9/23/10 Fallacies of Logical Structure I. Fallacies of Logical Structure Kelley says that these fallacies involve subtle logical errors with the argument itself. Dont all of the fallacies involve subtle logical errors? Didnt the other fallacies occur with
PL 111 FOUNDATIONS OF LOGICAL REASONING
DR. R. E. FITZGIBBONS
BRIDGEWATER STATE COLLEGE
SPRING 2009
LOGIC
What logic is
As an academic discipline, logic studies the criteria for differentiating sound arguments from unsound
arguments.
Logic is the academic
Todays Topics (11/18)
I. II. III. IV. V. VI.
Necessary Conditions Sufficient Conditions Necessary and Sufficient Conditions Symbolizing Sufficient Conditions Symbolizing Necessary Conditions Symbolizing Necessary and Sufficient Conditions Propositional Lo
Todays Topics (9/30)
I. II. III.
Review Logically True Propositions Validity and Logically True conclusions Logically Inconsistent Propositions Validity and Logically Inconsistent Premises
IV. V.
3/4/11
I. Review
An argument is valid if and only if it is
Todays Topics (9/28)
I.
Two Ways that a Conclusion can Follow From a Set of Premises
II.
Valid Arguments
a)
A Test for Validity Validity and Form Invalid Arguments Valid vs. Invalid Arguments
b)
III.
IV.
a)
Valid & Invalid Arguments: True Premises, True C
Todays Topics (10/26)
I. II. III. IV. V. VI. VII.
Truth-Values Truth-Functional Connectives The Truth-Table for Conjunctions The Truth-Table for Negations The Truth-Table for Disjunctions The Truth-Table for Conditionals The Truth-Table for Bi-Conditional
Todays Topics (11/2)
I. II. III. IV.
Argument Forms Logical Relations Using Truth-Tables to Test for Validity Validity and Form
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I. Argument Forms
Like a propositional form, an argument form represents a general pattern for an endless number of argu
Todays Topics (9/16)
I. II.
a.
What is a fallacy? Subjectivist Fallacies
Subjectivism Appeal to majority Appeal to emotion Appeal to force
b.
c.
d.
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I. What is a fallacy?
Defined broadly, a fallacy is any error in reasoning. In logic, the term is no
Todays Topics (11/9)
I.
a.
Two Common Valid Argument Forms
Modus Ponens Modus Tollens
b.
II. III.
A Point about Validity Some Other Rules of Inference
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II. Two Common Valid Argument Forms
Modus Ponens names a particular argument form: pq p
In argu
Todays Topics (12/2)
I.
Immediate Inferences
a. b. c. d. e. f. g.
Taking the Converse Conversion The Complement of a Class Taking the Obverse Obversion Taking the Contrapositive Contraposition Contradictories Contraries
I.
The Square of Opposition
a. b.
3
Todays Topics (12/2)
I.
Immediate Inferences
a. b. c. d. e. f. g.
Taking the Converse Conversion The Complement of a Class Taking the Obverse Obversion Taking the Contrapositive Contraposition Contradictories Contraries
I.
The Square of Opposition
a. b.
3
Todays Topics (10/5)
I. II. III.
Review of Validity Soundness The Conclusion of a Sound Argument is True
3/4/11
I. Review of Validity
When evaluating arguments, we should ask: a. Are the premises true?; and b. Does the conclusion follow from the premises?
Todays Topics 10/21
I.
Review
a) b)
Connectives Compound, Component, and Simple Propositions The Main Connective The Symbols of Propositional Logic Identifying Propositional Forms
c) d) e)
II.
Negation Conditionals Bi-Conditionals
III.
IV.
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I. a) Co
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Topics for Today (11-30)
I. II.
Categorical Syllogisms Using Venn Diagrams to Test for Validity
3/4/11
I. Categorical Syllogisms Examples
1. All whales are mammals. 2. All mammals are animals with lungs. 3. All whales are animals with lungs 1. No M
T opics of the Day
I.
Why study logic? What is logic?
a)
II.
What is an argument What is a good argument When do premises provide evidential support?
b)
c)
III.
a)
W hat logic is not
Logic is not psychology Logic is not rhetoric
b)
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I . Why Study Lo
Modus Ponens etc.
Modus Ponens
Modus Tollens
Affirming the Antecedent
Denying the Consequent
The Fallacy of Denying the Antecedent
The Fallacy of Affirming the Consequent
An if, then proposition is comprised of two partsthe if-clause and the then-clause.
1
This paper identifies all of the fallacies that you need to know
for the course. (There are hundreds of other fallacies.)
Quiz and PostTest Questions
Quiz and test questions will present you with little arguments (a short
paragraph as in the examples be
TRUTH FUNCTIONAL LOGIC
The new (revised by the Department of Philosophy as of Spring 2012) learning objectives for
PHIL 111 The Foundations of Logical Reasoning are less ambitions with regard to truthfunctional logic that earlier versions. Accordingly, th
Common Premise Indicators
These are premise indicators insofar as they precede one or more premises (reasons).
as indicated by
as shown by
as
because
clearly
follows from
for the reason(s) that
for
given that
in view of the fact that
inasmuch as
may be de
1
Categorical Syllogisms and Venn Diagrams
A categorical syllogism is an argument that
1. is comprised of exactly three categorical propositionstwo premises and one conclusion;
2. contains exactly three distinct terms, each of which occurs exactly twice;
Some Definitions Relative to Categorical Propositions
Contradiction
With regard to categorical propositions, propositions of the form All S is P and Some S is
not P are contradictories and propositions of the form No S is P and Some S is P are
contradicto
Categorical Propositions: Definitions and Venn Diagrams
Categorical proposition
A proposition is a categorical proposition if and only if it has one of the following forms:
All S is P
No S is P
Some S is P
Some S is not P
Universal categorical proposition
IfThen Translations
Below are some very common ifthen translations. These should be memorized so that
you can easily move from the ifthen formulation to each translation and then from each
translation back to its ifthen formulation. Finally, you should be
1
Simple IfThen Reasoning
I.
Introduction
An ifthen proposition is comprised (made up) of two distinct parts: (1) the if-clause
and (2) the then-clause.
The if-clause is the proposition that comes immediately after the if. Consider the
following.
If it is
Todays Topics (11/4)
I.
Logically Equivalent Propositional Forms Logically Equivalent Propositions Two Rules of Equivalence
a.
II. III.
Double Negation Contraposition
b.
IV.
Equivalence and Validity
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I. Logically Equivalent Propositional Forms
Two o
Todays Topics (10/19)
I. II.
Introducing Propositional Logic One way of Identifying the Form of Propositions Propositional Connectives Compound, Component, and Simple Propositions A Second Way of Identifying the Form of Propositions
III. IV.
V.
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I.
Todays Topics (12/7)
I. II. III. Deductive vs. Inductive Arguments Proof Evaluating Inductive Arguments Strength and Weakness IV. Ar guments fr om Sample V. Some Criteria for Determining the Strength of an Argument from Sample VI. Arguments from Sample an