# PHIL 210- Final Exam Guide - Comprehensive Notes for the exam ( 37 pages long!)

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PHIL 210

FINAL EXAM

STUDY GUIDE

Lecture 1: Deductive Arguments

Complex Statements

• Complex conjunctive statements can have claims that are true for many

situations/people.

• If any of the claims are false, then the entire statement is false

• Many ordinary sentences work like conjunctions of simpler claims

Compound Statements

• Conjunctive statement: a compound statement that contains two sub-statements, or

conjuncts, which is joined by the word “and” or “as well as”, conjunctions are true only

when all the conjuncts are true

• Disjunctive statement: a compound statement that contains two sub-statements, or

disjuncts, joined by words “or” or “alternatively”. A disjunction is true if and only if at

least one of the disjuncts are true

o Disjunctions (“or”) can be either inclusive or exclusive.

▪ if it is inclusive, at least one of the disjuncts are true. An inclusive

disjunction is when both disjuncts are true

▪ if it is exclusive, only one of the disjuncts are true.

▪ Typically, or should be used inclusively

• It is easier for a disjunctive statement to be true than for a conjunctive statement. A

disjunctive statement is true as long as one disjunct is true, whereas a conjunctive

statement requires all of its conjuncts to be true.

o Disjunctive statement

▪ 1. P or Q Either I love comedy, or I love horror

▪ 2. Not Q I don’t love horror

▪ 3. Therefore P I love comedy

• The premises of the valid argument are true, so the argument is

sound

o Constructive dilemma

▪ 1. P or Q Either I love comedy, or I love horror

▪ 2. If P then R If I love comedy, then I watch Bob’s Burgers everyday

▪ 3. If Q then S If I love horror, then I get excited for Halloween

▪ 4. Therefore, R or S either I watch BB everyday, or I get excited for

Halloween

Two types of conditional statements that are valid disjunctive argument forms

• Basic conditional

o If P then Q where P is the antecedent and Q is the consequent

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o The conditional is false when P is true but Q is false, and is true in all other

cases

o If I love Halloween (P) then I watch scary movies everyday (Q)

• Subjunctive conditional

o If P were to be true, then Q would be true

o You cannot assume that

▪ If P then Q,

▪ If Q then R

▪ Therefore, if P then R

• Modus ponens

o 1. If P then Q

o 2. P

o 3. Therefore Q

▪ 1. Either foxes are mammals, or rabbits are birds

▪ 2. If foxes are mammals, then vixens lactate

▪ 3. Rabbits are not birds

▪ 4. Therefore, foxes are mammals

▪ 5. Therefore, vixens lactate.

• Lines 1 and 3 imply line 4 by disjunctive statement, and 2 and 4

imply line 5 by modus ponens.

• Modus Tollens

o 1. If P then Q

o 2. Not Q

o 3. Therefore, not P

o To say that this is a valid structure is to say that any choices of P and Q that

make both 1. And 2. Come out true are guaranteed to make 3. Come out true

as well. There is no way for the conclusion to be false if the premise is true.

o If P, Canada is a republic, then Q, Canada has no monarch

o Then Not Q, it is not the case that Canada has no monarch

o Therefore, not P is true as well, so Canada is not a republic.

• Invalid conditional forms get their names from what the second premise does

• Denying the antecedent

o 1. If P then Q

o 2. Not P

o 3. Therefore, not Q

• Affirming the consequent

o 1. If P then Q

o 2. Q

o 3. Therefore, P

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