Course description

Logos School is once again offering an on-line Logic tutorial for the 2009-2010 school year. The instructor for this tutorial is James B. Nance.

In the fall of 2009, students will work through Introductory Logic, 4th edition by James B. Nance and Douglas Wilson. The students will learn about 1) Terms and Definition, 2) Statements and their relationships, 3) Syllogisms and Validity, 4) Arguments in Normal English, and 5) Informal Fallacies.

In the spring of 2010, students will work through Intermediate Logic, 2nd edition by James B. Nance. Students will learn about 1) Propositional Logic and Truth Tables, 2) Formal Proof of Validity, 3) Digital Logic, and 4) Truth Trees.

Tutorials will be held Tuesdays and Thursdays, from 8:10 to 9:10 am PST. At each session – using interactive software – the instructor will preview the lesson to be learned, offering suggestions for how to best grasp the concepts, and cautioning the students about difficulties or common errors to avoid. The students will come to the next session having watched the lessons on DVD, and having completed the assigned exercises (using the Logic Answer Keys). The instructor will answer questions, discuss ways to think about the material, and work through additional exercises together. About every other week the student will take a test (using the Logic Test Manuals), to be graded at home before the next session. The tests will be discussed, with questions answered and errors corrected.

Syllabus
Introductory Logic – Fall 2009
August 1 Payment for first semester due.
August 18 Software test session (8:10 am PST)
August 25 First day of regular sessions
November 24, 26 Thanksgiving week – no sessions on these days
December 1 Payment for 2nd semester due.
December 17 Final session for Fall semester.

Intermediate Logic – Spring 2010
January 5 First day of regular sessions
March 16, 18 Spring break – no sessions on these days
May 6 Final session

Course cost
Tuition costs are $400 for the year, payable in two $200 payments (due August 1 and December 1). A late fee of $25 will be assessed for payments received after this. Students will also need to purchase the Introductory Logic and Intermediate Logic textbooks, answer keys, test manuals, and DVDs, available through the Logos Press website.

Course registration
Go to the Logos Press website to purchase the course. Then contact James Nance by email at logiconline@logosschool.com, with “Registration for Online Logic Tutorial” in the subject line, letting him know that you wish to register a student for this course, and giving the following information:

1. Student name
2. Parent name(s)
3. Student birth date
4. Student email address
5. Parent email address (if different from #4)
6. Street address
7. Phone number
8. Mention how you heard about this course.

Other helpful information
This Logos School Logic website is available for students to interact throughout the week, post questions on the forum, and read Mr. Nance’s logic blog. Students will need to register as members on this website. A web page for student interaction is available exclusively to tutorial students.

“The reiteration of slogans, the distortion of the news, the great storm of propaganda that beats upon the citizen twenty-four hours a day all his life long mean either that democracy must fall a prey to the loudest and most persistent propagandists or that the people must save themselves by strengthening their minds so that they can appraise the issue for themselves.” — Robert M. Hutchins, from the Preface to The Great Conversation, 1951.

The Art of Reasoning is a very readable book, covering a fairly traditional range of topics: concepts and propositions, arguments, classical deductive logic, modern deductive logic, and inductive logic. I enjoyed reading and working through this book, and even though I have taught logic for many years, I learned several new concepts and approaches to explaining concepts more clearly from Kelley. I found the exercises to be creative and challenging. I especially enjoyed the section on Term Logic, which I had never studied before.

This book is written to about a high-school level of reading. An adult who has never studied logic before could teach himself the fundamentals of classical and modern logic quite easily from Kelley’s book. Each chapter has practice quizzes and exercises. Answers to practice quizzes are in the back. An instruction manual is also available.

Highly recommended for high school students and above.

(This review refers to the second expanded edition.)

“If . . . a proof that there are no proofs is nonsensical, so is a proof that there are proofs. Reason is our starting point. There can be no question either of attacking or defending it.”

– Miracles

“Reasoning is never, like poetry, judged from the outside at all. The critique of a chain of reasoning is itself a chain of reasoning: the critique of a tragedy is not itself a tragedy.”

– A Preface to “Paradise Lost”

I have often used Professor Kirke’s argument (from The Lion, the Witch, and the Wardrobe by C. S. Lewis) as an excellent example of a valid, deductive argument.

There are only three possibilities. Either your sister is telling lies, or she is mad,  or she is telling the truth. You know she doesn’t tell lies and it is obvious that she is not mad. For the moment then and unless any further evidence turns up, we must assume that she is telling the truth.

This argument can be analyzed in a number of profitable ways for the student of logic. We could symbolize it most directly as an extended Disjunctive Syllogism, in this form:

(L v M) v T     ~L • ~M     .:  T

We could also cast it (with minor editing) as an extended modus tollens, and so on. But for those who have not studied propositional logic, it might be clearer simply to consider this in terms of a genus and species chart, as follows:

Lucy claims to have gone to Narnia

Lucy’s claim is false       Lucy’s claim is true

Lucy is telling lies      Lucy is mad                                         .

The dividing principles should be clear. Lucy claims to have gone to Narnia. Her claim is either false or true. If her claim is false, then she either knows that it is false, or she does not. If it is false and she knows it, then she is telling lies. If it is false but she does not know it, then she is mad.

The Professor argues that Lucy’s claim is true by stating that there are only three final possibilities, as the chart shows, then removing two of them. Those who are familiar with the writings of C. S. Lewis will recognize this argument form. Consider this section from Lewis’s Mere Christianity, where Lewis is arguing that Jesus must be God:

We are faced, then, with a frightening alternative. This man we are talking about either was (and is) just what He said or else a lunatic, or something worse. Now it seems to me obvious that He was neither a lunatic nor a fiend: and consequently, however strange or terrifying or unlikely it may seem, I have to accept the view that He was and is God.

Apparently, Lewis desired his young readers of the Narnian Chronicles to learn logic, and particularly this form of argument, so that they would be able to analyze it in a much more serious form when they got around to reading his more theological literature.  And I say, the sooner the better.

Course description

Logos School is offering an on-line Logic tutorial for the 2008-2009 school year. The instructor for this tutorial will be James B. Nance.

In the fall of 2008, students will work through Introductory Logic, 4th edition by James B. Nance and Douglas Wilson. Topics include 1) Terms and Definition, 2) Statements and their relationships, 3) Syllogisms and Validity, 4) Arguments in Normal English, and 5) Informal Fallacies.

In the spring of 2009, students will work through Intermediate Logic, 2nd edition by James B. Nance. Topics include 1) Propositional Logic and Truth Tables, 2) Formal Proof of Validity, 3) Introduction to Digital Logic, and 4) Truth Trees.

Tutorials will be held Tuesdays and Thursdays, from 8:15 to 9:15 am PST. At each session – using interactive software – the instructor will preview the lesson to be learned, offering suggestions for how to best grasp the concepts, and cautioning the students about difficulties or common errors to avoid. The students will come to the next session having watched the lessons on DVD, and having completed and graded the assigned exercises (using the Logic Answer Keys). The instructor will spend the hour answering questions, discussing ways to think about the material, and working through additional exercises together. About every other week the student will take a test (using the Logic Test Manuals), to be graded at home before the next session. The tests will be discussed, with questions answered and errors corrected.

Syllabus
Introductory Logic – Fall 2008
August 1 Payment for first semester due.
August 19 Software test session (8:15 am)
August 26 First day of regular sessions
November 25, 27 Thanksgiving week – no sessions on these days
December 1 Payment for 2nd semester due.
December 2 Sessions resume
December 18 Final session

Intermediate Logic – Spring 2009
January 6 First day of regular sessions
March 17, 19 Spring break – no sessions on these days
March 24 Sessions resume
April 14, 16 Easter week break – no sessions on these days
April 21 Sessions resume
May 7 Final session

Course cost
Tuition costs are $400 for the year, payable in two $200 payments (due August 1 and December 1). A late fee of $25 will be assessed for payments received after this. Students will also need to purchase the Introductory Logic and Intermediate Logic textbooks, answer keys, test manuals, and DVDs, available through the Logos School Materials website.

Course registration
We will have a dedicated registration website. We will also put a note on the materials website directing people to the registration website. For now, simply contact Jim Nance by email at logiconline@logosschool.com, with “Registration for On-line Logic Tutorial” in the subject line, letting him know that you wish to register a student for this course, and giving him the following information:

1. Student name
2. Parent name(s)
3. Student birth date
4. Student email address
5. Parent email address (if different from #4)
6. Street address
7. Phone number
8. Mention how you heard about this course.

Other helpful information
This Logos School Logic website is available for students to interact throughout the week, post questions on the forum, and read Mr. Nance’s logic blog. Students will need to register as members on this website. A web page for interacting will be set up accessible only to tutorial students.

Logic is a tool given by God to help us order our reasoning and obey Him. Through our reasoning faculties God communicates to us. For example, the Scripture teaches that God has all power, and through deductive logic I can conclude that God has the power to save me. We see the sun rise and the rain fall, and through inductive reasoning we conclude that God is good. Through the process of reasoning we understand His revelation to us better.

We read that there is one God, and that the Father is God, the Son is God, and the Spirit is God; Through good and necessary consequence we conclude that there is one God, and He exists in three Persons: Father, Son, and Holy Spirit. We see that logic makes the implicit explicit, it reveals the truth already there. Logic properly used adds nothing to scripture, but it helps set forth clearly what is contained in scripture. This is because logic alone cannot give us truth. It must start with truths that are given to it in order to make conclusions based on that truth. The bucket doesn’t put the water in the well, it gets the water that is already there out of the well. This is what logic does.

Through the process of reasoning we apply universal law in particular obedience. For example, God commands all men everywhere to repent and believe. We take this universal law and through logic apply it to particulars: You are a man, therefore you must repent and believe. If people were allowed to reject logic, they could escape the application of God’s universal law to their particular situation; that is, they could get out of obedience: “The Bible says all men are to repent and believe; it doesn’t say I personally must.”

Let’s consider more the character of God in relation to logic.

First, logic is a reflection of who God is. We see this most in Jesus Christ, “the image of the invisible God” (Col. 1:15). Jesus is the incarnate logos of God: “In the beginning was the logos, and the logos was with God, and the logos was God” (John 1:1). I am not a Greek scholar, and so I won’t take this any further than to state the obvious: Jesus Christ is the Logos, the word from which we get the word logic. In the incarnation, the infinite God became a particular Man: “And the logos became flesh, and dwelt among us” (John 1:14). The logos who was God has infinite knowledge, is infinite in power and space and time. This logos became a particular man, a man with a particular height, with ten fingers and ten toes, who could bench press a particular weight.

In a similar way, in the process of reasoning, universal statements lead to particular statements. The universal truth that all men are sinners implies the particular truth that I am a sinner. Thus an abstract truth implies a very concrete truth; “I am a sinner” is an incarnation of “All men are sinners.” It is the process of logic that allows us to make these sort of incarnational conclusions from universal claims.

What it all comes down to is that God Himself is the foundation of Reason. He is a reasoning God. “Come, let us reason together,” He says in Isaiah 1:18. According to this verse, we can reason with God, and He can reason with us. He wants to teach us, He wants to teach our students, and He uses the gift of reason in order to do so. God in His grace has given us minds that reason just as He has given us eyes that see, so that we can receive the good things that He has for us. Reason is an attribute of God, and because He is perfect in His attributes, God cannot fail to reason well. We should imitate God in this, and seek to reason to the best of our abilities. For us, this means training, learning, and study.

God is an orderly, consistent God. Paul writes that “God is not a God of disorder” (I Cor 14:33). God is orderly, and order implies reason. Where there is no reason, there is only chaos.

God is also non-contradictory: He cannot lie (Numbers 23:19), He does not deny Himself (II Tim 2:13), and He is holy – nothing in Him contradicts His perfection. John Frame says about this: “Does God, then, observe the law of noncontradiction? Not in the sense that the law is somehow higher than God Himself. Rather, God is Himself noncontradictory and is therefore Himself the criterion of logical consistency and implication. Logic is an attribute of God, as are justice, mercy, wisdom, and knowledge.”

Now, we need to be careful with this. The logic which is an attribute of God is not an exact correspondence with the logic that we study in the classroom. Logic, as an art developed by men, is (or at least can be) a true reflection, but it is only a reflection of the perfect logic of God.

Logic is a study of the laws of reasoning, and Christ is the lawgiver. We will see this by considering how Christ is Lord over terms, statements, and arguments.

Terms are the verbal expression of ideas, or more concretely, names of things. Col. 1:16 says that “All things were created by Him and for Him.” By His word things are what they are. When we are defining terms and relating terms to each other, we are defining things that Jesus Christ has made, things that He cares about. Jesus created marriage. Does He care how we define marriage? Jesus created people. Does He care if we define a fetus as a person?

It follows that Jesus cares whether or not our definitions are good. If they are not, then we are not speaking of things as Christ made them. Logic teaches laws for defining terms, such as “the definition must state the essential attributes” and “the definition must not use words that are unclear.” Where do these laws come from? They are basically applications of the law of God: be honest, be helpful, love your neighbor as yourself.

Statements are claims to truth. Jesus is “the Way, the Truth, and the Life” (John 14:6), who is “full of grace and truth” (John 1:14). Truth is what God knows, that which corresponds to who He is and what He has made. God wants us to distinguish between truth and falsehood. Is it true that God has commanded all men everywhere to repent? Is it true that a husband should love his wife? Popular culture makes a lot of claims about how to know truth. Is it true that you are sitting in that chair? Really true? Do you think that’s air that you are breathing? Or is truth “simply electrical signals interpreted by your brain?”

When we are teaching students how to know the truth of statements, we are helping them to know more of who Christ is, what He really has done and is doing in the world, and what He wants us to believe.

Christ is Lord over arguments. Arguments are one means by which we come to know truth as truth. There are other means by which we know truth, including statements made by true authorities, such as the Bible. But God has given us the ability to reason in order that he may use our reason to lead us to truth. God has given us minds that reason so that we can receive His word, understand it, and apply it.

Much of the year in a logic class is spent learning rules for determining if an argument is valid or invalid. Consider this argument: “If you are a Christian, then you should read the Bible. You are a Christian. Therefore, you should read the Bible.” This is a valid argument. If the premises are true, then you must accept the conclusion as true. But where does the strength of that word “must” come from? Where do I get the authority to say that you must do something here? I would again argue that this is an ethical “must.” God has made words, and the logical reasoning carried across by those words reflects His rational character. “You must accept this as a valid conclusion” means that, if the premises are true, a denial of this conclusion is dishonesty, a rejection of how God has made the world and of who He is. In his book The Doctrine of the Knowledge of God, John Frame says, “The logical ‘must’ indicates a moral necessity. To say that someone ‘must’ accept a conclusion is to say that he ought to accept it, that he has an obligation to accept it.”

Consider this argument: “If you are a Christian then you must read the Bible. My Mormon friend reads the Bible. Therefore my Mormon friend is a Christian.” This is an invalid argument. Even if the premises are true, I am under no obligation, ethical or otherwise, to accept the conclusion as true. It would in fact be wrong for someone to require that I accept that conclusion based on that argument alone.

This question of right or wrong, true or false, correct or incorrect, comes down to a question of recognizing how Christ has made the world, and who He is. These examples should suffice to show how the laws of Logic reflect something about Christ’s laws of love, honesty, and truth.