2 Chapter 6: Categorical Logic

Patrick Hurley Categorical Logic 4.1

Patrick Hurley Categorical Logic 4.3

All, No , or Some?  In this chapter we learn how to evaluate claims about categories of classes. These are called categorical propositions. Categorical propositions are statements using the terms “All”, “No” and “Some”. We will learn two methods of evaluating short arguments (a.k.a. immediate inferences) comprised of categorical propositions. The first method of evaluation is the two ring Venn diagram method, which offers a way to visually represent and compare these claims. The second method is the Modern Square of Opposition, which is another handy visual way to test the validity of immediate categorical inferences.

While it may seem that claims involving categorical inferences are not very interesting (after all, isn’t it obvious that no cats are dogs?), this branch of logic touches on many important debates in our current world.  Consider, is it true that:  No men are women and no women are men?  Some political insurrections are not peaceful protests?  All human life begins at conception?  Some immigration is good for the country?

These claims and many others are controversial applications of categorical logic.

Our reading this week, which is in two parts, comes from A Concise Introduction to Logic, by Patrick Hurley.