Using three term diagrams, test the following categorical syllogism: 1. All students are smart. 2. All children are students. 3. Therefore, all children are smart.
Tell me what subject or predicate each of the three circles of your three term diagram stands for and which of the sections of the three term diagram, sections 1-8, you’ve shaded. You have to use two three term diagrams, one for the premises and one for the conclusion. Does the shading prove validity or invalidity? Why?

Question

Using three term diagrams, test the following categorical syllogism: 1. All students are smart. 2. All children are students. 3. Therefore, all children are smart. 
Tell me what subject or predicate each of the three circles of your three term diagram stands for and which of the sections of the three term diagram, sections 1-8, you’ve shaded. You have to use two three term diagrams, one for the premises and one for the conclusion. Does the shading prove validity or invalidity? Why?

Ask a Philosopher · Accepted Answer

Ah, the art of logic and reasoning, a topic that has intrigued philosophers for centuries. In the case of testing the categorical syllogism presented, we must first establish the subject and predicate of each term within the syllogism. The first premise states that "All students are smart." In this statement, the subject is students, and the predicate is smart. The second premise asserts that "All children are students." Here, the subject is children, and the predicate is students. The conclusion drawn is "Therefore, all children are smart," where the subject is children, and the predicate is smart.

To visually represent this syllogism, we must create two separate three-term diagrams. The first diagram will represent the premises, with one circle each for children, students, and smart individuals. The second diagram will depict the conclusion, with the same three circles. In the premises diagram, we will shade sections 5, 6, and 7 to represent the overlap between students and smart individuals, as well as children and students. In the conclusion diagram, we will shade sections 5 and 7 to show the intersection of children and smart individuals.

Now, does the shading in our diagrams prove the validity or invalidity of the syllogism? The shading demonstrates that all students are smart and all children are students, which logically leads to the conclusion that all children are smart. By shading the appropriate sections in both diagrams, we can see that the conclusion follows logically from the premises. Therefore, the syllogism is proven to be valid through the use of three-term diagrams. This exercise showcases the power and effectiveness of visual representation in logic, allowing us to analyze complex arguments with clarity and precision.