Logic in Scripture

Many syllogisms in the Bible leave a premise unstated. Arguments like this are called enthymemes. Using the rules of validity, we can determine what the assumed premise must be. We locate enthymemes by recognizing premise identifiers (for, because, since) or conclusion identifiers (therefore, thus, so, consequently).

For example, in Hosea 10:3, the people complain, “We have no king, because we did not fear the Lord.” Put these statements in categorical form, leaving the assumed premise blank:

No we are God fearers
∴ No we are king havers.

The terms “God-fearers” and “king-havers” will be the terms in the missing premise, since they each have only appeared once. The conclusion is a universal negative, and so the assumed premise must be universal, and (since the given premise is already negative) it must be affirmative (a valid syllogism cannot have two negative premises). The assumed premise must therefore be either “All king havers are God fearers,” or “All God fearers are king havers.” The major term “king-havers” is distributed in the conclusion, so it must be distributed in the premise. This means it must be “All king-havers are God fearers,” and the complete syllogism is this:

(All king havers are God fearers.)
No we are God-fearers
∴ No we are king havers.

This AEE-2 is valid. So the people in Hosea were assuming that the would have a king only if they feared the Lord.

Other arguments in scripture to analyze in a similar way are Job 17:4, Psalm 119:100, Ecclesiastes 2:17, Matthew 27:6, Mark 4:17, John 8:47, Romans 6:9, and Hebrews 7:25.

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