Tag Archives: symbolic logic

Analyzing a real argument

Mr. Nance,

I lead a group of young men in Intermediate Logic and they wanted to put their skills to use. They used an argument they pulled from chapter 1 of the book Defeating Darwinism. We tried several different ways of representing the propositions but always came up with an invalid argument. We really want it to be valid! What do we need to do? The original argument is: “If God created space and time, then He is outside of time. Therefore, He is not affected by time.” Any helpful hints will be very appreciated. Continue reading Analyzing a real argument →

The Biblical Biconditional

Intermediate Logic, Why learn logic?, ,

Symbolic logic has five standard logical operators, each of which has a standard translation in English:

negation is “not”
conjunction is “and”
disjunction is “or”
conditional is “if/then”
biconditional is “if and only if”

While the translations of the first four logical operators are frequent in English, the phrase “if and only if” is used very infrequently, and then only occasionally among mathematicians, philosophers, and lawyers.

For instance, while it is easy to find hundreds of nots, ands, ors, and if/thens in the Bible, the phrase “if and only if” is completely absent. However, for those who look carefully, biconditional reasoning is used several times in scripture. Keeping in mind that p if and only if q means if p then q and if q then p — and remembering other equivalences we have learned — the following verses all reflect biconditional reasoning: Continue reading The Biblical Biconditional →

If/Then Truth Table

Intermediate Logic,

One of the difficulties new students of symbolic logic must overcome is understanding the defining truth table for the conditional, the “if/then” logical operator. The defining truth table tells us what the truth value of the proposition is, given the truth value of its component parts. For the conditional, it looks like this:

p    q     p ⊃ q
T    T         T
T    F         F
F    T         T
F    F         T

One way to defend this is to look at real-life conditional propositions with known truth values, for which we also know the truth value of the component parts. We will take our examples from the Bible. Continue reading If/Then Truth Table →

“Not both” v. “Both not”

Mr. Nance,

I am having a hard time with problem 3 in Exercise 3 of Intermediate Logic.  For the first proposition, ~(J ⋅ R), the answer key says “Joe and Rachel are not both students.” For the second proposition, ~J ⋅ ~R, the answer key says “Both Joe and Rachel are not students.” Those sound the same to me. Continue reading “Not both” v. “Both not” →

The Dissection Lab & Logic

Logic, Why learn logic?,

Logic may be considered as a symbolic language which represents the reasoning inherent in other languages. It does so by reducing the language of statements and arguments down into symbolic form, simplifying them such that the arrangement of the language, and thus the reasoning within it, becomes apparent. The extraneous parts of statements are removed like a biology student in the dissection lab removes the skin, muscles and organs of a frog, revealing the skeleton of bare reasoning inside.

Continue reading The Dissection Lab & Logic →

Symbolizing Scripture

Intermediate Logic,

Translating Bible verses into symbolic form is sometimes fun and insightful.
Consider Exodus 21:18-19,

bible_with_books_med[1]“If men contend with each other, and one strikes the other with a stone or with his fist, and he does not die but is confined to his bed, if he rises again and walks about outside with his staff, then he who struck him shall be acquitted. He shall only pay for the loss of his time, and shall provide for him to be thoroughly healed.”

Recognizing this as a single logical proposition, it symbolizes as follows: Continue reading Symbolizing Scripture →

All those 1’s and 0’s

Intermediate Logic, ,
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.

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

Unit Four!

Intermediate Logic, , , ,


So, you have entered Unit 4! In this unit, you will be applying many of the tools you have learned up to this point to real-life arguments in written texts, texts that present what I call “chains of reasoning.”

This is a tough section, because we are no longer working with artificial arguments meant to teach the tools, but arguments that have been written in actual books from men like the philosopher Boethius, the Apostle Paul, Augustine, Martin Luther, and others.

Here are a few things you will want to note from the DVD for this lesson.

  1. This is a longer video, almost 50 minutes. Go get some popcorn.
  2.  I help you through the first two exercises, and work all the way through Ex. 28c. You’re welcome.
  3. Note that on the video, just before the 4 minute mark, I misspoke. I should have said that P ⊃ Q is equivalent to ~Q ⊃ ~P, but I accidentally omit the “not” (what appears on the screen is correct).
  4. Watch for the clip from the movie “Get Smart” at the very end. The screen will go dark for a moment; don’t let that fool you!