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.

Obverse changes the quality of the statement, and takes the complement of the predicate. It gives equivalent statements for all four forms of categorical statement:

All S is P  ≡  No S is non-P
No S is P  ≡  All S is non-P
Some S is P  ≡  Some S is not non-P
Some S is not P  ≡  Some S is non-P

Jesus uses the obverse in Mark 2:22, where He says,

“No one pours new wine into old wineskins… No, they pour new wine into new wineskins.”

The obverse is seen more clearly if translated into categorical form:

No new-wine pourers are non-new wineskin users. (No S is non-P)
All new-wine pourers are new wineskin users. (All S is P)

Jesus uses obverse again later in Mark 13:2 when he says,

“Not one stone here will be left on another; every one will be thrown down.”

In categorical form these statements could be written as:

No stones here will be stacked stones. (No S is P)
All stones here will be non-stacked stones. (All S is non-P)

Contrapositive switches the subject and predicate of the statement, and changes both to their complements. It gives equivalent statements for universal affirmative and particular negatives:

All S is P  ≡  All non-P is non-S
Some S is not P  ≡  Some non-P is not non-S

The contrapositive is used in Proverbs 13:24,

“Whoever spares the rod hates their children, but the one who loves their children is careful to discipline them.”

In categorical form, the contrapositive can be clearly seen:

All non-discipliners are non-children lovers. (All non-P is non S)
All children lovers are discipliners. (All S is P)

Paul uses something like the contrapositive in Romans 11:6 when he argues,

“And if by grace, then it is no longer of works; otherwise grace is no longer grace. But if it is of works, then it is no longer grace; otherwise work is no longer work.”

This is more obviously the contrapositive when the conditional statements are translated into categorical form:

All grace is non-work. (All S is non-P)
All work is non-grace. (All P is non-S)

You can see from these biblical examples that immediate inferences are used as something like single-premise arguments, one statement implying the next.


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