Fallacy of division
Encyclopedia
A fallacy
of division occurs when one reasons logic
ally that something true of a thing must also be true of all or some of its parts.
An example:
The converse of this fallacy is called fallacy of composition
, which arises when one fallaciously attributes a property of some part of a thing to the thing as a whole. Both fallacies were addressed by Aristotle
in Sophistical Refutations.
Another example:
Since the premises entail
a contradiction (6), at least one of the premises must be false. We may diagnose the problem as located in premise 3, which quite plausibly commits the fallacy of division.
An application: Famously and controversially, in the philosophy of the Greek Anaxagoras
(at least as it is discussed by the Roman Atomist Lucretius
), it was assumed that the atoms constituting a substance must themselves have the salient observed properties of that substance: so atoms of water would be wet, atoms of iron would be hard, atoms of wool would be soft, etc. This doctrine is called homeomeria, and it plainly depends on the fallacy of division.
If a system as a whole has some property that none of its constituents has (or perhaps, it has it but not as a result of some constituent having that property), this is sometimes called an emergent
property of the system.
Fallacy
In logic and rhetoric, a fallacy is usually an incorrect argumentation in reasoning resulting in a misconception or presumption. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor , or take advantage of social relationships between people...
of division occurs when one reasons logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
ally that something true of a thing must also be true of all or some of its parts.
An example:
- A Boeing 747 can fly unaided across the ocean.
- A Boeing 747 has jet engines.
- Therefore, one of its jet engines can fly unaided across the ocean.
The converse of this fallacy is called fallacy of composition
Fallacy of composition
The fallacy of composition arises when one infers that something is true of the whole from the fact that it is true of some part of the whole...
, which arises when one fallaciously attributes a property of some part of a thing to the thing as a whole. Both fallacies were addressed by Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
in Sophistical Refutations.
Another example:
- Functioning brains think.
- Functioning brains are nothing but the neurons that they are composed of.
- If functioning brains think, then the individual neurons in them think.
- Individual neurons do not think.
- Functioning brains do not think. (From 3 & 4)
- Functioning brains think and functioning brains do not think. (From 1 & 5)
Since the premises entail
Entailment
In logic, entailment is a relation between a set of sentences and a sentence. Let Γ be a set of one or more sentences; let S1 be the conjunction of the elements of Γ, and let S2 be a sentence: then, Γ entails S2 if and only if S1 and not-S2 are logically inconsistent...
a contradiction (6), at least one of the premises must be false. We may diagnose the problem as located in premise 3, which quite plausibly commits the fallacy of division.
An application: Famously and controversially, in the philosophy of the Greek Anaxagoras
Anaxagoras
Anaxagoras was a Pre-Socratic Greek philosopher. Born in Clazomenae in Asia Minor, Anaxagoras was the first philosopher to bring philosophy from Ionia to Athens. He attempted to give a scientific account of eclipses, meteors, rainbows, and the sun, which he described as a fiery mass larger than...
(at least as it is discussed by the Roman Atomist Lucretius
Lucretius
Titus Lucretius Carus was a Roman poet and philosopher. His only known work is an epic philosophical poem laying out the beliefs of Epicureanism, De rerum natura, translated into English as On the Nature of Things or "On the Nature of the Universe".Virtually no details have come down concerning...
), it was assumed that the atoms constituting a substance must themselves have the salient observed properties of that substance: so atoms of water would be wet, atoms of iron would be hard, atoms of wool would be soft, etc. This doctrine is called homeomeria, and it plainly depends on the fallacy of division.
If a system as a whole has some property that none of its constituents has (or perhaps, it has it but not as a result of some constituent having that property), this is sometimes called an emergent
Emergence
In philosophy, systems theory, science, and art, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems....
property of the system.
External links
- Logical Fallacy: Division The Fallacy Files