It’s logical!

It’s logical!

Do you remember the three kinds of reasoning we talked about before?Deductive…inductive…and…

informal!

Vs.Deduction Induction

• Reasoning from particular to general

Metal ‘A’ expands when hated; metal ‘B’ expands when heated; metal ‘C’ expands when heated.

∴ all metals expand when heated.

• More informative, but less certain than deduction.

• Goes from general to particular

All metals expand when heated.

‘A’ is a metal. ∴ ‘A’ expands when heated.• More certain, but less

informative than induction.

As a WoK… can logical reasoning be doubted?No! because of these three laws:a) Law of identity

a=ab) Law of non-contradiction

nothing can be a and -ac) Law of the excluded middle

everything is either a or -a

Can INDUCTIVE

reasoning be

doubted?

Can

DEDUCTIVE

reasoning be doubted?

Why?

Give a rational explanation to the

following…A man walks into a bar and asks the barman for a glass of water. The barman pulls out a gun and points it at the man. The man says

‘Thank you’ and walks out. What happened?

FallaciesA fallacy is a kind of error in reasoning. Fallacies should not be persuasive, but they often are. Fallacies may be created unintentionally, or they may be created intentionally in order to deceive other people. The vast majority of the commonly identified fallacies involve arguments, although some involve explanations, or definitions, or other products of reasoning. Sometimes the term “fallacy” is used even more broadly to indicate any false belief or cause of a false belief. 

All bull-fighters are brave people.Some brave people are compassionate.

All bull fighters are compassionate.

All dogs are mammals.Fido is a dog.

Fido is a mammal.

Truth Validity≠

TRUTH -

VALIDITY - Property of the whole SYLLOGISM when the conclusions follow the premises.

Property of STATEMENTS concerned with what is the case.

∴ The validity of an argument is independent of the truth of falsity of the premises it contains.

- No human being can run as fast as a thunderbolt.- If someone can run as fast as a thunderbolt, he is either non-human, or has been scientifically

modified.- The Flash can run as

fast (or even faster) than a thunderbolt.

- Therefore, the Flash is either non-human, or has

been genetically modified.

We can construct valid arguments for almost any combinations of true and false premises and conclusions. The only situation that is impossible is a valid argument with true premises and a false conclusion.[ T ] 1. All men are

mortal.[ T ] 2. Socrates is a

man.[T ] Therefore, Socrates

is mortal.[ F ] 1. All cups are green.

[ F ] 2. Socrates is a cup.

[ F ] Therefore, Socrates is green.[ T ] 1. All men are mortal.

[ T ] 2. Socrates is mortal.[ F ] Therefore, Socrates is

a man.

All whales are mammalsAll mammals have lungs.

Therefore, all whales have lungs.

All spiders have six legs.All creatures with six legs have wings.

Therefore, all spiders have wings.

If I owned all the gold in Fort Knox, I would be very rich.I do not own all the gold in Fort Knox.

Therefore, I am not very rich

[T][T][T]

Valid

[F][F][F]

Valid

[T][T][F]

Invalid

a)Two true premises and a true conclusion.

b)One true premise, one false premise and a true conclusion.

c)One true premise, one false premise and a false conclusion.

d)Two false premises and a true conclusion.

e)Two false premises and a false conclusion.

In the system of Aristotelian logic, the square of opposition is a diagram representing the different ways in which each of the four propositions of the system are logically related ('opposed') to each of the others.

Name Symbol English SSF

Universal affirmative

A Every S is P All S is P

Universal negative E No S is P All S is not P

Particular affirmative

I Some S is P Some S is P

Particular negative

O Some S is not P

Some S is not P

The Four Aristotelian Propositions

Propositions are contradictory when the truth of one implies the falsity of the other,

and conversely.For example, if the proposition “all industrialists are capitalists” (A) is true,

then the proposition “some industrialists are not capitalists” (O) must be false. Similarly, if “no mammals are aquatic” (E) is false, then the proposition “some

mammals are aquatic” must be true.

Propositions are contrary when they cannot both be true. 

An A proposition, e.g., “all giraffes have long necks” cannot be true at the same time as the corresponding E proposition: “no giraffes have long necks.”

Propositions are subcontrary when it is impossible for both to be false. 

Because “some lunches are free” is false, “some lunches are not free” must be true.

Two propositions are said to stand in the

relation of subalternation when the truth of the first

(“the superaltern”) implies the truth of the

second (“the subaltern”),

but not conversely.

The truth of the A proposition “all plastics are synthetic,” implies

the truth of the proposition “some

plastics are synthetic.” However, the truth of

the O proposition “some cars are not

American-made products” does not

imply the truth of the E proposition “no cars are American-made

products.” 

What can you say about the Truth and Falsehood of the following propositions

given the information stated in the first of them?

1.a)Every aminoacid is an organic

compound. [T]b)No aminoacid is an organic compound.

[ ]c) Some aminoacids are organic

compounds. [ ]d)Some aminoacids are not organic

compounds. [ ]

2. e) No reptile is a hot-blooded animal. [T]f) Some reptiles are hot-blooded animals.

[ ]g) Some reptiles are not hot-blooded

animals. [ ]h) Every reptile is a hot-blooded animal.

[ ]

3.a)Some NY senators have been

trimphant candidates to the US presidency. [F]

b)Some NY senators have not been trimphant candidates to the US presidency.[ ]

c) Every NY senator has been a trimphant candidate to the US presidency. [ ]

d)No NY senator has been a trimphant candidate to the US presidency. [ ]

4. a) Some fuels are not polluting agents.

[T]b) Every fuel is a polluting agent.[ ]c) No fuel is a polluting agent. [ ]d) Some fuels are polluting agents.[ ]

Fallacies

Name Description and example

Ad ignorantiam

Hasty generalisation

Post hoc ergo propter hoc

Ad hominem

Circular reasoning

Special pleading

Equivocation

False analogy

False dilemma

Loaded question

Two kinds of reasoning

Deductive Inductive

Definition

Example

Value

1. A man is lying dead in a field. Next to him there is an unopened package. There is no other creature in the field. How did he die?

2. Anthony and Cleopatra are lying dead on the floor of a villa in Egypt. Nearby is a broken bowl. There is no mark on either of their bodies and they were not poisoned. How did they die?

3. A man rode into town on Friday. He stayed three nights and then left on Friday. How come?

4. A landscape gardener is given instructions to plant four special trees so that each one is exactly the same distance from each of the others. How would he arrange the trees?

5. Connect the crosses using only four straight lines and without taking your pencil off the paper.

X X X

X X X

X X X

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