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.

Logic is not (as some erroneously believe) the science of thinking. The term “thinking” includes several operations of the human mind, many of which would fall under the domain of psychology rather than logic. But there are three mental operations which are usually associated with logic: apprehension, judgment, and reasoning.

Apprehension is the mental operation by which an idea is formed in the mind. If you were to think of a sunset or a baseball, the action of forming that picture in your mind is apprehension. The verbal expression of apprehension is called a term.

Judgment is the mental operation by which we predicate something of a subject. To think, “That sunset is beautiful” or “Baseball is the all-American sport” is to make a judgment. The verbal expression of judgment is the statement (or proposition).

Inference (or reasoning) is the mental operation by which we draw conclusions from other information. If you were to think, “I like that sunset, because I enjoy beautiful things, and that sunset is beautiful” you would be reasoning. The verbal expression of reasoning is the logical argument.

Formal logic is more properly defined as the science of reasoning. Students of formal logic analyze syllogisms to determine their validity, or develop proofs to establish a given conclusion. Logic students also learn how to define terms and make accurate statements, because these tools are necessary to learn in order to reason properly. But in so doing they are working more in the realm of informal logic, the branch of logic which is important, but which is only indirectly related to reasoning.

In defending the teaching of Formal Logic, Dorothy Sayers notes, “Another cause for the disfavor into which Logic has fallen is the belief that it is entirely based upon universal assumptions that are either unprovable or tautological. This is not true. Not all universal propositions are of this kind.”

I want to make two comments. First, it appears that Sayers is committing the fallacy of apriorism here. The discreditors of Logic attack it by arguing that the universal assumptions upon which Logic is based are unprovable or tautological (and are thus worthless). She implies, in what appears to be a hasty generalization, that they are attacking all universal propositions (when she argues that not all universal propositions are of this kind), when in fact they are only attacking some of them. Maybe I am missing something here, but it seems that the universal propositions she defends may not be the same ones the discreditors are attacking.

Second, if I were to respond to the discreditors given her assumption, I would argue this way: “Do you really believe that all universal propositions are unprovable or tautological? Then how about that claim? Is it unprovable, or tautological?” All universal propositions are unprovable or tautological is itself a universal proposition, and is thus open to the same refutation. Thus this attack on universals lays itself wide open to a classic reductio.

It would be an instructive exercise to take Logic or Rhetoric students through a defense of Sayers claim that not all universal propositions are unprovable or tautological. Ask your students, “How do we know the truth of universal propositions?” Discuss the value of an inductive defense of universals. Discuss also the proving of universals by authority, by definition, and by deduction from other universals.

In her essay “The Lost Tools of Learning,” Dorothy Sayers has identified for many classical Christian schools of our day an outline for a modern education following the medieval Trivium: Grammar, Logic, and Rhetoric. I am interested in what she says about Logic and the Dialectic Stage, and plan to occasionally post some thoughts about these and related topics. I will start my posts with a comment she makes that I have found helpful in my own teaching of Logic.

In describing a student of the medieval Trivium, Sayers writes, “Secondly, he learned how to use language; how to define his terms and make accurate statements; how to construct an argument and how to detect fallacies in argument.” This short statement gives us what I have come to believe are the four primary lessons to be learned in a Logic class, and in the proper order.

First, the logic student learns about terms, which are the building blocks of statements. They learn what a term is, how terms differ from words, the methods and rules of defining terms, and how to use the tools that relate terms to one another, such as genus and species charts.

Second, the logic student learns about statements. They learn what a statement is, how to identify the different types of statements, how to relate statements to one another, and how to determine the truth of a given statement.

Third, the student learns “how to construct an argument.” Logical arguments are built out of statements, which are connected as premises to make conclusions. Students learn how to distinguish between valid and invalid arguments, what validity means, and why it differs from truth. Once they are able to identify valid arguments given to them, they learn how to construct valid arguments of their own.

Fourth, the logic student learns “how to detect fallacies in argument.” A fallacy is an invalid form of argument. They learn to identify not only the formal fallacies discovered by the rules of validity, but also informal fallacies such as ad hominem and post hoc.

Thus, Sayers has given us the outline of a complete introductory logic curriculum. I would only add that we should not limit our learning of the above to categorical logic, but include the tools of propositional (or symbolic) logic as well. Students should be given the powerful tools of relating symbolic propositions, determining the validity of propositional arguments, and learning how to construct propositional proofs.

In our doctrine class we discuss classical arguments for and against the existence of God. One such argument is the Problem of Evil and goes something like this: “If God exists, then he is both perfectly good and infinitely powerful. If he is perfectly good, then he is willing to prevent evil. If he is infinitely powerful, then he is able to prevent evil. But if evil exists, then God is neither unwilling or unable to prevent it. Evil does exist. Therefore God does not exist.” We use a shorter truth table to show that this argument is indeed valid (or perhaps we write a proof for it). The students who have taken logic know that if an argument is valid, but the conclusion is false (as this obviously is), then at least one of the premises must be false. This leads to a fruitful discussion about which premise is false, and why. Is God infinitely powerful but not able to prevent evil because he cannot interfere with the free will of men? This is the choice of many modern evangelicals. Does God’s perfect goodness require that He is always willing to prevent evil? Reformed scholars would say no, and give counterexamples such as the crucifixion.

How do you take formal logic and apply it to real life during the dialectic stage? In other words, how do you move from the theory into practical application of what has been learned?

First, the obvious. We must teach logic-it’s definitions, theories and techniques-so that the students fully grasp these concepts. By its very nature logic is immediately applicable; every area of study in which conclusions are drawn from premises employ the techniques of logic. So students who fully understand these techniques will make their own application, just as students who understand mathematics, grammar, or the sciences naturally find applications of those subjects in their daily lives.

Second, we must teach tools of logic. These include techniques such as determining assumed premises in enthymemes, applying immediate inferences, identifying formal and informal fallacies, defining terms, developing and answering dilemmas, and using truth tables. The teacher must, for the students’ sake, distinguish all these tools from those lessons which are merely the means to an end, such as mood and figure, Venn diagrams, formal proofs, and so on. These latter lessons are helpful in their place, but everyone should honestly recognize their limited applicability outside of the classroom.

Third, we must give students examples of logic being applied. The teacher should not immerse the student in too many highly-symbolic lessons without occasionally surfacing for a breath of application in ordinary language. To be sure, as a symbolic language, logic, like mathematics, has a certain elegance or even beauty. But God has given us logic in order to apply it to the world around us, and we must lead students in showing how this is done. Point out to your students examples of informal fallacies in the newspaper, analyze enthymemes in the Bible to uncover the assumptions, show how Jesus uses and gets out of dilemmas, analyze Aquinas’s arguments with shorter truth tables.

Fourth, we must review and apply the tools of logic throughout the secondary curriculum. The students should see some of these being applied in different way in all their other classes. Certainly, courses like Geometry and Rhetoric will overtly re-teach many of the techniques learned in the logic class, but every subject will use some of the tools. Do not all teachers define terms for their students? Do not all draw premises form conclusions? All secondary teachers should learn enough logic to use the tools appropriate to their particular subjects.