A good argument is a logical idea with clear and acceptable premises. When we make an argument, it should not have fallacies and must be well structured, because if the premises are not true, the conclusion will not be clear. Also, a good argument does not just mean I agree with it. One of the most common mistakes in critical thinking is considering an argument acceptable only because we agree with its conclusion. This way of thinking shows a closed mind, as if we believe we know all the truth and anyone who disagrees must be wrong. It stops us from learning from other opinions and goes against true critical thinking. During a conversation, my neighbor claimed that all students who play sports are healthy, and since he plays soccer, he must be healthy. It is a categorical syllogism. However, my father challenged this by saying that not all athletes are necessarily healthy; some people play sports for social reasons or due to peer pressure, not just for their well-being. I used a disjunction, saying that my neighbor could be healthy, or perhaps he enjoys soccer for fun, but it does not guarantee his health. Then, Ana added that if my neighbor plays soccer, he will always stay in good physical shape, which is a conditional statement. I replied with a conjunction, saying that although my neighbor plays soccer, he also spends so much time studying, which might affect his health. By applying categorical logic to connect the categories (athletes and health) and propositional logic to analyze the relationships between statements, we helped Ana understand that her argument was too broad and didn’t consider all possibilities.
A valid argument in propositional logic could be:
Premise 1: If you study regularly, you will improve your grades. (p → q)
Premise 2: You study regularly. (p)
Conclusion: You will improve your grades. (q)
In categorical logic, we can express relationships like:
All S are P: All athletes are healthy.
No S are P: No athletes are unhealthy.
Some S are P: Some athletes are healthy.
Some S are not P: Some athletes are not healthy.