A bar B = U AB,BA
(~AbarB) = (~AuB), (B u ~A)
~(A bar B) = AvB, ~(A.B)
~(~Abar~B) = (~Av~B), ~(~A.~B)
~(~AbarB) = (~AvB), ~(~A.B)
~(A.B) / ~B = NO
~(A.B) / ~A = NO
~(A.B) / A = ~B
~(A.B) / B = ~A
(A.B) / B = ~A
(~A,~B) = ~A, ~B
~(A.B) = NO
~(~A.B) = NO
~(
Proofs (1)
Reviewing the Inference Rules
Last time we learned this set of Inference Rules:
GENSLERS INFERENCE RULE FORMS
S-Rules (S-1 through S-6)
I-Rules (I-1 through I-6)
(P Q) P, Q
~ (P Q) ~P, ~Q
~ (P Q) P, ~Q
~ (P Q), P ~Q
~ (P Q), Q ~P
~P P
(P Q), ~P
All of our S-Rules - make an inference which starts with one line
According to our inference rules for proofs, a false conjunction with one false conjunct implies that - the
consequent is false/the other conjunct is false/the other conjunct is true - ( NO
Induction Versus Deduction
Deduction concerns whether arguments are valid or invalid, i.e., whether their premises support their
conclusions with absolute certainty.
Induction concerns whether arguments are strong or weak, i.e, whether their premises supp
Basic Building Blocks (1)
First Impressions
At the beginning of a logic class, I often ask students about initial impressions. 'What is logic?', I ask.
'What is critical thinking? Who thinks they have an answer?' Sometimes I'll get some good answers, and
Inductive Probability (1)
Probability and Possibility
Probability is an idea which resides somewhere between two other ideas: actuality and possibility.
Actuality is an idea very tangible and familiar to us; it simply represents the way things are. We con
Fallacies
Bad Reasoning
Types of Bad Reasoning
(Intentional or Unintentional)
Bad Reasoning
Formal Problems
Inconsistency
Informal Fallacies
Formal Fallacies
Formal Fallacies
FORMALLY invalid arguments
sometimes have names (some Latin!)
sometimes very
Formal Fallacies (1)
When Arguments Go Bad
This week we begin looking at fallacies. Fallacies may at first appear to be good arguments, but they
aren't. Sometimes they are described as pseudo-arguments. Fallacies occur when people deliberately try
to dece
Venn Diagrams (1)
The Modern Square of Opposition
You may recall that in last week's learning module reading we focused especially on relationships among
the following four statement types:
All S are P.
(Universal Affirmative)
No S are P.
(Universal Negat
Counterexamples (1)
The Purpose of Counterexamples
In the Calculator Example we demonstrated that an invalid argument form was invalid by substituting
different 'content' for certain parts of an argument. We may call this activity creating a
counterexampl
Categorical Logic (1)
Overview
This section of the course is primarily concerned with statements, arguments and relationships
involving categories (also known as classes, sets, groups, and other synonyms). As categories are
composed of individual members
How to Approach Informal Fallacies (1)
Informal Fallacies
Studying informal fallacies is far messier than studying formal fallacies. Given most any argument form to
consider, almost all modern logicians will agree about whether it exhibits a formal fallac
Argumentation (1)
Opening Comments
Like fallacies, the activity of argumentation reflects a real-world concern of logic. The activity of
argumentation might be considered from either of the two opposite directions from which you will
encounter it: 1) maki
INFORMAL FALLACIES
according to
The Power of Logic*
Fallacies Involving Irrelevant Premises
Argument Against the Person
Premises: Instead of providing a rational critique of a statement (or argument), attack the person
who advances it.
Conclusion: The sta
Inductive Reasoning
Making Educated Predictions
Induction: The Basics
Validity, soundness, strength & reliability
Induction vs. deduction
Induction and science
(See Inductive Reasoning)
Valid, Sound, Strong or Reliable?
VALID: Arguments which have a true
Inductive Reasoning (1)
Opening Comments
Most of the arguments we study in this class are deductive arguments. Deductive arguments intend to
establish their conclusion with absolute certainty. Other arguments, however, may establish their
conclusions with
Gensler vs. POL
Two Classification Schemes
for Informal Fallacies
Broad Informal Fallacy Groupings
According to Gensler
circularity, ambiguity, emotional language or
irrelevance (5 types)
neatly expressed in premise-conclusion format
(6 types)
both cor
Midterm Review
Study Tips and Logistics
Quizzes
Study Quizzes 1 - 5. Any quiz question may be a test
question (except short answers with hints)
Complete uncompleted attempts - more questions!
View questions and answers for completed quizzes at
Submissi
Chris Weigand, Instructor
Logic & Critical Thinking
INDUCTIVE SYLLOGISM FORMS
(For LogiCola Exercises PI and PB)
NAME
Statistical
Syllogism
FORM
N percent of As are Bs.
x is A.
This is all we know about the matter.
Its N percent probable that x is B.
Sam
Categorical Logic
relationships among categories and things in
categories
involves both statements & arguments
formalization: translations into WFFs
interesting facts about some kinds of categorical
statements
Statements of
Categorical Interest
1.Some
The Calculator Example (1)
Arguments as Calculators
Logic is primarily a study of arguments. One of the first ways I go about helping students to understand
the study of arguments is to compare arguments to calculators. An argument is like a calculator (o
Probability
A Mechanism for Inductive Reasoning
Overview
Last week: basic principles of inductive
reasoning
This week: mechanism of inductive
reasoning
HOW probable is probably?
Well calculate some numbers.
Calculation Methods
COUNTING method
simple to un
Other Venn Diagrams (1)
The following is just for fun or extra practice; it is NOT REQUIRED. After you see it, see my suggested answers on the
next page in this learning module. If you have questions, feel free to ask them in the course discussion area!
B
Chris Weigand, Instructor
Logic & Critical Thinking
Calculating Pairs of Probabilities
Key Formulas, Definitions and Reminders
(For LogiCola Sets PP, PO & PC)
(A and B below represent events)
Probability of (A and B) = Prob (A) x Prob (B given A occurs)
P
Venn Diagrams
A Tool for Examining
Categorical Logic
With Venn diagrams we can.
represent many types of categorical
statements / forms
represent many types of categorical
arguments / forms
test categorical arguments / forms for validity
draw cool pictures
Chris Weigand, Instructor
Logic and Critical Thinking
MORE ON CALCULATORS
An argument is like a calculator or information processor. In this analogy, the first seven
situations shown below are possible, but not the last situation. The last two situations
Other Venn Diagrams Answers (1)
Here are my suggested answers for Other Venn Diagrams.
On this diagram, how would you represent each of the following statements?
1.
Nothing is in only one circle.
ANSWER: Shade areas 2, 6 and 8, since those are the only ar
Fallacies are deceptive errors of thinking.
A good argument should:
1. be deductively valid (or inductively strong) and have all
true premises;
2. have its validity and truth-of-premises be as evident as
possible to the parties involved;
3. be clearly sta
All logicians are millionaires.
all L is M
Gensler is a logician.
g is L
Gensler is a millionaire.
g is M
Syllogistic logic (our first system)
deals with such arguments; it uses
capital and small letters and five words
(all, no, some, is, and not).
Logi