by Nathaniel Bluedorn, Copyright November 19, 2001, all rights reserved. 411 views
Personal History: James Nance graduated from Washington State University in 1984 with a bachelor of science degree in mechanical engineering, and a minor in mathematics. He worked as an engineer at Boeing for five years before moving to Moscow, where he now teachs at Logos School. He is an elder at Christ Church, and writes for Credenda Agenda. He also speaks at education conferences and trains teachers in dialectic and rhetoric.
Family Info: He is happily married to Giselle since 1988. They have four children: Jamie (12), Josiah (10), Jacqueline (8), and Jonathan (5). All the children attend Logos school. Jamie plays the flute, Josiah the trumpet, Jacqueline the violin. Giselle is the pianist. Jonathan just bothers everybody else when they are trying to practice. James plays no musical instruments, though he does enjoy singing. He enjoys acting, reading, traveling, working on an electric vehicle with his physics students, and playing with his children.
Accomplishments: He is the author of "Intermediate Logic", co-author of "Introductory Logic" (and accompanying videos, test booklets, etc), contributing author of "Repairing the Ruins," and author of "Rhetoric I" (a rhetoric course on CD). He can also balance a tower of twelve upright Jenga blocks!
This is my twelfth year at Logos School. I currently teach Logic (8th grade), Rhetoric and Christian Doctrine (11th grade), Calculus and Physics (12th grade). I have taught a variety of other math, science, and Bible classes. I love to teach, and my favorite class is definitely Logic. I did not teach Logic my first year at Logos. At that time it was taught in tenth grade along with Debate, and the school board was considering backing it up to eighth grade. Doug Wilson visited my seventh-grade Pre-Algebra class and taught a sample lesson (on conditional arguments), and afterward asked me if I thought Logic should be taught to that class the next year. I said yes, upon one condition: they let me teach it. I was quite thankful when the school board agreed, and had to scramble a bit to develop a year-long course for that grade, out of which my logic texts came.
My first glimmers of interest had, I think, three sources. First, my grandfather was always something of a puzzle-solver, tongue-twisterer and riddle-spinner, and I believe he got my mind going in those lines of thought from a very young age. Second, I must confess that I was always something of a Star Trek fan, and probably first heard the word "logic" from the lips of Leonard Nemoy. Third, I was no doubt introduced to concepts of formal logic first in different math courses, especially geometry, which I thoroughly enjoyed. I took my first formal logic course at college (Philosophy 201), followed by a digital logic course and various computer classes toward my ME degree. When I was at Boeing, I had a good friend who was interested in popular fallacies, which he and I would banter about. Then when I moved to Moscow, I took summer courses in Reasoning and Rhetoric at New St. Andrews College.
Logic is the science and the art of reasoning. As a science, formal logic provides us with the standards of proper reasoning. As an art, logic provides us with specific skills to help us use proper reasoning in daily life. But of course, these depend upon each other and support each other. Let me back up a bit and explain.
Note first that logic is the science of reasoning, not of thinking in general. A lot of thinking, not all of it improper, occurs apart from logic. Memory and imagination, though they are related to it, are not strictly logic. Logic has to do with reasoning, that is, drawing conclusions from other information. When a student learns logic, he learns how to distinguish good reasoning from poor reasoning.
For example, that this is improper reasoning: "If one contracts anthrax, then one will get flu symptoms. I have flu symptoms, therefore I must have contracted anthrax." The logic student learns that this is an example of a general fallacy called affirming the consequent, which is the same form of bad reasoning occuring when one thinks this way: "If you are a Christian, you will go to church. My neighbor goes to church, so he must be a Christian!" The practicality of this comes not only from knowing that the reasoning is fallacious, but also in knowing WHY it is fallacious, and in naming the fallacy.
Similarly, the logic student learns that this is proper reasoning: "If one contracts anthrax, then one will get flu symptoms. Joe never had flu symptoms, so he must not have had anthrax." This valid argument is an example of modus tollens, and follows the general form "If p then q, not q therefore not p." In logic we learn that whenever we follow this form of argument, we are reasoning validly. From this we see that the practicality of logic rests firmly on the philosophy, which is represented in those symbols that one sees in textbooks! So I would reject the false dilemma presented in the question. Logic IS philosophical, it IS used by computer programmers, and partly because of BOTH of these facts, it is eminently practical.
Note that I just described a small corner of logic; namely, two forms of conditional argument, which is a type of propositional reasoning, which is one branch of deductive logic, which itself is only a branch of formal logic on the larger tree of logic. Logic is a vast area of study, governing all of our reasoning.
I have been asked by many people if logic is useful. Usually by this question they are really asking, "Should I spend the money, time, and effort to teach myself or my children logic?" In itself this is a reasonable question. But many people ask it in scepticism, thinking that they don't need to teach their children logic. After all, we can all reason more or less correctly without studying logic, can't we?
I might respond by asking this related question: How is English grammar useful? Why should we learn it? After all, we can all speak more or less correctly without studying English grammar! The answer, of course, is that the study of English grammar provides us with rules which lay out the standards for proper speaking. These rules help us both to learn to speak correctly and to identify the errors made when someone speaks improperly. In exactly the same way, the study of logic provides us with rules which lay out the standards of proper reasoning. These rules help us to reason correctly and to identify the errors in reasoning made by ourselves and others.
How is this useful to ordinary people? We are all created in God's image as creatures who reason. We all reason all the time – even the most "ordinary" among us. Whenever we read a textbook, listen to a discussion about politics, or try to persuade our friends of a doctrinal position, we find ourselves drawing conclusions from other information. Whenever you say "because" or "therefore" you are reasoning at some level. Logic helps us to make sure that in such situations we are reasoning properly. Isaac Watts said it well: "Logic helps us to strip off the outward disguise of things, and to behold them and judge of them in their own nature."
As Christians who are given the word of God to read and proclaim, it is especially important that our reasoning is clear and correct. The Bible is packed full of propositions, and a complete study of logic helps us to interpret those propositions correctly. For example, no student of logic would fall prey to the idea that the doctrine of the Trinity is illogical or self-contradictory. This teaching – that there is both only one God and that the One God eternally exists in three Persons – makes no logical fallacies and has no contradictions. That it is beyond our comprehension is one thing, but that we can apprehend it without inconsistencies is very much another.
The study of logic helps us to apply universals to particular situations. This is important in the application of the Bible, since (for example) the commands of scripture are given in the forms of universals. "God commands all men everywhere to repent" is a universal statement. It requires the syllogism, "You are a man, therefore you must repent" to make its application. If logic were rejected, we could not apply the Bible to ourselves or others.
Finally, people will try to convince us of things which are not true. The study of logic will provide us with an additional defense against such error. It does this in many ways: teaching about popular fallacies to avoid, training in identifying standard errors in logical arguments, practice in writing counterexamples to demonstrate their failings, as well as helping the student to remain objective and think in a straight line. Dorothy Sayers said it well: "For we let our young men and women go out unarmed, in a day when armor was never so necessary. By teaching them all to read, we have left them at the mercy of the printed word. By the invention of the film and the radio, we have made certain that no aversion to reading shall secure them from the incessant battery of words, words, words. They do not know what the words mean; they do not know how to ward them off or blunt their edge or fling them back; they are a prey to words in their emotions instead of being the masters of them in their intellects." Logic helps students to be masters of words in their intellects.
I would say this to prospective logic students: Logic is fun and challenging, like the solving of puzzles. Formal logic, like most other subjects, can be learned to some degree by anybody with the patience to study. They will need patience to learn the vocabulary and techniques of logic, to solve the problems and correct some errors in their thinking. They will need to find a good curriculum which teaches logic to the level of their interest. They may need to find someone who can answer the questions that arise in their studies. Thankfully, there are a number of excellent sources available for learning logic.
Is learning logic easy? That depends entirely are how deeply you want to learn it. Because we all use logic to some degree in our daily life, much of practical logic is already familiar to us and simply needs a name attached to it. When one is introduced to a common line of reasoning, a typical response is, "That makes sense." For example, we learn in logic that this is a valid pattern of reasoning: If P then Q. P, therefore Q. When we learn to substitute statements for the P's and Q's, we see that this form of reasoning is used everywhere. Jesus uses it in the gospels when the leper comes to him and says, "If you are willing, you can make me clean" "I am willing," says Jesus. "Be clean."
We see that logic exercises our abstract reasoning skills, that is, the recognition of patterns found in concrete examples. In this way it is similar to mathematics. Let me explain in more detail. When a child first learns arithmetic, they are learning the first level of mathematical abstraction: the abstraction of number representing a number of concrete things. When they can grasp "three" without having to think of three apples or three blocks, they are at that first level. Later, when the math student begins to learn algebra, they are on the second level of abstraction: variables representing numbers (such as x = 3). Now this seems to me to be similar to logic. When a small child is learning to speak, words are the first level of abstraction. They are at this level when they can think of the abstraction "dog" without having to think of a particular dog, and can use it in a statement like "Some dogs are brown." Logic is the second level of abstraction: using a letter to represent a word (in categorical logic) and later an entire statement (in propositional logic). In fact, such letters representing words and statements in logic are also called variables.
For this reason, I believe that the prospective student will be ready for logic about the same time that he is ready for algebra. The necessary abstract reasoning skill for these two disciplines is roughly equivalent. When people ask me how to prepare their grammar-stage child for logic, I encourage them to concentrate on teaching the subjects at that child's level. Fill their minds full of truth, so that when they begin to reason at the next level, they have a store of truth from which to reason. There is no real need to push the introduction of logic back to the early elementary years, as so many overly eager people try to do. But when the child is around eleven or twelve years old, and moving into algebra, the diagraming of sentences in English, and methods of interpretation in Bible, then they are ready for formal logic. Beyond simply concentrating on learning their other subjects, older elementary students can and perhaps should be given some introduction to logic. This can be done formally through books like "Logic, Anyone?" by Beverly Post, or more informally through the playing of games like Mind Trap, Mastermind, Clue, and even Chess.
I have authored (or co-authored) two logic textbooks: Introductory Logic, and Intermediate Logic. To go with these I have written answer keys and test booklets, and filmed teaching videos. But to clearly explain the material taught in these two texts, I should give an overview of the branches of logic.
Logic can be divided into two main branches: formal and informal. Informal logic includes the learning of informal fallacies, such as ad hominem ("You can't believe what Farmer Jones says about the Bible; He hasn't studied in seminary") and post hoc ("You should keep this chain letter going: Bill didn't, and the next week he broke his leg."). It could also include methods of defining terms. Formal logic has two main branches: induction and deduction. We will consider induction in a later question. Deduction has several branches, two of which are categorical logic and propositional logic. Categorical logic is the logic developed by Aristotle, the logic of syllogisms ("All men are mortal. Socrates is a man. Therefore Socrates is mortal."). Propositional logic is the logic of truth tables, of modus ponens and modus tollens, and modern digital electronics.
Here is the main difference between categorical and propositional logic: In categorical logic the basic unit of thought is the category or the term, terms such as men, mortals, and Socrates. The conclusions of categorical arguments connect terms together into categorical statements. Such statements usually use individual letters to abbreviate terms, e.g. "Some men are not lawyers" is abbreviated Some M are not L. In propositional logic, however, the basic unit of thought is the proposition, such as "Jesus is God" or "Jesus is Man." Variables are here used to represent enitre propositions. So the propositional argument "Jesus is God. Jesus is Man. Therefore Jesus is both God and Man" can be abbreviated simply as: G. M. Therefore G & M. That provides a brief but sufficient overview of logic to explain what is in the textbooks.
The Introductory Logic text was written by Doug Wilson and myself. It is primarily concerned with categorical logic, along with some informal logic. It has four main sections: Statements and Their Relationships, Syllogisms and Validity, Arguments in Normal English, and Informal Fallacies. Each section has five to ten chapters, with exercises. Intermediate Logic concentrates on propositional logic, along with methods of defining terms. The main sections are: Definitions, Propositional Logic, Formal Proofs of Validity, and Truth Trees. This second book is slightly larger than the first, but otherwise has a similar format. The covers and descriptions of these books can be viewed on-line at www.logosschool.com. The texts have been written for the junior high or high school student. I have tried to make them clear, complete, and concise.
The videos are simply me teaching through the lessons in the texts. On the videos I work through problems in the text, as well as doing additional examples, giving hints for solving problems and avoiding errors, and other helps. Students using the videos should probably watch the appropriate portion of the video with the text open before them, then read that portion of the text again on their own, then do the exercises, reviewing any part of the video lesson, if necessary. After a certain number of sections are done this way, the student should then take the exam corresponding to that section.
It would be best if you could ask my students what they think! But if they are being honest with me, then yes, on the whole my students think logic is fun. I had the pleasure of overhearing two of them several years ago at a teacher training conference. A conference attendee stopped these two eighth-grade boys and asked, "Which is your favorite class?" Without hesitation and in unison, they answered "Logic!" Students have often expressed to me how much they enjoy it, and years later students remark how much they appreciate what they learned in logic.
How are my students different after a year of logic? I suppose the most obvious difference is that they use formal means to do what they otherwise would do informally: argue, ask questions, point out errors in the reasoning of others, and so on. They can tell the difference between premises and conclusions; they can distinguish arguments that are sound from those that are merely valid (or merely true); they not only know when someone is being illogical, but they can name the fallacy being made, and produce a counterexample to demonstrate the error; they can distinguish with more confidence what is explicitly stated in an argument from what is being assumed; they can define terms more readily and without the typical errors made by others; and in general they are more confident in their reasoning and speaking.
As to the other questions, I must admit that some parents have told me that their child has, upon learning the name of a particular fallacy (usually ad baculum), pointed out that they are commiting the same. And yes, some of my former students have indeed started rock bands – though I hope they did so for logical reasons! This perhaps reminds us that the study of logic does not change hearts; education is not our savior. If we teach logic to devils, we get clever devils. Thus logic (and any other subject) should be taught from a Christian worldview, along with the proclamation of the gospel and the exhortation to use our learning to the glory of God, leaving the results up to him.
Inductive logic and deductive logic are the two main branches of formal logic. Inductive logic, or induction, deals with arguments of likelihood and probability. Inductive logic draws conclusions from experience, conclusions which go beyond the premises but which can be strengthened by further experience as more data is made available. For example: Observations tell us that hammers fall faster than feathers, and big rocks dropped from a high bridge fall faster than coins. We conclude, inductively, that heavier objects always fall faster than lighter ones. Note that this conclusion is universal, and goes far beyond the initial observation. But then we see a video of an astronaut on the moon dropping a feather and a hammer, and see that they fall at the same speed. We find ourselves modifying our initial conclusion as we gather more data. This is the process of inductive reasoning. You can see that inductive logic is the logic of the experimental sciences.
The conclusions of inductive reasoning are either strong or weak, depending on how well the evidence supports the conclusion. The conclusions of deductive arguments, on the other hand, are either valid or invalid. If valid, the conclusion follows necessarily from the premises. If the premises are true and the argument is valid, the conclusion must be true. For example, if God commands all men everywhere to repent, and you are a man, then you must repent. This is a valid, deductive argument. If the premises are true, the conclusion is certain. Inductive conclusions go beyond the premises, but deductive conclusions are contained within the premises. Finally, deductive arguments, to be valid, must employ universal premises (such as "All men must repent"), which the arguer believes his hearers will accept as true. Such premises are generally called axioms.
Here is a chart which summarizes the differences:
| Deduction | Induction |
| Based on axioms | Based on experience |
| Arguments are valid or invalid | Arguments are strong or weak |
| Conclusions are certain | Conclusions are probable |
The reader may see from this why it is important for Christians to understand the difference between induction and deduction. Consider apologetics, defined by John Frame as "the discipline which teaches Christians how to give a reason for the hope which they have." If we are seeking to argue that the triune God of the Bible exists, should we seek to argue inductively or deductively? Should we argue based on our own experience, or upon axioms revealed in God's word? Should the conclusion of our argument be, "Thus, to a high degree of probability, God exists," or should it be, "Therefore, if you accept what I have said earlier, then God certainly exists"? These are two very different approaches, and they illustrate the importance of understanding the difference between these two types of reasoning.
First, I would make sure that I understood exactly what they meant by "using logic." So many disagreements, especially between brothers in Christ, come about precisely because we are not careful to define our terms beforehand. By "using logic" do they mean starting with fully comprehended premises, putting all of our arguments into formal syllogisms or truth tables, and rejecting any conclusion which does not make complete sense to us? Then I would agree that we shouldn't always "use logic" when interpreting God and the Bible. We cannot fully comprehend all of the premises, because God is beyond us; His thoughts are higher than our thoughts. One of my premises in interpretation is that God is infinite in His attributes; I believe this, but I by no means fully comprehend it. Some of our arguments will not fit nicely into logical form, at least not if we are arguing like the scriptures do. For often the Bible uses poetry and metaphor to explain God and the things of God. "God is a rock and His works are perfect" does not fit nicely into a syllogism.
And sometimes, for those who receive all of God's word as true, the conclusions do not make complete sense to us, though we must still believe them because they are in the Bible. For example, I believe that God is absolutely sovereign over all events, including the actions of free men. All the days ordained for me were written in His book before one of them came to be, and before a word is on my tongue He knows it perfectly (see Psalm 139). At the same time, I believe that men are free to do what they want, and are fully responsible for their actions. Judas betrayed Jesus, the Jews called for His death, and Pilate condemned Him to be crucified, as God ordained that they would (Acts 2:23), yet they are still responsible for their sins and will answer for them in the judgment. God foreordained even sinful actions, yet He is not the author of sin. I believe all this, without fully understanding how it all works. If that means I am not "using logic" then so be it.
However, if by "using logic" they mean that we should make sure that our premises are true, that we are arguing validly, and that we avoid real contradictions, then of course we should use logic when interpreting God and the Bible. That is why God made us as rational beings, so that we could understand His word. Charles Hodge said it well: "Revelation is a communication of truth to the mind. But the communication of truth supposes the capacity to receive it. Revelations cannot be made to brutes or idiots. Truth, to be received as objects of faith, must be intellectually apprehended." Cornelius Van Til made a similar point when he wrote, "The gift of logical reason was given by God to man in order that he might order the revelation of God for himself."
The use of logic can be a great help to interpreting the scriptures, if we use it correctly and submissively. Isaac Watts, a logician as well as a hymn writer, wrote that "Logic helps us to strip off the outward disguise of things, and to behold them and judge of them in their own nature." Gordon Clark makes the point even stronger: "The use of logic is not optional. Logic is so fundamental, so basic, that those who attack it must use logic in order to attack logic. . . . They must assume its truth, in order to declare it false. They must present arguments if they wish to persuade us that argumentation is invalid. Wherever they turn, they are boxed in." We cannot escape the use of logic, and we should not try. What would happen if we succeeded? We would spout out absurdities and nonsense.
Again, let's define our terms. What do you mean by "everything"? Do you mean every thought that comes into my head? Do I need to prove that God wants me to wear my white shirt instead of my blue one before I can put it on? Then yes, that is too high of a standard. Nobody could live that way.
More practically, I have some beliefs which I cannot prove from the Bible, but which I nonetheless firmly hold. For example, I believe that God has called me to minister as a teacher at Logos School in Moscow, Idaho. I believe this firmly enough to pass down without a second thought offers made to me to work elsewhere. But I would be hard pressed to produce a deductive argument for this belief of mine from the Scriptures.
I would also add that our most basic axioms are not to be proved but must simply be believed. All foundational premises are unprovable – we explain truths in terms of other truths, and them in terms of others, but we cannot back up forever. Eventually we will reach our starting point, our presuppositions. Such presuppositions are not provable, but are rather used to prove everything else.
However, if you mean that I should learn to defend my major beliefs of faith and practice deductively from the scriptures, then I would agree. That is not too high of a standard. I hold to the Westminster Confession of Faith at this point: "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." Logic is what helps to establish that good and necessary consequence.
1 • Gary Hatchell • May 17, 2008 • 2:22 PM
We are going to homeschool our kids next year. They are ages 7 and 10. Is this too early to start logic? If not, what is a good resource to use?
2 • Nathaniel Bluedorn • May 19, 2008 • 11:41 AM
I’d recommend the Building Thinking Skills books from The Critical Thinking Company. James Nance’s Introductory Logic course would be too advanced for your children right now.
3 • Annetta • May 26, 2008 • 7:44 AM
Building Thinking Skills Book 2 would be good for your 10 year old.