Chapter 12 Varieties of Parthood: Ontology Learns from Engineering

Abstract

The abstract discusses mereology, which is the study of parts and wholes, and how it's applied in ontology (the branch of philosophy dealing with the nature of being). It points out that while some aspects of mereology are widely accepted, others are more controversial. The paper criticizes the tendency for oversimplification in this field and suggests that a closer look at how parts are used in engineering could provide valuable insights.

In engineering, understanding how different parts of an artifact fit and work together is crucial. The paper highlights the complexities and challenges in defining what exactly constitutes a 'part' of something, especially considering that the definition can change depending on the stage of the artifact's life. This can lead to practical issues, such as having multiple bills of materials (lists of parts needed) for different stages of a project.

Additionally, the concept of a 'material feature' in engineering, which refers to a characteristic part of a material, is discussed. This concept is somewhat related to, but not exactly the same as, the mereological concept of a part. This exploration aims to clarify and enrich the understanding of how parts are viewed and used in different contexts, particularly in engineering.

12.1 Introduction

The introduction of this paper contrasts the long history of humans creating and assembling artifacts with the relatively recent philosophical interest in the concept of parts and wholes. Since the first tools were made, people have been intuitively understanding and using the idea of parts combining to form a whole, especially in fields like engineering and construction. However, philosophers only began to focus on the part-whole relationship in the late 20th century, with the development of formal theories known as 'mereology'.

The introduction highlights the work of philosophers and logicians like Edmund Husserl, Stanisław Leśniewski, and Alfred North Whitehead, who contributed significantly to the formal understanding of mereology. Despite these advancements, the paper argues that philosophical theories on parts and wholes are too narrow to fully encompass the wide range of part-concepts used in practical applications, particularly in engineering.

The author suggests that a better understanding of parts and wholes requires looking beyond philosophical theories to real-world applications, particularly in engineering. This approach would provide a more diverse and accurate understanding of how parts are perceived and used in different contexts. The paper aims to review the limitations of current philosophical views on mereology and to emphasize the importance of incorporating empirical data from fields like engineering to enhance our understanding of the part-whole relationship.

12.2 Philosophical Mereology

The section "Philosophical Mereology" in the paper discusses how mereology, the study of parts and wholes, was initially developed for mathematical purposes, specifically as an alternative to set theory and as a framework for geometry. However, by the late 20th century, mereology became a crucial tool in ontology (the study of being) and metaphysics, with many philosophical debates involving mereological concepts.

Despite its importance in philosophy, the paper argues that the mereology used by philosophers, which heavily relies on algebraic assumptions, is often irrelevant to engineering practice and theory. Engineering, which deals with the practical assembly and function of parts in artifacts, presents its own complex set of mereological problems. These problems are not adequately addressed by the abstract mereology favored by philosophers.

The author contends that there is a significant gap between the "pure" mereology of philosophers and the "applied" mereology of engineers. This gap arises because philosophical theories on mereology have become too abstract and detached from practical applications like engineering. The paper emphasizes the need for philosophers to understand and articulate the differences between these two approaches to mereology. By doing so, philosophical theories can be more aligned with real-world considerations and applications, particularly in engineering contexts.

12.3 Uncontroversial Principles of Parthood

In "Uncontroversial Principles of Parthood," the paper discusses basic principles that define the relationship between parts and wholes in mereology (the study of parts and wholes). These principles are:

Irreflexivity (IRREFL): This principle states that if A is a part of B, then A cannot be identical to B. In simple terms, a part of something cannot be the same as the whole.

Irreflexivity (IRREFL): Consider a wheel of a car. The wheel is a part of the car, but it is not identical to the entire car. So, in this context, the wheel (A) is a part of the car (B), but the wheel (A) is not the same as the car (B).

Asymmetry (ASYMM): If A is part of B, then B cannot be part of A. This means the relationship of being a part cannot be reciprocal or mutual between two entities.

Asymmetry (ASYMM): If you think of a leaf on a tree, the leaf (A) is a part of the tree (B), but the tree (B) cannot be a part of the leaf (A). The relationship is not reciprocal.

Transitivity (TRANS): If A is part of B and B is part of C, then A is part of C. This principle demonstrates how the part-whole relationship can extend across multiple entities.

Transitivity (TRANS): Consider a brick in a wall of a house. The brick (A) is a part of the wall (B), and the wall (B) is part of the house (C). Therefore, the brick (A) is also a part of the house (C).

To further clarify the part-whole relationship, the paper introduces additional concepts:

Coincidence (Def.COIN): A coincides with B if either A is identical to B, or if A and B are not identical but have the exact same parts.

Coincidence (Def.COIN): If you have a collection of LEGO bricks assembled into two different shapes, Shape A and Shape B, and they consist of the exact same LEGO bricks, then Shape A coincides with Shape B. They are different as wholes but have the same parts.

Ingredient (Def.INGR): A is an ingredient of B if A is part of B or A coincides with B. This definition includes the case where A and B are identical.

Ingredient (Def.INGR): In a smartphone, a microchip (A) is an ingredient of the smartphone (B) because it is part of the smartphone. If the smartphone and its protective case are identical in every part (which is unlikely but for the sake of example), they are also ingredients of each other.

Disjointness (Def.DISJ): A is disjoint from B if nothing is an ingredient of both A and B. This implies that there are no common parts between A and B.

Disjointness (Def.DISJ): The engine of a car (A) is disjoint from the car’s trunk (B) as there are no common parts or ingredients between the engine and the trunk.

Supplementation (SUPPL): If A is part of B, then B must have a part that is disjoint from A. For example, if the frame is a part of a bicycle, there must be other parts (like wheels) that are not part of the frame.

Supplementation (SUPPL): If you consider a page (A) in a book (B), the page is part of the book. According to SUPPL, the book must have parts that are not the page, like other pages or the cover, which are disjoint from that particular page.

These principles are considered uncontroversial and foundational to understanding the part-whole relationship in mereology. They help to distinguish the part relation from other similar relations and provide a clear framework for analyzing complex structures made of multiple parts.

12.4 Contentious Principles

The section on "Contentious Principles" in the article discusses two advanced principles in mereology (the study of part and whole relationships) that go beyond basic principles and have stirred debate among philosophers. These are:

Mereological Extensionality (EXT): This principle states that things which coincide (have the same parts) are identical. It's similar to the idea in set theory that sets with the same elements are the same. However, this principle faces challenges when considering objects like a casting made from metal, where the sum of the metal parts could have formed other things, or a dry stone wall, which is not the same as the mere sum of its stones because rearranging the stones destroys the wall.

Universal Composition (UC): This principle suggests that any collection of individuals, no matter how random or unrelated, forms a further individual, or a mereological sum. This leads to bizarre conclusions, like the existence of a whole composed of unrelated parts such as Napoleon's left foot and someone's left hand at different points in history.

These principles, especially UC, lead to absurd scenarios and ontological issues, like the existence of strange combinations that have no basis in common sense or practical reality. The article critiques these principles for being too far removed from practical considerations and real-world applications, particularly in fields like engineering. The article also touches on the debate about under what conditions a collection of parts forms a whole, with UC and Radical Atomism (RAT) representing two extreme positions in this debate. The article suggests that these philosophical debates have become disconnected from common sense and practical application.

12.5 Ambiguities of ‘Part’

The section "Ambiguities of ‘Part’" discusses the complexities and subtleties in the use of the term 'part' in philosophy, especially in mereology, the study of part-whole relationships. This complexity arises from the different ways the term 'part' is used, which can lead to misunderstandings or oversimplifications.

Distinction between 'is part of' and 'is a part of': This distinction is crucial in understanding mereology. For example, the paint on a car 'is part of' the car but wouldn't typically be referred to as 'a part of' the car, unlike more distinct components like the engine or steering wheel. This distinction reflects the flexibility of 'part of' in everyday language compared to 'a part of.'

Mass Terms vs. Count Terms: The term 'part' is used differently with mass terms (like 'paint' or 'steel') and count terms (like 'car' or 'elephant'). In mass terms, 'part' refers to components of a mixture (like gases in air), while in count terms, it refers to distinct elements or components of an object.

Singular and Plural Use of 'Part': The term 'part' can be used both singularly and plurally, but its use can be grammatically complex. For example, "women are an important part of the electorate" (not "parts of the electorate"), illustrating how 'part' is used with plural terms.

Interchangeability with 'Some of': In many cases, 'part of' can be interchanged with 'some of.' For example, part of the air in a cabin is the same as some of the air in the aircraft. However, for singular items, 'one of' is used instead of 'some of.'

Conception of Material Constitution: This concept, important in engineering, deals with objects being made of materials or matter. For instance, an engine casting is made of alloy, and a stone wall is made of stones. In complex artefacts, the relationship between parts (count terms) and materials (mass terms) can be intricate and is often overlooked in philosophical discussions.

The article highlights the need for a more nuanced understanding of the term 'part' in philosophical discussions, particularly in mereology, and suggests that this understanding should be informed by practical applications, such as in engineering.

12.6 More Specific Part-Concepts

12.6.1 Physical Part

The section "More Specific Part-Concepts" focuses on the concept of a physical part, or p-part, in mereology. This concept is useful for understanding how certain parts relate to a whole in a physical context. Here's a concise explanation:

Physical Part Concept (p-part): This concept refers to a part of an object that, if separated from the rest, could exist as a physical object in its own right. For example, each half of a metal bar can be considered a physical part of the whole bar. Even if not currently detached, these halves have the potential to be separate physical entities.

Causal Internal Connection: A p-part is usually internally connected in a causal sense but isn't necessarily a maximally connected whole. This means that the parts are linked in a way that they could function or exist independently if separated.

Example of Physical Part vs. Non-Physical Part: If a metal bar is divided into alternating sections (1–2 cm, 3–4 cm, 5–6 cm, etc.), each section is not a p-part of the bar because separating these sections results in multiple objects, not a single physical object. To form a new p-part, these sections would need to be fused into a cohesive unit.

Connected vs. Disconnected p-parts: The concept might be further refined to distinguish between parts that are physically connected and those that are not, though this distinction needs more exploration.

Relation to m-parts (mereological parts): All p-parts are also m-parts, but the reverse is not true. Mereological parts do not necessarily have internal causal cohesion, which distinguishes them from p-parts.

This concept of physical parts is particularly useful in practical fields like engineering, where understanding the physical and functional relationships between parts of an artifact is essential.

12.6.2 Salient Part

The section "Salient Part" in the paper discusses a specific type of part known as an s-part, or salient part. Here's a concise explanation:

Salient Part (s-part): This concept refers to a part of an object that is particularly noticeable or prominent due to certain characteristics. These characteristics can include geometric prominence, material, or qualitative differences from adjacent parts.

Examples of Salient Parts:

The lower part of an aircraft fuselage painted a different color than the upper part, such as a white upper and a blue lower. The distinct line separating these two colors is designed to be visually noticeable and may convey a message, like speed or elegance.

Carburetor bulges on older sports cars, which may have originally been a functional feature, but over time they became associated with power and speed. As a result, designers began to include them for their symbolic value, even if they weren't functionally necessary.

Intentional vs. Incidental Salience: A part can be salient either by design (intentional) or as a by-product of its function or structure (incidental). In some cases, what starts as an incidental feature can gain symbolic or aesthetic significance and become a deliberately included design element.

In summary, s-parts are not just physically distinct parts of an object, but they are also significant due to their ability to stand out and be recognized for specific reasons, often related to their appearance, function, or symbolic meaning.

12.6.3 Engineering Parts: D-A-R-T

The section "Engineering Parts: D-A-R-T" in the paper delves into how engineers view and categorize parts of an artifact, focusing on the different stages of an artifact's life-cycle. Here's a concise explanation:

Engineering Parts (e-parts): These are parts of an artifact that are of interest to engineers. Not every physical part (p-part) of an artifact is necessarily relevant from an engineering perspective.

Different Roles in Artifact's Life-Cycle:

Design Parts (d-parts): Parts that are conceptualized as individual units during the design phase of an artifact.

Assembly Parts (a-parts): Parts that are treated as separate entities during the assembly process.

Repair Parts (r-parts): Individual parts that are considered and manipulated during repair and maintenance activities.

Retirement Parts (t-parts): Parts that are handled as distinct entities when an artifact is retired or dismantled.

D-A-R-T Acronym: Represents the four roles parts can play (Design, Assembly, Repair, Retirement) in the lifecycle of an artifact.

Multiple Bill of Materials Problem: This issue arises due to discrepancies in how a part is treated at different life-cycle stages. For example, what is a d-part in design might not be an a-part in assembly. This leads to challenges in documenting the mereology (study of part-whole relationships) of complex artifacts across their entire lifecycle.

In summary, engineers categorize parts of an artifact based on their roles at different stages of the artifact's lifecycle. These categorizations are crucial for understanding how parts are conceptualized, assembled, repaired, and eventually retired, and they help engineers manage the complexity of artifacts through their entire life-cycle.

12.6.4 Functional Part

The concept of a "functional part" (or f-part) in engineering refers to a component of an artifact that performs a specific, unified function within the whole system. This concept is crucial in engineering, but it can be challenging to define precisely.

For example, consider a screw head. Its role, or function, is to brace the screw against the material it is supposed to secure. This makes the screw head an f-part, as its function is clearly defined and essential for the operation of the screw.

On the other hand, not all physical parts (p-parts) of an artifact are functional parts. For instance, the left-hand half of a car does not qualify as an f-part. It doesn't have a distinct function like the screw head does. Simply being a segment of the car doesn't constitute a specific function.

A good example of an f-part is a car's windscreen. Its function is to provide forward visibility while protecting the occupants from wind during motion. This function is independent of the part itself and could theoretically be performed by another mechanism, such as a force field, although such alternatives may not be practically feasible.

In summary, f-parts are components of an artifact that have a distinct and essential function in the operation of the whole system. They are a key focus in engineering, as they directly relate to how an artifact performs its intended tasks.

12.7 Material Features

The section titled "Material Features" in the paper discusses a concept related to but distinct from material parts. Material features, like holes, slots, grooves, edges, and cavities, are integral to both natural objects and artificial artifacts, including those in engineering. Unlike material parts, material features are not typically made of matter themselves but are defined by their surrounding matter.

For example, the cross-shaped recess in a screw head that allows it to be turned by a driver is a material feature, as is the helical thread on the screw. These features, like the hole in a washer, are crucial for the functioning of these objects but are not made of material themselves.

Material features share similarities with material parts: they are individual entities located in space, have geometrical shapes, and can have specific functions in engineering. However, they differ in key ways: they generally don’t consist of matter like material parts and they are ontologically dependent on their adjacent material. This means that a material feature cannot exist without the surrounding material that defines it. For instance, a tunnel is a significant engineering feature but is nothing without the material that encloses it.

The concept of material features is extremely important in engineering. They are as crucial as parts because they often define the functionality of an object or a structure. The importance of these features is highlighted in feature-based design in manufacturing engineering. Despite their differences, material features and material parts are closely related, and sometimes the same term is used for both. This close relationship and their functional importance explain why material features are often considered quasi-parts of the objects they depend on.

12.8 Processes and Their Parts

The section titled "Processes and Their Parts" in the paper focuses on the significance of processes in engineering and philosophy. Processes, which include motions, chemical reactions, and physical changes, are fundamental to the functioning of any artifact that involves change. This is why a branch of engineering is specifically dedicated to process engineering.

The paper suggests that, from a philosophical perspective, processes might be more fundamental than static objects (continuants). The key distinction between processes and continuants is that processes have temporal parts or phases, meaning they have distinguishable segments over time. For example, a football match or an explosion has early and later stages, which can be considered as temporal parts of the process. In contrast, objects like chairs or human beings, while they exist over time, don't have such divisible temporal segments within their existence.

Additionally, just like physical objects, processes can also have spatial parts. However, unlike static objects, the parts of a process can undergo significant changes and movements over time.

The paper acknowledges that we are quite adept at intuitively understanding and dissecting the parts of events and processes, as often done in the analysis of historical events, natural disasters, or even biographies. However, the paper points out that relatively little philosophical thought has been devoted to adapting the principles of mereology (the study of parts and wholes) from mathematics and logic to the domain of processes.

12.9 Parts at a Time

The section titled "Parts at a Time" in the paper discusses how, unlike processes that have temporal parts, continuants (objects that persist over time) have parts at specific times and over time periods. This means that continuants can gain, lose, or change parts throughout their existence.

For example, a young man may have a full head of hair, but may become bald in old age. Similarly, a house may initially not have an extension, but one might be added later. In the case of a car needing a new clutch, the old part is removed and replaced with a new one. Some parts of a continuant are permanent (lasting throughout its existence), while others are temporary or even intermittent.

A unique aspect of some artefacts is that they spend more time dismantled into component parts than assembled as a whole. This is common in objects like guns, musical instruments, and complex tools. Additionally, some parts may come into existence solely based on the configuration of other parts, either permanently or temporarily.

The paper points out that the study of how parts exist in continuants at and over time is of great interest to engineers but has been largely overlooked by ontologists (philosophers who study the nature of being). Understanding these dynamics is not only practically important for engineering but also poses intriguing theoretical questions.

An illustrative example is provided from Plutarch's "Life of Theseus," where the ship of Theseus is maintained over time by replacing its old timbers with new ones. Philosophers debate whether the ship remains the same ship or becomes a different one. Thomas Hobbes further complicates this by imagining someone collecting the replaced parts and reconstructing the “original” ship, raising the question of which ship is the “real” one. This dilemma highlights the complex interplay of parts in a whole over time and how clarity in understanding this relationship can help resolve philosophical and practical disputes.

12.10 Conclusion

The conclusion section of the paper addresses the development and application of mereology, the study of parts and wholes. Mereology, which is about a century old, has been an important part of modern analytic ontology, enhancing its scope. Initially developed for mathematics and physics, mereology introduced features that sometimes hinder its application in other areas. These features led to controversial positions in ontology, such as denying the existence of commonly accepted objects or suggesting bizarre, unrealistic entities.

The paper suggests a solution: simplifying the formal understanding of part and whole to include only essential logical properties that define the concept of part. This approach would leave room for the development of more specific part-concepts, tailored to different contexts and needs. By doing so, mereology can be made more adaptable to the requirements of various sciences.

This recommendation benefits both ontologists and other scientific disciplines. Ontologists can apply their expertise in conceptual clarity to practical problems outside philosophy, while the challenges of real-world problems can strengthen their theoretical understanding. This approach fosters a mutually beneficial relationship between ontology and other fields, ensuring that mereology remains a versatile and applicable theory across different domains of knowledge.