would lead to absurdity.

Thirdly, even in cases of schizophrenia one rarely arrives at the conviction of being something like a character from the realm of literary fiction, and therefore completely passive, entirely reliant on a transcendent source, and totally controlled. However, some patients do have an experience to the effect that some of their thoughts have been “inserted”—that they themselves have not generated them, but instead someone else has inserted them.Footnote 8 Yet one would hardly expect the phenomenon of thought insertion to be an argument for a person actually being a purely intentional entity. One would rather have to conclude that in this condition one can have the illusory experience of being a purely intentional object.

A fourth implication is that ontological reflection on the structure of the human person shows that it cannot be a purely intentional entity. For we are dealing with consciousness, which from the formal-ontological point of view, as we have already argued, is a process constituted by conscious experiences. If it were a purely intentional entity, this process would require being grounded in some conscious being that is no longer (purely) intentional. If this entity were to be you the reader, this would mean that you yourself are not a purely intentional entity; if someone else, then the schizophrenic experiences described above would have to be considered veridical.

Let us further ask here about interruptions to the stream of consciousness, such as dreams or comas: if these in effect exist, how do we know this?Footnote 9 Ingarden writes, on the one hand, about—paradoxically—“a peculiar experience of non-consciousness” (Ingarden, 2016, p. 657). On the other, he emphasises that “in experiencing an interruption in our experiences, we do not experience any kind of interruption in our existence itself” (Ingarden, 2016, p. 664). So, in addition to the process of consciousness, there is the self, which is, from an ontological perspective, a certain subject who is the fulfiller of acts, so to say. Nevertheless, the self cannot be a purely intentional object, for the same reasons. See also the comments in Sect. 4.2 below, where we seek to highlight the problematic absence of the subject from the BMM-model.

A fifth point to emerge is that the BMM-model assumes that personality change is not possible. Yet this sort of change is confirmed both by everyday first-person-based experience and by empirical research conducted into the therapeutic process. For example, the effectiveness of cognitive-behavioural therapy (which includes Socratic dialogue!) has been confirmed for patients with various personality disorders.Footnote 10 Reductions in, for example, social isolation, engagement in high-risk activity, aggression, anxiety, hopelessness, depression or eating disorders, as well as the emergence of greater mindfulness and emotion regulation, are indisputable mental changes, and these are related not to the surface, but to the depth of a person’s psychical constitution. Personality changes are, therefore, empirically confirmed.

Both the arguments raised earlier, and those just above, reinforce the thesis that the BMM-model represents an account of persons that is irrelevant and inadequate. It is undermined both by the untenable assumption of an intentional mode of existence for persons, and by everyday first-person-based experiences—as well as by empirical research into personality change. Hence, the BMM-model should not serve as a basis for philosophical explanations.

At the same time, the relevance and adequacy of philosophical research itself is by no means a straightforward issue. Wójtowicz and Skowron (2022) have proposed that a philosophical work’s claim to relevance should be based on a good match between ideas (in the sense of Ingarden’s ontology). In this case, we are dealing with the idea of a person and the idea of a virtual object. The BMM-model proposes to match up these two. Nevertheless, they do not exhibit any common content on which such a model could be built. Thus, one is left with the impression of artificially transferring the properties of virtual objects onto persons, which at best leads to extremely speculative considerations that then have little to do with the object of interest itself—namely, actual persons. To invoke a model that is surely relevant here, it is worth relying not on conceptual analysis, but on eidetic intuition, as distinguished and used by phenomenologists. The latter makes it possible to construct adequate models, as it is just this sort of intuition that enables insights to be on target. Such intuition is nothing mysterious: the experience, one way or another, of reaching the core of the matter at hand is one shared by all philosophers, be they of an analytical or a non-analytical orientation. It also allows us to be wrong in philosophy. This, of course, is to affirm that being wrong is indeed possible there. After all, probably no contemporary philosopher claims to possess anything like the infallibility of the Stoic sage anymore. Timothy Williamson captures this well when he points out that modelling in philosophy is itself an art:

Another respect in which rigorous-minded philosophers may find the method of model‐building alien is that selecting and interpreting models is an art—in science as well as in philosophy. It depends on good judgment, honed by experience. One must distinguish simplifications which abstract away inessential complications from those which abstract away crucial features of the phenomenon, and genuine insights from mere artefacts introduced for mathematical convenience (Williamson, 2017, p. 169).

Braddon-Mitchell and Miller (2020, p. 3827) also propound another surprising thesis, which is that the SP-relation is not necessarily symmetrical. This is because from the perspective of Freddie today, he is the same person as Freddie a month ago to the degree of, say, 0.8, but from the perspective of the latter, Freddie a month ago is not necessarily the same person as Freddie a month later to the same degree—he may be so to the degree of 0.5. This is a serious argument against SP-gradability. Any relation pretending to be a relation of sameness should meet certain minimum requirements if it is to merit being called “sameness”. Among such minimum requirements is symmetry. As Frege already noted, identity-like relations serve, among other things, for counting: e.g., the relation of having-the-same-income-as enables us to count income groups, in the sense of sets of people earning the same amount. Similarly, the SP-relation is used to count people. If we learn that A is the same person as B, but B is not the same person as C, then we know that there are at least two people. However, when someone adds that B is not the same person as A, we stop understanding what is being discussed.

4.2 A critical discussion of desire-first views

The BMM model is intended to be metaphysically parsimonious—meaning that, as we mentioned in Sect. 2, the authors position themselves amongst the proponents of a desire-first approach, which is defined in contrast to a metaphysics-first one. The desire-first view is essential to the overall reasoning of Braddon-Mitchell and Miller; hence, we shall discuss it in detail here.

Desire-first views come in multiple varieties, but Braddon-Mitchell and Miller (p. 3821) distinguish one thing they have in common. This concerns direction of explanation. As a person-phase, we care about the future of other person-phases, but not because they bear the SP-relation. It is the other way around. That is, it is because we care about a future person-phase that we can talk about an occurrence of the SP-relation. Thus, the SP-relation is based on certain conative attitudes, as the authors call them. In particular, the authors indicate two types of such attitude, without excluding other possibilities: the first is reaching out to the future, the second looking back at the past. These attitudes are additionally supplemented by factors relevant to the occurrence of the SP-relation. Among them the authors mention “psychological similarity”, “bodily continuity” and “organismic continuity”, without pretending to have furnished an exhaustive list. They then call these factors candidate properties of conation, or CPCs for short.

These CPCs are, in fact, candidates for the SP-relation—although the authors do not indicate which CPCs, in their opinion, are necessary, and which not, for the latter. Remaining neutral on this, they also do not specify all the conditions needed for two person-phases not to accidentally merge on account of some CPC. However, for a given object to be a continuer of an actual person-phase as a future person-phase, these phases should at least be connected by cognitive attitudes. The authors only claim that for a relation to be a CPC, it must be the case that a person-phase “could organise its conative attitudes of extension and origin around that relation under conditions of full rationality and relevant knowledge” (p. 3821). Why do person-phases desire any CPCs at all? For example, why do some person-phases desire psychological continuity? The answer the authors give is that these primary and primitive attitudes of anticipation and origin are the decisive factor:

Here is one part of the story we find plausible: there are primitive conative attitudes of anticipation and of origin: primitive attitudes of, on the one hand, anticipating the experiences of certain future person-phases and, on the other, of taking some past person-phases to be one’s origin. Here, again, there is something of an inversion of the order of explanation. Rather than its being the case that person-phases have attitudes of anticipation and origin towards other person-phases because those person-phases bear some particular relation (such as psychological continuity) to the person-phase in question, instead, it is the attitudes that are primitive, and some CPC, such as psychological continuity, is one that a person-phase cares about because the primitive attitudes are ones that in fact track that relation (p. 3822).

Braddon-Mitchell and Miller treat person-phases as being composed of separate, unrelated experiences. In their arguments employing Freddie and his fellows as examples of persons, they sometimes call those experiences “memories” (p. 3816, 3809). “Memories”, as we know, consist of various mental states and—what is important—only selected “reasonable” conative states: i.e. those involving precisely CPCs. Even if such extreme assumptions about the structure of persons and of consciousness were to be explanatory of something, the question of their elementary truthfulness will remain open. It is no argument to say that the BMM-model assumptions are “more parsimonious” than those of a metaphysical account, if it turns out that the BMM-model is a fictional creation and has little to do with real consciousness and the real personal structure of human beings. Similarly, accepting the existence of dwarfs can explain a number of phenomena more parsimoniously, but there are no dwarfs, so this explanation is entirely cosmetic.

We believe that talking about “desires” and “beliefs”—that is, de facto, certain acts and states of consciousness—as if they were atomic mental phenomena, is an oversimplification. The authors discuss “desires” without the person who nourishes those desires. By analogy, there is no perception without what is perceived, and the one who perceives it. There is no “perception of a particular tree” that would not be a perception of a particular subject. Every act of consciousness intrinsically extends between two poles: on the one hand, the intention of the act (what it is directed at, what it reveals), and on the other, the subject out of which all of the acts come, which carries them through to their completion. It is also subjectivity that gives unity to the stream of consciousness: the perception of the same tree and the same phenomena is not an atom that can be added to this or that person-phase of this or that person. However, the perception of the same tree is, therefore, a perception that pertains to this and not another person, because without a subject there is no perception at all. Perception of the same tree by two different subjects amounts to two different perceptions. Only the tree remains the same. Thus, it makes no sense to talk about acts without taking into account these two essential poles that they involve. It would be like talking about a triangle that does not have three angles or three sides. A triangle is not the sum of “three sides + three angles + the way they are connected”, but a single object having these characteristics. Similarly, it is an illusion to speak of any object as an extensional sum of its features: e.g., of an apple as something identical to a particular “shape + certain colours + certain smells + certain tastes + …”. Even to think of an extensional set of five elements, we must posit them as a particular whole, a specific new single object, as otherwise it would be impossible to distinguish these five loose elements from, for example, two sets: a two-element and a three-element one. Meanwhile, the desire-first approach reduces consciousness and the person to a loose bundle of unrelated features, and tries to convince us that the subject can be simply forgotten about as it apparently does not figure in the argument.

The BMM-model, along with almost all of the explanations its authors put forward, is therefore reliant on psychological atomism: the subject is taken to be the mere sum of its mental states—in the sense of sensations, experiences, thoughts, desires, and so on. With this comes the possibility of such “memories” forming different entities, as the subject, on this view, is the extensional sum of its sensations (mental states), which, while remaining invariant, can be conjoined with others. Thus, a given thought (e.g., “I am thinking about my psychological continuity”), observation (e.g., “I can see a tree in the yard”), or desire (e.g., “I would like a drink of water”, “I wish I had psychological continuity”), can be placed in any juxtaposition with others, and the collection of these will “form” a subject. If we change the content of this entity, it may turn out that John will be created, instead of Freddie. According to the desire-first approach, particular “desires” (conative states) connect such characteristics together. Such “desires” are the only link between person-phases, “gluing” the latter to other phases belonging to one and the same person. Therefore, according to the authors, the backup can be regarded as a continuation of a particular person-phase—after the mysterious “revival”, of course. A propos this, the following question then arises: how can “desires” be copied, and immobilized in the copy? An entity, on the desire-first approach, is a jigsaw puzzle of certain elements, and many different entities can be configured out of a given set of them. Apparently, it is only necessary for there to be an anticipation of something, or a look back towards a point of origin. Yet this fails to distinguish between thoughts and desires about something specific (e.g., “I want to eat this apple”), and thoughts and desires about something general (e.g., “I want to be a good person”).

Moreover, we encounter a highly actualistic conception of the (hidden) subject in the BMM-model, in that the authors do not devote a single word to distinguishing between mental states that are “alive”, or actualized at a given moment (e.g., during the creation of a backup, or in a given person-phase), and ones that are just in play potentially, in that they are only “in the background” of the stream of consciousness (as with abilities, predispositions, and certain attitudes of mind—e.g., that someone is able to speak some foreign language, even when they are not currently doing so). Where, we might ask, are these states “located” at the moment of a given person-phase? In this way, the lack of basic experience of, and knowledge about, the subjectivity of alleged persons in the BMM-model fosters an appearance of eliminability on the part of the subject, making the latter look metaphysically superfluous where these considerations are concerned.

In addition to arguments pertaining to the ontological ineliminability of the subject, we also wish to draw attention to a pragmatic drawback to the desire-first view. By our lights, most subjects would not choose to take on the risk involved, were they to be acquainted with the assumptions underlying the BMM-model. First, the authors remain silent about what Freddie’s family, wife, children and friends have to say about all of this. Will Freddie’s wife recognise that the “Freddie in the suitcase” is her husband? We rather doubt it. Next, of course, we can imagine a situation where Freddie signs a contract with a mine (after all, it is all about money…), and the contract guarantees that his copy will be identical to (i.e. the same as) him. In Freddie’s place, we would start to ask for details, and it would turn out that the “travelling salesman” shows him a suitcase with a device in which his copy will be kept. Freddie will not recognise that what is in the suitcase is him (unless something is wrong with him). He will, let us assume, find out that it is him when the copy is rebooted. What is it that will come to be in the rebooted copy that is not in the suitcase? Well, it turns out that what will show up there is the subject of all those acts and experiences that were recorded and deposited as frozen in the suitcase. There is no other way to revive these “memories” than as experiences of some numerically different subject. If this entity is not there (actually in the suitcase), then its role will be fulfilled by a body or brain, or some other device, in another suitcase. Thus, the problem of the identity (sameness) of Freddie and his copy necessarily raises the question of the identity (sameness) of a subject, of a brain or a body, and thus cannot but bring into play additional ontological elements.

Generally speaking, it is not so important that we entertain certain thoughts and not others, but rather that we can think, not that we desire this or that, but rather that we can continue to desire, and so on. This “I can do something” presupposes precisely the living subject. Even at a linguistic level, verbs and other expressions denoting acts of consciousness generally point to a subject. The self is not made up of, or reducible to, disconnected thoughts, desires, or other events (memories?). The metaphysics of the subject can only be dispensed with if there is no such thing as a subject, and this is something the authors have not even given consideration to. In short, they could be said to be practising psychology without a subject, and philosophy without an ontology.

Having outlined our critique of the BMM-model, we now move on to our proposal of viewing the authors’ arguments from the standpoint of the holistic topological-dynamic model of persons proposed by Kurt Lewin.

5 Kurt Lewin’s topology of persons, and the personhood of Freddie

5.1 Not only time, but also the space of persons: Lewin’s topological psychology

In seeking to define the two main thoughts that motivate desire-first views, Braddon-Mitchell and Miller invoke a set of desires oriented towards notions of extension of oneself and extension from one’s origin. At first glance, they have in mind extension as something spatial that extends into some kind of space in a person’s life. Even so, they opt instead for a temporal characterisation. Well, the current person-phase looks ahead with its desires and wishes, for example, in order not to lose its personal identity in the future. On the other hand, looking back at the past it may desire to preserve, for example, its social status associated with its origin. As we know, both sets of desires are treated as primary and fundamental to the desire-first view adopted by these authors. ​Persons, however, extend not only in a temporal sense but also a spatial one (which is something that Braddon-Mitchell and Miller need not reject), as well as in many other ways vital for discussing the SP-relation. It is not only time that is important for personhood—as we mentioned earlier when discussing the time of consciousness—but also its space. To render the totality of the personal situation adequately, we must also render the spatial aspects of what it means to be a person. This is what Lewin did in his book Topological Principles of Psychology.

Before discussing the relevant details of Lewin’s proposal as these relate to our further arguments to be developed here, let us say a few words about spatiality and its related science, topology. The latter is a branch of modern mathematics. Intuitively speaking, it is a generalisation of geometry—something like a highly general form of geometry. The generalisation in question consists in an extending of the class of permissible transformations. When we consider figures such as appear in school geometry we already have in play, as part of our understanding, certain transformations of them that define their geometry. For example, when we consider a square, and ask when it remains the same square and when it becomes a different one, the answer of a student who has learned school geometry will be that it is the same when it looks the same—that is, when its shape does not change, and when it has equal sides. Why does the pupil answer this way? Because the criteria of sameness for squares are encoded in the invariants of transformations of that square. School geometry assumes that we can move the square, rotate it, or both move and rotate it, and these define the relevant criteria of sameness: the shape and length of the sides, these being the invariants of rigid transformations. However, what happens if we change these transformations and consider not only rigid transformations but a broader class of them—that is, the class of bicontinuous transformations?

Here—with bicontinuous transformations—the identity criteria change. A circle in a plane will be the same as the edge of a square, and the edge of a square will be the same as an ellipse’s edge. That is because a circle can be continuously transformed into the edge of a square, and the edge of a square into that of an ellipse. We can think of these continuous transformations as transformations of rubber objects: such objects can be squeezed (but not too much), stretched, and twisted, but not torn. Hence, sometimes topology is also called rubber-sheet geometry. Topological transformations, bijective and bicontinuous transformations, are technically called homeomorphisms. Homeomorphic objects are indistinguishable: hence, one often hears jokes about topologists not distinguishing, despite apparent differences in shape and sometimes also size, between a coffee cup with one handle and a French doughnut: after all, one can be continuously transformed into the other.

Among the invariants of school geometry are shapes, side lengths, angles, etc. But what is an invariant of topological transformations? What is certain to remain unchanged if we homeomorphically transform an object? The shape may change, but the size also changes. As Lewin (1936, p. 53) characteristically puts it: “A drop of water and the Earth are, from a topological point of view, fully equivalent”. However, the qualitative properties of the transformed objects will not change—including, for example, their connectedness. Connectedness, intuitively speaking, is the qualitative property of being in one piece. The psychological equivalent of connectedness is the Gestalt: i.e. the parts of the personality that are strongly fused together in virtue of being closely yet dynamically interdependent. Such fusion can be understood in terms of the notion of there being a path that can connect any two parts of the Gestalt. In other words, there are no barriers between parts in the Gestalt. In general, connectedness intrinsically corresponds to the impossibility of tearing a given whole into two disconnected parts or, precisely, the possibility of connecting every two points present in a connected object. Connectedness is an invariant of topological transformations. The invariants of topological transformations are called topological properties.

Another topological property is dimension as this pertains to a given object: objects with different dimensions, such as a one-dimensional interval and a two-dimensional surface, are topologically different. Dimension is some kind of intrinsic, qualitative characteristic of an object. For example, in the case of an interval one can only take a single path from one point to another. By contrast, with a connected two-dimensional surface two points can already be connected by multiple paths. At first glance, it seems that as the dimension of a space increases, its size increases. However, this is not the case; an increase in spatial dimension really means an increase in complexity and richness.

Among the written symbols of the alphabet, the letters (necessarily written in a sans-serif font – that is, without any tails) L, N, S, U and W are topologically identical. The appropriate transformation that demonstrates this consists in stretching them appropriately (as if they were made of a rubber band)—each can be stretched to resemble the letter I. The letters I and Y, however, are not topologically identical, because there is one point in the letter Y that splits the letter into three parts. That is, when this point is removed, the letter splits into three connected components. This is the connection point of the three branches of the letter Y. The letter I, meanwhile, does not have any such a point that would split it into three connected parts: the removal of one point can only ever break it in two. The topological invariant is the number of such connected components.

Topology, as we see above, is essentially a science of continuity, as topological invariants are invariants of—precisely—continuous transformations. Hence, when we take up the problem of personal identity and point to relations of psychological continuity or bodily continuity, it is topological phenomena that will naturally show up as pertinent. These are not just quasi-technical terms. They have their content. Continuity is not a trivial concept, and its proper definition is provided precisely by topology. We will not offer any strict topological definitions here: they would be too technical, so we prefer to stop at the level of intuitive description. Nevertheless, the lesson of topology is that if we are ho** to discuss continuity in philosophical terms, including the continuity of persons, then to do so we must first have some picture of the structure of persons. Why? Well, for example, any function from a discrete space into any other space is continuous. This continuity depends on the specific structure of the discrete space. From here, we may conclude, as Lewin did, that the topological structure of persons is important, and that it is this that captures the totality of their situation without reducing it to one particular set of terms or another (as when, for instance, we just take them to be composed of person-phases or moments).

Lewin came up with the idea of using intuition, concepts and topological-spatial techniques in the context of elaborating his view of persons when it became apparent that the drawings he made on his blackboard, examining persons individually and in certain groups, corresponded to certain real personal relationships. These drawings represented precisely the spatial relationships he encountered in the context of his holistic construal of what it means to be a human with a personality. A prisoner may have a very limited spatial field in which to move their body, yet the space of their mental life need not be rigid or constricted by strict edges as is the space of their possible bodily movements, where this is straightforwardly constrained by the prison walls. They can deal with the problem of personal identity by studying the various philosophical works of Derek Parfit and Roman Ingarden, and pass more and more deeply into the space of this problem, thus expanding the space of their life, which is related neither to their future nor to their past—although it does constitute their present life. These spatial components, such as the demarcation of one part from another by some boundary, exert several effects on persons, as well as on their surroundings. (Freddie, as was mentioned in Sect. 4.2, is not alone; he is together with his environment!) Hence, they can be identified and distinguished within the space of some given person.

Consider, following Lewin, the example of two children whose living spaces are shown as in Fig. 1 below. The life space of the child labelled C in the circle in figure (a) contains few opportunities for free movements. On the other hand, the life space of the child labelled C in figure (b), as we can see, is much more open to these. The children differ both in their possibilities (for example, one can tie his shoelaces, the other cannot) and in respect of the space of what is forbidden to them. The more numerous the regions of what is forbidden, and the fewer abilities, the smaller the degree of freedom (possible locomotion) evinced in the space of life. Child development is largely a gradual expansion of the region of the possible. Hence, adults tend to have a larger space for free movement than children.

Fig. 1
figure 1

Differences in the space of free movement; C—child, f—forbidden region, i—region inaccessibile.  (A redrawing of an illustration from Lewin, 1936, p. 45. Redrawing courtesy of Sławomir Świderski.)

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Figure 1 offers, we think, a good introduction to the topological-spatial way of capturing personality. Note that it does not matter at all in this drawing whether it is an ellipse or a circle. What is significant is that the space is bounded. That is, it is enclosed in a certain area. In other words, what matters is that the closed curve divides the area into two parts: the inner and the outer, being the boundary of both. The child’s life space (a) is bounded. That is, there is also something outside it. Inside it is the representation of the child itself (the letter C in the circle). The circle in which the child is enclosed represents the boundary between itself and its environment. What is important in respect of the whole situation is the position of the regions and how they relate to each other, not their shape. Nor does it matter whether the regions in question relate to children’s skills, to elements of morality (what is forbidden), to their dreams, or something else entirely belonging to the totality of their lives. What is discernible, on the other hand, irrespective of any material specification, is a certain structure, a certain arrangement of regions within and beyond the person, and certain relations pertaining to the positions of regions in space.

This arrangement of positions, or of possible places, is an arrangement of qualitatively related parts, and has nothing to do with the quantitative calculus with which mathematics is commonly—and wrongly—associated. (Besides, the latter corresponds to the quantitative rather than qualitative way in which Braddon-Mitchell and Miller also themselves argued when they assigned specific numbers to measure how much of a person was present in someone, as well as in their account of the calculus of decision making in which, in the context of the BMM-model, Freddie was obliged to participate independently of his own will.) The parts of mathematics that are sensitive to qualitative reasoning, especially those such as topology, can be used to describe qualitative phenomena. Undoubtedly, the phenomenon of the person is one with many plainly non-measurable, though cognisable and precisely graspable, aspects. This is particularly evident in the case of Braddon-Mitchell and Miller’s analysis of the problem of the relationship between degrees and continuity, and possible degrees of continuity. Comparing this with Rene Thom’s (2018) analysis of the problem of discontinuous jumps with continuous parameter change gives, we think, an accurate picture of the difference between thinking in terms of qualities and of quantities.Footnote 11

Lewin (1936, pp. 182–187), when he was looking for some measure of the differences that distinguish an adult from a child, considered, among other things, the degree of differentiation—that is, the number of distinguishable regions. The issue of differentiation with respect to persons is structurally similar to the problem of the gradability of the SP-relation. Could the number of regions be what distinguishes one person from another? This number, as it turned out, depends on the degree of accuracy of the examination. Well, the regions of a person Lewin distinguished were based inter alia on a certain qualitative feature. Nevertheless, it may turn out upon closer examination that a region which was originally homogeneous and did not admit of any further qualitative differentiation, upon closer examination shows further regions as its sub-regions. Hence, the conclusion is that more qualitative methods of comparing people—in terms of differentiation rather than the number of regions—are needed. This is because it is objectively impossible to compare people according to the number of regions they have. A similar objection can be made to the approach of the BMM-model. Is it possible to compare being Freddie to the degree of 0.8, and John to the degree of 0.2, to being Freddie to the degree of 0.7, and Annie to the degree of 0.3? If we consider degrees of being the same person, they should not be measured, as Braddon-Mitchell and Miller suggest, by numbers between 0 and 1. Suppose the authors want to differentiate instances of being the same person. In that case, they need to first determine the structure of persons, so that using this structure they can qualitatively describe the gradability of the SP-relation.Footnote 12 Lewin (1936, pp. 185–186) hints at how this could be done when he points to the dynamic unity of the person, which is co-constructed via their degree of differentiation, the degree of dynamic separation of neighbouring part regions, and the special structure of their life spaces.

5.2 A more realistic topology of persons

From the example given above, of two children with different spaces pertaining to skills and taboos, we can obtain, albeit tentatively, a sense of just how holistic Lewin’s account is. A person is a region in his or her life space. The life space consists of all the psychological facts that affect the person at any given moment. Regardless of how they exist, both the person and his or her life space are a dynamic system of dependencies. The person and the life space influence each other. The person is not an isolated point, separated from his or her environment. On the contrary, it also constructs itself in relation to the environment. What occurs and happens inside a person depends on the state of the person and the state of the person’s life space. Hence, Lewin in effect formulated the popular claim that a given person’s behaviour is a function of the state and environment of that person. In slightly different language, the person is always within a certain force field from which he or she cannot be separated. Any account of the person that separates them from this field is a certain abstraction of the person, if not a reduction of the person, and thus fails to account for the totality of their ontological situation.

At the same time, a person is not a homogeneous region of a life space. On the contrary, it is a differentiated energy system. The differentiation here consists in the fact that in the person, as in the life space, there are parts of the kind called “regions”. The person differentiated from the life space is a Jordan curve, a curve topologically identical to a circle. This curve allows the person to be distinguished from his or her environment—that is, to distinguish the inside and outside of the person. There is significant differentiation within the person, though this is dependent on the current moment: the state of the person and of the environment. Nevertheless, when persons are in a state of comfort, and without tension, Lewin is able to distinguish several fundamental regions in respect of them. Firstly (see Lewin’s original drawing below, in Fig. 2), right at the person’s edge, from within the person, there extends the motor-perceptual region M, or the region of bodily agency. The M region is used for communication and interaction with the environment; its sub-regions are, for example, the senses, and it also includes bodily acts such as looking, smiling, speaking and moving. Region M also includes a person’s clothes: this is because something’s touching our clothes is treated as its touching our body. Moving from the outside of the person, along the path to the inside, immediately after the regions in the M boundary sphere have been passed we come to the inner personal regions. Those closer to the M-sphere are the peripheral intrapersonal regions, and those closer to the person’s centre are the central parts. The necessity of distinguishing the more central parts has been confirmed by experiments “on psychological satiation: actions which belong to more central strata are ceteris paribus more quickly satiated” (Lewin, 1936, p. 180). When more central parts of a person are touched, outbursts of anger occur less frequently than when more peripheral parts are touched. The explanation for this regularity in the topology of the person is that the zone between the central parts and the environment is stronger than that between the peripheral parts and the environment. From this example alone, we can see how topological explanations work in the context of the metaphysics of persons.Footnote 13

Fig. 2
figure 2

E—environment, M—motor-perceptual region, I—inner-personal region; p—peripheral parts of I, c—central parts of I. (A redrawing of an illustration from Lewin, 1936, p. 177. Redrawing courtesy of Sławomir Świderski.)

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The structure of a person, then, is a dynamic-energetic system that depends, as we have already mentioned, on many factors, including individual differences, the current state of the person, and the state of the environment. In a state of relative calm, and in an undemanding situation, the peripheral regions of the intrapersonal are easily accessible from the environment, as they are not separated by a firm boundary, while the central regions are more strongly separated from the environment. (Because the true centre of the person is not easily reached, it is protected.) We see these facts reflected by Lewin in Fig. 3 below (see case (a)). When we consider a person under stress, the self-control mechanisms make the strongest boundary protecting the interior of the person already move to the motor-perceptual sphere, and the interior of the person becomes more coherent; that is, the peripheral parts and the central parts are more connected (Fig. 3, case (b)). In an instance of extreme tension on the part of the person, there is a regression with respect to their interior: the intrapersonal regions merge, and there ensues a primitivisation of the person (Fig. 3, case (c)). Of course, the dynamics of the person are not such that they are becoming a new and different person all the time. They remain relatively constant, but the elevated tension associated with falling in love, or with a family tragedy, will nevertheless significantly affect their dynamic system. Moreover, the characteristics of this arrangement may constitute personality attributes—something which adds to the exploratory power of Lewin’s proposal. For example, a person whose dynamic arrangement of regions is relatively well-balanced is, according to Lewin (1936, p. 187), a person with a harmonious character.

Fig. 3
figure 3

Lewin’s description of dynamic relationships within a person. The person is (a) in an easy situation of relative calm, (b) under stress, and (c) in a high state of tension. (A redrawing of an illustration from Lewin, 1936, p. 181. Redrawing courtesy of Sławomir Świderski.)

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5.3 Dimensions of the life space

As we mentioned earlier, our initial intuition regarding the dimension of a space takes the form of thinking of it as a characteristic pertaining to the size of a given space (“the higher the dimension, the bigger the space”), but this is not a good intuition. The dimension of a given space is an intrinsic property of that space that determines how complex it is. Among the basic intuitions about dimension, we will point to two. Firstly, a point has dimension 0, a line has dimension one, a surface has dimension 2, a solid has dimension 3, and so on. Moreover, a one-dimensional segment is bounded by zero-dimensional points, a one-dimensional line bounds a two-dimensional surface, and a two-dimensional surface bounds a three-dimensional solid. An n-dimensional object is generally bounded by an (n-1)-object. Dimension is, therefore an inductive concept.

Changing the dimension makes a difference, and brings with it important consequences. In two-dimensional space, any path going from a point outside a circle to a point inside that circle must intersect the edge of the circle. A path without this property will be found in three-dimensional space without difficulty. The higher the dimension, the greater the possibility of connections and locomotion between parts in a given space. Dimensionality is, therefore, a certain measure of possible connections in space. Hence, for Lewin, who sought to study personhood holistically, dimension could hardly be a matter of indifference. Nevertheless, the answer to the question of how many dimensions an adequate account of persons should contain is not obvious. Lewin indicated that for many applications a two-dimensional representation of the person will be sufficient, but also that a third dimension, at least, will be needed when aiming for ever higher degrees of irreality:

A daydream, a vague hope, has in general less reality than an action; an action sometimes has more reality than speech; a perception more than an image; a faraway “ideal goal” is less real than a “real goal” that determines one’s immediate action (…). Action itself can be of very different degrees of reality. Processes which concern strong needs of the person and in which he has to surmount strong physical or social barriers have usually a high degree of reality. Among the quasi-conceptual processes one can for instance distinguish carefully planned consideration of the ways and means which lead to a certain goal from free play of phantasy, which is more irreal (…) (Lewin, 1936, p. 198).

The introduction of dimension-related characterisations into the topology of personhood is not just a spontaneous conceptual exercise. There are a number of experiments where the degree of reality is relevant to personhood (Lewin, 1936, p. 197). These concern levels of aspiration, the formation and changing of our goals, memory, emotional processes, and play. It is not necessary to go into details to see that there is a difference between one’s own emotions and those experienced by the superhero in a film, or between the memory structure of living people and that of Freddie and all his copies in the BMM-model. The development of information technology and new media has made us see even more vividly than before that the boundary between the real and the virtual is important, even if it is not sharp.

It should be noted that such degrees of irreality, which are essentially dimensions in the topology of persons, correspond in Ingarden’s ontology to successive iterations (e.g., the bringing into existence of further intentional objects by those already themselves brought into existence) and versions of intentional objects. It is the intentional objects that have the least existence in themselves. And the further we go in considering an object in its existential heteronomy, the more unreal it is: Freddie conceived by a copy of Freddie that was conceived by a further copy of Freddie exists in a weaker sense than the original Freddie. For this reason, intentional objects are explicitly called fictions. They are, as it were, a shadow cast by consciousness on reality, but they are not reality itself. Nevertheless, they have an actual effect on a person’s life. Hence they must exist and have an adequate representation in the person’s life space. The dimensions that pertain to persons therefore correspond to degrees of intentionality: the higher the dimension, the stronger the existential intentionality.

The successive, increasingly unreal dimensions of the life space are characterised by a significant change in the structure pertaining to persons, as what we witness is ever greater fluidity between their regions. In increasingly unreal contexts, one can do, basically, whatever one wants. Hence, the barriers between regions in a person’s environment show less and less resistance. Such barriers also become less defined and more easily permeable. This is because a high degree of unreality allows for enormous freedom—and that goes for the conceptual order represented there, too. In a completely imaginary world, freedom increases immeasurably, regardless of whether it is a world imaginatively conceived as real, or the world of concepts. Going further, the boundaries within the person are weakened as dimension increases. Hence, intrapersonal tensions are discharged more quickly. Tension in one region passes more easily to other regions, as the boundaries are thinner. Also, the boundaries between the space of life and the person become blurred: the world around the person depends more on their needs than on objective contexts. Under the influence of psychedelic substances, the sense of unity with the world is so strong that it may not even be possible to distinguish the person from their environment. The higher the dimensionality of the person, the more they will merge with their life space and the more difficult it will be to distinguish them from the latter.

5.4 Freddie’s backups in higher dimensions

Freddie’s life space contains at least two dimensions: the first may be characterised as a sort of near-reality, while the second pertains to something exhibiting a high degree of unreality—namely, intentionality. Braddon-Mitchell and Miller postulate that to be Freddie is to be like you the reader, or us the authors of this paper. Hence, he must contain some basis for being a person and, in this context, some real life space that is his. For we are persons. The second dimension is that in which Freddie’s life space is highly unreal. In this dimension, there is a mine in which Freddie is employed, and there are certain socio-economic relations that underpin the hypothetical calculations of Freddie that Braddon-Mitchell and Miller invoke to justify their thesis. Based on the description supplied by the BMM-model, it is impossible to determine whether there are also other dimensions to Freddie’s life space. Nevertheless, from a purely theoretical perspective they are, of course, possible: even getting rid of Freddie’s ability to reboot would represent a new dimension, closer to the real and somewhat further away from the unreal. Let us therefore assume, without prejudging whether there are any more dimensions or not, that Freddie’s life space has at least two of them; we shall call the first one “the real dimension” and the second one “the unreal dimension”.

Just as in purely mathematical spaces, an increase in dimension leads to an increase in possible connections, so in the BMM-model the introduction of a life space of dimension 2 has significantly increased the possibilities—including making Freddie’s backup and restart possible. Everything possible in dimension 1 is also possible in dimension 2, but not vice versa. The real dimension does not allow people to be backed up or reincarnated. Dimension 2 opens up this possibility, as the boundaries between the regions of the environment in Freddie’s life space liquefy. They liquefy because all of that space exists in a different way to how it exists in dimension 1: it exists more intentionally. The transition to dimension 2 is a kind of firing up of fantasies and a bringing to life of otherwise remote scenarios—scenarios that can include new and surprising pathways for personal unfolding, such as the sort of decision-making processes Freddie carries out when, from dimension 1, he evokes Freddie from dimension 2.

So far, we have been concerned with the dimension of Freddie’s life space, yet the question can be asked of where Freddie himself is located in respect of these two different dimensions. And how many dimensions does Freddie himself have? In the first dimension, Freddie is a real person, just like each of us. In the second, he is not like us. We, after all, are not in a position to back up and reboot ourselves. Freddie is therefore located in both the first and the second dimension, as if at the same time. The Freddie of the first dimension must be linked to the Freddie of the second by multiple dynamic relationships. The real one can execute decisions based on considerations pertaining to the unreal one, while the unreal one can suddenly disappear when the real one receives, say, a pin-prick and stops fantasising. There is, thus, a series of flows between dimensions. If this were not the case and, for example, Freddie from the first dimension were a dynamically separate region from Freddie from the second dimension, then Freddie would simply be a schizophrenic—at least according to Lewin’s proposed definition of schizophrenia. A schizophrenic is a person who consists precisely of two dynamically separated regions belonging to different dimensions (Lewin, 1936, p. 201). If there were more dimensions, then Freddie would have as many personalities as dimensions. However, the BMM-model does not designate Freddie as being a schizophrenic, or someone with multiple personalities. He is therefore linked dynamically to his regions from different dimensions. This is possible because he is located in each of them, albeit that he is slightly different in each. He differs in his parts. More precisely, Freddie himself, qua person, corresponds to a multidimensional region. He has as many dimensions as the dimensions of his life space.

Freddie, being the multidimensional region that corresponds to his own life space, for the purpose of investigating the hypothetical problem of taking or not taking some risk, builds in another dimension, one in which he is able to entertain possibilities that (in dimension one) are completely unrealistic and impossible. It turns out that in this second dimension, the same Freddie considers various scenarios of going down the mine shaft that are a function of the interval between his backups. The two-dimensional Freddie concludes that in cases where he does not have backups being made very often, he will not take the risk. The Freddie of the first dimension may accept or reject these arguments. Nevertheless, neither he nor the Freddie of the second-dimension are different Freddies. They are the same person, just in different dimensions. The difference, then, is not a difference as to persons, but one pertaining to the dimension of the person and their life space.

Shifting between dimensions is nothing mysterious; it stems from the dynamic-topological structure of the person. By passing between dimensions, Freddie makes the situations of these dimensions overlap. Each of the dimensions in which Freddie lives has a relative importance for his life space. When Freddie flies off into pure fiction and considers the rebooted Freddie, then the relative importance of Freddie in the second dimension increases, and the importance of Freddie from the first dimension decreases. When Freddie shaves in the morning with a real razor (i.e. one that both Braddon-Mitchell and the authors of these words could really interfere with), and thinks about the good upbringing of his real children, then Freddie from the second dimension has less weight. Hence, we do not require such a strong SP-thesis to explain Freddie’s decision-making tendencies. It is enough to immerse Freddie in the topological model of the person, and point to dimension as it pertains to both the person and their life space, without making further explanatory appeals to the SP-thesis itself.

As Lewin points out, the transition between dimensions can be both an extension and a contraction of the life space. As we can see, this expansion or contraction is related not just to the temporal structure in which Freddie is immersed in the context of the BMM-model. Looking forwards to the future and back into the past are only one small part of the rich dynamics of personal life, which itself is irreducible to any one single aspect. Moreover, an increase in dimensional differentiation appears to signify a transition from childhood to adulthood (Lewin, 1936, p. 204). The structure of the young child’s life space resembles the intermediate dimensions of the adult’s space structure: dimensions lacking a strongly marked degree of either reality or unreality. The dimensions of the young child are also not so very different from those of the adult. The development of the person, i.e. its structural extension, consists in, among other things, the differentiation of successive dimensions! From this perspective, although immortal, Freddie is a poor wretch, because in the BMM-model he has been structurally and ontologically squeezed into the eternal position of a child! (And Freddie, just like us, would surely want to grow up.)

The BMM-model provides a putative explanation of Freddie’s decision-making tendencies. This explanation, as we have shown, is based on many overlooked assumptions of an ontological and a methodological nature. Although he was supposed to serve as a model of persons, Freddie becomes a caricature of them. Although he may have gained a coveted immortality, he remains stuck in the prison of an eternal childhood. Although he is able to store copies of himself and recreate himself anew, he cannot change—where this would mean having to become to some extent someone else, of course. His inner life and practical preoccupations are reduced to looking forwards and backwards for the sake of maintaining his continuity. Both the experiential data—as it were—furnishing us with a sense of the changes taking place, and real personal changes confirmed by research, together with the overall dynamic-topological view of persons, suffice to cast the BMM-model in an unfavourable light. In addition, there is our own concern (a kind of practical intention of sorts) not to be what Freddie is—and this so that Freddie can remain!

Many will say that we are being unfair in our criticism: it is well known that philosophers are often inclined to make light of the controversial assumptions they themselves entertain, and ultimately they can always argue that they are defending no more than a thesis about what is hypothetically implied: if we assume this and that, then by necessity, we must also affirm this and that. The authors of the BMM-model (p. 3810) suggest that when backups are not made very regularly, or when the time gap between backup processes is too large, this im**es on judgements about SP in the sense that our intentional miner will declare that he prefers his newer version to the older one because it is more him. But is it not enough to simply state that our everyday real life brings with it personal changes, and that we are not immutable entities? Just what implications does this have for personal identity? If someone were to claim that “I am me practically 100% just now, whereas I was less me ten years ago, and even less 30 years ago”, would they be right in their assertion—and would they actually do so?

6 Conclusions

Contrary to their explicitly proclaimed theses, the authors of the BMM-model implicitly make a whole series of extreme ontological, topological and methodological assumptions. Due to their over-simplifying and reductive character, these stand in the way of any attempt to arrive at a correct and realistic account of human persons within their framework. In their view, the characteristics of a person have no structure or form of the kind associated with a system or hierarchy. The only order and structure that show up in this conception are determined by the relation of temporal ordering of “earlier/later”, and the extensional containment of cross-sections which, according to the authors in question, are said to be the same as the “person at time t”. The above statements follow from a direct juxtaposition of the structure and topology of persons as seen by Lewin with the hypothetical topologies of the BMM-model.

As regards methodological issues, we have pointed to the lack of agreement between the assumptions of the thought experiment described by the authors of the BMM-model and the broader scientific and philosophical context relevant to the issue at hand. Mere alignment with the conceptions of objectual identity over time popular in analytic philosophy is insufficient. We have presented arguments that demonstrate the incompatibility of these experimental assumptions with what are currently the best physical theories (i.e. quantum mechanics). The consistency noted with perdurantism, exdurantism and endurantism therefore suggests that the frame of reference adopted for this thought experiment is too specific, and represents a poor choice when it comes to the task of making sense of personal identity.

The SP-thesis looks controversial at first glance. After all, a person would like to remain the same person, regardless of the time that has passed and any intrapersonal changes that have taken place in the meantime. Any parent will admit that giving different names to their child, depending on whether they are now more Johnny or more Adam, is perverse, to say the least. If my answer to the question of what my name is this morning is that I am a part Adam, a part George and a part Barry, it will be somewhat surprising. Note that the very notion of a parent then becomes more fuzzy as a concept: if I, as a father, have become a different person, for the most part I can no longer be the same parent for my child. The pragmatic difficulties that arise as consequences of the SP-thesis are manifold. The authors themselves point out several, and we have raised many others. On the other hand, the gradability of the SP-relation follows trivially from the definitions of Freddie’s copy adopted in the BMM-model. The only problem is that these definitions have nothing to do with giving an adequate description of human persons.

In this article, we have set out to consider the BMM-model critically, pointing out, among other things, its unreality and discrepancy with personal experience, and demonstrating the methodological flaws of the thought experiment presented there. Nevertheless, our criticism is not directed at any unreal and hypothetical considerations pertaining to persons and their lives. On the contrary, esca** into unreal, fictional, phantasmagorical states—i.e. states that exist increasingly (existentially) heteronomously—is one way of knowing the person as such. Moreover, as Lewin (1936, p. 202) himself stated, “[o]n the whole, processes within the more irreal planes seem to have a closer dynamic relation to the core of the person and to his central needs”. The higher regions of imaginary and unreal reality are thus able to reveal the most important parts of persons, albeit in a different way than thought experiments do. Our criticism, then, is not so much of the general method employed, but rather of its lack of grounding in a holistic view of personhood and the broader philosophico-scientific context for the latter—and thus concerns its inadequacy. Philosophical caution and illusory metaphysical neutrality cannot justify overtly metaphysical views. On the contrary, persons should always be considered in terms of the totality and richness of both intrapersonal and environmental structures. Our thesis is that when Braddon-Mitchell and Miller write about degrees of the SP-relation, they are at best writing about degrees qua dimensions of a person and their life space in the sense of the topology of persons proposed by Lewin.