After a Twitter exchange with someone who was particularly challenged with regard to logic, I promised to post some basic lessons in logic (I’ve been teaching the subject for many years).

I begin with a basic discussion of the nature of argumentation, which is one of the primary ways in which reasoning operates: it makes connections between statements.

(And apologies for getting into teacher mode here…)

Aristotle founded the discipline of Logic.
Aristotle founded the discipline of Logic

ARGUMENTATION

Argumentation is the method of Philosophy, and Logic is the science of argumentation. To make an argument is to provide reasons (the premises) in support of a claim (the conclusion).

Examples:

1) Berger is innocent, because the killer would have had blood all over him, and there wasn’t a drop of blood on Berger that night.

2) Mr. Conners, the gentleman who lives on the corner, comes down this street on his morning walk every day, rain or shine. Consequently, something must have happened to him, since he has not shown up today.

In example 1, the conclusion is “Berger is innocent.” The proof for this, the reasons provided, are the other two propositions: “The killer would have had blood all over him,” and “there wasn’t a drop of blood on Berger that night.”

In example 2, the conclusion is “something must have happened to [Mr. Connors].” How do we know this? What’s the proof? Well, the other two statements: “Mr. Connors comes down this street on his morning walk every day…” and “he has not shown up today.”

NOTE: Arguments are provided for claims/statements that need to be proved or demonstrated. Plain matters of fact, statements that are obviously true, those that can be verified through sense experience—these do not need to be argued for. “I am wearing shoes,” for example, doesn’t need to be argued for, since it can easily be verified simply by looking at my feet.

TWO KINDS OF ARGUMENTS

There are two kinds of arguments, formal and informal arguments (and thus two branches or subcategories of Logic). In a formal argument, we are trying to establish that the conclusion is necessarily true, that it can’t possibly be false. In an informal argument, we’re trying to establish that the conclusion is probably true.

Examples of Formal Arguments:

1) Every student who made 90 percent or better on the midterms has already been assigned a grade of A. Margaret already has her A, for she made 94 percent on her midterms.

2) If Congressman Smith were honest, he wouldn’t have taken bribes and lied about it; but he did take bribes and lie about it, so he’s definitely not honest.

In these examples I’m not trying to argue that Margaret probably got an A in the class or that Congressman Smith is likely dishonest. I’m arguing that these are necessarily the case. In each argument, if the premises are true, then the conclusion has to be true: If it’s true that “every student who made 90 percent or better on the midterms has already been assigned a grade of A,” and it’s true that Margaret “made 94 percent on her midterms,” then it has to be true that she’s getting an A.

Examples of Informal Arguments:

1) Sarah studies hard, and she’s bright, so she’s bound to do well in the class.

2) It’s likely going to rain: the barometer is falling and storm clouds are moving in from the west.

In example 1, the conclusion, “Sarah is bound to do well in the class” is supported by the two premises, but the premises don’t guarantee the truth of the conclusion. For example, other factors might come into play that prevent her from doing well. Likewise, in example 2, the premises provide support for the conclusion, they make it probable that the conclusion is true; but the conclusion doesn’t necessarily follow from the premises.

IDENTIFYING ARGUMENTS

It’s important for us to be able to identify arguments, to know when evidence is being given in support of a claim. This, for example, is not an argument:

‘Neo’ is the hacker alias of Thomas Anderson, and ‘Neo’ is an anagram of ‘One.’ An anagram is a word that’s produced by rearranging the letters of a different word.

No claim is being put forward; nothing is being proved here. This is simply a description, and not an argument.

Fortunately, we often have indicator words to tell us that we’re in the presence of an argument. There are both premise and conclusion indicators:

Premise Indicators

Since
Because
For
Given that
Assuming that

 

Conclusion Indicators

Therefore
Thus
So
Consequently
Hence

Berger is innocent, because the killer would have had blood all over him, and there wasn’t a drop of blood on Berger that night. (Premise indicator)

Sarah studies hard, and she’s bright, so she’s bound to do well in the class. (Conclusion Indicator)

Every student who made 90 percent or better on the midterms has already been assigned a grade of A. Margaret already has her A, for she made 94 percent on her midterms. (Premise Indicator)

Mr. Conners, the gentleman who lives on the corner, comes down this street on his morning walk every day, rain or shine. Consequently, something must have happened to him, since he has not shown up today. (Conclusion Indicator, Premise Indicator)

NOTE: Just because you find an indicator word doesn’t mean that you are looking at an argument; and just because you don’t find an indicator word doesn’t mean you’re not looking at an argument.

Examples:

Ever since he was little, Billy wanted to be a notary public, even though he doesn’t know what it is.

Not an argument: “since” here is not an indicator.

Martha must be depressed again. She only eats a lot when she’s depressed, and I just saw her wolf down three cheeseburgers.

This is an argument, even though there are no indicator words. “Martha must be depressed again” is the conclusion. The other two statements are the premises.

Francisco de Goya, The Sleep of Reason Produces Monsters
Francisco de Goya, The Sleep of Reason Produces Monsters

IDENTIFYING ARGUMENTS EXAMPLES

See if you can identify the premise and conclusion indicators in the following, then determine whether or not the example expresses an argument. Find the final conclusion, if it is an argument.

1. California is more populous than New York; New York is more populous than Ohio; therefore, California is more populous than Ohio.

2. He won’t be driving recklessly, for he only does that when he’s upset, and he’s not upset.

3. Bill’s in trouble. He shot a deer, and they’re not in season.

4. Toward evening, clouds formed and the sky grew darker; then the storm broke.

5. Since all seniors are immodest, and all arrogant people are immodest, all seniors are arrogant.

6. Lincoln could not have met Washington. Washington was dead before Lincoln was born.

7. Terry, Sherry and Barry were all carded at JJ’s, and they all look as though they’re about thirty. Chances are I’ll be carded too.

8. Jones won’t plead guilty to a misdemeanor, and if he won’t plead guilty, then he’ll be tried on a felony charge. Therefore, he’ll be tried on a felony charge.

9. I guess he doesn’t have a thing to do. Why else would he waste his time watching daytime TV?

10. Some pesticides must be unsafe for humans to consume, since some pesticides are toxic, and whatever is toxic is unsafe for most humans to consume.

Answers will appear in a subsequent post.

3 thoughts on “Logic Part I: The Nature of Argumentation

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