A Nugget from the World of Logic

A riddle

In the wake of generative AI, by the year 2040, the whole human world has been overtaken by excessive reliance on AI tools. People have stopped using their own minds while machines have started using theirs. In this scenario, an old professor uses a puzzle to make new friends. Thanks to social media, everybody knows where to find the professor. You seek him out, looking for a meaningful conversation with an intelligent person.

You’re in the coffee shop where the professor usually sits. You’re excited about befriending a real human being. However, before the professor allows you to sit and chat with him, he poses the following riddle and asks you if you think it’s logically and certainly true.

First attempt

You know from your experience with cats that the answer to the professor’s riddle is pretty straightforward, and you reply with the following.

Unfortunately, your answer is incorrect. Many times, our lived experiences and beliefs are not logically accurate. Because you believe that cats can’t be afraid of mice, you think the argument in the riddle is invalid. But as soon as you announce your answer to the professor, he shakes his head dismissively, hands you a book on logic, and walks out of the coffee shop.

With a strange feeling of curiosity, you open up the book and find an iconic argument of Aristotle.

Diving deeper

Strangely, while there can be infinite ways in which we can reason in any human language, it’s reassuring that some philosophers have dedicated their lives to studying the forms of valid and invalid reasoning. Knowing that only a handful of valid forms exist is even more reassuring. But what is a form?

Let’s return to the iconic argument.

A form can be thought of as a general shape or template where anything particular that can be ignored for a while gets abstracted away. Within logic, the form of an argument refers to its logical structure, abstracted from the specific content or meaning of the statements involved. It’s like the blueprint or skeleton of an argument that remains consistent even if we replace the specific details or content.

Notice (in the slide above) how the term “human” is replaceable by another symbol. It can be thought of as a placeholder. For the time being, let’s replace it with a green rectangle. For a logician, what gets placed inside those green rectangles doesn’t matter. When it comes to logical arguments, a form is a structure in which it doesn’t matter what particular terms we use inside the argument; what’s important is the consistent arrangement of those terms relative to each other. The premise is that if we successfully place our terms in the right form, that argument holds true. Can we introduce more placeholders in Aristotle’s argument?