# Immediate Inference Cheat Sheet

Equivalent Immediate Inferences of the four Categorical Statements:

All S is P
=  No S is non-P  (obverse)
=  All non-P is non-S  (contrapositive)

No S is P
=  All S is non-P  (obverse)
=  No P is S  (converse)

Some S is P
= Some S is not non-P  (obverse)
= Some P is S  (converse)

Some S is not P
= Some S is non-P  (obverse)
= Some non-P is not non-S  (contrapositive)

Immediate inferences work in reverse:

All S is non-P
= No S is P  (obverse)

All non-S is non-P
= All P is S  (contrapositive)

No S is non-P
= All S is P  (obverse)

Some S is non-P
= Some S is not P  (obverse)

Some S is not non-P
= Some S is P  (obverse)

Some non-S is not non-P
= Some P is not S  (contrapositive)

Immediate inferences can be combined:

No non-S is P
= No P is non-S = All P is S  (converse, obverse)

Some non-S is P
= Some P is non-S = Some P is not S  (converse, obverse)

Other translations:

All non-S is P
= All non-P is S  (contrapositive)

No non-S is non-P
= All non-S is P  (obverse)

Some non-S is not P
= Some non-P is not S  (contrapositive)

Some non-S is non-P
= Some non-S is not P  (obverse)

All of this and more is included in this complete Immediate Inference Chart.

# Alternate Answers for Exercise 27

I have received several inquiries regarding other possible solutions to the syllogism translations in Introductory Logic Exercise 27. Though the Teacher’s Edition offers only one solution per problem, there are in fact many possible correct answers to each question.

Here is one more reasonable possibility for each: Continue reading Alternate Answers for Exercise 27

# Some Uses of Immediate Inference in Scripture

Logic students sometimes struggle with understanding and remembering immediate inferences. The more opportunities they have to see them used, the more likely they are to grasp them. Consequently, I want to give some examples of immediate inferences used in the Bible. Two equivalent immediate inferences for categorical statements are obverse and contrapositive. Continue reading Some Uses of Immediate Inference in Scripture

# The Square of Eli

One of my greatest delights as a teacher is learning something new from my students. That happened today in my logic class, when Eli, Lily and I wandered down a rabbit trail of immediate inferences. We had used two immediate inferences to write a statement equivalent to some other statement, and realized that we could have gotten to that same answer using two different immediate inferences.  Eli asked if there was some “triangle of immediate inferences” that we could go through and end up where we started. After some playing around, we discovered, not a triangle, but what I will call The Square of Eli: Continue reading The Square of Eli