24.5 What Are Syllogisms?

24.5 What Are Syllogisms? Syllogism: Any two-premise argument. A syllogism is a two-premise argument. For example, this form of argument is called the disjunctive syllogism, because it’s a nifty valid argument using a disjunction: Disjunctive Syllogism: from PvQ and ~P

24.6 Aristotle’s A E I O

24.6 Aristotle’s A E I O Since Aristotle’s day it’s been common practice to label Aristotle’s forms with the first four vowels of the Latin alphabet: A, E, I and O. A == All Ps are Q. I == Some

24.7 The Square of Opposition

24.7 The “Modern” Square of Opposition So far you’ve learned Aristotle’s method for categorizing syllogisms. The beauty of it is that it’s exhaustive: there are only 256 different possible categorical syllogisms, and exactly 15 of them are valid. So we

31.3 Existential Instantiation

31.3 Existential Instantiation The last proof method for quantifiers that we need to learn is how to reason from an existential. Say we know that (1) all the pets are mammals, and (2) there exists a pet. We want to