PL2003Symbolic Logic
Assignment #1key.
1a)
P
P
P'
(P P' )
1b) (P (Q R' ) S)  not a wff.
1c) (P' )  not a wff.
1d)
Q
P'
Q
(P' Q)
R'
(P' Q) R' )
1e) (P' )  not a wff.
2a)
P' T
QF
RT
(P' Q) F
R F
(P
PLUY 2004 Symbolic Logic
Assignment #1. Due Thurs Feb 4.
1. Indicate which of the following strings of symbols qualify as wffs in PL. For those that
qualify, draw their construction trees.
(a)
(b)
(c
Chapter 16: Introducing PL Trees
Ex1. (P Q), (P' Q'), (P' Q') R
Truth table would contain 27 = 128 rows!
Tautologically invalid!
R nowhere occurs in premises.
Premises are not taut. inconsistent.
Chapter 14: The Language of PLC
Motivation:
Ex1. (1) If Jack bet on the Cardinals, then Jack lost his money.
(2) Jack did bet on the Cardinals.
VALID
(3) So Jack lost his money.
(1) If Jack bet on the
Gdel's 1st Incompleteness Theorem
Gdel's 1st Incompleteness Theorem.
Let N be a firstorder formal theory of arithmetic that is recursively
axiomatizable. If N is consistent, then it is negation incom
PL2004 Symbolic Logic
Assignment #2. Due Thus Feb 11.
1. For each of the pairs of wffs below, construct a truth table that includes them and indicate
whether or not they are truthfunctionally equival
Chapter 36: Functions
Motivation: Ultimately, to formulate simple arithmetic as a formal theory.
Def. 1. A function f : D R is a map from one set of objects D to another
R such that one or more objec
Chapter 34: Definite Descriptions
A definite description is a phrase that doesn't contain
a name and that aims to designate a particular thing.
Ex.
"The Queen of England"
"The smallest prime number"
"
Chapter 32: Identity
Let R be a twoplace relation and suppose a, b, c are objects that stand in it.
Def 1. R is transitive just when, if a has
R to b, and b has R to c, then a has R to c.
Exs.
is
hea
Chapter 30: Soundness and Completeness for QL Trees
Soundness of QL Trees
If a QL argument is not qvalid, then the corresponding QL tree will never close.
Let:
"QL" mean "QL treeentails"
Let:
"QL" m
Chapter 29: QL Trees
(a)
A

A
Add A to each open path containing A.
Check it off
(b)
(A B)

A
B
(c)
(A B)

A
B
Add A, B to each open path containing (A B).
Check it off
(d)
(A B)

A
B
Add A, B
Chapter 27: QValuations
The vocabulary V of a set of QL wffs is the set of
constants and predicates that appear in those wffs.
A "qvaluation" for a set of wffs with vocabulary V does three things:
1
Chapter 28: QValidity
In PL:
The PL wffs A1, ., An tautologically entail the PL wff C just when
there is no PL valuation that makes A1, ., An true and C false.
An argument in PL is tautologically val
Chapter 17: Rules for PL Trees
Unpacking Rules:
(a)
A

A
Add A to each open path containing A.
(b)
(A B)

A
B
(c)
(A B)

A
B
(d)
(A B)
Add A, B to each open path containing (A B).
A
(e)
Add A, B to
Chapter 25: Introducting QL Trees (Informally)
Recall the tree method:
To show that A1, ., An C is tautologically valid, show that A1, ., An, C is
tautologically inconsistent.
How will this work for Q
Chapters 23, 24: QL Translations
Let:
"F"
means
"is wise"
Domain = people
xFx
"Everyone is unwise."
xFx
"Not everyone is unwise."
or
"Someone is wise."
xFx
vC(.v.v.) is true iff vC(.v.v.) is true.
xFx
Chapter 18: PLC Trees
Further PLC Rules:
(f)
(A B)
A
B
(g)
(A B)

A
B
(h)
(A B)
A
B
(e)
A
B
(A B)
A
B
A
B
Add a fork with A, B as separate branches to each open
path containing (A B).
Add A, B to eac
Chapter 26: The Syntax of QL
Alphabet:
a, b, c, m, n, o, ., ck
individual constants (k 0)
w, x, y, z, ., vk
individual variables (k 0)
A, B, C, ., P0k
0place predicates (propositional atoms) (k 0)
F,
Chapters 21, 22: The Language of QL ("Quantifier Logic")
Motivation:
(1)
Fido is a cat.
(2)
All cats are scary.
(3)
Fido is scary.
In PL:
Valid argument!
Let P = Fido is a cat.
Q = All cats are scary.
PLUY 2004 Symbolic Logic
Prof: Jonathan Bain
Ofce: LC124
Spring 2016
T/Th 8:3010:20
Hours: Weds 12
RH425
faculty.poly.edu/~jbain/logic
I. Description
This is an introduction to the methods and appl
Chapter 8: The Syntax of PL
I. Syntactic Rules for PL
A. Alphabet (13 symbols)
(1) P Q R S '
simple propositions
(2)
connectives
(3) ( )
punctuation
(4) ,
additional punctuation
B. Grammar: What cou
Chapters 12, 13: Tautologies and Tautological Entailment
A wff of PL is a tautology if it takes the value true on every valuation of its atoms.
A wff of PL is a contradiction if it takes the
value fal
Chapter 11: Truth Functions
A way of forming a complex sentence out of one or more constituent sentences
is truthfunctional if fixing the truthvalues of the constituent sentences is
always enough to
17. Quantum Gravity and Spacetime
Theory of Matter
Relativistic Quantum Field Theories (RQFTs)
Quantum Electrodynamics (1940's)
RQFT of electromagnetic force.
Matter fields: leptons, quarks.
Force
PLUY 2274 Space and Spacetime
Paper #1. Due Tues Feb 23.
Instructions:
(a) Choose one of the following topics and respond to it in an essay of no less than 5 pages (not
including title page and bibli
PL2273  Space and Spacetime
Study questions on Einstein (Huggett, Chapter 14)
The Problem of Space, Ether, and the Field in Physics
1. What are two ways of regarding concepts, according to Einstein?
04. Zeno (5th century B.C.)
Recall: Euclid's theory of space:
! Is it consistent?
! Is it true of the actual world?
General Form of Zeno's Critique (reductio ad absurdum):
! The following argument i
PL2273  Space and Spacetime
Study questions on Poincar (Huggett, Chapter 13)
Space and Geometry
1. Why does Poincar claim that, if there were no solid bodies in nature, there would be no geometry?
2.
PL2273  Space and Spacetime
Study questions on Kant  Part 1 (Huggett, Chapter 11)
Concerning the Ultimate Foundation of the Differentiation of Regions of Space
1. According to Kant, what does a regi
PL2273  Space and Spacetime
Study questions on Leibniz and Clarke (The LeibnizClarke Correspondence  Huggett, Chapter 8)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
What is Leibnizs Principle of Suf