Wholes and parts

Introduction – Wholes and Parts

Aristotle’s quote (above) expresses a deep philosophical problem that has persisted to this day – a question about wholes and parts . . . their reality, properties, and relations . . . a specialized study called mereology.

On what grounds do we differentiate the objects of our experience? How do we group the smaller or less inclusive into the larger or more inclusive ones? How discrete is one object when compared to another? Which of the objects of our experience exist in the world, and which are creations of our minds?^[11]

These are not trivial questions because the way we answer reflects our view of what is ‘real’, and therefore worthy of scientific investigation.

For a more detailed philosophical; account of this topic see the Stanford Encyclopaedia of Philosophy article on mereology.

Historical background

Mereology, the branch of philosophy that deals with the study of the compositional properties of the world in relation to wholes and parts, has a rich and complex history that has evolved over centuries. The philosophical exploration of the nature of parts and wholes dates back to ancient times, but it was not until the 20th century that mereology as a distinct discipline began to take shape. This essay aims to provide a formal and comprehensive overview of the development of mereology, tracing its key milestones and contributors from antiquity to the present day.

The origins of mereology can be traced back to the ancient Greek philosophers, particularly Parmenides and his student Zeno. Parmenides’s famous paradoxes, such as the paradox of the heap and the paradox of Achilles and the tortoise, raised fundamental questions about the nature of parts and wholes and the relationship between them. These paradoxes challenged traditional notions of unity and plurality and laid the groundwork for the development of mereological theories in later centuries.

In the Middle Ages, scholars like Aristotle and Thomas Aquinas continued to grapple with questions of composition and unity, laying down the foundation for further exploration of mereological concepts. Aristotle’s discussions of substance and attributes, form and matter, and the hierarchical structure of reality all contributed to the development of mereological thought.

The early modern period saw a resurgence of interest in mereology, with philosophers such as René Descartes and Gottfried Wilhelm Leibniz incorporating mereological considerations into their metaphysical systems. Descartes, for example, distinguished between the material world of extended substances and the immaterial world of thinking substances, highlighting the fundamental divide between parts and wholes in his dualistic framework.

In the 20th century, mereology emerged as a distinct branch of philosophy with the groundbreaking work of Polish logician and philosopher Stanislaw Leśniewski. Leśniewski developed a formal system of mereology based on the principles of part and whole, leading to the establishment of mereology as a formal discipline within symbolic logic. Leśniewski’s contributions laid the groundwork for later developments in mereological theory and set the stage for a renewed interest in the study of parts and wholes within analytic philosophy.

One of the most influential figures in contemporary mereology is the American philosopher David Lewis. Lewis’s counterpart theory, outlined in his seminal work “Parts of Classes,” proposed a radical rethinking of the relationship between individuals and their parts, challenging traditional notions of identity and existence. Lewis’s theory of counterpart relations and modal realism opened up new avenues for exploring the nature of composition and the boundaries of objects in the world.

Another key figure in the development of mereology is the Australian philosopher Peter Simons. Simons’s work on ontological dependence and mereological essentialism has reshaped the way philosophers think about the relation between parts and wholes. His distinction between mereological wholes and sums, as well as his exploration of supervenience relations, has greatly influenced contemporary debates in metaphysics and ontology.

Contemporary mereology is a vibrant and diverse field, with scholars drawing on a wide range of philosophical traditions and methodologies to explore the nature of composition and unity in the world. From formal approaches grounded in symbolic logic to more speculative inquiries into the nature of parts and wholes, contemporary mereologists continue to push the boundaries of our understanding of the fundamental structure of reality.

In conclusion, the history of mereology is a testament to the enduring fascination with the nature of parts and wholes and the intricate relationships that define the composition of the world. From the ancient Greek paradoxes to the formal systems of modern logic, mereology has evolved into a sophisticated and multifaceted discipline that continues to shape contemporary debates in metaphysics and ontology. As philosophers grapple with questions of unity, identity, and existence, the study of mereology remains a vital and dynamic area of inquiry that promises new insights into the fundamental nature of reality (AI Sider July 2024).

Polysemy & conceptual analysis

There is a lack of clarity in what we mean when we make a statement like ‘the whole is more than the sum of its parts’ – or we say that something has been ‘reduced’ to something else. Both claims are ambiguous because they can be interpreted in several ways – they have multiple meanings (polysemy).^[2]

Aristotle’s simplified statement – that ‘the whole is more than the sum of its parts’ – is one of unhelpful generality because we can defend or deny its claims according to what is meant by ‘whole’, ‘sum’ and ‘part’. The number three, for example, might be considered a combination of the numbers one and two, but to claim that three is more than the sum of one and two does not make sense. In contrast, the unified functional agency of an organism is clearly more than the sum of the heap of molecules out of which it is composed.

Such claims must therefore be examined on their individual merits.

In contemplating parts and wholes, we are immediately confronted by an ancient philosophical paradox (dilemma, contradiction, antinomy) – the problem of the one and the many.

We can, on the one hand, claim with equal validity that the world consists of a variety of things . . .  just look around. On the one hand, there is a long philosophical tradition that reduces this complexity to one thing. Perhaps atoms, or maybe energy, number, space-time, or information? The appeal of the ‘one’ is that it provides security – an eternal sameness in a world of apparent difference and change. The ‘one’ provides a bedrock or foundation. It is fundamental or, in philosophical terms, ontologically prior to everything else. The ‘many’ is really only the ‘one’ in many guises.

We will not solve this problem here – but we can look at one of its manifestations.

Part & Whole

Our common sense tells us that objects can be mental and/or physical: that is, they can exist in the world, or in our minds, and perhaps both. When I see a table, I am seeing the image on my retina of a table that actually exists in the world?

To think and experience is to think and experience something. Mental activity is always about something, it is intentional.

We need units of thought – let’s call them concepts. As a matter of psychological necessity, we use concepts of generality and particularity. We might call this the detail or grain of our thought. Examples of very general concepts would be matter, space, time, or music. Then, to establish particularity, it becomes psychologically helpful to break up the generalities into units that act as building blocks out of which we can then construct a framework of thought.

These units are standards or yardsticks against which we measure and construct other things. Sometimes there seems to be a single foundational unit, like the atom of Democritus, the brick of a house, or the biological notoriously-difficult-to-define species. Biologically at the microscopic scale we have cells. Sometimes we just use a range of convenient units without placing emphasis on one as being fundamental to all the others. The unit of music is the crotchet, perhaps (whole note), as a foundational note that can be added to, or subdivided. The unit of time is, perhaps, the second or minute, while ‘now’ is contentious. Number systems seem to rest on the building block of a single unit, number one. Spatial measures, like centimetres, metres, miles and so on, seem to lack a foundational unit.

Perhaps it is a feature of our mental processing that we need objects to which we tether our thoughts. And, since we intuitively recognize the importance of these anchors, they take on special significance in our experience.

Principle 1 – our minds focus on units of experience and thought, some of which are representations of the external world. Science attempts to maximize the intelligibility of the relationship between our representations and the external world

Black-boxing

Another characteristic (innate limitation?) of our human minds is that we cannot think of everything we know and have experienced, all at once. We overcome this by concentrating on particular aspects, events, circumstances, or parts – and that means taking all else for granted. This is sometimes expressed scientifically as the principle of ceteris paribus or other things being equal.

When we assume that the universe is the largest possible physical ‘whole’, everything within it is, in some sense, no matter how obscurely, related to everything else. It follows that if we are to understand and explain the universe in its entirety then the most effective way of doing so is to provide some kind of total circumscription – otherwise we will be leaving some parts out and the explanation will be incomplete. But describing the entire universe scientifically in all its complexity seems an impossible task so, according to cosmologist Stephen Hawking: ‘

Instead, we break up the problem into bits and invent a number of partial theories. Each of these partial theories describes and predicts a certain limited class of observations, neglecting the effects of other quantities . . .’ . . . but . . . ‘ If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution by investigating parts of the problem in isolation’.^[6]

Hawking has, it seems, has arrived at Aristotle’s insight – that the whole is more than the sum of its parts. 

Our difficulty with this insight is more one of psychological resistance than intellectual persuasion. Aristotle made a compelling argument that an organism, as unit of functional organization, is more than its material constituents. But we still find this a mental barrier – how can the organism possibly be more than its associated parts?

Context, open & closed systems

This presents us with a further philosophical difficulty. What would a total circumscription of the universe look like? And even if physics were to provide a summary of the universe in a neat equation – this would only be a summary of everything as understood by (in the context of) physics.

It seems important to state our particular viewpoint, the context, aspect, or perspective from which we are approaching such a question.

Perhaps another way of expressing this difficulty is to regard it as a matter of context: what exactly is under consideration and what is not? Are we dealing, explicitly or implicitly, with an open or closed system?

This relates to the analytic and synthetic approaches to explanation. To be objective we can study an object or event within its total context, or we can isolate it from this context in order to manipulate or consider a limited range of variables.

Let’s try to tease out some basic distinctions and ideas.

Part – a part is generally related to and explained in terms of the whole of which it is a part. This simply follows the semantics: if it is a part then it is a part of something else; that is, our understanding of a part depends on its role within a wider context. To understand and explain an ant as a part, rather than a whole, we need to know how it interacts with other ants and its environment

Whole – again, following the semantics, a whole is generally (though perhaps not so strongly as the part) related to and explained or analysed in terms of its constituent parts To understand and explain an ant as an individual organism we need to know about its parts and the way they interact

Paradoxically, every^[3] object in the universe (apart from the universe itself) can be both a whole and a part. An ant is a whole individual but it is also a part of a colony . . .  and so on. This creates a cognitive dissonance since we feel intuitively that something cannot be these two things at the same time, both a whole and a part.

If you break a rock in two, do you then have two rocks – or one rock in two parts? Like a visual illusion this cognitive illusion occurs because we contemplate situations from one viewpoint at a time, not several at once. This situation becomes further complicated when we include the temporal properties of actuality and potentiality. When we ask ‘Which came first, the chicken or the egg?‘ we waver between considering the wider context by ‘looking forward’ to a destination and whole (becoming a chicken), or ‘looking backward’ to an origin and part (the egg) that gave rise to the chicken. Similarly, we might think of an acorn as either having the potential to produce a tree (see purpose) or of a tree as having the potential to produce acorns . . .  even though both apply.

Our minds continuously flip-flop between past, present, and future – between history and potentiality, anticipation and retrospection – and between wholes and their parts.

This does not mean it is impossible to consider an object in terms of both its wider context and constituent parts. 

There is a famous logical dilemma. Wholes are of two different kinds: those which contain themselves as members and those which do not. The set of all of the people in a room does not contain itself because all the people together do not make another person. However, all the piles of sand in the world put together would constitute an additional collective pile of sand. A proper part of an object is a part that is not identical to the whole. This leads to various errors and ambiguities, notoriously Bertrand Russell’s 1901 paradox in set theory concerning the set of all sets that do not contain themselves as members, such that the condition for a set to contain itself is that it should not contain itself.

Can we draw any general conclusions from these observations about the way the human mind works?

Analysis vs synthesis

It is a characteristic of explanation that we do not explain an object in terms of itself: explanations proceed either to component parts or a broader context. Using metaphorical hierarchy-talk, explanations can proceed in two ‘directions’ – by ‘upward’ synthesis or ‘downward’ analysis. Almost any item in the universe can be divided into smaller parts or united into larger wholes, and that is how we explain things.

When a whole is explained in terms of its parts we refer to this as analysis. Analysis adopts the mental perspective of the whole. It is the whole that is, as it were, demanding the explanation.

When we explain something (as a part) in terms of a wider whole or context we refer to this as synthesis. Synthesis thus adopts the mental perspective of a part within something greater.

For example, ‘A house is an assemblage of bricks‘ (analysis). ‘My legs are attached to, and mobilize, my body‘ (synthesis).

As we have seen, almost all objects in the universe (and our minds) are both wholes and parts. So, just as we can analyze an object into progressively smaller and smaller or less inclusive parts in an infinite analytical regress (or until a least-inclusive ‘rock bottom’ foundational or fundamental situation is reached), so we can also synthesize them into ever more inclusive wholes in an infinite synthetic regress (or until an all-inclusive ‘rock top’ is reached).

This raises interesting questions and possibilities concerning the metaphorical symmetry of explanation.

Analytical reductionism

The Western world has, for several hundred years, been living through an intellectual phase of intellectual preoccupation with analysis. Like other fashions and phases it is not questioned, it is simply taken for granted, the given way of proceeding. Bertrand Russell, who had a profound influence on analytic philosophy, describes this ‘direction’ of explanation as follows:

‘. . . the last of my initial prejudices, which has been perhaps the most important in all my thinking. This is concerned with method’ . . . ‘to start from something vague but puzzling, something indubitable but which I cannot express with any precision. I go through a process which is like that of first seeing something with the naked eye and then examining it through a microscope. I find that by fixity of attention divisions and distinctions appear where none were at first visible . . . analysis gives new knowledge without destroying any of the previously existing knowledge. This applies not only to the structure of physical things, but quite as much to concepts . . . belief in the above process is my strongest and most unshakable prejudice as regards the methods of philosophical investigation’.^[10]

Russell was echoing the second principle of Descartes:

‘ . . . to divide each of the difficulties that I was examining into as many parts as might be possible and necessary in order best to solve it’.

Here we have two key proponents of a Western intellectual tradition, sometimes called analytical reductionism and its statement of conviction about a particular manner of intellectual investigation . . . analysis.

It is a method that lies at the core of scientific procedure and gives its name to a strong tradition in Western philosophy – ‘analytic philosophy’. The principle is simple: to comprehend or explain either a physical object or a concept (a whole) we must investigate its parts and their relations.

Let’s extend, using a thought experiment, Russell’s analogy of the microscope as a means of achieving explanatory focus.

Imagine you have an extremely powerful new scientific instrument like a combined microscope and telescope – we can call it a micro-macroscope. The first objects you see as you look into the instrument have no recognizable form. We can call them molecules. But when you adjust the instrument by zooming out you see the molecules seeming to coalesce into something that looks like a leg, then zooming out further you see that the previous object really was a leg, that the leg belongs to a person, zooming out more we see that the person is one among many people living in a city, which is part of a country, which is part of planet Earth, which is part of the solar system, the galaxy, and the universe. Perhaps you can also imagine a scientific future when further objects can be added at the limits of this caricature – at one extreme much smaller objects, smaller than fermions and bosons, and at the other extreme our universe merging into a multiverse.

The micro-macroscope gives us a way of thinking about and challenging our scientifically learned cognitive categories (see Immanuel Kant) and the way this cognitive focus translates into explanatory focus: it allows us to look at the landscape of the universe both ‘up’ and ‘down’, viewing the same scenery, but from different scales and perspectives.

Principle 3 – The physical units of matter have no intrinsic (ontological) precedence one over the other: an electron and a marigold possess existence (‘being’) equally

Hierarchical metaphor

The methods of analysis and synthesis attracts hierarchical metaphorical language.

When we proceed from the smaller to the larger, or from the less inclusive to the more inclusive then we compare this metaphorically to movement in space. We are looking in opposite ‘directions’, either ‘up’ (progressive inclusivity) or ‘down’ (progressive division) or maybe ‘forward’ (to greater inclusivity) or ‘back’ (to greater reduction).

With this metaphor of a spatial hierarchy we regard analysis as reduction, a ‘looking downwards towards the bottom’. But when we think synthetically by understanding and explaining how something fits into a wider context we say we are either ‘looking upwards towards the top’. If we can steadily and systematically ‘build up’ the universe from its fundamental particles into greater wholes and their relations, we can also ‘break down’ the universe from its totality into its simplest parts. Our explanations, including our scientific explanations, thus take us ‘up’ and ‘down’ the ladder of life or great chain of being. The scientific consequences of hierarchical thinking are discussed elsewhere.

The holon

The word ‘holon’ was coined by Arthur Koestler in The Ghost in the Machine (1967, p. 48) to designate the part-whole hybrid – something that is simultaneously both a whole and a part. He was clearly thinking in terms of organic systems:

‘Holons are autonomous, self-reliant units that possess a degree of independence and handle contingencies without asking higher authorities for instructions. These holons are also simultaneously subject to control from one or more of these higher authorities. The first property ensures that holons are stable forms that are able to withstand disturbances, while the latter property signifies that they are intermediate forms, providing a context for the proper functionality for the larger whole‘.

For our purposes ‘holon’ is a term expressing a duality of potential explanation of every object as simultaneously a whole that can be subdivided and analyzed in terms of its parts, and a part that can be synthesized into a wider whole.

Principle 2 – every object is a holon – it is simultaneously both a whole and a part: we can understand and explain it analytically, in terms of its constituent parts, or synthetically in terms of its place within a wider context

Principle 3 – the scientific need for explanation (like the philosophical requirement for rational justification or causal origin) leads to an explanatory regress which is either analytic (segregating into ever smaller parts or scope) or synthetic (combining objects into a progressively wider context)

More than its parts?

Now let’s look more carefully at the general question ‘In what possible sense can a whole be more than the sum of its parts?‘ How, for example, can a building be more than the materials out of which it has been constructed?

The prime example here is that of an organism. It might be claimed, for example, that an organism is more than the sum of its parts. But, if we remove all the molecules that make up its body then what is left?

Nothing is left.

Consequently, we might conclude that the claim that there is something else, something more, is either false or that the ‘more’ that is being asserted is something mysteriously abstract and immaterial . . . something that either does not really exist, or which should be ignored. If it is immaterial then it is likely some kind of illusion, something that isn’t ‘real’.

However, the ‘more’, it turns out, is not the molecules or matter of the organism but the relationship that exists among these material objects – it is their organization or structure – their particular spatial arrangement and mode of dynamic interaction.

A dead organism is a collection of organic molecules. A living organism is a functional structure with agency – it can reproduce, metabolize, grow etc. It is this functional organization that makes an organism an organism and not a collection of molecules. This is the abstract and immaterial ‘more‘ that turns molecules into a living organism.

Aristotle’s formal cause

For many scientists this is a step too far. The more described here is akin to Aristotle’s form that was rejected by scientists during the Scientific Revolution as being too philosophically abstract. He had postulated four causes (different kinds of reasons that are offered as scientific explanations – the ‘becauses’ of existence and change) – the material, efficient, formal, and final causes. The Scientific Revolution rejected the formal and final causes as too philosophically abstruse, if not outright mistaken. But today, as in Aristotle’s day, and in spite of modern scientific advances, we are still forced to accept that in addition to the matter of the universe there are abstract (immaterial) properties and relations that have causal efficacy and are as real as matter itself.

Though scientific pride might still prevent us from accepting two of Aristotle’s ’causes’ – his formal cause and telos – it is nevertheless time to acknowledge that scientific explanation, especially in biology, incorporates abstract properties and relations within its explanatory realm.

Novelty in nature occurs, not only through the arrival of new matter, but with the emergence of new forms of matter as new properties and relations.

More than this. Immaterial properties and relations have causal efficacy. It is only organic molecules unified and integrated into a particular set of properties and relations that can express agency.

Principle 4 – only by studying parts and their dynamic relations can we really come to grips with physical reality: parts alone are not sufficient

Principle 5 – a collection of physical objects is not something in physical addition to the objects themselves, what is extra is something abstract (that is real) – it can be regarded as a power or property that is real but not physical

Principle 6 – though all physical objects consist of matter, the abstract (immaterial) organization of this matter generates properties and relations that can have causal influence on physical structure

Now, from Principle 6 we can see that although we can indeed describe social and biological phenomena in terms of their physical components there is additional information, as new properties and relations, that must be accounted for. Further, even given full physico-chemical knowledge it may not be (or would be nigh impossible) to build up from scratch or anticipate these new properties.

Most scientists would agree that a chair and the arrangement of molecules out of which it is made are one and the same. But, as Aristotle pointed out over 2000 years ago, it is not just molecules, but their organization that give rise to the particular immaterial properties and relations (the form) that we call ‘chair’.

Key points

To survive in a complex world our minds are continuously establishing units of experience as objects of understanding. These act as points of shifting focus as our priorities change. They are objects that may or may not correspond to physical objects in the world and they are under continuous re-classification and re-prioritization as our minds vacillate between past, present, and future – between actuality and potentiality – between anticipation and retrospection – all within a kaleidoscope of constantly reconfigured wholes and parts.

We explain a part in terms of the whole of which it is a part. This simply follows the semantics: if it is a part then it is a part of something else; that is, our understanding of ‘part’ depends on its role within a wider context. Similarly, a whole is generally (though perhaps not so strongly as the part) related to and explained or analyzed in terms of its constituent parts.

Every object in the universe (apart from the universe itself) can be both a whole and a part. This creates a cognitive dissonance since we feel intuitively that something cannot be these two things at the same time – that is, we tend to assess the situation from the point of view of the whole, or of the part, but not both at the same time. For simplicity we can call an object considered in the context of this cognitive dissonance a holon – it is simultaneously both a whole and a part: we can understand and explain it analytically, in terms of its constituent parts, or synthetically in terms of its place within a wider context.

When a whole is explained in terms of its parts we refer to this as analysis. Analysis adopts the mental perspective of the whole. We can analyze an object into progressively smaller and smaller or less inclusive parts in an infinite analytical regress (or until a least-inclusive ‘rock bottom’ foundational or fundamental situation is reached). It is the whole that is, as it were, demanding explanation. In contrast, when we explain something (as a part) in terms of a wider whole or context we refer to this as synthesis. We can also synthesize parts into ever more inclusive wholes (wider contexts) in an infinite synthetic regress (or until an all-inclusive ‘rock top’ is reached). Synthesis thus adopts the mental perspective of a part examining its role within a broader context.

This discussion on parts and wholes has two important outcomes for science:

First, analysis and synthesis are often described hierarchically in metaphorical spatial terms. This has created a perception of the entire body of knowledge and, indeed, the world as hierarchically organized. We find it natural to view things top-down or bottom-up. Traditionally this hierarchy took the form of Great Chain of Being that expressed moral worth. The unifying God was at the top, followed by humans in their various classes, then animals, followed by plants, then rocks, and the devil in a fiery underworld. Modern science has tended to reverse this ladder with ‘fundamental’ particles the foundation on which all else rests. Historically our scientific emphasis has been on analysis rather than synthesis. For most scientists it is more scientifically significant that we humans are composed of stardust – of simple atoms and molecules – than that life combines these objects into living and unified functional agents.

PlantsPeoplePlanet argues for a flat ontology – that there is no ‘preferred’ viewpoint on existence – see aspect theory.

Second, by looking closely at the more of ‘the whole is more than the sum of its parts’, especially as it applies to living organisms, we are confronted, as was Aristotle, with the fact that immaterial factors, like properties and relations (organization) can have causal efficacy: that formal cause is not, as most scientists have believed since the Scientific Revolution, an immaterial nonsense, metaphysical mystery, or philosophical obfuscation.