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1) Fallacy of Equivocation2) Fallacy of Amphiboly3) Fallacy of Composition 4) Fallacy of Division

Equivocation ("to call by the same name") is classified as an informal logical fallacy. It is the misleading use of a term with more than one

meaning or sense (by glossing over which meaning is intended at

a particular time). It generally occurs with polysomic words

(words with multiple meanings).

Fallacy of Equivocation

An equivocation trades upon the use of an ambiguous word or phrase in one of its

meanings in one of the propositions of an argument but also in another of its meanings in a second proposition.

The fallacy of equivocation occurs when the conclusion of an argument depends on the fact that a word or phrase is used, either

explicitly or implicitly, in two different senses in the argument. Such arguments are either invalid or have a false premise, and in

either case they are unsound.

Equivocation (Explanation)

Example

A feather is light.What is light cannot be dark.

Therefore, a feather cannot be dark.

Explanation:The argument is fallacious because the word “light” is first used as the opposite of “heavy” but then used as a synonym of “bright”.

ExampleJFK’s famous line:

“And so, my fellow Americans: ask not what your country can do for you – ask what you can do for

your country.”

Explanation: This is an example of equivocation and

therefore misleads the audience because the word “country” is used in two different senses. In its first occurrence it means “government” and in its second occurrence it means “nation” or “homeland.”

Example1. Some triangles are obtuse. Whatever is obtuse

is ignorant. Therefore, some triangles are ignorant.

Explanation:In the first argument “obtuse” is used in two

different senses. In the first premise it describes a certain kind of angle, while in the second it means dull or stupid.

2. Any law can be repealed by the legislative authority. But the law of gravity is a law. Therefore, the law of gravity can be repealed by the legislative authority.

Explanation:The second argument equivocates on the word “law.” In the first premise it means statutory law, and

in the second it means law of nature.

Example3. We have a duty to do what is right. We have a

right to speak out in defense of the innocent. Therefore, we have a duty to speak out in defense of the innocent.

Explanation:The third argument uses “right” in two senses. Inthe first premise “right” means morally correct, but

in the second it means a just claimor power.

4. A mouse is an animal. Therefore, a large mouse is a large animal.

Explanation:The fourth argument illustrates the ambiguous use

of a relative word. The word “large” means different things depending on the context.

Note

Equivocation is often confused with amphiboly. However, equivocation

is ambiguity arising from the misleading use of a word and

amphiboly is ambiguity arising from the misleading use of punctuation or grammar.

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Fallacy of Amphiboly

An amphiboly occurs when the construction of a sentence allows it to have two different meanings.

An amphiboly can occur even when every term in an argument is univocal, if the grammatical construction of a sentence creates its own ambiguity.

Amphiboly (Explanation)The fallacy of amphiboly occurs when the

arguer misinterprets an ambiguous statement and then draws a conclusion based on this

faulty interpretation. The original statement is usually asserted by someone other than the

arguer, and the ambiguity usually arises from a mistake in grammar or punctuation—a missing comma, a dangling modifier, an

ambiguous antecedent of a pronoun, or some other careless arrangement of words. Because

of this ambiguity, the statement may be understood in two clearly distinguishable

ways. The arguer typically selects the unintended interpretation and proceeds to

draw a conclusion based on it.

ExampleIt is said that we have a good understanding of our universe. Therefore, we know exactly how

it began and exactly when.

Explanation: The ambiguity here is what exactly “good understanding” means. The conclusion assumes a much better understanding than is suggested in the premise; therefore, we have the ambiguity fallacy.

A reckless motorist, Thursday struck and injured a student who was jogging through the

campus in his jogging boots. Therefore, it is unsafe to jog in your jogging boots.

Explanation:In this example, the premise (actually heard on a radio broadcast) could be interpreted in different ways, creating the possibility of a fallacious inference to the conclusion.

Example

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Fallacy of Composition The fallacy of composition involves an

inference from the attribution of some feature to every individual member of a class (or part of a greater whole) to the

possession of the same feature by the entire class (or whole).

Because the parts of a whole have a certain property, it is argued that the whole has that

property. That whole may be either an object composed of different parts, or it may be a collection or set of individual members.

Composition (Explanation)

The fallacy of composition is committed when the conclusion of an argument depends on the erroneous transference of an attribute from the

parts of something onto the whole. In other words, the fallacy occurs when it is argued that

because the parts have a certain attribute, it follows that the whole has that attribute, too, and the situation is such that the attribute in question cannot be legitimately transferred

from parts to whole.

ExampleEvery atom in this tea cup has mass. Therefore,

this tea cup has mass.Every component in this picket fence is white.

Therefore, the whole fence is white.

Explanation:In each case an attribute (having mass, being white) is transferred from the parts onto the whole, but these transferences are quite legitimate. Indeed, the fact that the atoms have mass is the very reason why the teacup has mass. The same reasoning extends to the fence. Thus, the acceptability of these arguments is attributable, at least in part, to the legitimate transference of an attribute from parts onto the whole.

Example1. The brick wall is six feet tall. Thus, the

bricks in the wall are six feet tall.2. Germany is a militant country. Thus, each

German is militant.3. Conventional bombs did more damage in

W.W. II than nuclear bombs. Thus, a conventional bomb is more dangerous than a nuclear bomb.

Proof:Show that the properties in question are the

properties of the whole, and not of each part or member or the whole. If necessary, describe the parts to show that they could not have the properties of the whole.

ExampleEvery course I took in college was well-

organized.Therefore, my college education was

well-organized.

Explanation: Even if the premise is true of each and every component of my curriculum, the whole could have been a chaotic mess, so this reasoning is defective.

NoteNotice that this is distinct from the

fallacy of “converse accident”, which improperly generalizes from an unusual

specific case (as in "My philosophy course was well-organized; therefore, college courses are well-organized.").

For the fallacy of composition, the crucial fact is that even when something

can be truly said of each and every individual part, it does not follow that

the same can be truly said of the whole class.

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Fallacy of Division The fallacy of division involves an inference from the

attribution of some feature to an entire class (or whole) to the possession of the same feature by each of its individual members (or parts).

The fallacy of division is the exact reverse of composition. As composition goes from parts to whole, division goes from whole to parts.

The logical form of fallacy of division is :1. A is part of B.2. B has X attributes.3. Therefore, A has X attributes too.

Types of Fallacy of Division

First type of fallacy of division:A person reasons that what is true for the whole must also be true for the parts. The person fails to justify that inference with the required degree of evidence.

Examples:1. The ocean when seen as a whole is blue in color, then each drop of water individually must also be blue in color. 

Types of Fallacy of Division

2. NaCl is not poisonous. Therefore, Na and Cl are not poisonous too.

3. The ball is blue. Therefore, all the atoms of this ball are blue too.

4. An airplane is made of Seattle. Therefore, all parts of airplane are made of Seattle too

5. Each atom of this pen is invisible. Therefore, this pen is invisible.

6. Water is made of hydrogen and oxygen. And water is liquid. Therefore, Hydrogen and oxygen are liquid too. 

Types of fallacy of DivisionSecond type of fallacy in division:

The other way in which someone can make a fallacy of division is through the assumption that the actions or beliefs of an entire population must represent the actions or opinions of each person in the population.

Examples:

1. America is fattest country on the earth. Therefore, are Americans are fat.

Types of fallacy of division

2. If a country is quite wealthy you will assume that each person within that country must also be wealthy.

3. Many Pakistani people love to talk. Hadia is Pakistani. Therefore, she loves to talk too.

4. Terrorist attacks committed by Muslims are in the name of Islam, therefore all Muslims are terrorists.

5. Israel has killed innocent people therefore all Israelis are murderers.

6. All politicians are corrupt. Hamid is a politician. Therefore, he is corrupt too.

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