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Chapter 1

PHI 1101 Chapter Notes - Chapter 1: Principle Of Bivalence, Logical Form, Enthymeme

Course Code
PHI 1101
Laura Byrne

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๎€Summary: logical strength and inductive and deductive arguments
๎€Logical Strength and Weakness
๎€Inductive arguments:
๎€Inductive Strength and Weakness
๎€Deductive arguments
๎€Deductive Validity and invalidity
๎€Deductively Valid Argument Forms
๎€1. Disjunctive Syllogism
๎€A disjunction is a complex proposition that has the form either p or q
๎€Either you had white milk or you had chocolate milk
๎€Either p or q (*note p and q are simple propositions that are combined
to form the complex proposition either p or q
๎€p and q are the disjuncts (simple propositions) of the disjunction
(complex proposition) either p or q
๎€example 1:
๎€Either you had white milk or you had chocolate milk
๎€You did not have white milk
๎€Therefore, you had chocolate milk
๎€Example 2:
๎€One is either a cat person or a dog person
๎€Socrates is not a dog person
๎€Therefore, Socrates is a cat person
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๎€Disjunctive Syllogism form
๎€Either p or q.
๎€Therefore, q.
๎€2. Reductio ad Absurdum
๎€One way to show that a proposition is false is to show that a
contradiction follows from it
๎€Socrates is an Olympian god๏ƒ show this is false
๎€(Note when we write out arguments in standard form, we can, for the
sake of clarity and convenience, label and number the premise(s) and
๎€P1: Socrates is a man
๎€P2: All men are mortal
๎€C: Socrates is a man
๎€Demonstrate that the proposition โ€œSocrates is an Olympian Godโ€ is
๎€Assume P1: Socrates is an Olympian God
๎€P2: Socrates died in 399 BC
๎€C1: Therefore, Socrates is immortal (by P2) and mortal (by P3).
๎€C2: Therefore, the statement โ€œSocrates is an Olympian Godโ€™โ€™ is false.
(By Reductio ad Absurdum)
๎€Explanation: the law of Non-Contradiction: contradictions cannot be
true. Therefore, any proposition that implies a contradiction cannot be true
๎€Now we can take this one step farther: if one proposition is false, its
negation must be true
๎€We know this by the law of the excluded Middle /bivalence(in classical
logical, true and false are your only values, there is no value in between)
๎€Therefore, we can demonstrate a certain proposition to be true, by
assuming it to be false, or assuming its negation and then deriving a
๎€Socrates is not an Olympian God (~Socrates is an Olympian
God)๏ƒ prove this is true
๎€Assuming its negation:
๎€It is not the case that Socrates is not an Olympian God
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