The fallacy of division is an informal fallacy that occurs when one assumes that something true of a whole must also necessarily be true of its parts (Hansen, 2020).
A simple fallacy of division example goes like this: Australian people are good at surfing. Matt is Australian. Therefore, Matt is good at surfing.
An informal fallacy differs from formal fallacies because the error doesn’t necessarily arise from the form of the argument but possibly from its content and context.
The fallacy of division is an informal fallacy that occurs when the attributes of a whole are assumed to apply to its parts. It is the converse of the fallacy of composition. It is also known as “false division.”
The fallacies of division and composition were first defined by Aristotle in On Sophistical Refutations:
“Fallacies connected with the use of some particular expression absolutely or in a certain respect and not in its proper sense, occur when that which is predicated in part only is taken as though it was predicated absolutely” (Aristotle, 1955, p. 27).
In a standard logical form, such arguments look like the following:
- A is part of B;
- B has property X;
- Therefore, A has property B.
Such reasoning can sometimes lead to correct conclusions, but that doesn’t change the fact that it’s fallacious.
Sometimes, what is true of a whole must also be true of its certain parts. For example, if my body is made up of atoms, then my arms are made up of atoms (Law, 2009).
This kind of reasoning is fallacious because this is not always the case.
Fallacy of Division vs Fallacy of Composition
The fallacy of division is often discussed with its counterpart: the fallacy of composition. Both of these are concerned with parts and composites:
- The fallacy of division projects the properties of the composite on a part.
- The fallacy of composition projects the properties of a part on the composite.
Hansen (2020) offers the following hypothetical argument to illustrate both fallacies:
- Every member of the investigative team was an excellent researcher.
- It was an excellent investigative team.
To conclude (2) from (1) would be to commit the fallacy of composition: just because something is true of the parts doesn’t necessarily mean it is true of the whole.
To conclude (1) from (2) would be to commit the fallacy of division: just because something is true of the whole doesn’t necessarily mean that it is true of its parts.
From this example, it is clear that informally fallacious thinking might often be quite reasonable and useful when we have limited information.
The fallacy of division can sometimes be useful. We should, however, be aware when we are committing it.
- The front door is a part of my house.
- My house is green.
- Therefore, the front door of my house is green.
It is clear why such reasoning is fallacious: we often say that a house is green even if the doors aren’t green. There is no reason to assume that all parts of the house are green. The front door may well be green, but that doesn’t change the fact that, in this argument, the conclusion does not logically follow from the premises. Such reasoning is an instance of the fallacy of division.
If we knew that the front door was green and assumed that the house must, therefore, also be green, we would be committing the converse fallacy: the fallacy of composition.
- The novel War and Peace by Leo Tolstoy is long.
- Chapter 20 of War and Peace is part of the novel.
- Therefore, chapter 20 must also be long.
The 20th chapter of this book may truly be long, but that doesn’t follow from the fact that the whole book is long. There is no logical necessity for each chapter to be long. Maybe the book has so many chapters that each is quite short. Maybe the other chapters are long, and this one is short. The point is that the conclusion does not logically follow from the premises, and the argument commits the fallacy of division.
- Water is wet.
- Water is made up of water molecules.
- Therefore, each water molecule is wet.
A single molecule cannot be a liquid and can not be considered wet. But this is just a physical fact. The argument still could have been valid even if it was not sound. In this case, however, the argument commits the fallacy of division: just because something is true of water does not necessarily mean that it is true of all of its constituents. The conclusion that each molecule is wet does not follow from the premises.
- Gothic cathedrals are built with stone.
- The windows are parts of Gothic cathedrals.
- Therefore, Gothic cathedrals have windows that are built with stone.
The conclusion immediately seems absurd. We know that Gothic cathedral windows were usually made with stained glass, not stone.
The problem with the argument, besides leading to a factually incorrect conclusion, is the fact that it commits the fallacy of division.
Saying that Gothic cathedrals are built with stone does not necessarily mean that all constituent parts of Gothic cathedrals are made of stone. The conclusion, therefore, does not follow from the premises.
- The human brain is capable of thinking.
- Neurons are part of the human brain.
- Therefore, each neuron is capable of thinking.
The argument leads to a weak version of panpsychism (Goff et al., 2022). Instead of viewing mentality as a fundamental feature of everything in the world, this argument claims that each part of the brain must be capable of thinking. The problem is that such reasoning is fallacious. The argument assumes that what is true of the whole must also be true of its parts. Hence it commits the fallacy of division.
- The University of Oxford is the highest ranking university in the UK.
- The University of Oxford has a faculty of philosophy.
- The philosophy faculty of the University of Oxford must, therefore, be the highest ranking in the UK.
The conclusion may be true, or it may be false. But this would not change the fact that the argument commits the fallacy of division. Just because the whole university is the highest ranking does not necessarily mean that each of its faculties will also be the highest ranking.
- My friend group is passionate about sports.
- Matt is part of my friend group.
- Therefore, Matt must also be passionate about sports.
A may actually be passionate about sports, but that would not change the fact that this argument is fallacious.
It assumes that because something is characteristic of a group of people, it must be characteristic of each member of that group. The argument, therefore, commits the fallacy of division.
- According to the World Happiness Report, Finland is the world’s happiest country (Happiest Countries in the World 2022, n.d.).
- Noel lives in Finland.
- Therefore, Noel must be happy.
The premises may both be true, but the conclusion still does not logically follow from them.
Being the happiest country applies to Finland as a whole, but it does not apply to each individual who lives there. The argument simply assumes this and thereby commits the fallacy of division.
- English people are good at football.
- John is English.
- Therefore, John is good at football.
The first two statements may be true, but that would not make the conclusion true.
The argument is fallacious because it assumes that something true of a group (English people) must be true of each individual in that group (A in this case).
The argument, therefore, commits the fallacy of division.
10. Houses are visible therefore atoms are visible
- Houses are visible.
- Houses are made of atoms.
- Therefore, atoms are visible.
The premises are both true, but the conclusion still does not logically follow from them.
The argument commits the fallacy of division because it assumes that what is true of a composite must also be true of its parts.
The fallacy of division is an informal fallacy that occurs when one assumes that something true of a whole must also necessarily be true of its parts. Informal fallacies like this can occasionally be useful, but knowing how they work and why they are fallacious benefits our critical thinking abilities. Fallacious reasoning can be useful because it doesn’t necessarily lead to false conclusions, but unless that’s the only option we have, we should be weary of using it.
Aristotle. (1955). On Sophistical Refutations (E. S. Forster & D. J. Furley, Trans.) [Data set]. Harvard University Press. https://doi.org/10.4159/DLCL.aristotle-sophistical_refutations.1955
Goff, P., Seager, W., & Allen-Hermanson, S. (2022). Panpsychism. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2022). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/sum2022/entries/panpsychism/
Hansen, H. (2020). Fallacies. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2020). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/sum2020/entries/fallacies/
Happiest Countries in the World 2022. (n.d.). Retrieved December 8, 2022, from https://worldpopulationreview.com/country-rankings/happiest-countries-in-the-world
Law, S. (2009). THINKING TOOLS. FALLACY: DIVISION. Think, 8(21), 83–83. https://doi.org/10.1017/S1477175608000419