formal logic: squares of opposition

formal logic: squares of opposition

implication: to allude to something that is not stated but is implied by another truth. "Children should be seen and not heard" (in the context of a rebuke at church as in the book means that children are being noisy. It doesn't state this, it implies it.

inference: To infer (or deduce) something new from something we already know. "All men are mortal. Socrates is a man. Therefore Socrates is mortal."

1: Contradiction: The relationship of contradition examines the relationship between A (universal affirmitive) and O (Particular Negative).

2. Contrariety: The relationship of contrariety examines the relationships between A (Universal Affirmative) and E Universal Negative) propositions. They have opposing qualities.

3. Subcontrariety: Examines the relationship between I (particular affirmative) and O (particular Negative). They have opposing qualities also.

4. Subimplication (subalternation): examines the relationships between A (universal affirmative) and I (Particular Affirmative); and also E (Universal Negative) and O (Particular Negative) propositions. It examines the universal proposition first to see what it implies about the particular.

5. Superimplication (superalternation) examines A-I and E-O propositions too, but moving from particular to universal.

contrariety

A

E

contradiction

superimplication

subimplication

superimplication

sublimplication

contradiction

see pg. 330

O

I

1) contradiction is the relationship between A (Universal Affirmative) and O (Particular Negative), and E (Universal Negative) and I (Particular Affirmative) propositions.

2) Contradictory propositions cannot both be ture and the same time, nor can the both be false at the same time.

3) If one is false, the other must be true and visa versa.

Contrariety

subcontrariety

See pg 87 and page 349 on socratic dialogue.

Contrariety is the relationship between A (universal Affirmative) and E (universal negative) propositions.

They cannot both be true at the same time, but they can be false at the same time.

If one is true, the other must be false.

If one is false, the other may either be true or false.

Subcontrariety

Relationship between I (Particular Affirmative) and O (Particular Negative) Propositions.

Propositions can both be true at the same time.

Cannot both be false at the same time.

If one is true, the other may be true or false.

If one is false, the other must be true.

subimplication

see pg 100 (and 333)

1. Subimplication is the relationship between universal propositions and their particulars. A (Universal Affirmative) relates to I (particular affirmative); E(Universal Negative) relates to O (Particular Negative).

2. The truth of the universal implies the truth of the particular.

3. The falsity of the universal does not imply a truth value for the particular. When the universal is false, the truth value of the particular is unknown.

squares of opposition and inference analysis

Superimplication

see page 337 (114)

1. Superimplication is the relationship between particular and universal propositions. I(particular affirmative) relates to A (universal affirmative) and O (particular negative) relates to E (universal negative).

2. The truth of the particular proposition, does not assign a truth value to the universals.

3. The falsity of the particulars implies the falsity of the universals.

checking up: Homework comprehension?

Debate homework?

If there is time (4:30) =) Note taking on the next portion of the debate book. (with emails sent of notes to students not in attendance.)

see page 109 and 110; 335 and 336

1. Analyzing the implications of your various beliefs can help you avoid holding contradictory beliefs.

2. Holding and acting upon contradictory beliefs can cause frustration and inner conflict.