Aristotelian and Predicate Logic

Definition:

A formalization of thinking, similar to the way in which geometry formalizes drawing. The classic logical statement is:

All Men Are Mortal.
Socrates was a man.
Therefore, Socrates was mortal.

This form of statement is called a syllogism. From these basic building blocks is it possible to analyze statements for validity. For example: I went to the store and I did not go to the store is not true — or — at best — it may be nonsense.

On top of simple transformations, this kind of logic includes the ability to spot items that take the form of a syllogism but are invalid, as well as predicate logic, where ideas in a paragraph may be converted to symbols and evaluated. The symbolic logic version of the “going to the store” example is A AND (NOT A), which can not evaluate to true.

As every conclusion is false, regardless if A is true or false, the total statement must be false. This is a trivial example, but knowing how to do symbolic logic can be incredibly powerful when evaluating more complex prose, like requirements or combinations of inputs.

A context where I used this skill:

I was consulting with an ecommerce company that allowed its users to create a custom catalog. We found we had several different possibilities — the customer catalog could exist, it could be inactive, out of date, the user might not be signed up for regular catalog access, and so on. We held a meeting before the code was created and I took the requirements, which were in plain English, and turned them into a table. For every possibility in the table we created a user who had those conditions, so the developers could ‘poke’ test before turning the system over to the testers. Through this process we found entire ‘boxes’ in the table that had no pre—defined correct behavior!

Result: Thanks to the decision table, we got better results out of the gate, could test more quickly, and had more confidence in our coverage. (To the extent that such a term has a meaning). Creating the decision table was easy, but seeing the symbols pop up in my mind — the idea to create the table — that came through practice.

How I’d recommend someone learn this skill:

My senior year in high school I took a course in Logic at Hood College at night. It was fantastic. The book we used for the course was Harrison’s Logic and Rational Thought. I would suggest a quick Google search and some reading on symbolic logic, predicate logic, and Aristotelian logic. The Great Courses have a course on reasoning that covers Aristotelian logic through predicate;; it looks interesting.

Additional resources:

By: Matthew Heusser

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