4 INDEPENDENT PROBLEMS WITH AN
ARGUMENT
1. One or more premises is false.
2. The claim is false: the truth of the premises does not
provide the support claimed for the conclusion.
3. The premises are irrelevant to the truth of the
conclusion.
4. The suppo
An argument is DEDUCTIVELY VALID if it has no
counterexample.
That is: it is not possible for the premises to be true and
the conclusion false. That is: any situation in which the
premises are true will also make the conclusion true.
An argument can be de
Today, we begin Ch.3: Propositional Logic
From here on out, we restrict our attention to deductive
logic.
We restrict our attention to a certain class of deductive
arguments: arguments in "propositional logic."
By the end of this chapter:
We will have a
FIVE IMPORTANT OPERATORS
A sentential operator is truth-functional if the truth or
falsity of a compound sentence containing that operator is
completely determined by the truth or falsity of its
component sentences.
Conjunction:
Bo Jackson played baseball
LPS/PHIL 29
Heis
TRANSLATING CAN BE TRICKY!
7 hints for working through rough spots
1.
q if p is translated: p q. Not: q p
With the conditional (), ORDER MATTERS!
An example:
You will do WELL if you STUDY
is translated:
S W
Chapter 3, Lecture 3
Page 1 of
TRANSLATING MULTIPLY-COMPOUND
SENTENCES
When translating an English sentence with more than one
truth-functional operator, always go from the outside
in: translate one operator at a time and start with the
major operator.
If Miami beats CORNELL and Penn S
TESTING ARGUMENTS FOR DEDUCTIVE VALIDITY
The BIG IDEA OF FORMAL LOGIC:
A (particular) argument is DEDUCTIVELY VALID if it has
an instance of a valid form.
An argument form is VALID if and only if there are no
instances of that form in which all the premis
SHORTCUTS with TRUTH TABLES
So far, weve always used the full truth-tables. We can
take a shortcut using the partial truth table method.
Simply restrict your attention to the relevant rows, and skip
the others!
Chapter 3. Lecture 7
Page 1 of 14
The econom
Why arent we done?
1. Truth tables can be unwieldy.
(R&T) (P Q) & (T (~U & ~V), P Q
2. (LPS 30): There are other kinds of deductively valid
arguments where T-tables do not work.
3. A theoretical reason. Truth tables do not well
represent our actual reason
Conjunction Introduction [&I]: From any statement p
together with any statement q, we may infer p&q.
p
q
p&q
q
p
p&q
Page 1 of 10
If there's oxygen and there's heat and there's combustible
material, then there will be fire. There's oxygen. There's
heat. T
2 More Basic Rules of Inference
Our system of rules of inference is currently incomplete:
there are valid argument forms for which we cannot yet
generate a proof. We need two more rules.
S
C
O
P
E
1. (AL) C
2. A
3.
4. C
5. A C
A
H ["hypothesis"]
1,3 E
2-4
7 DERIVED RULES OF INFERENCE:
Not necessary for the completeness of the propositional
calculus
Derivable from our 10 Basic Rules
Modus Tollens [MT]: From any statement pq and ~q,
we may infer ~p.
Page 1 of 14
If air sacs play a role in respiration, then
A THEOREM IS A STATEMENT FORM THAT IS
PROVABLE WITHOUT ANY GIVEN PREMISES
1.
pq
2.
p(p&q)
3. (pq)(p(p&q)
H
1 A BS
1-2 I
An important theoretical fact: a statement form is a
theorem iff it is a tautology.
A consequence: p is a contradiction iff _ is a
theo
The Logicians Promise: My approved kinds (or
forms) of arguments will not lead you from believing
something true into believing something false.
TRUE Premises
Logicians Approved
Arguments
TRUE Conclusions
ButGarbage In, Garbage Out!
Ch.8, Lecture 1
1/17
D
Definition: a FALLACY is a faulty argument or a faulty
kind of argument.
Lets distinguish four classes of types of fallacies: fallacies
of relevance, semantic fallacies, deductive fallacies, and
inductive fallacies.
III. A person commits a DEDUCTIVE FALLA
SOME EXAMPLES: IDENTIFY THE FALLACY
If Matt Holliday is really safe at home, then the Rockies
deserve to be in the playoffs instead of the Padres.
Matt Holliday is not really safe at home.
The Rockies do not deserve to be in the playoffs
instead of the P
LPS/PHIL 29 is the first course in a three course sequence
that covers the fundamentals of formal and informal,
inductive and deductive logic.
BUT WHAT IS CRITICAL REASONING OR
LOGIC?
A first stab: Logic is the study of reasoning, or thinking
Not psycholo
ARGUMENT STRUCTURE
4 Steps:
1. Circle all premise and conclusion indicator words
[since, etc.].
2. Bracket and number every statement.
3. Identify the premises and conclusions, including
intermediate conclusions.
4. Put the argument into standard form, us
The Logicians Promise: My approved kinds (or
forms) of arguments will not lead you from believing
something true into believing something false.
TRUE Premises
Logicians Approved
Arguments
TRUE Conclusions
ButGarbage In, Garbage
1/11
SEPARATING ARGUMENTS F
Heis
PHIL/LPS29
Our 10 Basic Inference Rules
p q
p
q
[E]
~p
p
[~E]
p
.
.
.
q
p q [I]
[
I]
pq
p q [E]
[
I]
pq
q p [E]
p q
p r
q r
r
[
E]
p q
q p
p q [I]
p&q
p
[&E]
p
p q
p&q
q
[&E]
q
p q
p
q
p & q [&I]
~p
p
.
.
.
q&~q
[~I]
Our 7 Derived Rules
p q
~q
~p
[MT
Our Basic Inference Rules I: Non-Hypothetical Rules
p q
p
q
[E]
p&q
p
[&E]
p
p q [
I]
pq
p q [E]
p&q
q
[&E]
q
p q [
I]
pq
q p [E]
~p
p
[~E]
p
q
p & q [&I]
p q
p r
q r
r
[
E]
p q
q p
p q [I]
Heis
PHIL/LPS 29
Our 10 Basic Inference Rules
~p
~p
p
p
.
.
.
q&~q
[~I]
[~E]
p&q
p
[&E]
p
p q [I]
pq
p q [E]
p&q
q
[&E]
q
p q [I]
pq
q p [E]
p
q
p & q [&I]
pq
pr
qr
r
[E]
pq
qp
p q [I]
p
.
.
.
q
p q [I]
pq
p
q
[E
Our 7 Derived Rules
pq
~q
~p
[MT]
pq
qr
p
EXAM #1 (PRACTICE)
LPS/PHIL 29 (Fall 09)
J. Heis
THE EXAM IS WORTH 100 POINTS. YOU HAVE 50 MINUTES.
I. DEFINITIONS AND QUESTIONS [39 pts total]
A.
Fill in the blank: Definitions [5 pts each; 20 pts total];
1. A deductive argument is _.
2. A counterexample
HOUR EXAM #2 (PRACTICE)
LPS/PHIL 29 (FALL 2009)
J. Heis
THE EXAM IS WORTH 100 POINTS. YOU HAVE 50 MINUTES.
I. DEFINITIONS AND QUESTIONS. [30 pts total]
A.
Fill in the blank: Definitions [5 pts each; 15 pts total].
1.
A counterexample to an argument form i
LPS 29 FALL 2009: PRACTICE FINAL ANSWERS
Part I. Chapters 1, 2, and 8
A. Definitions and Questions
(1) Complete the denition: an inductive argument is is an argument in which the
premise(s) are not claimed to lend absolute support to the conclusion. Inste