**The Prison of Logic**

Define what you think it means to be logical. Do you consider yourself to be logical?

Opening Question:

to define correct reasoning

to distinguish good arguments from bad ones (don't confuse the word 'argument'

to pick out flaws and weaknesses in reasoning

to create rules which enable us to test whether our reasoning is coherent and consistent.

Logic Attempts:

Concerned with the rules for determining when an argument is valid

Structures arguments in a formal way

Does not concern itself with the truth - only validity and the process of reasoning

Produces knowledge based on reason rather than experience

Types of Logic 1: Deductive Logic

__________ is a 12th grade student at CHS. (premise)

All 12th grade students at CHS study taxidermy. (premise)

Therefore, _____________ studies taxidermy. (conclusion)

A Simple Example of a Valid Argument:

The three statements together are called an ARGUMENT

If the conclusion follows logically from the two premises, the argument is said to be VALID

If the conclusion does NOT follow from the premises, it is INVALID

Deductive Logic

If you study taxidermy, you learn how to stuff dead animals.

___________ knows how to stuff dead animals.

Therefore, _____________ has studied taxidermy.

Is the following example valid or invalid?

The argument is INVALID, because the conclusion does not follow from the premises.

Let's try another.....

Is the following example valid or invalid?

All 12th grade students are clever.

____________'s dog is a 12th grade student.

Therefore, __________________'s dog is clever.

Is the following example valid or invalid?

The example is VALID, even if the premises are not TRUE.

Most arguments are not simply articulated in one, two or three premises. Many take multiple premises and intermediate conclusions to reach a final conclusion.

Is the following example valid or invalid?

The use of symbols helps logicians distance themselves from the vague language that can be used in syllogisms.

A SYLLOGISM is an argument in which a conclusion is based on two premises.

Symbolic Logic

All 12th grade students are clever.

____________'s dog is a 12th grade student.

Therefore, __________________'s dog is clever.

All A is B

All C is A

All C is B

No matter what words you put in to replace the symbols, the result is VALID

If you change the symbolic construction of the syllogism, however, the result may INVALIDATE it:

Symbolic Logic

All A is B

All C is A

All C is B

All A is B

All C is B

All C is A

-OR-

Lazy students never do their homework.

______________ never does his homework.

Therefore, _________________ is lazy.

Symbolic Logic

All A is B

All C is B

All C is A

1. All Italians eat spaghetti.

Giovanni Rossi eats spaghetti.

Therefore, Giovanni Rossi is an Italian.

2. No Martians have red noses.

Rudolph has a red nose.

Therefore, Rudolph is not a Martian

Using Euler Diagrams

3. Some monks are Tibetans.

All Tibetans are good at yoga.

Therefore, some monks are good at yoga.

4. Some astrologers are frauds.

Some frauds are not wealthy.

Therefore, some astrologers are not wealthy.

5. All bobos have dogs.

No doctors have dogs.

Therefore, no bobos are doctors.

Euler Diagrams

7. All rookies are red-heads.

All red-heads are runners.

Therefore, all rookies are runners.

8. No alphas are betas.

No gammas are betas.

Therefore, no gammas are alphas.

Euler Diagrams

1. Jenny goes to Oxford University, so she must be smart.

2. Drugs should be legalized because they only harm the addict.

3. Graham is a politician so he is probably lying.

4. Since it is natural to eat meat, there is nothing morally wrong with it.

Enthymemes: Incomplete Arguments with Assumed Premises

Make up your own VALID syllogisms to illustrate each of the following:

1. 2 true premises and a false conclusion

2. 1 true premise, one false premise, and a true conclusion

3. 1 true premise, one false premise, and a false conclusion

4. 2 false premises and a true conclusion

5. 2 false premises and a false conclusion

Daily: Writing Syllogisms

Inductive Logic

the reasoning we use when we make generalizations or analogies

We use experience and empirical knowledge and make inferences from that experience.

fundamentally different from the pure reason of deductive logic, which is independent of any empiricism

How would you respond to the following question: Will your next ToK class be interesting?

What do you base your answer to that question on?

Inductive Logic 1: Generalizations

Inductive logic is not concerned with absolute certainty

It has two main features:

It gives good reasons for supporting a conclusion, but it does not guarantee that conclusion

Its conclusion contains information that is not in the argument

Inductive Logic 1: Generalizations

Look back at the ToK class example.

Is your conclusion guaranteed?

Is there any info in the conclusion that is not in the argument?

Inductive Logic 1: Generalizations

Take the following example:

In every country's capital city there is an IB school.

Test One: Sufficient Number

on what numerical info is the statement based?

Was it based on info from every country in the world, most, or just a few?

Is it a generalization from a widely-traveled educator, or someone who has only traveled to 20% of the world's capital cities?

What numerical info is acceptable as sound evidence for generalizations?

Inductive Logic 1: Generalizations

3 Tests for Soundness

Test 2: Varying Circumstances

Is the generalization based on information evidence from all parts of the world, or is it localized?

In every country's capital city there is an IB school.

Test 3: Exceptions

Has a thorough and reliable search for exceptions been made?

In every country's capital city there is an IB school.

When we reason (induct) by analogy, we compare two things which are similar in some ways and then infer that they are similar in other ways too.

Inductive Logic 2: Analogies

Ex: ACRE:LAND

1. distance:space

2. kinsfolk:family

3. gallon:liquid

4. degree:thermometer

5. year:birthday

Inductive Logic 2: Analogies

Areas of knowledge that may use analogies are: Ethics, Economics and History

Read the story on the handout, then mark each of the following statements as True, False, or Unknown

Inductive Logic Flaws: Insufficient Evidence

In pairs, define each of the following and provide two examples (turn in your work):

post hoc ergo prompter hoc

ad hominem

circular reasoning

special pleading

equivocation

argument ad ignorantiam

false analogy

false dilemma

loaded questions

Informal Reasoning: Fallacies

identify & clarify vague/ambiguous statements

indicate unstated assumptions or biases

help us identify unstated premises

make us aware of the strength & validity of analogies or comparisons

The Value of Logic

Logic Can Help Us...