Thinking Clearly: Logic

Why do we need to think clearly?

Katherine Klingseis Dr. Charles Rice

1. OrderLogic helps you to

think in an orderly way.

Like all objects in our world, thought has a form and structure.

Thought also follows certain rules and laws which can be learned.

2. PowerLogic has the power to

prove a point and to persuade people.

Logic is the science of argumentation.

Logic can also be used to lead people to wicked conclusions. Knowing logic helps to defend you from manipulation by others.

A Face You Can Trust

3. Reading 4. WritingLogic will help to

show you the structure of books, so you can read more effectively.

Logical thinking leads to clear, understandable writing.

All religions and faiths must be logical to be believable.

Faith goes beyond logic, but cannot go against it.

Logic assists faith in three ways:1. Logic clarifies and defines beliefs.2. Logic shows what other beliefs and actions

necessarily follow from faith.3. Logic shows why particular beliefs are

reasonable, thus giving further reasons for people to believe; that is, logic strengthens faith.

5. Religious Faith

6. Recognizing Contradictions 7. Certainty

Logic teaches us which ideas contradict each other.

Avoiding contradictions makes our thought clearer and our lives more peaceful.

The principles of logic are unchanging and always true.

Logic can help clarify situations that are confusing by providing us with a reliable “rule” for measuring what we do know.

The most important use of logic is for helping us to find the truth.

Logic helps us find truth by:1. Teaching us to define what we are talking about2. Teaching us to give good reasons for what we

are talking aboutTruth is valuable to us because it:

1. Helps us to change the world2. Helps us to change ourselves3. Helps us to know for the sake of knowledge—

our natural curiosity.

8. Finding Truth

The Parts of Right Thinking

1. Terms – the words used 2. Premises – the reasons given3. The Conclusion – the argument made

An argument has three parts:

1. The terms must be clear – all the words must make sense and be used correctly

2. All the premises must be true – each reason given must be correct

3. The argument must be valid – the conclusion must make sense

To be true all three parts must work:

1. “What do you mean?” All the terms should be clear and

unambiguous

2. “What is the point?” All the premises should be true

3. “How do you prove it?” The argument should be logically valid

To make sure an argument checks out, we should ask:

All these rules are common sense

Terms

Meaning what you say.

Only human beings can ask this questionAnimals cannot use abstract termsComputers can only manipulate words and

numbers in relation to each other

Terms answer the question “what is it?”

Quantity/ExtensionHow many things or

individuals are included in the term?

How many different types of things are included in the term?

What does the term mean?

What other words can describe the term?

All terms have quantity and qualityQuality/

Comprehension

Animal

Mammal

Primate

Human Beings

The more general the term, the more things it includes; the more specific, the fewer things it includes

1. How clear is the term?

2. How many meanings does the term have?

3. Is the term literal or metaphorical?

4. Does the term refer to a group or a particular thing?

Speaking clearlyStep 1: Classify the terms

a. Make sure the terms do not overlapBad division:

Dividing “music” into “rock,” “rap,” “pop,” “alternative,” “country,” and “jazz.”

Good division: Dividing music into “Baroque,” “Classical,” “Romantic,” and “Modern.”

Bad division: Dividing “teenagers” into “jocks” “preps,” “goths,” “geeks,” and “nerds.”

Good division: Dividing “teenagers” into “junior high-age,” “high school-age,” and “graduate-age.”

Step 2: Divide terms from each other

b. Use the same standard of division

All definitions should be:1. Neither too broad nor too narrow2. Clear, literal, and brief3. Not negative or circular Bad:

“Big blue wobbly thing that mermaids live in: sea.”

“Dog: not a cat.” Good:

“Medium-sized insectivore with protruding nasal implement: aardvark.”

Step 3: Define terms

Mistakes regarding terms

Logical Mistakes

1. Changing the meaning of a word during an argument.

Who's on Stage?

2. Using the wrong word order. “Would you rather a cannibal ate you or a

shark?”

3. Stressing or accenting words. “We don’t have to tell the whole truth, you

know.”

4. Exaggerations or understatements “You need to clean your room.” “Oh, so you want

me to be your slave!”

5. Misrepresenting your opponent’s position“You think we should all be brainless idiots!”

Mistakes in using language

1. Attacking the person who is making the argument

“What do you know? You’re only a kid.”

2. Citing an irrelevant authority “According to 75% of all convicted felons, the

American justice system is unjust.”

3. Threatening or shaming the person4. Appealing for pity or acceptance5. Relying on ignorance

“He can’t prove he earned that money, so he must have stolen it!”

Mistakes of Diversion from the point

1. Applying a general rule to a special case. “Water is good for you, so take a drink from Lake Erie.”

2. Taking a special case and generalizing it. “I was stung by a bee at camp, so I don’t go camping

anymore.”

3. Claiming that what is true of a part is true of the whole. “Every actor in this movie is great, so it must be a great

movie.”

4. Claiming that what is true of the whole is true of a part. “She goes to Willard High School, so she must be

awesome.”

5. Seeing in black and white.“You have to be either a Republican or a Democrat.”

6. Stereotyping. “I can’t stand all these teenagers with their loud music! ”

Mistakes of Oversimplification

Grace Bride

What errors are in these arguments?

Fr. John’s Opponents

Why I hate religion but love JesusJefferson Bethke

Response: Why I love religion and JesusFr. Pontifex

1. Conclusions that do not follow. “It’s raining today, and I’m sad today, so the rain must

make me sad.”

2. Assuming the conclusion before it is proven. “The accused will be given a fair trial before we

execute him.”

3. Expecting a simple answer to a complex question. “Are you dumber today than you were yesterday?”

4. Arguing in a circle. “How do I know there’s a God?” “The Bible says so.”

“How can I trust the Bible.” “Because God says it’s true.”

5. Contradicting yourself. “I will not tolerate intolerance!”

d. Mistakes in Arguing

1. Making a Hasty Generalization. “The Browns keep losing this season. They’ll

always be losers.”

2. Assuming that what comes before is the cause of what comes after.

3. Jumping to conclusions based on what a person does not say.

4. Selecting only the evidence that supports an argument.

5. Slanting the question. “Shouldn’t a woman be free to choose?” “Isn’t all

human life sacred?”

e. Mistakes in Connecting the Facts

1. Claiming to refute an argument by refuting its conclusion.

2. Claiming that refuting an argument refutes its conclusion.

3. Ignoring an argument or answering a different argument.

4. Giving an explanation instead of proof.5. Being cruel to our opponents in debate.

f. Mistakes in Replying to Arguments

Premises

Giving good reasons.

We write a proposition as a declarative sentence.Ex.: All the students at Calvert High School are

human.We must identify in every proposition a

subject and a predicate.Subject – what we are talking aboutPredicate – what we say about the subject

Propositions are either true or false. Finding the truth is the main goal of logic, so

finding true propositions is essential for finding truth.

Premises may also be called propositions.

Peter Kreeft again:“One of the best remedies for bad

reading and writing is good logic, especially the analysis of propositions. For thinking clearly, expressing your thoughts clearly (in writing or speaking), and interpreting another’s expressions (written or spoken) clearly are three arts that are very closely allied; no one of them can be done well without doing the other two. And the part of logic that is most directly related to this is the part that studies propositions.”

Simplifying premisesTo make an

argument easier to understand, you can re-phrase each premise into one of the four classic forms:

1. Universal affirmative “All men are mortal.”

2. Universal negative “No men are mortal.”

3. Particular affirmative “Some men are

mortal.”

4. Particular negative “Some men are not

mortal.”

Here’s another way to think of the forms:

Quality

Affirmative Negative

Quantity

UniversalAll ___ are ___. All ___ are not ___.

ParticularSome ___ are ___.

Some ___ are not ___.

The Conclusion

Proving your point.

To reach the conclusion, we must use the great power of human reason.

1. We can gain knowledge beyond our experience based on what we do know.

All objects with great mass emit a gravitational pull, certain dark areas of the universal emit a gravitational pull, therefore these dark areas (black holes) must have mass.

2. We can know universal truths. “All human babies come from human

mothers.”

3. We can know necessary and unchangeable truths.

The sum of all interior angles in a triangle is 180 degrees.

Deductive Reasoning allows us to reach conclusions with certainty:

Rule 1: Whatever is universally true of a subject must be true of everything contained in that subject.For example: All men are mortal, I am a man, therefore I am mortal.

Rule 2: Whatever is universally false of a subject must be false of everything contained in that subject.

Rule 3: Two things identical with the same thing are identical with each other.

The rules of deductive arguments are always and everywhere true.

Rule 4: If one thing is identical with something that a second thing is not identical with, then the first and second things are not identical with each other.For example: No men are angels, I am a man, therefore I am not an angel.

Rule 5: A thing cannot be the opposite of itself.

Rule 6: A thing either has a certain attribute or it does not have it.In other words, a premise is either true or false.

How to detect an argument

The premises are the evidence, reasons, or proof for an argument.

The conclusion is what the argument is trying to prove.

Before the premises:BecauseSinceForAsIfFollows fromFor the reason that

ThereforeHenceIt follows thatConsequentlyWhich shows thatSoThen

Some key words that come before the parts of an argument:

Before the conclusion:

How to distinguish an argument from an explanation:

An explanation simply gives the cause of something.

An explanation does not try to prove anything, but only states what is the case.

A good argument is one whose terms are all clear, whose propositions are all true, and whose logic is valid.

A valid argument gives us certainty about its conclusions. The certainty of the conclusion depends upon

the premises.So we know that a conclusion is true when

the premises are all true and the logic is valid.

Elements of a good argument

Then at last, we have found the truth!(even without the Lasso of Hestia)