What is formal fallacy committed in the following syllogistic argument? All Professors are Academicians.
Some Academicians are Activists.
Therefore, Some Activists are Professors.
$A I I$
Syllogism Analysis
The problem asks to identify the formal fallacy in the given syllogistic argument. First, let's break down the argument and determine its structure (mood and figure).
Argument Structure
Identify the terms:
- Major Term (P): Professors (Predicate of the conclusion)
- Minor Term (S): Activists (Subject of the conclusion)
- Middle Term (M): Academicians (Appears in both premises)
Analyze the premises and conclusion:
- Premise 1: All Professors are Academicians. This is a universal affirmative statement. Form: All P are M.
- Premise 2: Some Academicians are Activists. This is a particular affirmative statement. Form: Some M are S.
- Conclusion: Therefore, Some Activists are Professors. This is a particular affirmative statement. Form: Some S are P.
Determining the Mood
The mood is determined by the types of statements in the argument (A for universal affirmative, E for universal negative, I for particular affirmative, O for particular negative), in the order: Major Premise, Minor Premise, Conclusion.
- Major Premise (All P are M): A
- Minor Premise (Some M are S): I
- Conclusion (Some S are P): I
Therefore, the mood of the syllogism is $A \ I \ I$.
Determining the Figure
The figure is determined by the position of the middle term (M) in the premises.
- Major Premise: P is subject, M is predicate (P - M)
- Minor Premise: M is subject, S is predicate (M - S)
The structure P-M, M-S corresponds to Figure 4.
Identifying the Fallacy
The specific form of the argument is $AII-4$. Now, let's check for validity by examining the distribution of terms. A term is distributed if the statement refers to all members of the class designated by that term.
- In Premise 1 (All P are M): 'P' (Professors) is distributed, 'M' (Academicians) is undistributed.
- In Premise 2 (Some M are S): 'M' (Academicians) is undistributed, 'S' (Activists) is undistributed.
The middle term 'M' (Academicians) is undistributed in both premises. This violates a rule of valid syllogisms, which requires the middle term to be distributed in at least one premise.
The formal fallacy committed is the Fallacy of the Undistributed Middle.
Conclusion
The mood of the syllogism is $A \ I \ I$. This corresponds to the identified structure. The argument commits the Fallacy of the Undistributed Middle, making it invalid, despite having the mood $A \ I \ I$. Option A correctly identifies the mood $A \ I \ I$.
Important Questions from Syllogism
Statements:
1. All heroes are winners.
2. All winners are lucky people.
Inferences:
I. All lucky people are heroes.
II. Some lucky people are heroes.
III. Some winners are heroes.
Which of the above inferences can be logically deduced from statements 1 and 2?Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?
(i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.- Given below are four statements.
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class. - Based only on the truth of the statement ‘Some humans are intelligent', which one of the following options can be logically inferred with certainty?
Given below are two statements and four conclusions drawn based on the statements.
Statement 1: Some bottles are cups.
Statement 2: All cups are knives.
Conclusion I: Some bottles are knives.
Conclusion II: Some knives are cups.
Conclusion III: All cups are bottles.
Conclusion IV: All knives are cups.
Which one of the following options can be logically inferred?
