Philosophy 12A, Lecture 5, Notes
Scribe: Simon Mo
Contents
Finish Handout
1
Logical Concept in TFL
2
Tautologies + Contradictions
Joint Truth Table
2
Consistency and Inconsistency
Entailment
Equivalence
2
3
3
4
Finish Handout
Conclusion There will be a lo
104
Symbolic Logic Study Guide: Practice Tests and Quizzes
Medium
Large
Medium
Small
Large
Small
Small
Small
3.4. Solutions to Tests
3.4.1. Test One Solutions
Problem 1.
(A v ( B C) ) ( B v (A v B)
A (B C) B (A v B)
A B C B A B
A B C B
(C B) (B A)
(
02/26/2017
LESSON 1: logical consequence, valid arguments and sound
arguments.
1. What does it mean when we say that sentence S is a logical
consequence of sentence T?
logical consequence: S is a logical consequence of T if, whenever T
is true, S must be
Translate the following sentences into FOL:
1. c is to the right of d only if b is to the right of c and left of e.
2. If e is a tetrahedron, then its to the right of b if and only if it is also in front
of b.
3. If b is a dodecahedron, then if it isnt in
announcements
syntax and truth tables for PL
on bCourses as of yesterday:
chapter 2: the syntax of propositional logic
1
2
announcements
last week
on bCourses as of yesterday:
chapter 2: the syntax of propositional logic
handout 1: truth tables for the co
Announcements
Validity
Reminder: first problem set due Friday
1
2
Announcements
Announcements
First set of course notes now
available on bCourses.
My office hours will generally be Wednesdays 3-5.
But this week they will be Wed 1-2 and Thurs 4-5.
3
4
Logi
Announcements
Validity
(and some other basic concepts)
Reminder: first problem set due today at 5pm
1
2
Announcements
Announcements
Next problem set will be posted
later this afternoon
Dont email me problem sets.
3
4
Logic is mostly about validity.
5
Val
welcome to
Introduction to Logic
We will be studying arguments from an abstract
point of view. The primary aim is to learn is how to
distinguish valid arguments from invalid arguments.
The aim here is to develop the skill of
deductive reasoning.
We will b
2.3. THE DISTINCTION BETWEEN USE AND MENTION
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2.3 The distinction between use and mention
Here is something so obvious that it might not even seem worth mentioning:
When you use language to communicate, you are not necessarily talking about language.
Fo
(P Q)S)(P Q)S)
logical equivalence
Suppose P is true and Q is false.
What is the truth value of the whole?
A = True
C = not determined
, , , ,
1
2
(QP)(PP)R)
(QP)(PP)P)
Suppose P is true and Q is false.
What is the truth value of the whole?
A = True
B =
interpretations, valuations
1
2
If a set of wffs is consistent, then every pair
within the set is consistent.
True or False?
3
Last time: consistency
, , , ,
If a set of wffs is inconsistent, then every
pair within the set is inconsistent.
True or False?
semantics, truth trees
1
Last time: we upgraded our definitions of various basic
notions like validity, consistency, and logical equivalence.
, , , ,
2
define consistency in terms of validity?
An interpretation for PL is a function I that takes each
sente
question
Overall, how difficult did you find the
first quiz?
consistency, interpretations, valuations
A - really easy
B - some effort required, but not
difficult
C - moderately difficult
D - really difficult
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2
Dont forget to read chapter 3 in particular