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## Introduction to Logic

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### Introduction to Logic Dr. Pedro Poitevin IDS 108-08 – PowerPoint PPT presentation

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Title: Introduction to Logic

1
Introduction to Logic
• Dr. Pedro Poitevin
• IDS 108-08

2
Consistency
• A set of beliefs is consistent if the beliefs are
compatible with each other.
• A set of beliefs may itself be consistent while
not being consistent with the known facts.
• A set of beliefs is consistent if these beliefs
could all be true in some possible situation.

3
Example 1
• It would be wrong to censor violent programs on
television, because peoples behavior isnt
really affected by what they see on the screen.
All the same it would be a good idea to have more
programs showing the good side of our national
way of life, because it would change the ways of
some of the people who are always knocking down
our country.

4
Example 2
• During the last five years I have been involved
in three major accidents and several minor ones,
while driving my car. After two of the major
accidents, courts held me responsible. But
basically Im a thoroughly safe driver Ive

5
Example 3
• The surface of the earth is flat (apart from
mountains, oceans, and other relatively small
bumps and dips). When people think they have
sailed round the earth, all they have really done
is to set out from one place and finish up in
another place exactly like the one they started
from, but several thousand miles away.

6
Example 4
• I have invented an amazing new sedative that
makes people faster and more excited.

7
Exercise 1A
• You know that human beings normally have two
legs. Try to convince yourself that they
normally have five.

8
Exercise 1B
• Are the following sets of beliefs consistent?
• Ive never drawn anything in my life. But if I
sat down to it now, it would take me two minutes
to produce a drawing worth as much as anything by
Picasso.
• I knew I would never get pregnant. But somehow
it just happened.
• There is no housing shortage in Lincoln today
just a rumour that is put about by people who
have nowhere to live.
• Walter joined the friendly club two years ago,
and has been one of its most loyal members ever
since. Last year he paid for the holidays of
precisely those club members who didnt pay for
their own holidays.

9
Beliefs and Words
• Many sentences do not naturally state beliefs.
(eg What time is it?)
• One sentence may have two different meanings.
(eg Tariq is a Persian carpet importer.)
• One sentence can be used on different occasions
to talk about different things. (eg Tomorrow
will be rainy.)
• The sentences that do express beliefs are called
declarative sentences.

10
Declarative Sentences
• A declarative sentence of English is a
grammatical English sentence which can be put in
place of x in
• Is it true that x?
• Example The price of beef has fallen.
• We call a string of words grammatical if most
speakers of the language would accept it as
correctly formed.
• A sentence may be slightly off from being
grammatical. In that case we say it is a
perturbation of a grammatical sentence.
• A sentence is a selection violation if it puts
concepts together in impossible ways but is
otherwise grammatically okay.

11
Examples
• These pages must not be removed or defaced.
• Your breast will not lie by the breast
• Of your beloved in sleep.
• The very so not was, wasnt it?
• echo foxtrot golf hotel
• Did you be angry with Sally?
• Her train was decorated with silver gorgeous
lace.
• Government hastening collapse of economy.
• By swaggering could I never thrive.

12
Selection Violation Examples
• The pianist then played a red hat topped with
geraniums and wisdom.
• He ate a slice of boredom.
• Nothing spoke her more than a hot bath.
• The civilization of the ancient Persians
fervently knew at least two inches.

13
Selection Violation and Poetry
• Selection violations are easy to recognize by
their bizarre and poetic feel.
• In fact, they play an important role in poetic or
metaphorical writing.
• By committing a selection violation deliberately,
a writer can force her readers to forget the
literal sense of what she says since they can
make nothing of her words if they take them
literally, they have to notice the colors and the
overtones.

14
Exercise 3A
• Classify the following sentences
• Colorless green ideas sleep furiously.
• Furiously sleep ideas green colorless.
• Please pass me a butter.
• I bet theres dozens of people youve forgotten
to invite.
• singing each morning out of each night my father
moved through depths of height
• My father moved through theys of we
• You cant do nothing with nobody that doesnt
want to win.
• His face was calm and relaxed, like the face of
an asleep child.
• Not, Father, further do prolong
• Our necessary defeat.
• 10. Time and the bell have buried the day.

15
Exercise 3B
• Which of the following are declarative sentences?
• Twice two is four.
space provided.
• Would you believe youre standing where Cromwell
once stood?
• Thats true.
• I promise not to peep.
• Blackmail is wicked.

16
Ambiguity
• Lexical ambiguity occurs when a single word can
be understood in more than one way.
• Example I thought it was rum.
• Structural ambiguity occurs when the words in the
string can be grouped together in different ways.
• Example I heard about him at school.
• Ambiguity of cross-reference it occurs when a
word or phrase refers back to something mentioned
elsewhere, but it isnt clear which thing is it
that it refers to.
• Example Tasmins stuck at home with a migraine,
but Diane said shed be dealing with the Kaplan
file today.

17
Exercise 4A
• What kinds of ambiguity occur in the following?
• Launching the ship with impressive ceremony, the
Admirals lovely daughter smashed a bottle of
champaign over her stern as she slid gracefully
down the slipways.
• Miss Crichton pluckily extinguished the blaze
while Herr Eckold pulled the orchestra through a
difficult passage.
• The font so generously presented by Mrs Smith
will be set in position at the East end of the
Church. Babies may now be baptized at both
ends.
• The Government were strongly urged to take steps
to put a stop to the growing evil of methylated
spirit drinking by the Liverpool justices at
their quarterly meetings.

18
Exercise 4B
• Rewrite each string in two non-ambiguous ways.
• I shall wear no clothes to distinguish me from
my fellow citizens.
• He only relaxes on Sundays.
• He gave each guest a glass of rum or gin and
tonic.
• Most of the nations assets are in the hands of
just one person.
• Dogs must be carried.

19
Referential Failure
• Suppose that the greatest thing that can be
conceived doesnt exist outside our minds. Then
it is not as great as it would have been if it
had existed. Therefore we can conceive something
greater than it which is impossible. Therefore
our original supposition is incorrect.
• - Anselm

20
• Adjectives like fat, funny, happy, expensive,
heavy, unpleasant, etc. are scaling adjectives.
One can be fatter, or happier than someone else.
Ones jokes may be funnier than someone elses.
Some things are heavier than others, and some
events are more unpleasant than others.

21
• Some adjectives are not scaling.
• Examples straight, silent, perfect, daily.

22
Bizarre Situations
• Example the two cerebral hemispheres of the
human brain are joined by a structure called the
corpus callosum. Surgeons sometimes cut through
the corpus callosum in order to control epilepsy.
• People whose corpus callosum has been severed are
quite normal in most ways, but they show one or
two strange symptoms.
• Suppose we show an object to such a person, and
then ask the person to indicate what we showed
him or her by writing a mark on a piece of paper.
• If the object fell in the left half of his or her
field of vision, then the person can answer our
question with his or her left hand but not with
his or her right.
• If the object fell in the right half then the
person can answer with his or her right hand but
not with his or her left.
• Does a person with a severed corpus callosum, who
can see a mouse to the left of him or her, know
that he or she is seeing a mouse?
• It seems her or she knows with one half of his or
her brain but not with the other.
• In this case, is it appropriate to say simply
that he or she knows?
• In a bizarre situation it may be impossible to
say whether a sentence is true-not because we are
stupid or lack the facts, but because language
fails us.

23
• A witness in the case of Thumptmann v. Thumper
states that Mr. Tumper hit Mr. Thumptmann three
times with the camera tripod, and Mr. Thumptmann
fell to the floor.
• What the witness actually saw was that Mr.
Thumptmann fell to the floor just before Mr.
Thumper came into the room, and Mr. Thumper hit
him three times with the camera tripod before he
could get up.
• After the office party, a man admits to his wife
I did kiss some of the girls.
• In fact, he kissed all nineteen of them.
• After another office party, another man boasts to
his wife All the girls kissed me.
• In fact there were no girls at the party.

24
Possible Situations
• In logic, a situation is described as possible if
it could have been the actual situation,
forgetting what we know about the world.
• There are some limits to what could have been
two times two could never have been equal to
four.
• One of the smartest philosophy books of all time
starts If kangaroos had no tails, they would
topple over and proceeds to work out the details
of how to make sense of the meaning of that
sentence.

25
Applications
• Counterfactual reasoning is the art of reasoning
with possible situations.
• Counterfactual reasoning helps us distinguish
between concepts that appear to be the same
concept.
• Distinguishing between concepts is very useful,
for a variety of reasons.

26
Mistake and Accident
• How to distinguish between mistake and accident?
• Imagine a situation in which an accident has
occurred, but no mistake has occurred.
• Example You have a donkey, so have I, and they
graze in the same field. The day comes when I
conceive a dislike for mine. I go to shoot it,
draw a bead on it, fire but as I do so, the
beasts move, and to my horror yours falls.
• This is clearly an accident, but I didnt make a
mistake.
• Nevermind the fact that the situation hasnt
happened, we have made it clear that the two
concepts are not the same.

27
Exercise 8
• Distinguish between the following pairs of
sentences
• The senator was lying.
• What the senator said was untrue.
• Its in your best interests to go to Corsica.
• It would do you good to go to Corsica.
• He knows Im at home.
• He thinks Im at home, and I am.
• 4. Brutus killed Caesar.
• Brutus caused Caesar to die.
• 5. A crow is a kind of bird.
• The word crow is used to denote a kind of bird.