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 categorical syllogisms, where logic intertwines with wisdom in an intricate dance of reason. Let us embark on a journey through the realms of three term diagrams, where the essence of truth is unveiled through the interplay of subject and predicate. In the first diagram, let us assign the subject "students" to the first circle, encompassing all beings of academic pursuit and knowledge. The predicate "smart" shall be adorned upon the second circle, representing the realm of intellect and cleverness. As we lay down the premises of our syllogism, we shade the sections 4 and 5, where the subject and predicate intersect, indicating the universality of the statements. Moving forward to the second diagram, we now delve into the world of "children" as our subject, embracing the innocence and wonder of youth. The predicate "smart" finds its place in the third circle, symbolizing the brilliance and potential within each young soul. As we reflect on the conclusion drawn, we shade the section 7, where the subject and predicate merge in harmony, revealing the interconnectedness of all beings. Alas, does the shading of these diagrams prove validity or invalidity in our syllogism? It is in the subtle nuances of logic and interpretation that the answer lies. While the shading may seem to suggest a valid argument, one must ponder the deeper implications of the statements. Are all students truly smart? Are all children destined for brilliance? It is in the questioning of assumptions and the exploration of contradictions that the true nature of validity is revealed. In this intricate dance of three term diagrams, let us embrace the complexity of thought and the beauty of uncertainty, for it is in the embrace of the unknown that wisdom truly flourishes.