APHI 210 Introduction to Logic
Chapter 6 Proofs
Introduction (See also Quick Reference, Basic Rules of Proof, pp.158-159)
The aim of a PROOF SYSTEM is to demonstrate the validity of a given argument in such
a way as to show why the argument is valid
o A

1
Phi 210
Brad A-G
Lecture #4
In-class assignment on Tues; Quiz on Thurs. (transl., det.
status and det. validity or invalidity)
HW: pg. 57#s 3,5; pg. 66 sec I #s 2,3,5
Difference between statements and arguments:
Statements make claims; arguments aim to

PHI 210
Brad A-G
Agenda for 1st day
1. Go through syllabus
2. Brief intro to subject
For Tuesday:
i.
ii.
Please buy the book, Modern Logic, at the
University bookstore.
Homework: Please read Ch. 1, pgs. 3 11,
in Modern Logic.
Note 1: The first 2 chapters

Phi 210
Brad A-G
Lecture #3
Turn in HW.
The homework answers will be posted on Blackboard. If you have questions
about the hw, you should come to one of our office hours.
We are translating sentences of English into LSL (the language of
sentential logic)

28 October 2013
APHI 210
APHI 210 Introduction to Logic
Chapter 5 Formal Semantics
Introduction
Formal Semantics for SL and QL
o SEMANTICS: Related to meaning; formal in the sense that for a given language,
the semantics in question gives a mathematical

210
Homework #2
Brad A-G
#3 R(SR)
RS
R(SR)
TT
T
T
T
T
T
T
Tautology
#5 (F&G)H)(FvG)H)
FGH (F&G)H)(FvG)H)
TTT
T
TT
T
TT
T
T
TT
T
T
T
T
T
contingent
1
#2 (A&B)C, BD, C~D: ~A
Q: Is #2 valid or invalid?
ABCD (A&B)C, BD, C~D: ~A
T
T
T
For ~A to be false we req

210
Brad A-G
Homework assignment #1answers
2. If its Tuesday and its not Belgium, I am lost.
T: It is Tuesday
B: It is Belgium
L: Im lost
(T & ~B) L
6. The applicants may examine their dossiers only if they
have not already waived their right to do so and

210
Brad A-G
In-class assignment #1
For each of the problems, below, decide if they are a statement or an
argument. If a statement, after translating it into LSL, determine its
status, viz., as contingent, contradictory or tautologous. If an argument,
aft

210
Brad A-G
Today: Turn in HW; review; In-class assignment. Thurs: Quiz in which
you will be asked to do the following: i) translate; ii) if a statement,
determine the status; if an argument, determine the validity or
invalidit

210
BRADAG
HW:pgs.9899,#s4,12,13;p.108,#s6,9,12
WEVENOWMOVEDONTOPROOFS!
Recall: We are now moving from semantic consequence, |=, to logical
consequence,|.
Recalltherelationshipbetweenlogicalandsemanticconsequence,forany
argument,P1,Pn:C,
(A)IfP1,Pn|=Cthen

210
BRADAG
Turn in HW (Nota bene (note well), HW answers are posted on Blackboard)
Notes: There will be a review session in class on Thursday that will be led by Kali,
as I will be away giving a talk. There will be an in-class assignment on Tuesday
and a

APHI 210 Introduction to Logic
Chapter 1 What is Logic?
Introduction
LOGIC is the business of evaluating arguments
A logical argument is structured to give someone reason to believe some conclusion
(1)
(2)
()
It is raining heavily.
If you do not take an

APHI 210 Introduction to Logic
Chapter 4 Quantified Logic
Introduction
Introduction to Quantified Logic (QL)
o So-called because it allows for logical operators for expressions of quantity (all,
every, some, or none), called quantifiers
Sometimes also r

APHI 210 Introduction to Logic
Chapter 2 Sentential Logic
Introduction
SENTENTIAL LOGIC (SL) is a formal language that represents entire sentences
2.1
Sentence Letters
In SL, capital letters are used to represent basic sentences, these are known as
SENT

APHI 210 Introduction to Logic
Chapter 3 Truth Tables
Introduction
TRUTH TABLES: A method of evaluating both sentences and arguments of SL
3.1
Truth-Functional Connectives
TRUTH-FUNCTIONAL CONNECTIVES: A connective of a compound formula is truthfunction

‘ angwmwmnxvmm Mammal n W” m-
.
ii
2i
What Is Logic?
1 Arguments
Symbolic logic is usually described as the study of the difference between valid
and invalid arguments, so we begin with an explanation of this terminology. An
argument is a piece of