It’s logical!. Do you remember the three kinds of reasoning we talked about before?...
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Transcript of It’s logical!. Do you remember the three kinds of reasoning we talked about before?...
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It’s logical!
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Do you remember the three kinds of reasoning we talked about before?Deductive…inductive…and…
informal!
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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.
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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
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Can
INDUCTIVE
reasoning be
doubted?
Can
DEDUCTIVE
reasoning be
doubted?
Why?
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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?
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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.
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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≠
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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.
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- 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.
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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.
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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
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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.
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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.
NameSymbol 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
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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.”
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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.[ ]
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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
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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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http://www.youtube.com/watch?v=vRJUvFG8gbE
http://www.youtube.com/watch?v=ytWGiOuzpe4&feature=related
http://www.youtube.com/watch?v=k0xgjUhEG3U
http://www.youtube.com/watch?v=GNN6-OekWvI&feature=related
http://www.youtube.com/watch?v=Dln3DJEcghY
http://www.youtube.com/watch?v=DQ24HdCPN9E&feature=related
http://www.youtube.com/watch?v=ZsoMIbXfA0g&feature=related
http://www.youtube.com/watch?v=m4foH4HCzKA&feature=related
http://www.youtube.com/watch?v=im4TYITM0VE