4. The whole world – and its parts
At the beginning of this paper I made the rather trite remark that the world is the totality of whatever is in the world. However, the remark rests on assumptions which bear further scrutiny. The majority of reductionist programmes, and particularly physicalist reductions, make the assumption that the world can best be described in terms of its most fundamental parts and the relations between these parts. In itself, this is as philosophically unobjectionable as any other specification of a fundamental ontological domain; however, we should be wary of the stronger metaphysical thesis that the world is constructed “bottom-up” from these fundamental entities. If, as Quine suggests, all entities are theoretical posits projected onto the distribution of matter and energy in spacetime, then the “fundamental entities” of this or that theory can be seen as the smallest meaningful subdivision of some area of the world, and the way we establish this subdivision depends on the domain of our investigation (and thus, entities that are fundamental in one area of investigation can be subject to reduction in some other area1). Rather than a bottom-up construction from fundamental entities and relations, this would rather suggest a top-down subdivision of the world into fundamental entities and relations. This corresponds to the distinction between use of the term ‘world’ with the sense ‘specified domain of a given ontology’ and with the sense ‘putative general domain which founds any ontology’. In the second sense, there’s no reason whatsoever to hold that ‘the world’ should be a collection or a composite of individuals: it could just as well be taken as an individual with differentiable parts. Preference for one account or the other depends, once again, on one’s metaphysical assumptions: the constructivist account is more congenial to presentism, serious tensing, and endurantism, while the bottom-down account is more likely to appeal to four-dimensionalist eternalists.
4.1 Set-theoretical and mereological descriptions of the world
Whether the world is one thing or many is perhaps a matter of idle metaphysical speculation; however, there’s a clear distinction between treating the world as a collection of unit sets and constructions on unit sets and treating it as an individual that is a composite of individuals and parts of individuals2. Set-theoretical approaches construct their ontologies from logically atomic elements upwards, while mereological approaches can either construct their ontologies bottom-up from mereological atoms or define a given level as ‘atomic’ when giving a top-down account of the parts of some individual. As an illustration, take the scientific realist view that the world consists of elementary particles and the relations obtaining between them. On the set-theoretic account of this view, “the world” and the domain of elementary particles is co-extensive – everything is either an elementary particle or a collection of elementary particles, from which it follows that no thing is not either an elementary particle or a collection of elementary particles3. Given a set-theoretical expression, scientific realism is apparently constrained to eliminative physicalism; and while many scientific realists are eliminative physicalists, there’s no prior metaphysical reason for claiming that scientific realism should entail eliminative physicalism.
A mereological account allows us greater freedom: the view that the world consists of elementary particles can be given as stating that any individual is either an elementary particle, or has a proper part that is an elementary particle. On the set theoretic interpretation, any individual is identical to either an elementary particle or a collection of elementary particles; on the mereological interpretation, any individual is either an elementary particle or is correlated with an elementary particle. While this disallows individuals that have no elementary particles as proper parts, it evidently doesn’t disallow that an individual can have both proper parts that are elementary particles and proper parts that are not, though any proper part that is not an elementary particle is nonetheless correlated with an elementary particle. As no individual can exist unless it is has a proper part that is an elementary particle, individuals are ontologically dependent on elementary particles, but we’re no longer obliged to hold that there are only (sets of) elementary particles – as individuals, tables and benches have the same ontological standing as collections of elementary particles, rather than being constructions on sets of elementary particles. In the classical ontology these ‘individuals’ could be described as sets or classes of unit sets of elementary particles, but classlike entities are ‘suspect’ on a mereological account – they are at best fusions of elementary particles4. However, an individual isn’t the fusion of solely those proper parts that are elementary particles, but of all its parts, however they might be described. Furthermore, while a fusion of elementary particles describes the physical base of – say – a table (‘the mass of matter that is a table’) at some time, there is no guarantee that the table as a continuant will comport the same fusion of elementary particles at some other time. Similarly, the masses of matter that constitute the physical bases of the table’s proper parts (top, legs, joints…) at some time might well have been part of some other individual at some previous time – and particularly if the table is made of wood. These distinctions are drawn by Peter Simons5 from Frederick Doepke’s arguments against various objections to apparent superposition; a few pages later (p. 214), Simons makes the following comments on the “reductivist” view that “only the ultimate constituents of which continuants are made [are real], everything else being a logical construction from such ultimate reals”:
“While this attitude rightly emphasizes the importance of material constitution, it overlooks the fact that parts are not always ontologically prior to their wholes. A whole put together out of independently pre-existing parts, and continuing to exist by mere default of anything happening to destroy it, such as a pile of stones, is such an ontologically posterior whole. But interesting integrated wholes, like organisms, possess properties and operate according to laws which are relatively independent of the particular material constituents happening to make them up at a particular time.”
A table has parts – legs, a top – that, at any instant, depend ontologically on the fusions of elementary particles which constitute their material bases. However, this doesn’t coincide with the functional dependence6 of the table’s parts on the table itself as a continuant. Insofar as it allows for a distinction between ontological and functional dependence, the mereological account is more accommodating than the set-theoretical account7.
In a formal ontology, the domain is defined on all objects that have some property or quality; thus, given that the natural language term “world” can only be set as the widest scope of universal quantification, “the world consists of elementary particles” can only be given as the universally quantified disjunction
(x) x is an elementary particle x is a collection of elementary particles
where things that are not individual elementary particles can either be constructed as sets of such unit sets, or eliminated. So, once we’ve set our domain, we must either redescribe the putative entities and relations of any non-regimented language in terms of the entities and relations of the explicit ontology, or simply banish them. This would be unproblematic if the non-regimented domain were restricted – thus, if we limit ‘the world’ to ‘the physical world’, the scientific realist view can be given as a universally quantified conditional:
(x) x is a physical entity (x is an elementary particle x is a collection of elementary particles)
which states no more than what the realist holds to be physical reality. “The world consists of elementary particles and collections of elementary particles” would seem, on a superficial analysis, to have the conditional form “if any thing is in the world, then that thing is an elementary particle or a collection of elementary particles”. However, this conditional is grammatically superficial and logically misleading: if the non-regimented domain (“the world”) is entirely unrestricted, then the apparent conditional can only be analysed as the simple disjunction we gave above: “(x) x is an elementary particle x is a collection of elementary particles” – in other words, the non-regimented domain is a phantom.
On a mereological account, the Universe8 is an individual that is the sum of all other individuals, whatever they may be; at its widest setting, the Universe is the fusion of all such objects. If we take the Universe as an individual corresponding to the non-regimented domain of ‘the world’9, then the pseudoconditional given in the preceding paragraph can be given as a true conditional: if any individual is a proper part of the Universe, then either that individual is an elementary particle, or it has an elementary particle as a proper part. Thus, and while the Universe is correlated with and dependent on elementary particles, we can avoid an account in which the world simply dissolves into the domain of elementary particles.
4.1.1 Disparate wholes, ontological neutrality, and utility
The accounts given above are, of course, no more than an illustration – as I remarked, the view that “the world consists of elementary particles and the relations obtaining between them” is so simplistic as to be a straw man (and in my comments I give no sustained development of the kinds of relation obtaining between individuals, or between an individual and its parts; a more serious account would also examine fields, or spacetime points, regions, and vectors, or alternative formal models, such as quantum logic). In more general terms, however, the ontological neutrality of the mereological approach and its inclusiveness with respect to ‘disparate wholes’ are certainly of use when dealing with particular areas of our day-to-day experience, whatever our views on ‘ontological fundamentalism’. When dealing, for example, with professional organisations (corporations, administrative organs….), such an approach would allow us to analyse organisations as composite individuals10, and would not disallow that we found them on, for instance, a formal ontology of spatiotemporal regions. Given its tolerance for disparate wholes, the organisation can be described as a sum of physical objects, locations, processes, events etc.; furthermore, the mereological approach can distinguish between synchronic organisational descriptions of ‘management structure’ based on ‘professional posts’, and the diachronic operational processes which effectively realise the organisation’s objectives (thus permitting clarification of operational malfunctions arising from confusion between the two). Given its ontological neutrality with respect to individuals that lie partially outside a given domain, it can allow for the observation that the human resources of the organisation are proper parts of human individuals, and can clarify the finalities corresponding to the human individual both with respect to the organisation and with respect to the individual’s wider social context. Indeed, in this final respect a mereological analysis allows us to resolve the apparent distinction in management theory between organisations and their human component: the organisation is an individual that has proper parts that are human, but that also has proper parts that are artefacts, concrete processes, punctual events, causal explanations, operational forecasts, definitions of posts, and what-have-you.
As mereological analyses are arguably ontologically neutral with respect to set-theoretic models we can – if we wish to set a limit to our ‘deep’ ontological commitment – found a clear existential distinction using the usual tools of model theory, while allowing superficial or instrumental commitment to disparate mereological composites. Thus, for instance, we could allow superficial commitment to disparate composites while setting our deepest limit of ontological commitment by some intensional definition with a clear scope such as ‘spacetime regions’11. On our deepest level of commitment, individuals would be constructed from unit sets and sets of unit sets of such regions; their properties and relations would be given by functions on and between these sets. We could thereafter give a local ontology (such as an ontology of tools, or an ontology of professional organisations) by allowing the corresponding compositional criterion that any individual is either delimited by a spacetime region or has a proper part that is delimited by a spacetime region. This would allow us to project or map the various individuals of the local ontology onto spacetime regions: individuation would be a matter of occupying some more-or-less well-defined region12 while identification could rely on putative causal relations obtaining between one region and another13. In an ontology of – say – professional organisations, the general belief that the organisation consists of human agents using certain tools to perform some kind of operation in the real world of space and time restricts problematic entities, properties, or relations to what is largely social or conceptual (mental events, intentions, beliefs, desires, values; but also algorithms, processes, and teleological finalities); and such things are generally associated either with human individuals, or with the tools employed by such individuals. As we can give no clear spatiotemporal localisation for such things, it would seem difficult to accommodate them as discrete individuals in the classical ontology without reducing them to spatiotemporal regions occupied by agents and tools; however, a parallel mereological account allows superficial commitment to the problematic entities as proper parts of individuals without identifying them with those individuals. On the mereological account, any individual would be, or would have a proper part that is, a spacetime region – thus, following the analysis given in section 4.1, any individual is correlated with a spacetime region; from the modal remark that no individual can be neither a spacetime region nor have a part that is a spacetime region it follows that, on this account, individuals would be ontologically dependent on spacetime regions14. From the point of view of deep ontological commitment, an evident explanatory gap would remain concerning what kinds of relation the troublesome mental and conceptual entities might entertain with a spatiotemporally localised individual or individual sum of individuals (as in the purported causal relations obtaining between intentions or objectives and certain courses of physical action); however, the mereological approach could give a pragmatic account of such relations in terms of functional dependency within the local ontology.
4.2 Unity or multiplicity?
In section 3.3.1 I remarked that in the limited areas of professional discourse, those who are linguistically and culturally competent can generally distinguish which kinds of thing are ‘real’, in the sense of ‘having immediate import’, from that which is irrelevant or inappropriate to the ends of professional discourse: indeed, those who confuse what is appropriate or relevant to their professional context with what is not are frequently held to be ‘unrealistic’. This is evidently not a metaphysical judgement – the purportedly guilty party isn’t accused of commitment to things that don’t exist – but is rather functional: the guilty party is confusing that which is functionally dependent on the characteristics and finalities of the professional context with that which is dependent on the characteristics and finalities of some other, more ‘personal’, context. Sociolectal competence is almost invariably a matter of ‘register’: certain domains are appropriate to the sociolect, while others are not. Thus, while an agent might well be competent in the sociolect specific to a given professional situation, this doesn’t imply that she is in some way eliminating entities or situations outside the professional context, or reducing them to the entities and situations appropriate to the professional context15. General linguistic competence subsumes the specific sociolect, and allows the agent to function in a wide range of more or less well-defined situations. In this respect, and while the ontology of a professional organisation might distinguish that which is functionally dependent on the finalities of the organisation from that which is not, it is existentially non-exclusive (and it’s this characteristic that allows us to set a deeper ontological commitment – such as a commitment to spacetime regions). The individuals who comprise the human resources of the organisation overlap the organisation insofar as they have proper parts that are proper parts of the organisation; however, as individuals, they have proper parts that overlap other social composites (family, couple, consumer…) – and in our day-to-day lives we find nothing worthy of remark in such non-exclusiveness.
When given with respect to some aspect of the world, classical ontologies prefer monotony. This isn’t just a matter of model theory – reduction to some fundamental kind or principle is as old as Democritus; concomitant with this is the realist16 view that at most one ‘version’ or account of reality is correct. On either a first-order or a set-theoretic model, and insofar as professional organisations are concerned, any limited or local ontology would dissolve into our most general ontology; if we take the full range of things and situations people can hold as ‘real’ outlined in section 1.2, either these things and situations are susceptible to reduction in terms of the most general ontology, or they should be eliminated. A classical first-order ontology sets its widest limit with respect to some given extension or intensional description, and thereby regiments all things whatsoever over which the theory is supposed to range – and if the theory is metaphysical, then whatever cannot be regimented under the ontology is not part of ‘the world’. In the place of the loose, catholic multiplicity of things that we talk about in our everyday lives with greater of lesser commitment in this or that context, we have either deep commitment to one kind of thing, or no commitment at all.
For those who are not metaphysicians, the unregimented domain is entirely sufficient to the ends of daily life – in the pursuit of our everyday goals, we tend to be less concerned with the descriptive than with the pragmatic and performative aspects of language. However, this doesn’t mean that there’s no pragmatic utility in a descriptive approach to the diverse areas of everyday life (as the pretensions to scientific status of anthropology, sociology, and psychology bear witness), and any descriptive approach that fails to account for the ontological status of the entities over which it ranges risks confusing the scope and the range of its descriptions and representations17 – and this is a major failing of concept-based “applied ontologies” in artificial intelligence and in knowledge representation. In this respect alone, the mereological approach to setting ontological limits allows greater flexibility than does a set-theoretic model. Perhaps more importantly, while the set-theoretic model allows that only one account or version of reality is correct, the mereological account can allow us to construct overlapping versions18; furthermore, if mereology is indeed ontologically neutral with respect to the usual tools of model theory, and if we require some gauge of ‘deep ontological commitment’, such a version can allow that some general domain might underlap our various ‘versions of the world’.
‘World versions’ (cf. Nelson Goodman, “Ways of Worldmaking”, 1978) are not ‘alternative worlds’; nor are they – strictly speaking – ‘possible worlds’ in the tradition of Kripke, Lewis and their commentators. In Goodman’s initial formulation, ‘world versions’ are parallel accounts of reality that, while they may be mutually incommensurate or even incompatible, nonetheless correspond to observed phenomena or states of affairs. Traditional positivist first-order ontology tends to reduce the different accounts of reality to one preferred account (usually that of physical science); from the nominalist view that there is no ‘fact of the matter’ that might decide between competing accounts, Goodman suggests that different accounts give different ‘versions’ of reality that are specific to particular (pragmatic) contexts. Our ‘general understanding of the world’ encompasses several world-versions, depending on our different interactions with the world and our pragmatic objectives in talking about this or that part of the world – and in suggesting that the world has ‘parts’, Goodman draws on his own ‘calculus of individuals’; in terms of more recent developments; contemporary mereology allows us to give more precise formulations of the notion.
When considering the way different ‘world-versions’ might coexist in our widest understanding of reality, we can once again draw on the example of the distinction between a low, long, narrow table and a bench, and that between a table and a desk. Physical theory will describe the characteristics of each as physical bodies, but will not allow description of the functional distinctions between them; nonetheless, the ‘reality’ and even the ‘existence’ of tables, benches, and desks seems more directly evident to us than does the ‘reality’ of elementary particles. Discourse on tables and desks concerns a different ‘part’ – a different ‘version’ – of the world than does discourse on hadrons; though there is no reason why the ‘objects’ of such discourse should not be co-located (or rather, that the objects should not have common spatiotemporal parts) – if physical theory is correct, both tables and desks have parts that are hadrons. If, as Quine holds, ‘objects’ are epistemic posits, the various objects required by different versions of the world are theory-dependent entities – and if there is no ‘fact of the matter’ about which version effectively describes the world, then each version should be judged on its practical success in accounting for whatever ‘part’ of our experience it applies to.
A pluralistic approach to the construction of locally-fundamental ontologies is not without problems, the foremost being the problems of individuation and of our ability to identify ‘the same’ individual from one local ontology to the next (as is the case with human individuals occupying several, semi-exclusive social spheres). I’ve touched on several strategies that could be employed to overcome such problems, setting some basal domain to which individuation is correlated, employing mereological distinctions that allow one individual to be the sum or fusion of its parts from one ‘world-version’ to the next19.
However, the main problem with my present analysis is that it remains firmly attached to the view that there actually are motivated facts-of-the-matter about what is and is not real. I shall address this misapprehension in my forthcoming posts.
1 Roberto Poli of Trent University, Italy, has developed an account of ‘chronotopoids’ which largely corresponds to this notion (private correspondence).
2 Cf. Barry Smith, “Objects and Their Environments: From Aristotle to Ecological Ontology” in Frank, Raper and Cheylan (eds.), The Life and Motion of Socio-Economic Units, Taylor and Francis, 2001
3 Simplifying ‘thing’ to ‘object’ in the lay sense – for reasons of economy I’ll forgo further comment on the properties of such particles, on the relations between them, and on the status of spacetime (all of which should be taken into account if the view is the expression of a slightly more sophisticated scientific realism). An elementary particle is difficult enough to describe as a ‘thing’ – the term “material object” is of course entirely inappropriate; furthermore, if we wanted to be more precise, we should consider both particles and fields. The example given is, of course, so naïve as to be a straw man, but as my present intention is neither to defend nor to criticise scientific realism, it will – I hope – suffice.
4 This isn’t to say that we can’t give a mereological account that has the reductive force of the set-theoretic account – for example, we could hold that elementary particles are mereologically atomic, and that no individual that is not an elementary particle is a mereological atom, and that any individual is either a mereological atom or a fusion of such atoms (as are its proper parts, unless the proper part is a mereological atom).
5 Parts: a Study in Ontology, OUP, 1987, p. 212.
6 Cf. Simons, Op. Cit., p. 254. See also the well-known puzzle, due to Plutarch and Hobbes, of the Ship of Theseus.
7 Some have held mereology to be “ontologically innocent” (cf. Rolf Eberle, Nominalistic Systems, Kluwer, 1970; and notably David Lewis, Parts of Classes, Wiley-Blackwell, 1991); lack of space forbids me to develop the various arguments for and against the ontological neutrality of mereology and its innocence with respect to the objects of set-theoretic ontologies. Achille Varzi develops some of the arguments for and against ‘disparate wholes’ in his Stanford article on mereology: http://plato.stanford.edu/entries/mereology/.
8 Following Simons, the capitalised “Universe” distinguishes the mereological from the everyday use of the term.
9 But we should bear in mind Peter Simons’ warning against any too-hasty assimilation of mereological and everyday uses of the term “Universe” (cf. Op.Cit. p.134).
10 If a professional organisation is an individual entity, it’s evidently a composite individual.
11 Postulating unit sets and sets of unit sets of spacetime points would comport additional difficulties which I’ll discuss elsewhere.
12 Also allowing for discontinuous regions.
13 Cf. Quine, “Events and Reification” in LePore and McLaughlin (eds.), Actions and Events: Perspectives on the Philosophy of Donald Davidson, Basil Blackwell, 1985.
14 This parallels but doesn’t reproduce theories which hold that certain entities supervene on more fundamental entities. Nonetheless, Kim’s notion of “mereological supervenience” (cf. Kim, “Supervenience and Nomological Incommensurables”, American Philosophical Quarterly 15, 1978) is incompatible with Leśniewskian mereology as it takes as its basis that wholes are nothing but the sum of their parts.
15 Unfortunately, certain managers behave as if the agent should eliminate or reduce extra-professional concerns.
16 ‘Realist’ as opposed to ‘nominalist’.
17 Cf. the problems evoked in section 4.1.4 above which can arise in a professional organisation when middle managers confuse the synchronic organisational descriptions of ‘management structure’ based on ‘professional posts’ with the diachronic operational processes which effectively realise the organisation’s objectives.
18 Cf. Goodman, Ways of Worldmaking, Hackett, 1978).
19 In this respect the mereological account conforms to our usual understanding of, say, the relation between an individual and its temporal parts (cf. Theodore Sider, Four-Dimensionalism: an Ontology of Persistence and Time, OUP, 2001) but differs from usual strategies for identifying an individual across possible worlds (save for certain quasi-mystical many-world interpretations of ‘quantum mind’).