Programming Probability Worksheet

deductively valid,

deductively invalid,

inductively strong,

or inductively weak

Premises.

Epistemic probability.

Inductive probability.

Conclusion.

The stock of knowledge

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Week 2
Assignment 2
Write your answers to each question on paper (I’d use a pencil). You do not need to copy out
the questions themselves, just write (for example): (1)(a) [your answer].
Take a photo/scan your documents, and upload them into Canvas. You must upload your
answers by Saturday, April 10th, 5pm Irvine time. Late submissions will receive a zero.
Make your answers legible, and clearly indicate the question/part of the question you are answering. You must submit your own work. Include your name and ID number at the top of each
page. You may refer to your notes. The assignment is worth 40 points.
(1) The definition of an inductively strong argument we gave was this: an argument is inductively
strong just in case:
1. it is improbable that its conclusion is false given that its premises are true, and
2. it is not deductively valid.
Why do we need clause 2 in this definition?
(2) Put the following arguments into standard logical form and order them by the strength of the
evidential relation between premises and conclusion.
(a) Even though you might be tempted, never pick up a recently killed cottonmouth, because
its nerve reflexes enable it to bite for some time after death.
(b) This election is about great voter fraud, fraud that has never been seen like this before. In
Wisconsin, as an example, where we were way up on election night, they ultimately had
us miraculously losing by 20,000 votes. And I can show you right here that Wisconsin,
we’re leading by a lot, and then at 3:42 in the morning, there was this. It was a massive
dump of votes. Mostly Biden.
(c) There can’t have been a speed trap back there, because if there had been it would have
showed up on this radar detector, but nothing did.
(3) Classify the following six arguments according to whether they are deductively valid, deductively invalid, inductively strong, or inductively weak (there might, or might not, be one of
each kind).
(a)
(b)
I only have a bad day if work is stressing me out.
I only work on weekdays.
I’m having a bad day today.
Today is probably Wednesday.
If I bet on the Packers to win next year’s Superbowl, I’ll lose.
If I bet on someone other than the Packers to win
next year’s Superbowl, I’ll win.
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Week 2
(c)
After I return home in my car, I always leave my keys on my desk.
I sometimes leave my keys in my car by mistake.
My keys aren’t on my desk, and I’ve checked all my pockets,
and can’t find them there either.
I probably left my keys in my car the last time I drove home.
For the past two springs, herons have nested in the pine tree outside my house.
This spring, there is no nest in the tree.
It’s likely that herons have become extinct.
(d)
(e)
I’m sitting at home in my romoworking when the lights go out in my room.
I check the kitchen and bathroom lights, and they don’t work either.
I go round to my neighbor’s house, and their lights are off too.
There’s probably been a power cut in my area.
(f)
If an object is a cube, then it is red.
There is an object that is a red cube.
(4) Here is an argument:
(1) Walter is a man.
(2) Walter is 1500 years old.
(3) Walter has arthritis.
(4) Walter will not break the world record for cycling 100-miles tomorrow.
(a) Match the following terms to the statements in the argument to which they apply. Some
of the terms might apply to more than one individual statement. Some of the terms
might apply to multiple statements considered together.
•
•
•
•
•
Premises.
Epistemic probability.
Inductive probability.
Conclusion.
The stock of knowledge.
(b) Suppose I make the above argument, and someone says this to me: “your argument is
invalid. Since there can’t be a man who’s 1500 years old, it is a bad argument.”
Describe two things that are wrong with that response.
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Week 2
(5) Here are four arguments, and below each one, an additional statement. For each argument,
decide whether the additional observation strengthens or weakens the argument.
(a)
We need a new power plant.
The choices are either a boring natural gas-fired plant or a waste-to-energy plant
that serves both as a trash incinerator and a power plant.
Environmentalists are in favor of the waste-to-energy even though it would
pollute the air three times more than the natural plant would.
We should opt for the waste-to-energy plant.
Additional observation: the new waste-to-energy plant would replace an existing trash
incinerator that produces much more air pollution than the waste-to-energy plant would.
(b)
Pedestrians are less likely to be careful within crosswalks.
More pedestrians are struck in crosswalks than outside of crosswalks.
Additional observation: the overwhelming majority of pedestrians in high-traffic areas
cross streets in crosswalks.
(c)
Readers of popular magazines can’t understand some scientific issues.
Those issues are what a lot of readers would find interesting.
Magazines won’t publish a lot of things its readers would find interesting.
Additional observation: editors of popular magazines generally do not approve stories
about issues that cannot be well understood by those magazines’ readers.
(d)
In most cases in which a planet has been detected orbiting
a distant star, the planet’s orbit is oval.
The orbit of Earth and several other planets round our sun
is approximately circular.
Many comets orbiting our sun have been thrown into oval orbits by
close encounters with planets orbiting our sun.
Some of the planets in oval orbits around distant stars were
probably thrown into those orbits by close encounters
with other planets orbiting the same stars.
Additional observation: in most cases in which planets have been discovered orbiting a
distant star, more than one planet has been found orbiting this star.
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Week 2
(6) (a) Consider the argument below. Which of the following, if true, most weakens the argument?
At a large elementary school researchers studied a small group of children
who successfully completed an experimental program in which they learned to play chess.
The study found that most of the children who completed the program soon showed
a significant increase in achievement levels in all of their schoolwork.
It is likely that the reasoning power and spatial intuition exercised in chess-playing
also contributed to achievement in many other areas of intellectual activity.
(I) Some students who did not participate in the chess program had learned to play
chess at home.
(II) Those children who began the program but who did not successfully complete it had
lower preprogram levels of achievement than did those who eventually did successfully complete the program.
(III) Many of the children who completed the program subsequently sought membership
on a school chess team that required a high grade average for membership.
(IV) Some students who did not participate in the chess program participated instead in
after-school study sessions that helped them reach much higher levels of achievement
in the year after they attended the sessions.
(b) Consider the argument below. Which of the following principles, if legitimate, most
helps to justify the reasoning in the argument?
Some people talk up “alternative” treatments that don’t
do anything – they don’t hurt you, but they also don’t help
cure whatever they’re supposed to cure.
The problem is that people might use these “alternative”
treatments instead of those that actually work.
Promoting these alternative treatments is actually harmful.
(I) It is harmful to interfere with someone doing something that is likely to benefit that
person.
(II) A person is responsible for harm they do to someone even if the harm was done
unintentionally.
(III) A person who convinces someone to take a course of action is in part responsible for
the consequences of that action.
(IV) One should not promote a remedy if one believes that using that remedy will cause
harm.
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Week 2
(c) Consider the argument below. Which of the following, if true, most supports the
conclusion?
If newly hatched tobacco hornworms first feed on plants from the nightshade
family, they won’t eat leaves from any other plants thereafter.
Tobacco hornworms will feed on other sorts of plants if they feed on plants other than
nightshade just after hatching.
When a hornworm’s first meal is from a nightshade, its taste receptors become
habituated to the chemical indioside D, found only in nightshade,
and after this habituation nothing without indioside D tastes good.
(I) Tobacco hornworms that first feed on nightshade leaves show no preference for any
one variety of nightshade plant over any other.
(II) If taste receptors are removed from tobacco hornworms that first feed on nightshade
leaves, those hornworms will subsequently feed on other leaves.
(III) Indioside D is not the only chemical that occurs only in nightshade plants.
(IV) The taste receptors of the tobacco hornworm have physiological reactions to several
naturally occurring chemicals.
(d) Consider the argument below. Which of the following most seriously weakens the
argument?
The sole purpose of having teaching assistants perform services for the university
is to enable them to fund their education.
Teaching assistants should not be considered university employees, or entitled
to the usual employee benefits.
(I) The university employs adjunct instructors who receive compensation similar to that
of its teaching assistants.
(II) The university has proposed that in the interest of the economy, 10% of the faculty
be replaced with teaching assistants.
(III) Most teaching assistants earn stipends that exceed their cost of tuition.
(IV) Teaching assistants work as much and as hard as do other university employees.
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Week 2
(e) Consider the argument below. Which of the following, if true, most helps to strengthen
the argument?
Most of the new TV shows Wilke & Wilke produced last season were canceled
due to insufficient viewers.
Their new TV shows are all police dramas, and few police dramas have been
popular in recent years.
It is likely that most of the new TV programs Wilke & Wilke produce
for this season will be canceled.
(I) Wilke & Wilke have produced more new shows for this season than they produced
last season.
(II) Most of the shows that Wilke & Wilke produced last year were police dramas.
(III) None of the shows that Wilke & Wilke produced last year that were not canceled
were police dramas.
(IV) All of the new shows that Wilke & Wilke produced last year that were canceled were
police dramas.
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