Chapter 1 Independent work
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School
Toronto Metropolitan University *
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Course
105
Subject
Philosophy
Date
Apr 3, 2024
Type
Pages
3
Uploaded by GrandMoon11932
For each of the following, indicate whether it is the kind of sentence that falls within the
scope of this text—that is, is either true or false. If it is not, explain why not.
a. George Washington was the second president of the United States.
●
This sentence is false. George Washington was the first president of the United States.
It’s a historical fact, which makes it a statement that it either true or false
b. Turn in your homework on time or not at all.
●
This sentence is not a declarative statement; it is a command or instruction and does not
fall into the category of sentences evaluated as true or false in classical logic.
c. Two is the smallest prime number.
●
This sentence is true. Two is the smallest prime number because it is divisible only by 1
and itself.
d. George Bush senior was the immediate predecessor to George W. as president.
●
This sentence is true. George Bush senior (George H.W. Bush) was the immediate
predecessor to his son, George W. Bush, as President of the United States.
e. Sentence f below is true.
●
This sentence is not a declarative statement; it is a meta-statement referring to another
sentence, making it self-referential and not within the scope.
f. Never look a gift horse in the mouth.
●
This sentence is a proverb or aphorism, not a factual statement. It expresses advice and
does not fall into the category of sentences evaluated as true or false.
g. This sentence is false.
●
This sentence is paradoxical. If it is true, then it must be false, but if it is false, then it
must be true. It creates a logical paradox and does not have a determinate truth value.
2. For each of the following passages, specify what argument, if any, is being advanced.
Where the intent is probably not to express an argument, explain why this is so. Where
an argument is probably being expressed, restate the argument in standard form.
Analysis of Passages:
a. This passage presents an argument. The argument can be restated in standard form as
follows: Premises:
When Mike, Sharon, Sandy, and Vicky are all out of the office, no important decisions get
made.
Mike is off skiing.
Sharon is in Spokane.
Vicky is in Olympia.
Sandy is in Seattle.
Conclusion: 6. No decisions will be made today.
b. This passage does not express an argument. It provides a list of qualities or characteristics of
individuals but does not make any claim or inference.
c. This passage also does not express an argument. It provides information about the contents
of different drawers without making any claims or inferences.
3.
Which of the following are true and which are false? Explain your answers, giving examples
as appropriate.
a. False. An argument can be valid even if not all the premises are true. Validity is about the
logical relationship between premises and conclusions, not the truth of individual premises. For
example, the argument "All fish have wings; Nemo is a fish; therefore, Nemo has wings" is valid
(the conclusion follows logically from the premises), but one of the premises is false.
B. True. All sound arguments are indeed valid. A sound argument is a valid argument with all
true premises. Since a valid argument is one in which it's impossible for the premises to be true
and the conclusion false, having all true premises guarantees validity. However, While all sound
arguments are indeed valid, not all valid arguments are sound. Soundness calls for both validity
(the argument's structure is logically valid) and all proper premises. So, a valid argument may
want to have a false premise and still be valid, but it would not be sound. For instance, the
argument;”All pets can fly; my pet is a cat; therefore, my pet can fly”; is valid (the conclusion
follows logically from the premises), however it isn't sound because one of the premises is false.
c. True. If the conclusion of an argument is false, then the argument cannot be valid. Validity
requires that if all premises are true, the conclusion must be true as well. If the conclusion is
false, it means there exists at least one situation where the premises are true and the
conclusion is false, making the argument invalid.
d. True. This statement is a restatement of the definition of a valid argument. If all premises of
an argument are true, and the conclusion is true, then the argument is valid because it meets
the requirement that, if the premises are true, the conclusion must also be true for it to be
considered valid.
2. a. A valid argument with true premises and a true conclusion:
Argument: Premise 1: All cats are mammals. Premise 2: My pet is a cat. Conclusion: Therefore,
my pet is a mammal.
This argument is valid because the conclusion logically follows from the true premises. It's also
sound because all the premises are true, and the conclusion is true.
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