Hi I'm trying to discover any metaphysical necessities that connect the properties of a whole and the properties of its parts. I know the properties of the whole can be different than the properties of its parts, and am aware that both the fallacy of division and fallacy of composition are common errors in reasoning, but I am struggling to find out more about it. Would you be able to provide any philosophical references that explore such topics?
To understand the relationship between a part and a whole is one of the central aims of mereology (SEP). If you want to know more, start with that article.
There are philosophers who specialize in such theories. For instance, my shelves contain a copy of Mereology: A Philosophical Introduction by Giorgio Lando in which he discusses different uses of the word "mereology" and puts forth a philosophical thesis of mereological monism. It's a technical read, and he discusses a number of aspects such as mereological formalism, extensionalism, vagueness, and composition.
What Lando does is explore some of the metaphysical necessities that surround the notion of a part and whole. First, he talks about Classical Extenstional Mereology and presents the basic theses:
- parthood is transitive
- given some things, there is at most one thing composed by them
- given some things, no matter how heterogenous and disparate they are, there is at least one thing composed by them
He goes on to delineate a scope of narrow mereology:
According to the narrow understanding of mereology as a discipline I am going to adopt, essentiality, dependence, and supervenience lie beyond the explanatory scope... [the study] is only about the formal features of the relation of parthood, and about identity and existence conditions for wholes.
He draws a distinction between the discipline, the theory, and the philosophical thesis; then he discusses the relationship between his philosophical work and that of David Lewis.
He goes on to say:
The extremely accurate and extensive entry on mereology in the Stanford Encyclopedia of Philosophy by Achille Varzi... is an extremely valuable resource, in particular about the inferential relations between various mereological principles.
And goes on to make claims such as mereology is not logic, that it's imperfectly understood, and addresses the relationship between mereology and abstract entities. He goes on to exclude discussion of the Composition of Identity as a topic (his rationale explained in the appendix), and lays out the plan for the book.
While both the SEP article and the book are complicated reads, they are both thorough, and will go far beyond and above any answers you're likely to get on this site. Mereology is a discipline that has its fair share of convolutions that are NOT intuitive, and are often expressed in FOPL, and touches on enough philosophical thinking such as ontology and identity (SEP) as well that of Quine and others that your average arm-chair philosopher such as myself would have to put in a fair amount of work to even interpret source materials.
The only type of systems where the whole has the same properties than the parts are fractals.
Any other kind of system features emergence, which is a subjective quality (in facts, there are no systems in nature, everything is just fields, it is our subjective rational and physical capacities that grant systems of boundaries, between what is and what is not the system). Some features can be shared between a whole and a part (e.g. size), but not all, otherwise the whole is the same as the part.
For example, dots have no extension as such. But a system of two different dots can be represented by a line, which has an emergent feature: extension. And not only that, but also size and form.
Consider that dots, lines, sizes, extensions, countries, rainbows, clouds, rivers, or rocks are not part of nature. Those are just perceptions that depend on our own subjective capabilities and features, like our size, density, speed, scale, mass, charge, etc. Changing some of such properties could allow us traversing rock walls. So, rocks wouldn't exist, because we wouldn't perceive them.
Perhaps there are walls in front of our faces made of dark matter iron, but since we don't perceive them, they don't exist, so they are not systems. So, systèms are subjective features, and so is emergence.
Properties of the parts either:
- add, e.g. ferromagnetic elements, or cells in series;
- cancel, like how protons are positively-charged and electrons are negatively-charged, but a salt crystal is electrically neutral; or how water molecules are fast, but the water itself isn't.
The relationship between the parts also contributes properties of the whole:
- fast-moving molecules that move in different directions to their neighbours are hot;
- patiently-waiting people who stand behind each other form a queue;
- letters in one order call something evil, but in another order call it live.
Considering these three contributions allows you to predict the property of a system by considering its parts – though since there are vastly many more possible relationships between parts than there are properties of parts, it's usually easier to explain than predict the emergent properties of a system.