Table of Contents

 

     Preface                                                                                             

Practical Logic

Chapter 1  Necessary Background:  Biblical                                   

Chapter 2  Necessary Background:  Classical                                 

Chapter 3  Definition of Logic:  Purpose                              

Chapter 4  Definition of Logic:  Limitations                                   

Chapter 5  Foundational Patterns:  Deduction and Induction

Chapter 6  Foundational Principles:  Laws of Thought                   

Chapter 7  Patterns:  Premises and Conclusions                             

Chapter 8  Patterns Embodied in Language:  Guidelines                 

Chapter 9  Patterns Embodied in Language:  Premise Types

Chapter 10  Patterns Embodied in Language:  Diagramming

     Chapter 11  Principles:  Evaluation of Arguments                          

Chapter 12  Principles:  Informal Fallacies:  Composition              

Chapter 13  Principles:  Informal Fallacies:  Distraction                 

Chapter 14  Principles:  Informal Fallacies:  Ambiguity                 

Chapter 15  Review of Practical Logic                                           

Symbolic Logic

Chapter 16   Practical and Symbolic Logic:  Introduction               

Chapter 17   Categorical Logic:  Translation                                   

Chapter 18   Categorical Logic:  Distribution and Inference 

Chapter 19   Categorical Logic:  Square of Opposition                   

Chapter 20   Categorical Logic:  Mood and Figure                         

Chapter 21   Categorical Logic:  Rules for Validity                         

Chapter 22   Propositional Logic:  Propositions                             

Chapter 23   Propositional Logic:  Truth Tables                             

Chapter 24   Propositional Logic:  Shorter Truth tables                  

Chapter 25   Propositional Logic:  Inference and Replacement       

Chapter 26   Propositional Logic:  Basic Proofs                             

Chapter 27   Analogical Reasoning:  Definition or Description       

Chapter 28   Analogical Reasoning:  Some Directions          

Chapter 29   The Big Picture:  Refocusing                                      

Chapter 30   The Big Picture:  Definition and Translation              

Chapter 31   The Big Picture:  Larger Arguments                           

Chapter 32   The Big Picture:  Conclusion                                     

Appendix I   Categorical Logic Helps                                              

Appendix II   Propositional Logic Helps                               

Appendix III   Imitation Reading                                                    

Glossary                                                                                

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Chapter 1:  Necessary Background:  Biblical

 

Come now, and let us reason together, saith the LORD: though your sins be as scarlet, they shall be as white as snow; though they be red like crimson, they shall be as wool. Isaiah 1:18

 

            Every reader of this book reasons even as he reads this sentence.  Reasoning and thinking are inescapable.  Thinking is a necessity to human existence that is comparable to breathing.  Every thought that goes through your head is, in a sense, a use of your reason.  In the study of logic, we have before us the difficult and sometimes confusing task of thinking about our thinking.  Thoughts about thoughts can then become material for more thought about those thoughts.  I introduce this text with this consideration to help you realize that the study of reasoning is not always easy, and is often fraught with the most difficult and interesting philosophical questions. 

 

The history of the study of reasoning is, as a result, very philosophical.  Since my goals for this course lie in a different direction, we will not spend much time discussing the ins and outs of philosophical systems.  However, as some background is necessary, I will try to outline a Biblical perspective on human thought and reasoning, and then compare and contrast it with the classical or secular view.  Forgive me if this seems cursory; I admit it is only that.

           

In this book you will learn about some of the intellectual tools for thinking about your thoughts.  More particularly, you will learn to evaluate purposed thought (reasoning).  The most common manifestations of purposed thought are found in “arguments” or, perhaps a bit more technically, “syllogisms.”  In this kind of purposed thought there are two main parts:  the premises, or reasons, and the conclusion, or result.  I want you to be able to follow the reasons to the result, the premises to the conclusion.  Most importantly, however, I want you to do this outside the classroom, as well as in the exercises in this textbook.  I hope that the intellectual tools you pick up here will be handy enough for you to use them all your life.  But before we get down to the nitty-gritty of these principles and techniques, let me give you at least a little bit of background. 

 

Biblical View of Reason:

 

            Men are created in God’s image.  When Scripture teaches about God it teaches us also about ourselves, and when it teaches us about ourselves it teaches also about God.  In this, Scripture is teaching us that purposive thought in ourselves can be seen as a reflection of a purposing God, and that the purposes of God provide a basis for purposively reasoning man.  Man’s purpose is to glorify God and enjoy Him.  Enjoying God means knowing Him and knowing who He is and what He is like.  One of the first things that Scripture teaches us is that God is Truth—He is the fount of all that is true, good, or lovely.  Pursuit of God, then, is a pursuit of ultimate Truth—this is at least one reason why God gave us the ability to reason.  When men reject truth saying that they cannot know and that there is no truth, true (righteous) thought ceases (Romans 1).

 

            All truth and knowledge depend on God’s being, as does all of the creation.  Scripture is unequivocal about this.  This means that we cannot seek truth without seeking God; for man, there is no such thing as discovering truth on his own.  All of our thoughts depend on God.  This is strikingly illustrated in the language Scripture uses concerning truth.  Where autonomous human thinking tends to draw an impersonal line between true and false, Scripture speaks of truth and lies.  God’s Word is truth; Jesus Christ himself is Truth; if it is not God’s Word (or consistent with God’s Word) it is a lie.  Scripture teaches us that truth is ethical and personal, not merely intellectual.

 

            This ethical and personal approach to truth is demonstrated further in the Bible.  Scripture does not recognize all “reasoning” as good and legitimate.  Unrighteous human reasoning exists, as does righteous human reasoning.  Far from being amoral, reasoning is always ethically charged.  While there are examples of a positive reference to reasoning in Scripture (Paul’s defenses of the faith in Acts, etc.) we often find that the scribes and Pharisees are the ones “reasoning among themselves.”  Their reasoning is not necessarily invalid, but it is unsound and leads not to truth but to lies.  Reason is not a means for automatic ascension to knowledge, truth, and God; rather, it is a tool given to us by God, which we can use either to ascend to knowledge of Him or to descend to hell.        

 

            The epistles of the Apostle Paul are great examples of holy reasoning.  “Shall we continue in sin that grace may abound? Certainly not! How shall we who have died to sin live any longer in it?”  This reasoning is phrased as a question and is also rhetorically fashioned, but Paul is clearly engaging his God-given reason to explain salvation in Christ.  The argument is simple:  if you die to something, you leave it behind; if you died to sin in Christ, you left it behind.  Therefore, you cannot continue to live in something you died to.  He goes on to explain that we have died to sin in Christ, and if we died with Christ then we will also be raised with Him.  This is why we are to walk in newness of life.  There is much food for thought in these passages. 

 

            The book of Job presents another interesting example of reasoning in Scripture.  Job’s friends reasoned with him at length about God’s purpose in allowing him to suffer, only to find in the end that they were wrong.  Again, their reasoning was not necessarily invalid.  Most of their premises were even legitimate, so how did they go wrong?  At least one of the things that caused their error was their certainty that they could parse out the purposes of God.  Their error is in effect a warning to those who do seek knowledge, truth, and God Himself with reason, reminding them that while they can and will know what God reveals, they must not think they can know more.  Reason can tempt us to assume we have more knowledge than we actually have.

 

Reason, as a good gift of God, is subject (like all of the created order) to use or misuse by man.  One common misuse of reason is idolatry—worshipping the created thing instead of the Creator.  Most of the unbelieving world wants to use human reason, in one way or another, as an ultimate standard.  Christians, just as the Israelites were, are susceptible to the temptation to idolatry; to bring things to Reason as an ultimate standard is nothing less.  No matter how cogent our reasoning, we must hold our thought in submission to God and His Word.  When reason joins the worshipping chorus of creation and Scripture, it becomes a means to understanding and applying revealed truth; but when it is an ultimate standard, it becomes an idol.  I want to make this very clear.  I do not want you to study logic if you think that by it you can determine truth.  Truth is revealed.  Logic and reason are designed to help you understand revealed truth, and, by God’s grace, for that task they are very capable.

 

            The Proverbs speak often of wisdom, understanding, and knowledge as prize possessions.  Knowledge, understanding, and wisdom deliver man from sin and folly.  Did you know that if you learn well the discipline of logic and subject it to God’s Word, it will give you treasure and safety?  In Proverbs 8 and 9 Wisdom, personified, explains all of the bounty that is hers.  Right use of reason is at least one of the aspects of Godly wisdom.  Throughout the Proverbs the wise man is pictured as the one who sees and has understanding.  Reason, as we mentioned above, seeks understanding.  However, reasoning is not something done in a vacuum; it is not a system without premises.  If you do not have the first premise right, in fact, you cannot get any further.  The fear of the Lord is the beginning of wisdom.

 

            Colossians 2:3 says that all the treasures of wisdom and knowledge are in Christ.  In Christ we understand the mysteries and we know God.  But even beyond Who Christ is and what He accomplishes in His person (treasure beyond imagination), we have His specific example.  In His life on this earth Christ was not only a teacher of truth but a refuter of error.  He often confounds the scribes and Pharisees with His answers.  In His example, Christ shows us the right use of reason:  to glorify God and leave the unbeliever without an excuse.  Christ’s use of reason and language is our first example; following in His steps, other holy men of the Scriptures provided examples for us, as well.   

 

            The Apostle Paul also reasoned with unbelievers.  Notice that Paul didn’t just appeal to his personal experience, or to his faith, but he reasoned with them.  He became positively didactic when rooting out error in unbelievers and in the church.  He did see the Christian message as more than a set of true propositions, but he definitely didn’t see it as less than that.  “If there is no resurrection, we are worse than fools.”  In other words, “If there isn’t a truth to be argued for, there isn’t any good news.”  So an important use for reason is the defense of the faith against unbelief.  Those who worship God use reason; those who worship Reason are used by it.

 

            As in all things, God comes both first and last.  The fear of the Lord is both the beginning and the end of right thinking.  When you subject your thoughts to the Lord, He will give you the desires of your heart.  He will show you truth and knowledge, even beyond your years.  Scripture’s attitude toward human reason is ethical and personal.  Reason is a tool, and used well it serves God in beauty and truth; used sinfully, it condemns the one who uses it and all who listen. 

 

Summary:  Reasoning is inescapable, and it involves many philosophical questions. Though this is not my focus in the course, this chapter provides some necessary background to the study of reason.  The Biblical perspective on truth and reason is personal and ethical, and it reveals the fact that reason is a tool which can be used or abused.  Reason is abused when it is worshipped, or used by man to justify rebellion against God. 

 

Exercise 1:  Theory

a. Summarize the purpose of this book as stated in this chapter.

b. What is another word for “syllogism”?

c. Is reason a gift from God or a temptation to idolatry, or both?

d. What is the Biblical view of reason?

e. What, according to the Bible, is truth? 

 

Exercise 2:  Imitation

Read the first half of the book of Proverbs.  How does the writer reason?  Can you follow his reasoning?

 

Exercise 3:  Practice

Use a concordance or Bible search program to search for passages about reasoning, truth, and wisdom.   List the characteristics or qualities given for reasoning, truth, and wisdom.

 

Example:

 

Reasoning                                Truth                                        Wisdom

1. Another name                      1.God gives truth                     1. God gives spirit of wisdom

for pleading                             with mercy; Gen                      for making priestly garments

Job 13:6                                  24:27 & 32:10                         Exodus 28:3

2. continue                              2. etc                                       2. etc

                                               

 

 

 

Chapter 3:  Definition of Logic:  Purpose

 

 “Language is the dress of thought.”  Samuel Johnson

 

Logic, then, is the discipline you will learn in the following pages.  But what is logic?  As it turns out, the answer to this question is not as simple as you might expect.  The way you define the word reflects what you hope to accomplish with logic, and suggests its limitations as well.  While most definitions of logic are similar, there is some amount of variation from one author to another.  In this chapter I will set forth my answer to this question. 

 

            As I mentioned in the last chapter, there is a sense in which when we practice logic, we are thinking about thought.  Logic is not indiscriminately concerned, however, with all kinds of thought.  Logic teaches you how to evaluate thought processes such as those involved in defending a position or solving a problem; that is to say, logic is about purposive thought. By this I mean the kind of thinking that sets out specifically to accomplish something.  I do not mean random thoughts that cross a person’s mind.  So logic is “the study of purposive thought.”  This definition is workable, but let me refine it a bit more.

 

              The word logic comes from the Greek word logike or logikos, indicating something belonging to speech or to the reason. The fact that speech and language are part of the etymology gives us a clue about how we will actually use logic.  When you analyze purposive thought with logic, you are not going to be looking at arguments as they form themselves in someone’s head—that is impossible.  Rather, you will look at arguments embodied in language, whether spoken or written.  So we should add this to our definition.  Logic is “the study of purposive thought, as embodied in the spoken or written word.”  This definition is better, but I predict objections from students of logic who have been taught that logic is “the science of necessary inference.”  For them our definition is far too general.  There are a couple of ways to answer this objection, but instead let us refine the purposive-thought clause a bit first.  Logic applies common and standard forms and certain criteria of judgment to the purposive thought it evaluates.  In other words, there are principles and patterns specific to the discipline of Logic.   Logic is the study of the principles and patterns of purposive thought, as embodied in language spoken or written.

 

            This will be the operative definition of logic for this course.  It includes what we will study, and excludes what we won’t.  It will still be too broad a definition for some people’s tastes, but I believe even they must admit it as acceptable since it meets the requirements for definition set forth by the principles of logic itself.  The definition is neither too broad (including other disciplines besides logic) nor too narrow (excluding legitimate kinds of inference).  It is not negative, and it includes the essential attributes of the referent without using metaphorical or vague language.  This definition also has the advantage of being fairly close to the conventional use of the word.  The logic of computer programming, for example, does fit the definition, although it is not our specific focus in this book. 

 

            So how does my definition indicate what I think logic should do?  The phrase “embodied in language spoken or written” reflects the fact that I want you to learn to use logic practically.  Logic is a tool that needs to be used to be learned well, and to use it you must (obviously) have opportunity to use it.  By emphasizing the fact that arguments are embodied in language, and in language which we use every day, I hope to help you realize that you have many opportunities to use logic practically.  If your study of logic never meets the ground, you will be an expert in rarified reasoning and nothing else.  That is why we begin with practical logic in this book.  You will learn how to identify and diagram English arguments and give them a general evaluation, before you go on to the more abstract and precise science of symbolic logic.

 

            The phrase “of purposive thought” points to a couple of ways in which I expect you to use logic.  First, as we discussed earlier in this chapter, the study you will do here is not just of thought in general but rather of thought that is going somewhere and doing something.  Second, “purposive thought” is a rather general phrase but it helps us to include in the study of logic legitimate inferences that are sometimes excluded.  For example, those who define logic as “the science of necessary inference” exclude both induction and analogous reasoning, neither of which deal in necessary inferences[1].  I want you to be able to see both of these as legitimate and important rational processes, and to be able to evaluate them. 

 

            The phrase “principles and patterns” points to the systematic and evaluative aspects of logic.  Logic helps you to identify and distinguish sound reasoning from unsound.  In order to do this effectively, you will have to learn the patterns and the principles of sound reasoning.  Equipped with these tools you will be able to analyze reasons and arguments—both your own, and those of others.  The patterns will help you quickly classify arguments, so that they can be analyzed according to the principles appropriate to their form.  Principles and patterns are at the heart of logical analysis.

 

            The phrase “the study of” indicates what you will have to do to learn and to practice this discipline.  This study is an ongoing process which demands constant maintenance—in other words, it is a discipline.  The principles and patterns of purposive thought will eventually become second nature to you.  You have to think, and if you habitually use logic to help you in this process, eventually it will not be hard to maintain.

 

Summary:  The definition of Logic is foundational to the rest of this course:  Logic is the study of the principles and patterns of purposive thought as embodied in language spoken or written.

 

 

Exercise 1:  Theory

a. Memorize the definition of logic given in this chapter.

b. Outline how the definition helps us understand the purpose of logic.

c. Why is this definition better than some of the common narrower definitions?

d. What is purposive thought?

e. What does “embodied in language” mean?

 

Exercise 2:  Imitation

Read the first quarter of the book of Job.  What is Satan’s argument concerning Job?  What are Job’s friends trying to convince him of?

 

Exercise 3:  Practice

Think of five hypothetical examples of purposive thought.

 

Example:

 

I am trying to think of examples of purposive thought.  Purposive thought is thought that has a particular end in mind—it tries to accomplish something.  So it seems that trying to think of examples of purposive thought is an example of purposive thought.

 

Or,

 

As a Christian, I love Christ.  Christ says that if I love Him I will want to keep his commandments.  So, you can see, I want to keep his commandments.

 

 

 

Chapter 6:  Foundational Principles:  Laws of Thought

 

There are some who…assert that it is possible for the same thing to be and not be….  We can, however, demonstrate negatively even that this view is impossible, if our opponent will only say something; and if he says nothing, it is absurd to seek to give an account of our views to one who cannot give an account of anything, in so far as he cannot do so.  For such a man, as such, is from the start not better than a vegetable.  Aristotle, Metaphysics

 

         In this chapter we come to some foundational principles of “purposive thought.”  Some of you are probably already familiar with the phrase “the laws of logic.”  The meaning of this phrase is not always clear, but when it is, it most often refers to the three laws of thought.  These laws originated at the time of Plato and Aristotle in the schools of the Stoics and in their own writings.  They have traditionally been considered the three laws necessary to rational thought; that is to say, if these were not true there would be no thinking.  In recent years this has been questioned by science, and also by those who hold observation to be a higher court of appeal than reason.  In this case we see two different camps of unbelief holding up conflicting standards for truth.  One camp uses reason founded on the laws of thought as the ultimate standard; the other wants to use the scientific method, founded on the laws of physics and observation of physical phenomena, as the ultimate standard of reality.  Notice that unbelieving worldviews still need to have an ultimate point of reference if they want to keep thinking.  These two extremes are the result.  For the Christian, science and reason are not in conflict.  They are both legitimate thought processes and are both subject to the Word and will of God.  In this chapter I hope to show how the laws of thought and scientific or inductive reason can be reconciled, and what role each plays in forming a basis for logic.

 

  1. The Law of Identity:  A thing is itself and not something else.  If a thing is A then it is A. 
  2. The Law of Non-contradiction: A thing and its opposite cannot both be true at the same time and in the same respect.  If a thing is A then it is not not-A.
  3. The Law of Excluded Middle:  A thing is either true or false but not between.  Either A is true or A is false. 

 

These probably seem intuitively obvious—which is why they have been almost universally accepted throughout the years.  And, as long as you talk about deductive reasoning (moving from generals to a particular conclusion) they pose no problems.  The questions concerning their ultimacy have arisen with the increased interest in the scientific method and induction (reasoning from particulars to a general conclusion).  The deductive method involves putting general principles together to create a more particular conclusion.  An everyday example would be the following argument:  “Light switches turn on lights; this is a light switch; this turns on a light.”  Although your mind is able to skip most of these stages and go directly from the observation to the conclusion, at one point in time you were applying the deductive method to this situation in order to figure out how light switches worked.  However, before that process, you needed to get the general principle that light switches turn on lights from somewhere.  There are a couple of ways you could come up with this general principle.  First of all, someone could tell you that it is the case that these kinds of switches turn on lights.  You would then try this principle out and flip as many light switches as you could.  These particular instances of turning on a light switch and seeing a light come on begin to form an inductive process of reasoning in your thought.  You already have the conclusion “light switches turn on lights” in mind, but the more you test the principle and find it true the more certain you are of the reliability of the general rule, and the stronger your argument.  Here you see the difference that leads to the disagreement between those who deduct and those who induct.  If the premises of the deductive argument are true, and the reasoning valid, then the conclusion must be true.  If the premises of the inductive argument are true and the reasoning correct, the conclusion is merely strong.  Inductive arguments can seem to be inconsistent with the Law of Excluded Middle, since a strong or weak conclusion is not specifically identified as either true or false.  There is a potential for the principle to be false in one case (when you turn on the switch for the garbage disposal) while it is true in all the rest.  And while we aren’t saying that the same thing is true and false at the same time in the same respect, we are saying that it can be true at one time and false at another.  This doesn’t technically break the Law of Non-contradiction, but a system of reasoning that regularly makes arguments like this also isn’t the most perfect match for the rule.  So you see why induction (and science) and the three Laws of Thought can seem to be at odds. 

 

            But why are we discussing this, anyway?  As a logician, you will have to consider these questions.  What role do the laws of thought play?  Are they ultimate?  Are they practical?  Especially, how can we make induction jive with the laws of thought?  Should one of these methods of reasoning be considered supreme and the other subject to it?  My answer to that last question is that, since the Word of God governs both induction and deduction, we as Christians can reconcile these two seemingly disparate points of view as both being useful, without necessarily making one subordinate to the other.  The answer to the seeming dilemma is that deduction and induction deal with the world in different ways.  Deduction is essentially abstract and theoretical, dealing with universals or point-in-time questions. Induction is concrete and practical, trying to establish patterns and general principles among particular examples.  Don’t misunderstand; there are good and necessary purposes for both abstract and concrete purposive thought.  They actually build on one another.  And we find (and use) both in reasoning every day. 

 

            The Biblical basis for both is clear.  Scripture everywhere upholds the idea that we learn from our interaction with the created order around us.  From the illustrations in Proverbs that tell us to observe the ants, to the heavens that declare the glory of God, Scripture upholds the idea that the creation gives us many particular reasons to conclude that God is good and great.  In addition to the example of Scripture, we have the principle from God’s law that from the mouth of two or three witnesses a matter is established.  If you consider the Scriptures with this in mind, you will find that there are almost always at least two accounts of every event recorded in Scripture.  In the Old Testament we have four books that tell the story of Israel’s deliverance from Egypt and pilgrimage to the promised land—Exodus, Leviticus, Numbers, and Deuteronomy.  In the New Testament we have four Gospels.  Even God Himself reveals Himself by the mouths of two or three witnesses in the Creation and in His Word, as well as in His Triune nature where each of the persons always bears witness to the others: the Father and the Spirit to the Son (at Christ’s baptism), the Son to the Father throughout His earthly ministry, and the Spirit to both in the Word.  The principle of multiple witnesses confirming a matter comes from the very nature of God. 

 

            The deductive method of reasoning is also supported throughout Scripture.  Especially obvious are the deductive arguments of the New Testament epistles.  When you are reading these passages, one of the most valuable questions you can ask is, “What is the ‘therefore’ there for?”  In the next chapters we will learn to look for sign words that indicate the conclusion of an argument; we find many of them in Scripture.  There is another argument for deductive reasoning that is even stronger than examples of it from Scripture:  God’s nature itself is the foundation for the Laws of Thought.  God is Himself, the same yesterday, today, and forever (Law of Identity).  We also know that He doesn’t lie (Law of Non-contradiction).  Finally, God and His words are Truth, and all else is a lie (Law of Excluded Middle).  And so, the foundational principles of deduction are a reflection of God’s nature as well. 

 

            So what do we do with the seeming conflict between these two methods?  The short answer is, “nothing.”  God’s Word is our ultimate standard.  Reason, both deductive and inductive, is used in our understanding of Scripture, but a systematic philosophy of each is, luckily, not necessary to understand the meaning of Scripture which is “plain,” according to the creeds.  To satisfy the curious, however, we can point to the differences of perspective and purpose between the abstracting tendencies of deductive reason and the practical tendencies of inductive reason.  The practical inductive process is the one we most naturally use to form opinions and general rules for our everyday living (as in the light switch example).  We all know there will be exceptions, but we also count on a relative amount of consistency from one time to another and throughout time.  Time, then, is a factor in the inductive process.  Inductive principles are considered not at only one moment in time, or as being stationary in time.  They are fluid.  This is why we can only refer to the relationship between induction and deduction as a seeming contradiction.  The seeming contradiction between the Law of Excluded Middle and induction arises from the fact that induction is an over-time process, and deduction is a moment-in-time or outside of time process.  Induction doesn’t claim that a statement can be true and false at the same time in the same way.  It means that, over time, due to change, the object of knowledge can change, as can human perception.  The laws of thought state clearly that they are to deal with things that are not in motion or subject to change (i.e. “in the same place and in the same respect”). They are used to apply timeless or general truths to a particular situation.   

 

The inductive method collects data according to a hunch or hypothesis, which then becomes a principle when the argument is strong enough.  The inductive method relies on the laws of thought, as well.  If it were possible for a thing to be both itself and not itself at the same time and in the same way, no one would ever be able to collect the particular data for inductive proof.  Unfortunately, I have to leave this discussion here.  If your interest is piqued by this topic, more information on epistemology can be found in the bibliography or on the web site.  

 

As we begin in the next chapter to look for arguments in English, keep your eyes open for arguments that seem inductive versus those that seem deductive.  Both will appear in everyday reasoning, and both are important to the overall processes of purposive thought.  As Christians, we can easily reconcile what we learn from experience to what is ultimately true.  Truth is revealed to us both progressively, through time and space, and ultimately unchanging in God and His Word. 

 

Summary:  The laws of thought, (1) the Law of Identity, (2) the Law of Excluded Middle, and (3) the Law of Non-contradiction, are basic to all reasoning, although they have been questioned in recent years by proponents of the scientific method.  Although there are some initial seeming inconsistencies between induction (scientific reasoning) and deduction (traditional logic), the two methods are actually complementary.  The apparent inconsistency is the result of a difference in the way they interact with the world.

 

Exercise 1:  Theory

a. List, define, and give examples illustrating the three laws of thought.

b. What makes the inductive process and the laws of thought seem incompatible?

c. How can you reconcile the seeming conflict between the laws of thought and induction?

d. How are the laws of thought foundational to both induction and deduction?

e. Give a brief Biblical defense of both induction and deduction.

 

Exercise 2:  Imitation

Read the last quarter of Job.  God reasons by asking questions.  What is His point?  How does this book illustrate that the fear of the Lord is the beginning of wisdom?  Discuss Job 42:7.

 

Exercise 3:  Practice

Think of five real-life situations in which the laws of thought make rational communication possible.  If you get stuck, take a break and come back to it later.

 

For example:

 

At the grocery store they said that the total for all the items I wanted was $5.25.  The Law of Identity assures me that $5.25 is $5.25.

 

When my dad says he wants what is best for me I know that doesn’t mean he doesn’t want what is best for me, since the Law of Non-contradiction would then be violated.

 

If it is false that pigs are whales, I don’t have to worry that it might be partially true, since the Law of Excluded Middle says that things are either true or false but not in between.

 

 

 

Chapter 10:  Patterns Embodied in Language:  Diagramming

 

                        If the English language had been properly organized…then there would be a word which meant both “he” and “she,” and I could write, “If John or Mary comes heesh will want to play tennis,” which would save a lot of trouble.

                              A.A. Milne, The Christopher Robin Birthday Book

 

            This is the final chapter on the patterns of purposive thought in language.  In it you will learn two ways of diagramming the premises and conclusions which you are already learning to identify.  Diagrams are helpful tools in evaluation and understanding since their standard form can help to reveal differences, similarities, and irregularities of arguments.  They also help to systematize the connection between premises and conclusions.

 

            The first method of diagramming is the simple listing method.  When you begin to set up a diagram it will be necessary to change and distill the wording of the argument out of the language in which it occurs.  That means that sometimes a statement, as it occurs in English, needs to be changed a little to fit the diagrammatic system.  We’ve seen this at work already in chapters 5 and 7.  As we’ve also discussed in previous chapters, you have to identify premises and conclusions in the original language first.  Then you can begin the process of standardizing your premises. Here is a basic three-step process for doing so:  First, turn the language into indicative statements, removing as much of the “padding” language as you can, and arrange the argument so that all the premises come first and the conclusion last (whether or not this is the order in English).  Second, take terms[2] that refer to the same thing in English but are different in word order or detail, and change the word order and detail to make them alike.  Third, order and standardize—as much as possible—the tense and mood and type of verb in each statement.  The goal is not to change the English any more than necessary, so be careful in each of these steps.  Let’s look at the passage from C.S. Lewis again to illustrate this process:

 

If you asked twenty good men today what they thought the highest of the virtues, nineteen of them would reply, Unselfishness.  But if you asked almost any of the great Christians of old, he would have replied, Love.  You see what has happened?  A negative term has been substituted for a positive, and this is of more than philological importance.  The negative idea of Unselfishness carries with it the suggestion not of securing good things for others, but of going without them ourselves, as if our abstinence and not their happiness was the important point.  I do not think this is the Christian virtue of Love. 

 

            First step:  there are a number of arguments in this passage, as we considered in Chapter 8.  Since we already set forth the hypothetical inductive arguments in that chapter, let us turn to the third argument.  Arguments in this passage are already arranged according to the “premises first, conclusion last” pattern.  All we have to do is identify and list the premises and conclusion minus the non-essential padding language.

 

 

Second and Third Steps

Premise:

Good men today say the highest of the virtues is Unselfishness. 

Premise:

Good men (Christians) of old say the highest of the virtues is Love. 

Conclusion:

A negative term has been substituted for a positive.

 

First Step

Premise:

Of twenty good men today, nineteen of them would say the highest of the virtues is Unselfishness. 

Premise:

The great Christians of old would have replied, Love. 

Conclusion:

A negative term has been substituted for a positive.

 

 

 

 

 

 

 

 

 

 

 

You can see that the wording of the terms in the first box is different in each premise.  When we compare the two premises together and look at the rest of the passage we see that Lewis is making a comparison between good men today and good men of the past (specifically Christians).  Since this is the case, we are justified in standardizing the first term in each premise as “good men.”  The “highest of virtues” phrase is clearly implied in the second premise, so we can standardize the second term as well.  Then the third step in this argument is not that difficult.  We merely change the second premise’s verb from “reply” to “say,” which it was already obvious we needed to do.

 

            There is one further thing that we can do to make our analysis even more compact and easy to use—abbreviate some of the terms.  Like this:

T = good men today, V = highest virtue, U = unselfishness, O = good men of old, L = love,

N = negative term, P = positive term

 

Premise:  T say V is U 

Premise:  O say V is L 

Conclusion:  N has been substituted for P

 

 

 

 

 

 

 

Now once we do this, a terminology gap appears between the premises and the conclusion.  The terms in the conclusion are nowhere in the premises.  Have we identified and reproduced the argument correctly?  After looking at the original passage again, indeed, it seems that we have.  So the most likely solution to the problem is that there are assumed premises.

T = good men today, V = highest virtue, U = unselfishness, O = good men of old, L = love,

N = negative term, P = positive term

 

Premise:  T say V is U 

Premise:  O say V is L

Assumed Premise:  U is N

Assumed Premise:  L is P

Conclusion:  N has been substituted for P

 

 

 

 

 

 

 

 

 

The assumed premises are easy to overlook because they seem so intuitively obvious when you read the original text.  Lewis didn’t include them because it would have been unnecessary and it would have weakened his writing style.  However, when we want to look at the argument in detail it is important to see how the premises fit together and point to the conclusion, and that is why we need to make them explicit here. 

 

            The second method of diagramming, the arrow method, is specifically concerned with how the premises point to the conclusion (i.e., dependently or independently).  Think back to our discussion of dependent and independent premises in the last chapter.  The second method of diagramming is based on this distinction.  First, you follow all the steps above and abbreviate your terms, just as in the first method.  But then you add one step.  That is, you examine the premises and conclusion to see if the premises are dependent or independent and then you show the relationship in the diagram.  Here are a couple of examples.

 

Hypothetical Inductive (#2) Argument:   Lewis

 

O1 says L is V

O2 says L is V

O3 says L is V

Etc.

 

 

Therefore, O generally say L is V

 

 

T = good men today, V = highest virtue,

U = unselfishness, O = good men of old,

L = love, N = negative term, P = positive term

 

(T say V is U) + (O say V is L) + [U is N] + [L is P]

 

 

N has been substituted for P

 

 

      

 

 

 

 

 

 

 

 


In the diagram to the left you see that the deductive argument we’ve been diagramming throughout this lesson (brackets indicating assumed premises) uses all dependent premises.  None of the premises by itself points to the conclusion, but all of them, taken together, do.  In the hypothetical inductive argument from the same passage in Lewis we see that each points, independently of all the others, to the conclusion that good men of old, as a group, say that love is the highest virtue. The inductive conclusion grows stronger with each added premise, but none of the premises relies on any others in order to point to the conclusion.  Let’s look at two more examples of this diagramming method:

 

I am bored; therefore I am bored or it is Tuesday.

 

B = I am bored; T = it is Tuesday

 

B

 

 

 

Therefore: B or T

 

Jesus is the Christ: the Christ came to redeem His people, therefore Jesus came to redeem His people.

 

J = Jesus; C = Christ, R = came to redeem His people

 

J is C + C is R

 

 

Therefore: J is R

 

 

 

 

 

 

 

 

 

 

 


On the left we see an independent premise, and on the right, dependent premises.  These are, in fact, the examples from last chapter.  They illustrate, perhaps in a simpler way, how the arrow diagrams work. 

            The arrow diagrams have one added benefit which is worth considering.  Look back to Chapter 7 and consider the whale diagram.  This diagram illustrates the way in which an arrow diagram will allow you very flexibly to show relationships, not only between premises and conclusions, but also between individual supporting arguments in a passage.  It will also allow you to represent a situation in which an author presents both inductive and deductive reasons for a particular conclusion.  We will discuss this in more detail in Chapter 31.

 

            These two methods of diagramming are a middle way between the language itself and the more precise systems of symbolic logic which we will consider later.  As a middle way it is subject to some of the dangers and difficulties of a middle way. There is always a tendency to drift into one extreme or the other—either not changing the language enough for it to be diagrammed effectively, or changing it so eagerly into a systematic form that the meaning of the language is treated carelessly.  It is also important to note that this system of diagramming is not meant to work in the same way or do the same things as the symbolic logic you will learn in the second half of this course.  The purpose of these systems of diagramming is to help you see two things.  First you will see how premises are related to conclusions and how the basic structure of an argument works.  In this way it is actually similar to the more precise symbolic methods we will consider later.  The second purpose of practical logic is to help the student see arguments in everyday language, and understand how the argument he sees in the diagram relates to the argument he just read in a book or newspaper.  The diagrams of practical logic can only treat the structures and functions of reasoning in a general way, compared to that of symbolic logic, but they deal with the language more flexibly. 

 

Summary:  This chapter outlines two basic methods for diagramming arguments.  One is the “list method,” in which the premises and conclusion are listed with abbreviated standardized terms.  The second is the “arrow method,” in which arrows are used to represent the relationship between premises and conclusion.  Both of these methods are a middle way between the language itself and the more precise systems of symbolic logic you will learn about later.  Both help to clarify the relationship between premises and conclusions.

 

Exercise 1:  Theory

a. Give the three steps for the listing method of diagramming.

b. In the second and third steps, what is the balance that must be maintained?

c. What further information does the arrow method of diagramming give you than the listing method?

d. What, in practical terms, does “order and standardize—as much as possible—the tense and mood and type of verb in each statement” mean?

 

Exercise 2:  Imitation

Read the first half of The Hound of the Baskervilles by Sir Arthur Conan Doyle.  What kind of logic does Sherlock Holmes use? 

 

 

Exercise 3:  Practice

Diagram each of the following arguments, using both the listing and the arrow method, on a separate sheet of paper.

 

1.  The Lord is my strong tower and my deliverer, so God is my help in distress.

Assumed Premises: a tower gives protection, and protection and deliverance are help in distress.

 

2.  All my enemies have turned against me, but the Lord is my protector; therefore I shall not be put to shame (be overcome by my enemies).  Assumed Premise:  My enemies cannot overcome the Lord.

 

3.  Abel made his offering to the Lord by faith.  Enoch walked in faith and was taken.  Noah built the ark by faith.  Abraham and Sarah lived by faith.  By faith Isaac, Jacob, and Joseph blessed their children.  Moses, saved by the faith of his parents who didn’t obey Pharaoh, lived by faith.  Rahab acted by faith, and so did Gideon, Barak, Samson, Jephthah, David and Samuel, not to mention the prophets.  The saints who went before us lived by faith!

 

4.  This product will make your life better.  You want a better life.  Therefore, you want this product.

 

5.  How excellent is Thy loving-kindness, O God! therefore the children of men put their trust under the shadow of Thy wings.

 

6.  If a brother or sister is destitute and you send him away empty, merely wishing him well, it is good for nothing.  Therefore, faith without works is dead. 

 

 

Chapter 16:  Practical and Symbolic Logic:  Introduction

 

Obstinate people may be subdivided into the opinionated, the ignorant, and the boorish.  Aristotle, Nicomachean Ethics, VII

 

            Thus far in this course, I have emphasized the differences between practical and symbolic logic.  Now it is time to introduce symbolic logic and turn to the similarities between the two. Symbolic logic does not differ in kind from practical logic, merely in degree.  The main differences are that practical logic is broader and less logically precise, and that symbolic logic does not include inductive reasoning and requires more translation.  Now for the similarities.

 

            First of all, both types of logic deal with argumentation in language.  And, as a result, both deal with the translation of language into a peculiar logical format.  The first steps of eliminating padding words, regularizing the language, and listing out the premises and conclusion of an argument are very much the same.  In fact, if you diagram an argument according to the systems I set forth in practical logic (listing or arrow methods), your translation for symbolic logic is at least half done. 

 

            I will introduce two logical languages in this second half of the book.  The first is the categorical calculus.  This system is firmly grounded on the conceptual system of Greek philosophy.  The philosophical systems of both Plato and Aristotle were based on the essential reality of ideas and the “idea realm.”  Plato saw the essence of a thing as existing even apart from the physical object related to it (e.g., “treeness” exists, even apart from trees).  Aristotle found the essence of things in physical objects, but still distinct from them.  These “essences” were then conceived of in a certain logical hierarchy.  This hierarchy or ranking of ideas is the basis for the scientific genus/species relationship.  Genus and species are relative terms:  a genus is a broad classification, under which there occur a number of more particular groupings called “species.”  The term “mammals” is a genus for many species such as whales, cats, dogs, bears, cows, man, etc.  “Man,” which is a species of mammal, is also a genus for different kinds of men.  Notice at this point that there is a difference between a species and a part.  Caucasian is a species of mankind, while an arm is a part of a man. 

                  Man   (whole)

 

 

 

 

 

arm        hand      leg         chest

  

     head        foot     neck

                    (parts)

 

 

                              Mammal    (genus)

 

 

 

dog        cat          man    (genus)      cow        bear  (species)

 

 

 

Caucasian      Asian       African      Native American   (species)

 

 

 

 

 

 

 

 

 

 

 


The genus-species relationship is just one example of the classification and organization of thought that was so important to the Greeks and had such an influence on their intellectual and philosophical approach.  I mentioned this briefly in Chapter 2.

 

            Categorical logic is so named because it examines reasoning according to classes or categories of things.  For example, “all men are mammals” is a statement that tells us that the whole of the category of men is within the larger category of mammal. The Greeks understood all ideas in terms of categories.

 

            There are four relationships that can occur between categories.  The first, as we have already seen, is “All S are P,” as in the statement, “All men are mortals.”  The second is “No S are P,” as in “No men are reptiles.”  The third is “Some S are P,” as in “Some men are captains.”  The fourth is “Some S are not P,” as in “Some men are not captains.”  Pay attention to the relationships being described in these statements.  All S are P tells you that there is total overlap between two categories; in other words, all entities belonging to the first group are also members of the second.  No S are P tells you that there is no overlap between two given categories; that is, no member of the first is a member of the second.  The third relationship describes a situation with some overlap:  if some S are P, at least one member of S is also a member of P.  Lastly, some S are not P describes a relationship in which at least one member of the category of S is not a member of the category of P.  We will look at the categorical calculus in more detail in the coming chapters.

 

            The second symbolic system I will introduce you to is called Propositional Logic.  It is of more recent origin than categorical logic, although it has ancient roots as well.  The famous “if…then” arguments, Modus Ponens and Modus Tollens, are two of the immediate inferences of propositional logic.  While the categorical calculus is based in classification and categories, propositional logic is more language-based.  In fact, the word “proposition,” is a synonym for “statement,” which you will remember from your studies in practical logic is the term used to refer to premises and conclusions. 

 

            Propositional logic is especially good at dealing with types of statements called “compound propositions”—statements consisting of two or more simple propositions joined together by one of the logical operators (such as “and”see below).  The statement “all men are mammals” is a simple proposition.   The statement “all men are mammals and I am a man” is a compound proposition.  Propositional logic can examine these compound propositions to find out how the truth or falsity of the simple propositions affects the truth of the compound proposition.  In the compound statement above, for example, both simple propositions must be true in order for the compound proposition to be true as well.  In propositional logic there are a set number of “logical operators,” or connecting and modifying words that link simple propositions together to make compound propositions.  Each logical operator is expressed by means of a special symbol; you will learn more about this later.  The logical operators of propositional logic are not, and, or, if…then, and if and only if…then. 

 

            Both categorical and propositional logic are systematic enough that, once you learn the rules and some simple evaluation processes, you can use them to determine quickly and easily whether an argument is valid or invalid. Both of these systems deal exclusively with deductive reasoning.  They are more precise than the diagramming systems of practical logic, but they also present more challenges of translation.  For instance, the categorical calculus requires the logician to translate all statements into one of the four kinds of statement listed above (all S is P, no S is P, some S is P, and some S is not P).  When you do this the meaning of the original language is often quite clearly changed.  For example, the statement “Many people find symbolic logic too abstract” has to be translated into categorical logic as “Some people are symbolic-logic-too-abstract-finders.”  Besides the fact that this is bad English, the word “many,” which expresses a majority, has to be changed to “some” which only means “at least one.”  Additionally, the category “symbolic-logic-too-abstract-finders” isn’t particularly handy as a category.  Categorical logic will still work; it is just a little unwieldy and it tends to change the original meaning of the language.  Propositional logic, being language-based, is a little more supple in translation than categorical logic, but it still involves some difficulties.  Neither system incorporates inductive reasoning, although both often rely on it as foundational, as I mentioned before (Chapter 4). 

 

            In the coming chapters you will be immersed in a sea of symbolic logic.  The work you do here is very valuable.  To mentally handle and manipulate these statements, categories, and propositions will give you a much better and deeper understanding of how deductive reasoning works.  In the final chapters of this book we will combine the work done in these systems with the practical logic you have already learned, and with some basic analogous reasoning, in an attempt to give you as comprehensive and useful a logical system as possible in the short space we have here.

 

Summary:  Symbolic logic is more precise than practical logic, and our study of it will include two logical languages—the categorical and the propositional.  Categorical logic uses four types of statements to represent the relationship between categories of ideas.  For the Greeks, all ideas were ordered and classified according to categories.  Propositional logic deals with compound propositions (statements) and with how they work, both internally and with other propositions.  Both of these systems deal only with deductive reasoning, and although they are logically more precise than practical logic, they do present some translation problems.

 

Exercise 1:  Theory

a. What are the main differences between symbolic logic and practical logic?

b. What is the origin and basis of categorical logic?

c. Define genus and species.

d. How does a species differ from a part?

e. What is the main difference between the categorical and the propositional symbolic systems?

 

 

 

Exercise 2:  Imitation

Read three of Chesterton’s “Father Brown” stories.  Notice Father Brown’s innovative use of reasoning.

 

Exercise 3:  Practice

Come up with five genus-species relationships.  Here are some ideas:

 

Examples:

 

            Book                                                               Government

 

 


Bible   Dictionary    Textbook                   Family                Church            State

 

 

 

Chapter 27:  Analogical Reasoning:  Definition or Description

 

The roads by which men arrive at their insights into celestial matters seem to me almost as worthy of wonder as those matters themselves.  Johannes Kepler (as cited in Koestler, 1963, p. 261)

 

            You have now learned the basics of a couple of different symbolic systems of deductive reasoning, and have spent some time looking at everyday arguments, both inductive and deductive, in your study of practical logic.  Now I turn to the third kind (or pattern) of reasoning that I mentioned way back in the Preface—Analogical Reasoning.  Inductive and deductive reasoning are both linear in the sense that they move more or less in a straight line from premises to a conclusion.  Analogical reasoning is less linear, and would better be characterized as parallel, or lateral.  I think you will see what I mean as we continue.

 

            As a way to understand the difference between linear and parallel reasoning, consider the difference between definition and description.  A definition gives the basic identification of an object or idea, and distinguishes it from other objects or ideas.  A definition merely identifies an object, setting the boundaries for what it is and for what it is not; for what a word can mean and for what it does not mean.  For example:  a “car” may be defined by the dictionary as “a vehicle moving on wheels.”  Other entries are listed as well, but they are similarly bare of explanatory detail.  Definitions move a word from an unknown or uncertain context into a certain and definite context.  In other words, they classify.  Definitions have the narrowness of linear reasoning; they work by categories, and, in fact, definitions are an important part of linear reasoning, as we learned from a fallacy like equivocation.  Both definitions and linear reasoning have a single end in mind—that of intelligible order and classification. 

 

            Descriptions, on the other hand, are less concerned with classification, but generally give you more explanatory details concerning the object or idea under consideration.  The purpose of a description is to help you picture, visualize, or understand something.  Using the car example again, a description of cars might talk about sizes, colors, materials out of which cars are made, and how different cars are able to do different things (SUV’s as opposed to sports cars).  Notice that descriptions do identify things, but not necessarily according to classification.  Analogical reasoning is similarly broad, often with the goal of understanding the subtleties of something rather than classifying it.  When reasoning by analogy you compare two things as similar, and by doing so you form a connection which in turn brings a new dimension to your knowledge of the object under consideration.  By recognizing that one thing is like another in some way, you make a comparison that enhances your understanding of each.  And since this is what you are trying to do with analogous reasoning it, also, is considered purposive.

           

            Definitions and descriptions overlap in the information they provide, and, in a sense, rely on each other, but there is clearly a difference in method and emphasis.  Definitions directly seek out the classification and/or identification of objects, moving systematically in a line from identification to classification to categorization to conclusion.  Descriptions, on the other hand, begin with a basic description or definitional knowledge of a thing and then branch out in many directions in order to explore different aspects of the object under consideration.  Since this movement is not in any one direction but can consider things as disparate as the color of the object or its cosmic significance, it is better described as lateral than as linear.

 

            Now let us move to a more specific comparison of analogous reasoning with the inductive or deductive process.  In induction and deduction, the process moves from premises to a conclusion, or from reasons to a result.  Analogous reasoning moves from a source to target objects, but it doesn’t leave the source behind; rather, it ties the source and the target together.  Consider Christ’s comparison of the kingdom of heaven with leavening, found in Matthew 13:33:  “The kingdom of heaven is like leaven which a woman took and hid in three measures of meal until it was all leavened.”  The kingdom of Heaven, in this case, is the target, and the leaven is the source.  Christ expects his hearers to know something about leaven already (source) that he wants them to understand about the Kingdom (target).  So he compares the two.  Outside of context, this comparison is not very focused; but since this parable follows the parable of the mustard seed it would seem that Jesus might be making a similar comparison here.  And so the analogical network widens—by comparing the second parable with the first we can understand it better.[3]  In a sense, He is going on to the next issue.  If the mustard seed is an picture of how the Kingdom starts small and grows large like a tree, the yeast is a picture of how the Kingdom, like leaven in meal, is an agent that permeates everything.  Look at the diagram:

 

 

 

 

 

 

 


       

 

The contrast with the deductive and inductive processes is clear.  The example from Matthew 13 is a simple analogy or connection.  Yet even in this connection there is more than the simple formula shown in the diagram.  The connection also includes connotations of growth, bread, rising, food, and house-holding.  These form a more holistic and broader understanding of the Kingdom, and also add new significance to our use and understanding of leaven.  The connection itself remains very important even after you think you have understood all the important aspects of it.  You will learn more about this in the next chapter.     

 

            Analogous reasoning, then, is the comparison of objects or ideas in order to form intelligible connections that aid our understanding.  And, surprisingly, analogies are one of the most common forms of reasoning.  How often have you heard the phrase, “Well it’s like….” when someone is describing or explaining something?  Often when you are coming to understand something better, you might notice how it is like something else you know about.  Scientists often use analogous reasoning to help form their theories. The comparison of something they are investigating to something that is already fairly well understood is a standard aspect of forming theories.  It is also important in the courts, especially in a case-law system like ours.  By showing that your case is like some other case that has already been decided in the way you hope your case will be decided, you can persuade the judges to bow to precedent and decide the case in your favor.  Analogous reasoning is used in medicine when doctors compare the symptoms involved in two cases, in order to draw a connection that will afford clues about the case in question.  And, of course, pastors, teachers, and writers use analogies to describe and explain all the time. 

 

            As I suggested earlier, the goals of analogous reasoning are somewhat different from those of inductive or deductive reasoning, although they can still be seen as manifestations of purposive thought.  Inductive and deductive reasoning are both defined by the search for a specific conclusion, while analogical reasoning seeks to identify points of similarity, and to illuminate one object or idea in the light of some other object or idea.  Of course, analogical connections can lead to particular conclusions, as in the medicine or law examples above.  These kinds of analogical syllogisms go something like this:  A is like B in this or that way; B does a certain thing, therefore A should do the same or a similar thing.  You can see that this is almost a kind of deductive process—which leads me to one final point.  Analogical, inductive, and deductive reasoning form a matrix of interdependent relationships.  Deductive arguments are often formed from premises that are the conclusions of inductive arguments; and analogical reasoning is really the basis for inductive classification, in which objects or ideas get grouped together according to certain similarities—similarities which are noted by analogical process.  This is just one set of the ways in which these three are related to and rely on each other.  The analogical argument that uses deductive principles is another example.  The many intricate ways in which these three basic kinds of reasoning work together and within each other is beyond the scope of this book, but you should know that each of them plays a crucial role in human reasoning. 

 

            As I mentioned, analogical reasoning is more like description than like definition.  While a definition clearly classifies and sets the boundaries for an object or idea, a description tells you more about what the object is like—how it looks, feels, works, tastes, or sounds.  Deductive and inductive reasoning are both linear in that they always move from premises to a conclusion.  Analogical reasoning can move from a comparison to reasons to a conclusion, but at times the analogical process is merely descriptive, being a way to shed light on something new by comparing it to something old, or helping you remember a complex idea by associating it with something more basic.

 

Summary:  Analogical reasoning is descriptive, while induction and deduction are definitional.  The particular conclusions of both induction and deduction are concerned with classification.  Analogical reasoning can lead to conclusions, but it doesn’t need to; rather, it exists primarily for the comparison of one thing to another for the purpose of forming connections of structure or appearance.

 

Exercise 1:  Theory

a. Characterize in your own words the difference between definition and description.

b. How are induction and deduction linear?

c. How is analogical reasoning parallel?

d. What are a few of the most common uses of analogical reasoning?

 

Exercise 2:  Imitation

Read Chapter Four of Calvin’s Institutes of the Christian Religion.  Is man basically good?  Identify two comparisons, or instances of an analogical reasoning process, in this chapter.

 

Exercise 3:  Practice

Make as many connections as you can between the pairs of things listed below.  Write your answers in a matching-pairs format as shown in the first problem, below.  Some of these will require imagination.  The connections of Analogical reasoning often require imagination.

 

1. Christian living—investment money management

investing in the future (hope)—also investing in the future (hope)

treasure in heaven—treasure on earth

wise investment of time and  effort required—wise investment of the same required

service to God—service to God in money—service to money

life of God’s grace (gift, blessing, etc)—life of God’s grace (gift, blessing, etc.)

 

2.  Oranges—jackhammers

 

3.  Beautiful classical music—crisp cool mornings

 

4.  Harvest time—midlife crisis

 

5.  Children growing up—gardens

 

6.  Garden of Eden—Solomon’s Temple

 

7.  Riding a bicycle—being in politics

 

8.  A tree—a righteous man.

 

9.  Fruit—temptation

 

10.  Spoken words—waves on the shore

 

11.  Definitions—inductive and deductive reasoning

 

12.  Descriptions—analogical reasoning

 

 

 



[1] The inference that “Socrates is mortal,” drawn from the premises “All men are mortal,” and “Socrates is a man,” is a necessary inference—in other words, given that the premises are true, there is no way that the conclusion can not be true.   By contrast, induction produces arguments that are either strong or weak, not true or false.  And analogous reasoning is concerned more with illuminating comparisons than with hard-edged conclusions.

[2] In logic a “term” is one of the nouns, subject or object, of a statement.

[3]We constantly rely on analogical reasoning processes like this.  Understanding meanings and objects in context requires us to compare one thing with another, building connecting things into whole conceptual units.