Category Archives: Why learn logic?

Isaac Watts – The Value of Logic #1

Why learn logic?

watts[1]The first is, the depth and difficulty of many truths, and the weakness of our reason to see far into things at once, and penetrate to the bottom of them. It was a saying among the ancients, Veritas in puteo, Truth lies in a well; and, to carry on this metaphor, we may very justly say, that logic does, as it were, supply us with steps whereby we may go down to reach the water: or it frames the links of a chain, whereby we may draw the water up from the bottom.

Yet More Logic in Scripture

Introductory Logic, Why learn logic?,

bible_with_books_med[1]Logic students regularly struggle with immediate inferences, and (as is often the case when students have more than usual difficulty) they can begin to wax philosophical about the value of learning this particular concept. As an initial response to such students, I want to give a couple of 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. Otherwise, the wine will burst the skins, and both the wine and the wineskins will be ruined. No, they pour new wine into new wineskins.”

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

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.

Isaac Watts on Logic

Logic, Why learn logic?

“Logic is the art of using Reason well in our inquiries after truth, and the communication of it to others. Reason is the glory of human nature, and one of the chief eminences whereby we are raised above our fellow creatures, the brutes, in this lower world. Reason, as to the power and principle of it, is the common gift of God to all men… The design of Logic is to teach us the right use of our reason, or intellectual powers”  –  Isaac Watts, from Logic: The Right Use of Reason in the Inquiry After Truth

Incarnation Deduction

Intermediate Logic, Why learn logic?,

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

Logic, Why learn logic?,

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.

Logic in Scripture

Introductory Logic, Why learn logic?,

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.

Continue reading Logic in Scripture →

The Value of Learning Propositional Logic

Intermediate Logic, Why learn 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

Watch your assumptions!

Introductory Logic, Why learn logic?

In his Institutes of Oratory, the rhetorician Quintilian, in discussing the value of learning logic, mentions the “horn” problem, which evidently was this tricky syllogism:

“You have what you have not lost. You have not lost horns. Therefore you have horns.”

Initially I supposed that this was invalid, until I put it into categorical form:

All things you have not lost are things you have.
All horns are things you have not lost.
∴  All horns are things you have.

This is an AAA-1, and is thus valid. It could just as readily be written as modus ponens: Continue reading Watch your assumptions! →