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ToK:Logic

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Chris Kirby

on 30 August 2013

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Transcript of ToK:Logic

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...
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