Last week we considered examples of enthymemes in the Bible, and noted that we can use the rules of validity to determined their unspoken assumptions. In this post we will consider another form of logical argument.
If we look closely into the arguments in the Bible, we can see several examples of hypothetical syllogisms, arguments using “if/then” propositions.
The most basic valid hypothetical syllogism is modus ponens, which follows this pattern: If P then Q. P, therefore Q. This is the form of reasoning shown in Matthew 8:2-3,
And behold, a leper came and worshiped Him, saying, ‘Lord, if You are willing, You can make me clean.’ Then Jesus put out His hand and touched him, saying, ‘I am willing; be cleansed.’
The modus ponens can be also seen in Proverbs 23:13-14,
Do not withhold correction from a child, for if you beat him with a rod, he will not die. You shall beat him with a rod, and deliver his soul from hell.
Another valid hypothetical syllogism form is the modus tollens, which follows this pattern: If P then Q. Not Q, therefore not P. We see this form used in 1 John 2:19,
If they had been of us, they would have continued with us; but they went out that they might be made manifest, that none of them were of us.
Here is another modus tollens, in slightly different form, from 1 Corinthians 15:13,20:
If there is no resurrection of the dead, then Christ is not risen… But now Christ is risen from the dead, and has become the firstfruits of those who have fallen asleep.
We learn about hypothetical syllogisms in Introductory Logic, Lesson 31, and Intermediate Logic, Lesson 13.