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PHLA10H3 Chapter Notes -Color Blindness, Central Processing Unit, Reductio Ad Absurdum

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William Seager

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PHLA10 Reason and Truth
Exercise 1
Pg. 17
1. When is an idea or statement valid? (trick question)
A statement or an idea cannot be valid; they can only be true or false. Being valid or invalid are
properties of arguments, meaning that only they can be valid or invalid. Arguments can still be valid
even if the premises or conclusions are obviously untrue, or if the premises and conclusion are all false.
3. Invent an example of a valid argument that has false premises and a true conclusion. Invent an
example of an invalid argument that has true premises and a true conclusion.
Valid argument:
All dogs can fly.
Jack is a dog.
So Jack can fly.
Invalid argument:
If the dog is running, then the dog has four legs.
The dog has four legs.
The dog is running.
5. Which of the following argument forms is valid? Which is invalid? For each of the invalid ones,
construct an example of an argument with that form in which the premises are true and the
conclusion false:
(a) Valid
(b) Invalid
If Sam lives in Wisconsin, then Sam lives in the USA
Sam lives in the USA
Sam lives in Wisconsin
(c) Invalid
If Sam lives in Wisconsin, then Sam lives in the USA
Sam doesn’t live in Wisconsin
Sam doesn’t live in the USA

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(d) Valid
7. What does it mean to say that an argument is “circular”, that it “begs the question”? Construct an
example of an argument of this type different from the ones presented in this chapter.
When an argument is “circular” or that it “begs the question”, it does not give you a good reason to
accept the conclusion even if the premises and conclusion are true. If the premise was not accepted,
then the conclusion would not be accepted either.
The Earth is a planet.
Therefore, the Earth is a planet.
Pg. 34
1. What is the difference between deductive validity and inductive strength?
Deductive validity is either valid or invalid, there is no middle ground. An argument of this type is based
on whether the premises are true, which in turn indicate whether the conclusion is true. Furthermore,
deductive valid arguments cannot introduce new information in the conclusion that wasn’t already
there, while inductive strength arguments can conclude on things that are beyond what was in the
premises. Inductive strength can either be stronger or weaker depending on the sample size and the
unbiasedness of it.
2. What is the difference between induction and abduction?
Induction is taking a description of a sample and extending it to things outside the sample, for example
sending out polls to figure out what the country’s preference of political parties are
Abduction is reaching the best explanation possible based on evidence and reasoning.
3. What factors affect how strong an inductive argument is?
The factors affecting how strong an inductive are the sample size and the unbiasedness of the sample.
PHLA10 Reason and Truth
Exercise 2
1. Here's a little logical puzzle: you are in a strange land where everyone is either a
knight or a knave. Knights always tell the truth; knaves always lie. You meet two
of them, A and B. A says "we are both knaves". What are A and B? Prove it.
If A is right, then he has to be lying because he said that he is a knave as well. A cannot be a knight
because they cannot both be knaves or that would make his statement true. As thus, B must be a knight.
A is a knave and B is a knight.
2. What are the four main characteristics of God as Aquinas understood it?

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Aquinas characteristics of God are that he is a personal God, omnipotent (all-powerful), omniscient (all-
knowing) and omni-benevolent (all-good). Aquinas’ concept of God is also known as PKG.
3. What is the primary difference between the conception of motion that Aquinas
accepted and Newton's conception of motion?
Aquinas’ conception of motion was that there needed to be an outside force acting on it for it to be
moving and that that force had to be kept for the object to continue being in motion. Newton’s law of
motion says that an object’s acceleration will not change unless acted on by a force so it could remain in
uniform motion.
4. Explain why the "Birthday Fallacy" is a fallacy.
The “Birthday Fallacy” is considered to be a fallacy because the second premise does not necessarily
follow the first. While the first premise, every person has a birthday a day on which he or she was
born, is true, the second premise, there is a single day that is everybody’s birthday, does not mean that
everybody was born on the same day. The fact that there was a cause for the beginning of events does
not mean that it was the same cause for all the events.
5. What is the valid deductive logical form of a reductio ad absurdum argument?
If P is false, then A is true.
A is false.
P is true.
6. What is the difference between necessity and contingency?
Necessity means that an object exists in all possible worlds while contingency means that an object
doesn’t exist in all possible worlds.
7. What is a "necessary being"? Explain in terms of possible worlds.
A necessary being is something that exists in all possible worlds. It does not depend on anything for its
existence at any time from the past to the present to the future.
8. Why does Sober say that certainty is in the subjective realm while necessity is
Certainty is about how sure the person is of themselves about a particular statement and is as such
subjective. However, necessity has nothing to do with what a person thinks or believes and is therefore
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