The Republic and Protagoras both written by Plato, examines the topics of justice, soul, virtue, as well
as the relationship between the good and pleasure, and the weakness of the will through written dialogues
expressing his own insightful philosophical
DERIVATIONS: NATURAL DEDUCTION
Part 1
3.2 E1
Which inference rule justifies the following arguments? (mp, mt, dn or none)
a)
~R P
~R
P
b)
P ~Q
Q
~P
c)
NONE!
DN cannot be
used on a
sentential part
MP
e)
~S T
ST
~(~P Q)
PQ
f)
P (P ~P)
P
P ~P
NONE!
First y
UNIT 2: SYMBOLIZATION EXERCISES 1
Negation and Conditional
Symbolize each of the following sentences using the abbreviation scheme provided:
P: The Toronto Maple Leafs win.
Q: The Washington Capitals win.
R: The Vancouver Canucks win.
S: The Edmonton Oile
`
UNIT 1: REASON AND ARGUMENT
Answers to exercises
1.4 E 1
Some students will undoubtedly pass this course. Hence it is clear that some students in this
class will do the exercises, since nobody passes who doesnt do at least some of the exercises.
Some st
UNIT 2
SENTENTIAL LOGIC: SYMBOLIZATION
Answers to Exercises
2.4 E1
UNDERSTANDING THE MATERIAL CONDITIONAL
A LITTLE LOGIC PUZZLE: Discussion & Answers
Every card has a number on one side and a letter on the other. Suppose there is a rule:
If one side of a
PHL245 Unit 3: Introduction to Derivations in SL
I.
Arguments and Symbolic Form
So far our purpose has been to investigate whether or not a given argument is valid. Last week we
discussed two strategies for this:
a) Try and analyze the ways in which all o
Last Name:
Student Number:
UNIVERSITY OF TORONTO
Faculty of Arts and Science
AUGUST 2012 EXAMINATIONS
PHL 245H1Y
Duration - 3 hours
Examination Aid: Sheet with rules (provided)
Last Name _
First Name _
Student Number_
Answer all questions on the exam pape
DERIVATIONS
NATURAL DEDUCTION
Part 2 Solutions
3.11 E1
Which inference rule if any justifies the following arguments?
(S, ADJ, ADD, MTP, BC, CB or none)
a) R (P ~S)
(P ~S) R
_
(P ~S) R
b) (P Q) (S T)
_
ST
c) (P (S~Q)
_
~P (P
(S~Q)
sl
CD
e) Q ~(S P)
(S P)
UNIT 6
DERIVATIONS FOR PREDICATE LOGIC
6.1 Extending the Derivation System
Now that weve learnt how to symbolize sentences using predicates, operations and quantifiers, we need to
extend our derivation system to handle these new features.
New Derivation R
DEPARTMENT OF PHEOSOPHY
University of Toronto
PHI 245F: Modern Symbolic Logie '
. Assignment 1
Translation and Symbolization
Reading: Kalish, Montague, and Mar, chapter I, sectioris 1—2.
I. For each of the following expressions, state whether or not it is
University of Toronto
PHl. 2451: Modern Symbolic “Logic ' - '
Assignment 3 - - A
Translation and Symbolization
Reading: KMM,ch_ap. II, secs, 1-3.
',From each of the. following sentences obtain a symbolic sentence in the’official sense by
restoring parent
PHL 245 Assignment 1
Department of Philosophy,
University of Toronto Mississauga
Due: 11:59pm, October 5th, 2016
Task
Symbolize the following sentences. Submit electronically through the Logic2010 database. Submission details will be posted on Blackboard
PHL245: Modern Symbolic Logic
M: 1-2pm W: 1-3pm
Room: IB120
Department of Philosophy,
University of Toronto Mississauga
September December 2016
Instructor: Kevin Kuhl
E-Mail: [email protected]
Office: Academic Annex 217
Office Hours: Wednesdays 10:30
DEPARTMENT OF PHILOSOPHY
University of Toronto
PHI. 245: Modern Symbolic Logic
Assignment 2
Derivability and Validity
Reading: KMM, chap. I, secs. 35.
Show by constructing annotated derivations that the following arguments are valid.
1. (RaS)-+Q-R~>(~S->-
PHL245: Chapter 2, Section 8-11
Section 8 Truth-value analysis of sentences
-a symbolic sentence, like an English sentence, may have one of two truth values, truth (T) or falsehood
(F) but not both
Truth-value rules
(1) A sentence letter has the value cor
ERINDALE COLLEGE
University of Toronto
PHL 245 : hodern Symbolic Logic
Assignment 5
Abbreviated Derivations
I. Show by constructing derivations that the following arguments are valid;
1. pus/L5) . (o-+P)xxcmsre). RVQ 7
2 PVU+(~Q+~HAT) . 9(ovs) '~(T.A~S)V~
DEPARTMENT OF PHILOSOPHY
University of Toronto
PHI. 245 Modern Symbolic Logic
Assignment 8
Derivations
Reading: KMM, chap. 111, secs. 5-11.
1. Construct a dewitaon for each of the following arguments.
1. Afox'A [Gx v mph) . Axx A Hat-x) . Ax(Kx>Hx)
. Ax(F
Chapter 2 section 7-8
How to derive conjunctions, disjunctions, conditionals p. 83
(1) To derive a sentence PvQX
derive first PX
and QX
(2) To derive PQ where P is not a disjunction, use conditional derivation
(3) To derive a conjunction, derive first bot
ERINDALE COLLEGE
University of Toronto
PHL 2&5 : Modern Symbolic Logic
Assignment 4
Derivations
Reading: KMM, chap. II, secs. 34.
I. Show by constructing derivations that the following arguemts are valid.
ax u: a h) a: k1
P + R _. Q + P v R '-. R + P A Q
ERJNDALE COLLEGE
University of Toronto
PHI. 2453 Modern Symbolic Logic
Assignment #6 '
Truth-Value Analysis
Reading: Kalish and Montague, pp.87105.
I. It happens that a set of symbolic sentences is truth-functionally inconsistent if and only if
a truth-fu
ERMALE COLLEGE
University of Toronto
PHL 245s: ' Modern Symbolic Logic
Assignment 7
Translation and Symbolization
Reading: KMM, chap. 111, secs. 1-4.
For each of the following formulas, construct a grammatical tree and describe its granunaiical
structure.
Critical Reasoning Week 3: Arguments and
Argument Analysis More Precisely, Deductive
Arguments
Kevin Kuhl
Department of Philosophy
University of Toronto Mississauga
Announcements
Assignment 1 due next week, link is now available on
Blackboard while you c
UNIT 7
INTERPRETATIONS AND MODELS: SEMANTICS FOR PREDICATE LOGIC
7.3 EG1
a)
On the interpretations below, is the following true or false?
~Fa x(Fx G(xa)
Universe: positive integers
F1: a is a multiple of 4.
a0: 2
G2: a is divisible by b
The first conjunct