Fallacy of division

Information about Fallacy of division

A fallacy of division occurs when one reasons logically that something true of a thing must also be true of all or some of its parts.

An example:
  1. A Boeing 747 can fly unaided across the ocean.
  2. A Boeing 747 has jet engines.
  3. One of its jet engines can fly unaided across the ocean.


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.

Another example:
  1. Functioning brains think.
  2. Functioning brains are nothing but the neurons that they comprise.
  3. If functioning brains think, then the individual neurons in them think.
  4. Individual neurons do not think.
  5. Functioning brains do not think. (From 3 & 4)
  6. Functioning brains think and functioning brains do not think. (From 1 & 5)


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.

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Informal fallacies
Special pleading • Red herring • Gambler's fallacy and its inverse • Fallacy of distribution (Composition • Division) • Begging the question • Many questions
Correlative-based fallacies:False dilemma (Perfect solution) • Denying the correlative • Suppressed correlative
Deductive fallacies:Accident • Converse accident
Inductive fallacies:Hasty generalization • Overwhelming exception • Biased sample • False analogy • Misleading vividness • Conjunction fallacy
Vagueness and Ambiguity:False precision • Slippery slope • Continuum fallacy
Equivocation:Equivocation • False attribution • Fallacy of quoting out of context • Loki's Wager • No true Scotsman
Questionable cause:Correlation does not imply causation (Cum hoc) • Post hoc • Regression fallacy • Texas sharpshooter • Circular cause and consequence • Wrong direction • Single cause
A fallacy is a component of an argument that is demonstrably flawed in its logic or form, thus rendering the argument invalid in whole. In logical arguments, fallacies are either formal or informal.
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Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration.
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A fallacy of composition arises when one infers that something is true of the whole from the fact that it is true of some (or even every) part of the whole.
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entailment (or logical implication) is a relation between sets of formulae such that, if A and B are sets of formulae of a formal language, then A entails B if and only if every model (or interpretation) that makes all the members of A true, makes at least one of the members of B
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Anaxagoras (Greek: Αναξαγόρας, ca. 500 BC–428 BC) was a pre-Socratic Greek philosopher. He was a member of what is now often called the Ionian School of philosophy.
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In natural philosophy, atomism is the theory that all the objects in the universe are composed of very small, indestructible building blocks - atoms. Or, stated in other words, that all of reality is made of indivisible basic building blocks.
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Titus Lucretius Carus (ca. 99 BC- ca. 55 BC) was a Roman poet and philosopher. His only known work is the epic philosophical poem De Rerum Natura, On the Nature of Things.

Life of Lucretius

Very little is known about Lucretius' life.
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emergence refers to the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Like intelligence in the field of AI, or agents in distributed artificial intelligence, emergence is central to the theory of complex systems and yet very
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An informal fallacy is an argument pattern that is wrong due to a mistake in its reasoning. In contrast to a formal fallacy, the error has to do with issues of rational inference that occur in natural language; which are broader than can be represented by the symbols used in formal
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Special pleading is a form of spurious argumentation where a position in a dispute introduces favorable details or excludes unfavorable details by alleging a need to apply additional considerations without proper criticism of these considerations themselves.
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The gambler's fallacy is a formal fallacy. It is the incorrect belief that the likelihood of a random event can be affected by or predicted from other, independent events.
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The inverse gambler's fallacy is a term coined by philosopher Ian Hacking to refer to a formal fallacy of Bayesian inference which is similar to the better known gambler's fallacy.
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A fallacy of distribution is a logical fallacy occurring when an argument assumes there is no difference between a term in the distributive (referring to every member of a class) and collective (referring to the class itself as a whole) sense.
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A fallacy of composition arises when one infers that something is true of the whole from the fact that it is true of some (or even every) part of the whole.
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This article or section may be confusing or unclear for some readers.
Please [improve the article] or discuss this issue on the talk page. This article has been tagged since October 2007.
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Many questions, also known as complex question, presupposition, loaded question, "trick question", or plurium interrogationum (Latin, "of many questions"), is an informal fallacy.
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In logic, correlative-based fallacies, also known as fallacies of distraction, are logical fallacies based on correlative conjunctions.

A correlative conjunction is a relationship between two statements where one must be false and the other true.
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false dilemma—also known as false choice, false dichotomy, falsified dilemma, fallacy of the excluded middle, black and white thinking, false correlative, either/or fallacy, and bifurcation
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The perfect solution fallacy is a logical fallacy that occurs when an argument assumes that a perfect solution exists and/or that a solution should be rejected because some part of the problem would still exist after it was implemented.
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The logical fallacy of denying the correlative is an attempt made at introducing alternatives where there are none. In a way, it is the opposite of the false dilemma, which is denying other alternatives.

For example:

Policeman: "..

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The logical fallacy of suppressed correlative is a type of argument which tries to redefine a correlative (two mutually exclusive options) so that one alternative encompasses the other, i.e. making one alternative impossible.
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a Dicto simpliciter (Latin: "from a maxim without qualification" -- meaning 'from a universal rule') or ad Dictum simpliciter (Latin: "to a maxim without qualification" -- meaning 'to a universal rule') The a
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The logical fallacy of accident, also called destroying the exception or a dicto simpliciter ad dictum secundum quid, is a deductive fallacy occurring in statistical syllogisms (an argument based on a generalization) when an exception to the generalization is ignored.
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The logical fallacy of converse accident (also called reverse accident, destroying the exception or a dicto secundum quid ad dictum simpliciter) is a deductive fallacy that can occur in a statistical syllogism when an exception to a generalization is wrongly
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faulty generalization, also known as an inductive fallacy, is any of several errors of inductive inference:

Logic

The proportion PIE of the sample has attribute CAKE.

therefore

The proportion CAKE of the population has attribute PIE.
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Hasty Generalization, is a logical fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence. It commonly involves basing a broad conclusion upon the statistics of a survey of a small group that fails to sufficiently represent the whole
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An overwhelming exception is a logical fallacy similar to a hasty generalization. It is a generalization which is accurate, but comes with one or more qualifications which eliminate so many cases that what remains is much less impressive than the initial statement might have led
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A biased sample is a statistical sample of a population where some members of the population are less likely to be included than others. An extreme form of biased sampling occurs when certain members of the population are totally excluded from the sample (that is, they have zero
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False analogy is a fallacy applying to inductive arguments. It is often mistakenly considered to be a formal fallacy, but it is not, because a false analogy consists of an error in the substance of an argument (the content of the analogy itself), not an error in the logical
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The logical fallacy of misleading vividness involves describing some occurrence in vivid detail, even if it is an exceptional occurrence, to convince someone that it is a problem.
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