Identify the fallacy committed in the following argument: "American Indians are disappearing. That man is an American Indian. Therefore, that man is disappearing."
Understanding the Logical Fallacy in the Argument
The argument presented is:
- Premise 1: American Indians are disappearing.
- Premise 2: That man is an American Indian.
- Conclusion: Therefore, that man is disappearing.
This argument makes a common logical error by assuming that a property true of a whole group must also be true of every individual member of that group. Let's analyze the types of fallacies provided in the options to identify the specific error.
Identifying the Fallacy of Division
The Fallacy of Division occurs when one assumes that what is true of a whole must be true of its parts. In the given argument, the statement "American Indians are disappearing" refers to the group as a whole (perhaps meaning their numbers are decreasing over time, or their cultural identity is changing). The conclusion then wrongly applies this group property ("disappearing") to a single individual member ("That man"), implying he is literally vanishing or ceasing to exist. This is a clear example of dividing a property of the whole and applying it to a part.
Consider another example of the Fallacy of Division:
- The company is profitable.
- John is an employee of the company.
- Therefore, John is profitable (meaning John makes a profit).
While the company as a whole makes a profit, it doesn't mean every single employee is individually profitable in the same way.
Comparing with Other Fallacies
Let's look at the other options to see why they don't fit the structure of this argument:
- Fallacy of Composition: This is the opposite of the Fallacy of Division. It assumes that what is true of the parts must be true of the whole. For example, "Each atom in this chair is invisible, so the chair is invisible." This doesn't match the structure of the argument about the American Indian.
- Fallacy of Accident: This fallacy occurs when a general rule is applied to a specific case where an unusual circumstance ('accident') makes the rule inapplicable. For example, "It is generally wrong to injure others. Therefore, a surgeon operating to save a life is doing wrong." The argument about the American Indian doesn't involve applying a general rule to an exceptional case.
- Fallacy of Converse Accident (Hasty Generalization): This fallacy occurs when a general conclusion is drawn from an atypical specific case or a small number of cases. For example, "The first two people I met from that city were rude, so everyone from that city must be rude." The argument about the American Indian starts with a claim about a group ("American Indians are disappearing") and applies it to an individual, not the other way around.
Based on the analysis, the argument directly exhibits the characteristics of the Fallacy of Division.
| Fallacy Type | Description | Example Structure |
|---|---|---|
| Fallacy of Division | Assuming what is true of a whole is true of its parts. | The group G has property P. X is part of G. Therefore, X has property P. |
| Fallacy of Composition | Assuming what is true of the parts is true of the whole. | Each part of W has property P. W is made of these parts. Therefore, W has property P. |
| Fallacy of Accident | Applying a general rule to an exceptional case. | Rule R applies to all X. Y is an X with unusual circumstance A. Therefore, R applies to Y (incorrectly). |
| Fallacy of Converse Accident | Drawing a general conclusion from atypical specific cases. | Case 1 of type X has property P. Case 2 of type X has property P. Therefore, all X have property P (incorrectly). |
Conclusion on the Argument's Fallacy
The argument "American Indians are disappearing. That man is an American Indian. Therefore, that man is disappearing" commits the Fallacy of Division because it incorrectly assumes a property true of the group ("disappearing") applies individually to a member of that group ("That man").
Revision Table: Logical Fallacies Explained
| Fallacy | Core Idea | How it Applies (or Doesn't) to the Example |
|---|---|---|
| Fallacy of Division | Whole → Part | Applies directly: Property of the group ("disappearing") is assigned to an individual member. |
| Fallacy of Composition | Part → Whole | Does not apply: The argument goes from group to individual, not individual to group. |
| Fallacy of Accident | General rule → Exception | Does not apply: No general rule is misapplied to an unusual specific case here. |
| Fallacy of Converse Accident | Specific case → General rule | Does not apply: The argument starts with a claim about a group, not specific instances. |
Additional Information on Logical Fallacies
Logical fallacies are errors in reasoning that undermine the logic of an argument. They can be categorized in various ways, including formal fallacies (errors in the structure of the argument) and informal fallacies (errors in the content or context of the argument).
The Fallacy of Division is an example of an informal fallacy, specifically a fallacy of ambiguity or a fallacy of presumption, depending on how the term "disappearing" is interpreted and how the link between the whole and the part is assumed.
- Understanding fallacies helps in critically evaluating arguments presented in everyday life, media, and academic contexts.
- Identifying fallacies strengthens your own argumentation skills by helping you avoid making such errors.
- Many fallacies exploit ambiguities in language or make unwarranted assumptions about the connection between premises and conclusion.
Being able to distinguish between fallacies like Composition and Division is key to understanding how properties of wholes and parts relate in logical arguments. The crucial difference lies in the direction of the inference: from part to whole (Composition) or from whole to part (Division).
Important Questions from Argument Forms - Teaching
The Fallacy committed in the argument
"All textbooks are books intended for careful study. Some reference books are books intended for careful study. Therefore, some reference books are textbooks." is
- The space program deserves increased expenditure in the years ahead. Not only does the national defence depend upon it, but the program will more than pay for itself in terms of technological snipoffs. Furthermore, at current funding levels, the program cannot fulfil its anticipated potential”. What is the conclusion of the above argument?
All mortals are men.
Socrates is mortal
Therefore Socrates is a man.
Which of the following statements are true of the above argument?
(A) Above arguments is sound.
(B) Above argument is valid.
(C) Above argument is fallacious.
(D) Above argument commits the fallacy of undistributed middle.
Choose the correct answer from the options given below:"Environmentalists accuse us of blocking the plan to convert Antartica into a World park. In fact nothing could be further from the truth. Antartica is a huge continent teeming with life. It is home to millions of penguins, seals, seabirds and sea lions. Also great schools of finfish and whales inhabit its coastal waters."
Which fallacy is committed in the above argument?
Given below are two statements:
Statement I : An argument form that allows for a substitution instance having true premises and a false conclusion is an invalid form.
Statement II : Any arguments having true premises and a false conclusion is an invalid argument.
In the light of the above statements, choose the correct answer from the options given below :
