Adult Introduction

We all know intrinsically how to reason – it is part of our created being. Nevertheless, the powers of reason, like other innate abilities, can be strengthened and refined through exercise and instruction.

Our purpose here is to teach formal deductive reasoning – arguing from the general to the specific – in the form of a syllogism: a major premise, a minor premise, and a conclusion.

Each lesson begins with a story which develops certain concepts of reasoning. This is followed by exercises which use information from the story in order to explain and teach about logic and reasoning. The exercises build on the concepts developed in the story, while introducing some of the terminology, specialized expressions, symbols, rules and formulations, and the operations and procedures of formal logic. For quick confirmation or correction, each exercise is immediately followed by an answer.

• Bullets precede and separate each sentence which introduces a term, concept, or explanation.

• Bold underline italic marks important terms or expressions and definitions or explanations.

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Chapter 1[a]: Mystery Train

Our story concerns two brothers, Chaz and Zach (that’s Charles and Zachary, for those who don’t know nick names). Chaz and Zach are twins. They share the same birth date and the same bedroom, but each has his own things – clothes, books, models, collections. No, they are not identical twins – they don’t even look that much alike. Chaz is the older – by a few minutes – but Zach is the bigger – by an inch. Chaz has blond hair and blue eyes, whereas Zach has brown hair and green eyes. They both like baseball, but Chaz follows the National League while Zach follows the American League. They both like ice cream, but Chaz likes vanilla while Zach likes mint chocolate chip. You get the idea.

Oh, and one thing very important with regard to our story: they both like trains. They like to read about trains. They like to watch trains. They like to visit train museums. They enjoy model trains. They read model train magazines. And so you can imagine their delight one day when they came home from baseball practice and they went into their room to discover – lying in the middle of the room – a large plain cardboard box, and on the box was written, “Mystery Train.” It was not store-bought packaging – the words on the box were scrawled by hand with a felt tip marker. So someone must have put this package together himself. Their first and only guess was their dad – he did that sort of thing – they didn’t even have to ask.

As was their custom, whenever they encountered something new (such as this package), Chaz and Zach had to talk about it – sort of argue about it – before they even opened the package.

Chaz: “I wonder what’s inside, and I wonder why it’s labeled ‘Mystery Train.’”

Zach: “It is what it is. We won’t know until we open it. So let’s open it.”

Chaz: “Of course it is what it is. Everything pretty much is what it is. That’s pretty obvious. Can you name for me one thing that isn’t what it is? You can’t very well deny that what is, is.”

Zach: “True. But not everything ‘is.’ Everything either ‘is’ or ‘isn’t.’”

Chaz: “Well of course things can’t both exist and not exist.”

Zach: “Well, yes they can, just not at the same time or in the same way. This room at one time didn’t exist, but the house was built, and now here it is. This morning I was wearing clean pants. After baseball practice, those pants no longer exist.”

Chaz: “Yes they do. You haven’t changed your pants.”

Zach: “Yes I did – when I slid into second base, I changed my pants. Those clean pants no longer exist.”

Chaz: “So when mom tells you to change your pants, you can say you already did.’”

Zach: “I don’t think she’ll appreciate the subtlety.”

Chaz: “She will and she won’t at the same time.”

Zach: “But not in the same way.”

Chaz: “Okay, I get your point.”

Zach: “Okay, then back to my original point, which was that we ought to open the box.”

Chaz: “But don’t you want to spend a little time wondering what’s in it before we open it?”

Zach: “Why should I wonder? I already know what’s in it.”

Chaz: “What?”

Zach: “A mystery train.”

Chaz: “What’s that?”

Zach: “We’ll never know till we open the box.”

Chaz: “Okay, I give in, let’s open the box”

Zach: “We can’t do that.”

Chaz: “Why not?”

Zach: “Because I already did. Here’s a big envelope I found sitting on top of everything.”

Chaz: “Oh. I wonder what’s inside?”

Zach: “You can stop wondering. It’s instructions.”

Chaz: “You take all the wonder out of things.”

Zach: “Exactly.”

The instructions explained that dad would be away for a few weeks, and he wanted the twins to work together to reason out how to put together a very particular model railroad. The large envelope contained several smaller envelopes, each envelope numbered. The twins were to open the first envelope and complete the task before opening the second envelope and completing its task, and so on until they ran out of envelopes.

So what’s in that first envelope?

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Exercises:

• There are three fundamental laws of thought. Although the expression of these three laws will appear to be very simple and self-evident, all development of reasoning or logic stands upon the foundation of these three laws. One cannot attempt to deny these laws without necessarily using these laws – which is self-evidently contradictory, which is one of these laws. Hence these laws are undeniable and inescapable.

• In logic, a proposition is a sentence that says something which can be either true or false.

• The first fundamental law of thought is called the law of identity. The law of identity simply says that every proposition implies itself. In other words, whatever a sentence says, it says. Any given thing is identical with itself. Whatever something is, it is that something.

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1. What things did Chaz and Zach say which express the law of identity?

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Zach: “It is what it is …”

Chaz: “Of course it is what it is. Everything pretty much is what it is. That’s pretty obvious.”

≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈

• The second fundamental law of thought is called the law of excluded middle. The law of excluded middle simply says that everything proposed must either be or not be. In other words, logical thought does not allow for something between “is” and “is not” – logic doesn’t allow for anything between existing and not existing.

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2. What things did Chaz and Zach say which express the law of the excluded middle?

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Chaz: “Can you name for me one thing that isn’t what it is? You can’t very well deny that what is, is.”

Zach: “True. But not everything ‘is.’ Everything either ‘is’ or it ‘isn’t.’”

≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈

• The third fundamental law of thought is called the law of non-contradiction. The law of non-contradiction simply says that no statement can be both true and false at the same time and in the same respect. In other words, logical thought does not allow the contradiction where something can be both existing and not existing at the same time and in the same way.

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3. What things did Chaz and Zach say which express the law of non-contradiction?

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Chaz: “Well of course things can’t both exist and not exist.”

Zach: “Well, yes they can, just not at the same time or in the same way. This room at one time didn’t exist, but the house was built, and now it does. This morning I was wearing clean pants. After baseball practice, those pants no longer exist.”

Chaz: “Yes they do. You haven’t changed your pants.”

Zach: “Yes I did – when I slid into second base, I changed my pants. Those clean pants no longer exist.”

Chaz: “So when mom tells you to change your pants, you can say you already did.’”

Zach: “I don’t think she’ll appreciate the subtlety.”

Chaz: “She will and she won’t at the same time.”

Zach: “But not in the same way.”

Chaz: “Okay, I get your point.”

TO BE CONTINUED …