Introduction to Categorical Logic. logic10.ppt

Basic introduction to Aristotle's logic of categories, the classical standard for clear and rational thinking, useful for law, engineering, planning, and science and mathematics

2. Philosophy 103
Linguistics 103
Yet, still, Even further More and yet
more, etc., ad infinitum,
Introductory Logic:
Critical Thinking
Dr. Robert Barnard

3. Last Time:
•Venn Diagrams for Propositions
•Existential Import in Diagramming
•Traditional Square of Opposition

4. Plan for Today
•Review: Venn Diagrams for Propositions
•Modern Square of Opposition
•The Existential Fallacy

5. Today is DAY 10
•In 10 Days an embryonic Chick goes from
nothing to this:
HAVE YOU
DEVELOPED
AS MUCH
IN the LAST
10 Days???

6. REVIEW: THE 4 TYPES of
CATEGORICAL PROPOSITION
UNIVERSAL PARTICULAR
AFFIRMATIVE ALL S is PSOME S is P
NEGATIVE NO S is PSOME S is not P

7. REVIEW: A, E, I, and O
TERM Proposition Form Quantity Quality
A ALLS IS P UNIVERSAL AFFIRMATIVE
E NOS IS P UNIVERSAL NEGATIVE
I SOMES ISP PARTICULAR AFFIRMATIVE
O SOMES IS NOTP PARTICULAR NEGATIVE

8. Review: The Traditional Square of
Opposition

9. Subalternation
What is the relation between the UNIVERSAL and the
PARTICULAR?
•If All S is P, what about Some S is P?
•If No S is P, what about Some S is not P?
Subalternation claims that if the Universal is true, then
the corresponding Particular is true.

10. TRADITIONAL A and E
In Traditional Logic we need to capture the
Existential Assumption: That everything we can
name with a category term or description, exists!
X X
A
E

11. Traditional vs. Modern Categorical
Logic
The KEYdifference between Traditional
(Aristotelian) and Modern (Boolean)
categorical Logic is that Traditional Logic
ASSUMES that category terms all refer to
actual objects.
Modern Logic does NOT make the Existential
Assumption.

12. Thanks to: George Boole
•English Mathematician and
Grandfather of computer
Science.
•Wrote
The Laws of Thought (1854)
•Invented Boolean Algebra
1815-1864

13. Boole and the Existential Fallacy
•Boole recognized that many Syllogistic
Arguments assume that every category or
class referred to is NON-EMPTY.
•But it is possible to denote an EMPTY CLASS
•What Happens to Categorical Logic if EMPTY
CLASSES are allowed?

14. Traditional Square using Venn
Diagrams
X
X
The Existential
Assumption allows the
inference from
Universal to Particular

15. Where is the Fallacy?
Basically, the EXISTENTIAL FALLACY is this:
1.Deductive validity requires that it be IMPOSSIBLEto
infer a FALSE CONCLUSION from TRUE PREMISES.
2.Reasoning by SUBALTERNATION alwaysrequires that
the SUBJECT CLASS is non-empty.
3.It is POSSIBLEthat a UNIVERSAL Proposition is true
but has an empty SUBJECT CLASS
4.Therefore, it is possible to reason from True Premises
to a false Conclusion by Subalternation.
5.So Subalternationis INVALID.

16. BUT Hurley Disagrees with ME!!!
•The Author of our Logic Text claims that the
Existential Fallacy only occurs when the
subject is some sort of Mythic or Fictional
being.
•He thinks that traditional logic only sanctions
SOME sub-alternations.
•I disagree: I think Aristotle would not have
drawn the line in THAT place. I think that
relying upon individuals to decide on what is
Mythic or Fictional takes us beyond LOGIC.

17. Take THAT Patrick J Hurley!

18. Avoiding the Existential Fallacy
In order to avoid the Existential Fallacy
we need to modify traditional
categorical logic to remove the
existential assumption.
The Result is Modern or Boolean
Categorical Logic

19. The Modern Square of Opposition
Without the Traditional Existential Assumption, ONLY
Contradiction is Valid

20. Modern Square using Venn
Diagrams

21. Contradictories
Contradictory Propositions ALWAYS take
opposite TRUTH VALUES
•A and O are Contradictories
•E and I are Contradictories

22. Questions?

23. The Class So FAR (roughly)
Week 1 Week 2 Week 3 Week 4 Week 5
Basic Concepts I:
1) Arguments (
Premise/Concl
usion)
2) Propositions
(Simple/Compl
ex)
-Conditional
Props.
(Antecedent/C
onsequent)
-Truth values
Basic Concepts II :
1) Deductive/Ind
uctive
2) Valid/Invalid
3) Strong/Weak
4) Sound
5) Cogent
Informal Fallacies:
1) Fallacies of
Relevance
2) Fallacies of
Weak Induction
3) Fallacies of
Meaning and
Ambiguity
Laws of Thought:
Philosophical
Issues about the status
of
logical laws.
Meaning
1) Types of
Meaning:
Cognitive/Emo
tive
2) Intension vs.
Extension
3) Ambiguity and
Precision
4) Names vs.
Descriptions
Definitions
1) Lexical
2) Theoretical
3) Precising
4) Persuasive
Logical Form
Form and Validity
Deductive Forms
1) Modus Ponens
2) Modus Tollens
3) Disjunctive and
Hypothetical
Syllogism
4) Reductio ad
Absurdum
Formal Fallacies
Counter Example
Construction
Introduction to
Categorical
Logic
Aristotle’s Categories
Leibniz, Concepts, and
Identity
Analytic –Synthetic
Distinction
Essence and Accident
Necessary and
Sufficient
Conditions
Introduction to
Categorical
Logic
Categorical Propositions
1) Parts and
Characteristics
2) Conditional and
Conjunctive
Equivalents
3) Existential
Import
Venn Diagrams for
Propositions
Existential Import in
Diagramming
Traditional Square of
Opposition
Modern Square of
Opposition
The Existential Fallacy

24. Next Week
Tuesday: Mid Term Exam
Thursday: Immediate Inferences in Categorical
Logic

25. Test Format
The Midterm will be 150 Points
•Section 1 (30 points) Basic Concepts/Vocabulary
•Section 2 (30 Points) Fallacies
•Section 3 (30 Points) Categorical Logic Concepts
•Section 4 (60 Points) Applications