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Midterm

PHI 1101 Study Guide - Midterm Guide: Co-Premise, Modus Ponens, Deductive Reasoning


Department
Philosophy
Course Code
PHI 1101
Professor
Laura Byrne
Study Guide
Midterm

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Course Content/Knowledge
Statement
a sentence used to make a claim. Statements are capable of being either true
or false.
Commands, questions and expressions of volition are not statements because
they are not sentences capable of being true or false.
Example
o Socrates is a man.
The Law of Contradiction
states that it is impossible for both a proposition and its negation to be true
at the same time
Example
o Lassie is a dog and Lassie is not a dog contradict one another. Both
statements cannot be true
The Law of the Excluded Middle/Bivalence
states that every proposition must be either true or false. In other words,
any middle position between truth and falsity is excluded.
It follows from this law that for any given proposition and its negation, one
must be true and the other one false. If a proposition is true, its negation
must be false. If a proposition is false, its negation must be true.
Examples
o If the statement Lassie is a dog is true, then its negation Lassie is not
a dog is false
o If the statement Socrates is a man is false, then its negation Socrates
is not a man is true
Set
A group of statements. Sets are capable of being consistent or inconsistent.
A set of propositions is consistent if and only if it is possible for all of the
sentences in that set to be true at the same time. In another words, a set of
propositions is consistent if these propositions do not contradict one
another.
Sets can be false and consistent
Examples
o The set Lassie is a doog and Lassie barks is consistent
o The set  Socrates is a man and Socrates is a woman is inconsistent
because the two statements contradict one another
o The set Socrates is immortal and Socrates is an Olympian god is
inconsistent
Inference
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a logical relationship between two thoughts that occurs when one thought
supports or justifies or makes it reasonable to believe another.
When we infer q from p we move from p to q because we believe that p
supports, justifies or makes it reasonable to believe q is true
Inference indicators: Since, thus, implies, consequently, because, it follows
that, given that
Examples
o Ollie was out all night and Ollie is sleeping is simply a set. No
inference is made.
o Ollie is sleeping because Ollie was out all night. An inference is made
between the two thoughts.
Argument
a set of statements that claims that one or more of those statements, called
the premises, support, or justify, or make it reasonable to believe that
another of those statements, the conclusion, is true.
Example
o Socrates is a man. (premise one) All men are mortal. (premise two)
Therefore, Socrates is mortal (conclusion)
Logical Strength
An argument has logical strength when the premises, if true, actually provide
support for, justify, or make it reasonable to believe the conclusion is true.
Example of Logically Strong Argument Breakdown
A = B
X = A
X = B
Examples
o Logically Weak Argument - Sally has brown hair. Therefore, Sally is a
poor student.
o Logically Strong Argument - Socrates is a man. All men are mortal.
Therefore, Socrates is mortal.
Feature One Logical strength is independent of the truth of its premises.
Feature Two There are varying degrees of logical strength.
Sound Argument
An argument is sound if is logically strong and it has true premises.
Inductive Argument
In virtue of the logical form of an inductive argument, the truth of its
premises makes the truth of its conclusion probable. Probability is a matter
of degree as well too.
The logical strength and weakness of inductive arguments is called inductive
strength and inductive weakness.
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o When inductive arguments are logically strong, they are inductively
strong.
o When inductive arguments are logically weak, they are inductively
weak.
Examples
o I liked Sense and Sensibility. I liked Pride and Prejudice. Therefore, I
will like Persuasion. (probable but not guaranteed)
o I got a good mark in Philosophy in high school. I read the text book. I
attended all the lectures. Therefore, I will get a good mark in PHI
1101. (probable but not guaranteed)
Deductive Argument
In virtue of the logical form of a deductive argument, the truth of its premises
guarantees the truth of its conclusion.
The logical strength and weakness of deductive arguments is called
deductive validity and deductive invalidity.
o When deductive arguments are logically strong, they are deductively
valid.
o When deductive arguments are logically weak, they are deductively
invalid.
An argument is said to be deductively valid if and only if whenever all the
premises are true, the conclusion must also be true. A deductively valid
argument is one that can never have, at one and the same time, true premises
and a false conclusion.
Example
o Socrates is a man. All men are mortal. Therefore, Socrates is mortal.
Enthymeme
an argument in which the conclusion or one of the premises has been left
unstated
Examples
o Premise Unstated: (All men are mortal.) Socrates is a man. Therefore,
Socrates is mortal.
o Conclusion Unstated: All men are mortal. Socrates is a man.
(Therefore, Socrates is mortal.)
Sorites
a connected series of arguments in which the conclusion of one argument
also serves as a premise in another argument
Example
o P1: All men are mortal. P2: Socrates is a man. C1 and P1: Therefore,
Socrates is mortal. P2: Mortal men are not Olympian Gods. C2:
Therefore, Socrates is not an Olympian God.
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