1. Reasoning as a Way of knowing
Inductive and Deductive Reasoning

3. Essential Questions What is Logic or Reasoning?
How can new knowledge be acquired using inductive and deductive reasoning ?
What is more certain, the conclusions drawn from deductive or inductive reasoning?
What are some of the issues with depending on inductive reasoning as a way of knowing?

4. What is logic Formal type of reasoning.
Used as justification for a belief. An important source of reliable knowledge.
Two branches
Inductive reasoning – a series of specific of observations called premises leading to a general conclusion or generalization.
Deductive reasoning – a series of general premises leading to a specific conclusion
An argument is a connected series of premises
(statements or assumptions) that are used to draw a
conclusion.
Deductive reasoning or deductive logic

5. Which kind of reasoning is this?
All Christians believe in God John is a Christian John believes in God Peter is an atheist Peter’s father is an atheist Peter’s grandfather is an atheist Therefore Peter’s brother is also an atheist

6. Parts of a simple logical argument
Two or more premises
Some premises will be obvious and stated explicitly and some will be implicit.
Words or phrases such as “therefore,” “so,” “then,” “hence,” “thus” indicate that the conclusion follows.
Words or phrases such as “because,” “for,” “since,” “if,” “when” indicate that what it said next is a premise.

7. Distinguishing between Truth and Validity
Truth and validity are NOT the same.
Truth is a property of premises and conclusions.
Truth in TOK is the quality of being true or correct according to some ground or test (coherence, correspondence, pragmatic).
Truth is “true for all”.

8. A valid argument is one where the conclusion logically follows from the premises.
In an invalid argument the conclusion does not follow logically from the premises.
A fallacy is a mistake or invalid pattern in reasoning.
The validity of an argument is independent of the truth of the premises it contains.
A sound argument is one that is valid and its premises are true, making the conclusion true.

9. Relationship between truth and validity
The validity of an argument is independent of the truth or falsity of the premises. For example:
All panthers are pink (False)
Ms Jones is a panther (False)
Therefore Ms Jones is pink (False)
Both the premises and the conclusion are false, but the argument is valid.
An argument can also be valid when the premises are false and the conclusion is true. For example:
All ostriches are teachers (False)
Ms Jones is an ostrich (False)
Therefore Ms Jones is a teacher (True)

10. Determining the validity of an argument
Determining the validity of even simple arguments is difficult.
Venn Diagrams can be used.
The structure of this type of argument is always valid.
All A’s are B’s
Some A’s are C’s
Therefore some B’s are C’s
We can substitute in anything we like for A, B and C. C B A

11. The structure of this type of argument is always invalid
All A’s are B’s
All B’s are C’s
Therefore all C’s are A’s
Just because the A falls inside B and B falls inside C, it
doesn’t follow that all C’s are A’s. A B C

12. Try to identify valid and invalid arguments
Work in pairs, use Venn diagrams if necessary and see if you can identify whether the arguments are valid or invalid for #1-10 on the sheet
When you are finished the activity above, turn over the page and look at arguments #1-5

13. Make up your own arguments…
Make up your own simple arguments that have:
Two true premises and a true conclusion.
One true premise, one false premise and a true conclusion
One true premise, one false premise and a false conclusion
One false premise and a true conclusion
Two false premises and a false conclusion
Two true premises and a false conclusion.
Determine the validity of the arguments you wrote.

14. Comparing Deduction and Induction

15. Issues with Inductive Reasoning
When a specific set of observations leads to a general conclusion.

16. Knowledge Issue: 1 We can’t totally rely on sense perception.
Our brain which perceives (interprets) the sense can be tricked.
Our brain can misinterpret what we sense – optical illusions.
We have a natural tendency to look for meaning in what we see.
Expectations, culture, context, age and memory influence perception.
Humans are limited by the range of frequencies we can hear and see.

17. There are two things your brain can potentially perceive in this picture. What are they?
Hint: Try tilting your head to the right, the world begins with 'L’. LIAR

18. Knowledge Issue: 2 How many examples do you need to observe
before a general conclusion can be drawn?
In science to improve the certainty of the conclusions drawn from induction many repeated observations are made.
But how many times should an experiment be repeated?

19. Up until 1697 every swan observed in Europe was white, leading to the conclusion that all swans are white.
In 1697 Dutch explorer William de Vlamingh traveled to Western Australia and saw a flock of black swans along a river (Swan River which runs through Perth).
This discovery forced Europeans to revise their accepted belief that all swans are white.
The black swan story is one of inductive reasoning.
Story reminds us that just because you have never seen something, it doesn't mean it doesn’t exist.

20. Knowledge Issues: 3 Knowledge Issues: 4
Statistics can be misused, distorted, and misinterpreted especially if they make generalizations beyond what the data allows.
Knowledge Issues: 4
We believe something because we have a good reason for doing so – a justification for that belief.
Since induction involves moving from the observed to the unobserved, there is no way to justify a conclusion on the basis of previous experience.

21. Knowledge Issue: 5
Since inductive reasoning produces a general conclusion (a generalization) you can’t guarantee the truth of a conclusion made.
How we sense/observe our world is affected by our emotional state and this will affect the general conclusions we draw.
Also our observations can be influenced by intuitive hunches. Ie., one terrorist is muslim, another terrorist was muslim etc …therefore terrorists are muslims
Example from Vicki – Al Gore Book
" The Assault on Reason" by Al Gore, it talks about how politics of fear can subvert wise decision-making, degrade democracy, and etc. Claim made by Gore which says: "Fear is the most powerful enemy of reason."

22. Knowledge Issue: 6
There is a danger that a hasty generalization will be
made.
For example: You are visiting France on holiday and you are served in a restaurant by a rude waiter, you may infer that all French waiters are rude. This is a hasty generalization.
Even well-established generalizations can let you
down.
For example: Since my neighbor’s dog is always friendly to me, it will not bite me today. But it is possible that it could.

23. What is a good generalization?
Look at a reasonable number of instances. If you see one dog swimming, this is not enough to conclude that all dogs can swim.
Look at a variety of circumstances. Look at a variety of different breeds of dogs swimming.
Actively look for counter examples. Ask if anyone has seen a dog that can’t swim.
Demand more evidence (coherence) to support surprising claims.

24. Issues with Deductive Reasoning

25. Knowledge Issue: 1
The truth of the conclusion is dependent on the truth of the
premises.
All students are lazy
I am a student
Therefore
I am lazy
The premise “all students are lazy” is not true for all and can be disputed with the statement “some students are not lazy”.
What makes it not true is the use of the word “all”.
Therefore the truth of a conclusion depends entirely on the correctness of the premises.
To be called true it has to be true for all

26. Knowledge Issue: 2
The argument goes round and round and never reaches a
conclusion because one or both parties can’t understand the
reasoning.
The wording of premises can:
Be interpreted in different ways
Be hard to understand
Cause you to make assumptions
Be ambiguous or abstract
Use language that is not clear
Be influenced by your personal beliefs
Be influenced by your expectations and perceptions
First clarify the important words by finding out exactly what
they mean and be very clear in the language used.

27. Knowledge Issue: 3 Disagreements about the truth of a premise
There are two types of disagreements:
Factual dispute – disagreement over the facts which can usually be resolved by looking in a book, on the Internet etc.
Merely verbal dispute – where an ambiguous term conceals the fact that there is no real disagreement. Disputes like this are not often easy to spot and can be resolved by clearing up the ambiguity.

28. Knowledge Issue: 4 There are no selfless acts.
I saved a child from a fire.
Therefore saving a child is not selfless
A generalized premise or conclusion uses words like “all” or “no,” “none,” “always,” “never,” “everyone,” and “everywhere”
Each makes a statement about every single instance, or in other words every single act in the world is not selfless.
It hard to know if the first premise is true. How many examples of selfish acts would you need to describe before you could state with any certainty that the premise is false.

29. The word “some” is imprecise and can stand for numerous possibilities between “all” and “none”. It refers to a particular instance or a number of instances. It is not a generalization.
“I talked to you on Wednesday” is better than “Sometimes I talk to you” because it is easy to determine if it is true.
Other confusing words are “couple,” “few,” “many,” “almost all,” “nearly everyone”.
In order to prove that the premise “Some teenagers are not lazy” is true you need to prove that there are no instances of teenage laziness. Impossible!!! So, the premise “Some teenagers are not lazy actually implies that teenagers are lazy.
An implication is a logical relationship between two ideas, stated in the form “A implies B”. Therefore for any valid implication if “A” is true then “B” must also be true.

30. Knowledge Issue: 5 Belief Bias
Formal reasoning focuses on the structure of the argument not the content.
Focusing on the content can lead to a belief bias; the tendency to believe an argument is valid simply because you agree with the conclusion.

31. Lateral Thinking – Creative Reasoning
Being able to think in a way that does not involve formal inductive or deductive reasoning.
Lateral thinking or thinking outside the box.
For example:
A women is lying dead in a field. Next to her is an
unopened package. There is no other living thing in
the field. How did she die?
Which do you think is easier: having the courage of your convictions, or having the courage to question your convictions?
Riddle = jumped from a plane, parachute didn’t open

32. Bibliography http://www.edwarddebono.com/about.htm
Theory of Knowledge Course Companion, Dombrowski, Rotenberg and Bick, OUP
Theory of Knowledge for the IB Diploma, van de Lagemaat, Cambridge
Theory of Knowledge, Alchin, Hodder Murray