Arguments and Their Structure
Solutions
Week 2
For the following exercises, identify the component statements:
1. If all else fails, go with your gut.
All else fails.
2. Unless you pull it together, Im leaving and Im taking the dog with me!
You pull it
Arguments and Their Structure
Week 2
For the following exercises, identify the component statements:
1. If all else fails, go with your gut.
2. Unless you pull it together, Im leaving and Im taking the dog with me!
3. If at first you dont succeed, try aga
PHILOSOPHY 120 Q1
Problem from Class of 14 November
At the end of class, I was trying to prove the following problem, but in the end
had an issue with having to do a I, but having the variable not being truly
arbitrary. Heres a better proof of that proble
INTRODUCTION TO
PHILOSOPHY
G.E. Moore and Weak Scepticism
Announcements
2
1. Reading for Tuesday: Jonathan Vogel, Cartesian
Skepticism and Inference to Best Explanation.
2. Ive posted a Tips sheet for writing a
philosophy paper on Canvas.
Your
TA will be
Below is a sample midterm from a previous class. I post it so that
you can get a sense of the format and the instructions, and
perhaps be motivated to study. The answers are at the bottom.
But please dont think that if you simply memorize the answers,
you
Criteria to determine whether an argument is good
1) Are the premises true?
2) Are the premises providing strong logical support for the conclusion?
Deductive validity states an argument is good because it answers 2) with the strongest possible
support
Ha
Weve seen that even if a sentence is not a statement, it can contain a statement, in which case we
call the contained statement a component statement
Component Statement
A series of words in a statement is a component statement if substituting it by any
Remember the recipe for determining the form of an argument
Identify all the premise and inference indicators
Identify all the logical terms such as
And, or, ifthen, if and only if, not, every, all, some, no, none, is/are, etc
In statement logic, we f
Modus Ponens (MP)
pq,pq
Modus Tollens (MT)
p q, q p
How to reason about the statement operator &
When we accept / affirm a conjunction such as A & B, we accept that both A is true and B is true
A and B are known as conjuncts
When we deny a conjunctio
P unless Q
is the same as
P if not Q
Conditional Proof (CP)
From a derivation of Q from the supposition of P, infer P Q.
When you do a deduction that contains suppositions, you can never appeal to something that is
indented to the right more than the st
The definition of wf is a recursive definition
A Recursive Definition contains three things:
Base case
Accepting axiomatically that some things satisfy the definition.
Recursive rules
Rules that you can apply to generate more things satisfying the def
Any argument with logically inconsistent premises is formally valid
P. It is not the case that P. Therefore Q
By definition, this argument is formally valid if and only if the negation of the conclusion and the
premises are logically inconsistent.
By de
DONT NEED TO KNOW
Section 7.3: Supposition in natural arguments.
Section 9.2: Natural dilemmas.
Section 10.2: Natural reductio arguments.
Subsection 11.1.1: Rules of inference and equivalence rules.
Subsection 12.2.2. Axioms and the propositional calculus
When we write Px, we read it as x is P or x has property P
Lets make notation Px clear
When we write Px, P is called the predicate
X is the argument of the predicate
We will also call singular terms individual names on occasion.
For now, we will count t
PHILOSOPHY 100W:
INTRODUCTION TO
PHILOSOPHY
Introduction: Scepticism
Announcements
2
1. Reading for Tuesday: Descartes, Second
Meditation
2. Tutorials begin next week
3. Accessing audio recordings:
When
you click the Open in a New Tab link, click on
the
INTRODUCTION TO
PHILOSOPHY
Descartes and G.E. Moore on Scepticism
Announcements
2
1. No new reading for Thursday.
Descartes: Third Meditation
3
Descartess Cosmological Argument
1. I have an idea of an infinite and perfect God.
2. There must be as much rea
INTRODUCTION TO
PHILOSOPHY
Vogel on Weak Scepticism
Announcements
2
1. No new reading for Thursday.
2. I must leave immediately after lecture.
Knowledge and Reality
3
Do I know
right now
that I am not
a brain in a
vat?
Descartes and Moore respond
to the S
PHILOSOPHY 120
Stylistic Variants of conjunctions, disjunctions, equivalences
This handout is a companion piece to the one about stylistic variants of negations and
conditionals. The warnings given there also apply here: although the phrases I will give a
PHILOSOPHY 120 Q1
(Pelletier, Fall 2013)
MIDTERM EXAM
Directions: Answer all questions, putting your answers in the answer book
provided. You do not need to answer questions in the order they are asked, but
please label your work so that I know what quest
Answers to Phil 120Q1 Midterm (Fall 2013)
Je Pelletier
(First note that there are numerous correct ways to answer any of the questions on the exam. I give here just one possibility for each of the questions. . . except for Part III, where in two of the pr
Be aware of the importance of sequence searching and sequence
alignment
Appreciate the difference between sequence "similarity" and
"homology"
Be familiar with some common algorithms and scoring schemes used
in sequence alignment and sequence searching
U
Some More Hints for Translating into Predicate Logic: Pt. II
(Phil. 120, Pelletier)
Some stylistic variants of (x)Fx: there is an F, there are Fs, Fs exist, at least one thing is F,
some Fs, an F,
Some stylistic variants of (x)Fx: everything is F, every
Some Hints for Translating into Predicate Logic: I
(Phil 120, Pelletier)
You should read very carefully Sections 7.3 and 7.4 of The Logic Book, which contain a
discussion of some of the ins and outs of translation. In this handout I will just mention some
Still More Hints for Translating into Predicate Logic: Pt. III
(Phil. 120, Pelletier)
Indefinite Articles: In English the indefinite article is a (or an). Except for special uses such
as generics (like A snake is a reptile these generic uses most generall
PHILOSOPHY 120 Q1
(Pelletier, Fall 2013)
Review Session
27 November 2013
I. Construct derivations in PL+ for the following.
1. cfw_ xy(F xy F yx
F xx
2. cfw_ x(P x & y(Dy Lxy), x(U x Dx)
x(P x & (U y Lxy)
3. cfw_ x(F x Gx)x(Ix & Hx), x(Ix Hx)
4. cfw_ x
PHILOSOPHY 120
Stylistic Variants of negations and conditionals
This is a reminder about different ways to express our English connectives in symbolism.
There is nothing new in here, but you might use it as a way to jog your memory from your old
logic cla
Syllogistic Logic
15.1 Category Logic
15.1.1 - Aristotle's logic
We symbolize now using capital letters to stand for categories of things, not statements
o
In an argument, each of the premises and the conclusion is a categorical statement
Categorical stat
Philosophy 110
Introduction to Logic and Reasoning
Nicolas Fillion
Assistant Professor
Simon Fraser University
Lecture 6
More on Substitution Instances
First Rule of Inference and Deductions
1
More on Substitution Instances
2
First Rule of Inference and D
Validity and Argument Form Solutions
Week 3
1
Short Answer
1. We ask (i) Are the premises true? and (ii) Do the premises offer sufficient support for the conclusion? (for our purposesdeductive logicwe
ask whether the truth of the premises necessitates the
Validity and Argument Form
Week 3
1
Short Answer Questions
1. What two questions do we ask in order to determine whether a given
argument is good?
2. What does it mean to call an argument valid (in the general sense)?
3. Can an argument be true? Why or wh