Write a short note on read the following arguments carefully. Identify the formal fallacy committed by each and give suitable justifications to support your answer : All philosophers are scientists. Some scientists are not musicians. Therefore, some philosophers are musicians.

Identifying the Formal Fallacy:

The argument presented commits the formal fallacy known as the Fallacy of the Undistributed Middle.

Explanation of the Fallacy:

The Fallacy of the Undistributed Middle occurs when the middle term in a categorical syllogism (the term that appears in both premises but not in the conclusion) is undistributed. In other words, the fallacy arises when the relationship between the subject and predicate terms is not properly established across all instances of the middle term.

Analysis of the Argument:

1. All philosophers are scientists. (Premise)
2. Some scientists are not musicians. (Premise)
3. Therefore, some philosophers are musicians. (Conclusion)

Justification:

In the given argument, the middle term "scientists" is undistributed because it appears only once in the premises. While the first premise states that all philosophers are scientists, it does not establish any relationship between scientists and musicians. Similarly, the second premise states that some scientists are not musicians, but it does not establish any direct relationship between philosophers and musicians either.

Therefore, the conclusion that "some philosophers are musicians" is not logically supported by the premises. The argument fails to establish a valid connection between the subject term "philosophers" and the predicate term "musicians" through the middle term "scientists." The fallacy lies in assuming that because some scientists are not musicians and all philosophers are scientists, therefore some philosophers must be musicians. However, there is no direct logical connection between being a philosopher and being a musician, and hence, this argument commits the Fallacy of the Undistributed Middle.

Conclusion:

In conclusion, the argument provided commits the formal fallacy of the Undistributed Middle. This fallacy occurs when the middle term in a categorical syllogism is undistributed, leading to an invalid conclusion. In this case, the argument fails to establish a valid logical connection between the subject and predicate terms through the middle term, resulting in an invalid inference.