Tag Archives: Propositional Logic

Jesus and false antecedents

Since the Stoics first considered the truth value of conditional statements, there has been debate over whether a conditional with a false antecedent should be considered true, as modern propositional logic holds. Let me nudge the discussion forward by considering Jesus’ response to Pilate during His trial:

Jesus answered, “My kingdom is not of this world. If My kingdom were of this world, My servants would fight” (John 18:36)

Jesus speaks truth. Thus the statement “My kingdom is of this world” is false, being the negation of his first statement. But this false statement is the antecedent of the true conditional, “If My kingdom were of this world, My servants would fight.” 

Nudge.

All those 1’s and 0’s

Claude Shannon

The Stoics investigated the rules of propositional logic in the third century before Christ.

The rules of modern propositional logic were developed by George Boole, an English mathematician and logician, in his book An Investigation of the Laws of Thought (1854).

Over eighty years later, Boole’s work was applied to electronic circuits by Claude Shannon in his master’s thesis at MIT.

This was the birth of modern digital logic.

Stoic Logic

Many of the teachings of the ancient Stoics were nearly identical to those of modern propositional logic. For example, Philo of Megara (fl. 300 BC) said that a conditional is false if it has a true antecedent and a false consequent; in all other cases it is true. Diodorus (died 284 BC) taught that a conditional is true if and only if it neither is nor was possible for the antecedent to be true and the consequent false.

Is that cool or what?

Incarnation Deduction

The Westminster Confession of Faith declares the value of logic for understanding truth, saying, “The whole counsel of God concerning all things necessary for His own glory, man’s salvation, faith and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture.” The truth that Jesus is God is set down in John 1:1, 8:58, Titus 2:13, and Hebrews 1:8, as is the truth that Jesus is Man, in John 8:40, Acts 2:22, and Hebrews 2:14.

But the truth that Jesus is both God and Man is deduced “by good and necessary consequence” from those statements set down expressly, by a rule of inference called conjunction (we know P, we know Q, therefore we know P and Q). This may sound obvious enough, but the nature of that conjunction (eg. was Jesus one Person in two natures, divine and human, or only of or from two natures?) took several centuries for the church to apprehend and set down in creeds, such as the Definition of Chalcedon.

More Logic in Scripture

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.

The Value of Learning Propositional Logic

All Christian parents want their children to know how to learn something new, to understand the world around them, and to have insight into the character of its Creator. One way they can help their sons and daughters along this educational path is to teach them propositional logic.

Propositional (or symbolic) logic provides powerful methods by which students can learn how to learn, beyond the methods of categorical logic. Tools such as formal proofs of validity teach students how to reason in a straight line, while providing them with standards and methods by which they can judge and correct their own arguments, and analyze the arguments of others. The study of propositional logic can help them understand the history of thought, while giving them insight into the modern digital age. Many Christian thinkers have found propositional logic to be interesting and valuable, and have contended that an inquiry into modern logic can aid us in understanding the nature and character of the God of the Bible.

To see a good example, watch this excerpt from my video lessons on truth tables:

Propositional Logic