# The Square of Opposition (for logic nerds only!)

The Square of Opposition is a useful tool for representing and understanding the relationships between categorical statements with the same subject and predicate:

The relationships are defined this way:

Contrariety: The statements cannot both be true, but can both be false.
Contradiction: The statements cannot both be true, and cannot both be false.
Subcontrariety: The statements can both be true, but cannot both be false.
Subimplication: If the universal is true, the particular must be true.
Superimplication: If the particular is false, the universal must be false.

Students might be interested to discover that the square of opposition can be created for non-categorical statements as well. Continue reading The Square of Opposition (for logic nerds only!)

# Why Logic Test A and B?

Hello, Mr Nance!

Could you please explain to me why the tests and quizzes pack for the Introductory Logic has a test form A and a test form B for the same chapters? I am sure it is logical (pun intended) but I am not getting it and just want to be sure I am administering them correctly.

# Invalidity and truth

Mr. Nance,

I have a question on Intermediate Logic, Test 2, Form B, Problem 4. The question says: “An invalid argument can have true premises and a true conclusion, is this true or false?” The answer book says it’s true but the definition of an invalid argument would prove that statement to be false. Is there a typo or is that correct? Continue reading Invalidity and truth

# A Seeming Disagreement

Lesson 10 of Introductory Logic discusses the possibility that two statements delivered by different people may seem to be inconsistent, but upon further examination turn out to actually be consistent. We can call these seeming disagreements, and they can happen in one of two ways. Continue reading A Seeming Disagreement

# I Know London is the Capital of France

I teach logic online. In addition to my regular logic students I have several Classical Conversations tutors who audit my logic course. After I finish the lesson and my students leave, the auditors join the class live, turning on camera and mic, and we discuss the lesson. I appreciate these discussions, because I often learn as much from them as they do from me. Continue reading I Know London is the Capital of France

“Those, then, whose office it is to look after the interests of the state will refrain from that form of liberality which robs one man to enrich another.”

– Cicero, On Duties