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School
University of New South Wales *
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Course
1362
Subject
Philosophy
Date
Dec 6, 2023
Type
docx
Pages
11
Uploaded by DeanSpider3880
Example bank:
Fred ate the cookies,
because
Mary says she saw him eat them, and also
because
he has crumbs all
over his shirt!
1.
Mary says she saw Fred eat the cookies
2.
Fred has crumbs all over his shirt
3.
∴
Fred ate the cookies
How can Bob pass the exam, if he does not study? But I doubt he will study. So, Bob will not pass
the exam.
Rhetorical question + expression of doubt
imply hidden premises
1.
Bob will pass the exam only if he studies
2.
Bob will not study
3.
∴
Bob will not pass the exam
Social welfare does not help anyone. Giving money to people who do not work does not help
anyone, and this is what social welfare is.
1.
Giving money to people who do not work does not help anyone
2.
Social welfare is giving money to people who do not work
3.
∴
Social welfare does not help anyone
Your brother is struggling with his maths homework. So, you must give him a hand.
1. Your brother is struggling with his maths homework
2. ∴ You must give him a hand
If God did not want humans to sin, he could easily make sure that we do not. It
follows that God wants us to sin.
1. If God did not want humans to sin, he could easily make sure that we do not
2. ∴ God wants us to sin
As he apologised, you should forgive him.
1. He apologised
2. ∴ You should forgive him
“Any law that degrades human personality is unjust. All segregation statutes are
unjust because segregation damages the soul and degrades the personality.”
It is an argument, and the conclusion is "all segregation statutes are unjust".
‘Because’ is an argument marker
If Bob does not study he will fail his exam, and he will not study.
Gives reasons why bob will fail. Conclusion “Bob will fail his exam” is omitted
Greg was struggling with his maths homework. That’s why I gave him a
hand.
Not an argument, this is an explanation (WHY is not asked)
You should vote for party X. Party X will cut taxes, and therefore party X is
better for economic growth
Every event has a cause, and the beginning of the universe was an event that took place some 15
billion years ago. But what, if not an act of God, could be the cause of the beginning of the
universe?
An argument is valid just in case it is impossible for its premises to be true while its
conclusion is false.
True
Suppose that Fred gives you an argument for the conclusion that eating meat
is
morally impermissible
, and Mary an argument for the conclusion that eating
meat is
morally permissible
. Which of the following combinations is
impossible
?
Both arguments are sound
It is possible for a complex argument to be valid, even if one or more of its sub-
arguments are not
True
It is possible for a complex argument to be invalid, even if all of its sub-arguments
are valid.
False
Is the following argument valid or invalid?
If Bob studied, he passed his exam.
Bob passed his exam.
∴Bob studied.
Therefore, you should vote
for party X
Party X is better for
economic growth
Party X will cut
taxes
The cause of the
beginning of the
universe was an act of
God
Every event has
a cause
the beginning of the
universe was an event
that took place some 15
billion years ago
Invalid
Is the following argument valid or not?
If Bob studied, then he passed the exam.
Bob did not pass the exam.
∴Bob did not study.
Valid
Is the following argument valid or invalid?
Either Raji or Mary will come to the party.
Raji will not come to the party.
∴Mary will come to the party.
Valid
Is the following argument valid or invalid?
If the moon is made of blue cheese, then it is edible.
The moon is made of blue cheese.
∴The moon is edible.
Valid
Is the following argument valid or invalid?
Logicians are the most interesting people.
∴Logicians are the most interesting people.
Valid
Is the following argument valid or invalid?
If a really supremely powerful and supremely good God existed, then he would
not allow innocent people to suffer. But innocent people do suffer. So, a
supremely powerful and good God does not exist
Valid
Is the following argument valid or invalid?
Either the maid or the butler committed the murder, unless someone else had
access to the house during the night. No one else had access to the house
during the night, so either the maid or the butler committed the murder.
Moreover, the maid had no motive to commit the murder. So, the butler did it.
Invalid
Is the following argument valid or invalid?
Birds have wings and butterflies have wings. So, butterflies are birds.
Invalid
Is the following argument valid or invalid?
Since Melbourne is south of Canberra and Canberra is south of Sydney,
Melbourne is south of Sydney.
Valid – property of relation = ‘transitivity’ in logic
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Is the following argument valid or invalid?
If God did not want humans to sin, he could easily make sure that we do not. It
follows that God wants us to sin.
Invalid
All cats are mammals. Tibbles is a mammal. So, Tibbles is a cat.
This argument is of the form:
1.
All As are Bs
2.
x is a B
3.
∴x is an A
No reason to think that
the only
way for something to be a B is for it to be an A.
Cannot be fixed by supplying hidden premises.
The premise "Tibbles is a cat" would make the argument valid
The correct answer is: The argument is not valid as stated. There is no reasonable
hidden premise that would make this argument valid.
If Bob studies, he will pass the exam. But Bob will not study. So, Bob will not pass his
exam
This argument is not valid as stated, because we are not told that Bob will
pass
only
if he studies. The hidden premise "Bob will not pass the exam unless he
studies" would make it valid, and it is reasonable to assume.
Of course Raji will pass her exam, she has studied really hard!
1.
This argument is not valid as stated. It is reasonable to take the premise “if
Raji studied hard, then she will pass the exam” to be a hidden premise, and
that would make the argument valid.
If A then B
A
∴B
2.
This argument is not valid as stated. It is reasonable to take the premise
“everyone who studies hard passes” to be a hidden premise, and that would
make the argument valid.
All F are G
a is F
∴a is G
Platypuses are not mammals, because they lay eggs.
No F is G
x is G
∴x is not F
This argument is not valid as stated. The premise that no mammals lay eggs would
make the argument valid, and, although it is false, perhaps the reasoner does not
know that it is
Platypuses are not mammals, because they lay eggs. In polling places all over the
country, our party’s representatives asked departing voters who they had just voted
for. Most voters said they voted for our party, so we should win the election.
This argument is not strong, because the sample may not be representative.
I put a kiwi fruit in a tub of water, and it floated. To confirm, I did the same with
another one, and it floated too. So, kiwi fruits float in water.
This argument is strong, given the subject matter.
My friend got COVID-19, and treated it with zinc supplements. She recovered in a few
days. Therefore, zinc supplements are effective against COVID-19.
This is a weak argument.
Attempt to ‘inference to the best explanation’ but doesn’t consider any
alternative explanations of the evidence
My house just started shaking. It must be an earthquake!
This argument is strong: an earthquake would explain the evidence, and there are no
obvious alternatives on offer.
I know that WestConnex is digging a tunnel near my house. My house just started
shaking. It must be an earthquake!
This argument is weak, because vibration from the tunnelling is a more likely
explanation than an earthquake.
Consider the following exchange:
Mary: “This table is mostly empty space. It is made up of atoms, and atoms consist
of tiny sub-atomic particles, which orbit eachoth3er at huge distances (relative to
their own size).
Fred: “This can’t be right: if it were true, then the computer would fall right through
the table, and it does not”
Is Fred’s objection successful?
No
Fred’s conclusion is an absurdity. Conclusion does not follow on from Mary’s
claim.
In mathematics, a “set” is a collection of distinct objects, and is an object in its own
right. So, sets can be members of other sets. Bertrand reasons as follows:
“Suppose that there is a set, S, that contains all sets that do not contain themselves.
Then, does S contain itself? If it does, then it should not. And if it does not, then it
should. This is absurd. So, there can be no set that contains all sets that do not
contain themselves.
Is Bertrand’s reasoning successful?
Yes
Which of the following statements are false? Select all that apply
1.
Very few of our ordinary concepts are vague
2.
Slippery slope arguments are good arguments
3.
Even if there is no sharp line between cases where a concept P (sych as
“bald”, or “is a heap”) applies and cases where it does not, there can still be
cases where P definitely applies and P definitely does not apply
4.
Slippery slope argments exploit vagueness to create an impression of validity
5.
If there is no sharp line between cases where a concept P (such as
“bald”, or “is a heap”) applies, then we must either apply the
concept to everything, or refrain from applying it to anything.
Consider the following argument. Is it successful?
Human beings are conscious. Moreover, this has to do with the fact that they possess
an enormously complex brain and nervous system. But, a slightly simpler brain and
nervous system (such as that found in chimpanzees, for example) would also support
consciousness. More generally, if an organism O is conscious, then another organism
with a nervous system just slightly simpler than O’s will also be conscious. So, since
we can move by small decreases of nervous system complexity from human beings
all the way down to earthworms, earthworms are conscious.
Slippery slope argument - unsuccessful
Consider the following argument. Is it successful?
If we allow cloned human organs to be grown in laboratories for transplantation, then
soon we will find ourselves allowing the cloning of entire human beings, and before
long creating a genetically designed “master race”. We should not go down that
road.
Slippery slope argument – unsuccessful
Joe will play in the second round of the tournament only if kayla does
1.
(J ↄ K)
2.
(J v K) & ~(J& ~K)
3.
(K&J)
4.
(K ↄ J)
Mary's not playing in the second round of the tournament is a necessary condition for Kayla to play
Translation: if mary does not play, kayla does
HOWEVER; words 'necessary condition' mean it translates to:
If kayla plays, it must be that Mary does not
1.
~M ↄ K
2.
K ≡ ~M
3.
~(M v K)
4.
K ↄ ~M
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1.
What is the probability of rolling a 6 in one throw of a fair six-sided die?
a.
1/6
2.
What is the probability of not rolling a 6?
a.
5/6
3.
Rolling the die twice, what is the probability of a 6 both times?
a.
A = 6 first time, B = 6 second time
b.
P(A&B) = P(A) x P(B)
c.
1/6 x 1/6 = 1/36
4.
If you roll a fair six-sided die twice, what is the probability that it will come up at a 6 at least
once? (there's two ways to calculate this)
P (A v B) = P(A) + P(B) - P(A & B)
P (at least one 6 in two throws) = 1 - P(no 6 in two throws)
5/6 x 5/6 = 25/36
P(at least one 6 in two throws) = 1 - 25/36 = 11/36
5.
If your roll a fair six-sided die twice, what's the probability a 6 will come up exactly once?
a.
11/36 of at least once
b.
11/36 - 1/36 =
10/36
c.
P(6 on exactly one roll) = P(6 on first roll v 6 on second roll) - P(6 on first roll & 6 on
second roll)
1.
If you roll a fair six-sided die six times, what is the probability that it will come up 6 at least
once? (same question as number 4)
a.
5/6 x 5/6 x 5/5 … 5/6 to the power of 6
i.
(5/6)^6
b.
P(of not getting a 6 at all) = 0.33
c.
1-0.33 = 0.67 or 2/3
2.
Your school is running a lottery with 100 tickets and 1 winner. Suppose you buy 2 tickets in
the lottery. What is the probability that one of your tickets is a winner?
P(ticket 1 is a winner v ticket 2 is a winner) = P(ticket 1 is a winner) + P(ticket 2 is a winner)
1/100 + 1/100 = 2/100 OR 1/50
3.
Two of your local schools run lotteries, with exactly 100 tickets each, and only one winner.
Suppose you buy one ticket in each lottery. What is your probability of having at least one
winning ticket?
Outcomes are not mutually exclusive (as you could win both lotteries).
Formula for non-exclusive disjunctions: P(ticket 1 is a winner v ticket 2 is a winner) = P(ticket 1
is a winner) + P(ticket 2 is a winner) - P(ticket 1 is a winner & ticket 2 is a winner)
Moreover, since we know both lotteries are independent: P(ticket 1 is a winner & ticket 2 is a
winner) = P(ticket 1 is a winner) * P(ticket 2 is a winner) =
1/10,000
So:
P(ticket 1 is a winner v ticket 2 is a winner) = 1/100 + 1/100 - 1/10,000 = 199/10,000
To use a negation it is: negation of winning no tickets
P(winning at least one ticket) = 1 - P(winning no tickets)
P(winning at least one ticket) = 1 - P(ticket 1 is not a winner & ticket 2 is not a winner)
P(winning at least one ticket) = 1 - (99/100 * 99/100)
P(winning at least one ticket) = 199/10,000 OR 0.0199
4.
Two of your local schools run lotteries, with exactly 100 tickets and only one winner each.
Suppose you buy one ticket in each lottery. What is your proability of having two winning
tickets?
P(ticket 1 is a winner & ticket 2 is a winner) = P(ticket 1 is a winner) * P(ticket 2 is a winner)
P(ticket 1 is a winner & ticket 2 is a winner) = 1/100 * 1/100 = 1/10,000
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