Philosophy 103Linguistics 103

Yet, still, Even further More and yet more

Introductory Logic: Critical Thinking

Dr. Robert Barnard

Last Time:

• Introduction to Categorical Logic• Aristotle’s Categories• Leibniz, Concepts, and Identity• Analytic – Synthetic Distinction• Essence and Accident• Necessary and Sufficient Conditions

Plan for Today• Categorical Propositions– Parts and Characteristics– Conditional and Conjunctive Equivalents– Existential Import

Reminder !!!!!Thursday, September 13, 2007 4:00 PMBryant 209

Philosophy Forum Talk –

“Einstein on the Role of History and Philosophy of Science in Physics”

Dr. Don Howard – University of Notre Dame

Extra Credit: 1 page reaction, due in 2 weeks (9/27)

Categorical Propositions

Categorical Propositions relate one category (in whole or part) as indicated by the SUBJECT TERM to another category, indicated by the PREDICATE TERM (either affirmatively or negatively):

• All houses have roofs• Some buildings are houses• No eggs are shatterproof• Some people are not paying attention

UNIVERSAL CATEGORICAL PROPOSITIONS

A Categorical Proposition that makes a claim about the entire SUBJECT CLASS is called a UNIVERSAL CATEGORICAL PROPOSITION

• All Toys…• No Fish…• All Bugs…• No people from Georgia…

PARTICULAR CATEGORICAL PROPOSITIONS

A Categorical Proposition that makes a claim about one or more members of the SUBJECT CLASS is called a PARTICULAR CATEGORICAL PROPOSITION

• Some Eggs…• Some men…• Some Lithuanians…

QUANTITY

All categorical propositions are either:

UNIVERSAL or PARTICULAR

We call this the QUANTITY of the proposition.

AFFIRMATIVE AND NEGATIVE PROPOSITIONS

When a categorical proposition asserts the existence of a relationship between the Subject term and the Predicate term we say that the proposition is AFFIRMATIVE.

When a categorical proposition denies the relationship between the Subject term and the Predicate term we say that the proposition is NEGATIVE

QUALITY

All categorical propositions are either:

AFFIRMATIVE or NEGATIVE

We call this the QUALITY of the proposition.

THE 4 TYPES of CATEGORICAL PROPOSITION

UNIVERSAL PARTICULAR

AFFIRMATIVE ALL S is P SOME S is P

NEGATIVE NO S is P SOME S is not P

Questions?

THE UNIVERSAL AFFIRMATIVE

ALL S is P

TYPE A

If (x is S) then (x is P)

Conceptual Claim

THE UNIVERSAL NEGATIVE

No S is P

TYPE E

If (x is S) then (x is not P)

Conceptual Claim

PROPOSITIONS ABOUT INDIVIDUALSIn CATEGORICAL LOGIC a proper name denotes a class with

one member.• Socrates: the class containing Socrates• Al Gore: the class of Al Gore• Brad Pitt: The class containing Brad Pitt• …etc…

SO, a proposition like ‘Socrates is a man’ is really about the whole class Socrates, so…

It is a UNIVERSAL proposition!!!

Universal Propositions

1. All Dogs are Brown2. All Houses are residences3. No Pigs have wings4. No Cars are Airships5. No Humans have quills6. All Wisdom is not Folly7. John Jay was the first Chief Justice

THE PARTICULAR AFFIRMATIVE

Some S is P

TYPE I

At least one thing X is Both S and P

For at least one x (x is S) and (x is P)

Existential Claim

THE PARTICULAR NEGATIVE

Some S is not P

TYPE O

At least one thing X is S and not P

For at least one x (x is S) and (x is not P)

Existential Claim

Particular Propositions

1. Some Cats are red.2. Some Pigs are not Sows3. Some lettuce is not endive.4. Some Men are not Women5. Some Flowers are plants.6. Some Presidents of the United States served

two terms7. Some Ole Miss coaches used to win games.

EXISTENTIAL IMPORT

ONLY a proposition with EXISTENTIAL IMPORT requires that there be an instance of the SUBJECT TERM in reality for the proposition to be true.

• All Dogs have 4 Legs (Conceptual – no EI)• Some Fish are Red (Existential – EI)

QUANTIFIER AND QUALIFIER

The Term which determines the QUANTITY of the proposition is called THE QUANTIFIER

ALL – NO -- SOMEThe term that determines the QUALITY of the

proposition is called the QUALIFIER

ALL – NO – IS – IS NOT

A, E, I, and OTERM Proposition Form Quantity Quality

A ALL S IS P UNIVERSAL AFFIRMATIVE

E NO S IS P UNIVERSAL NEGATIVE

I SOME S IS P PARTICULAR AFFIRMATIVE

O SOME S IS NOT P PARTICULAR NEGATIVE

COPULATION!!!!Every Categorical Proposition has a Quantity and

Quality, a Subject term and a Predicate Term. There is one more part:

THE COPULA

All S is PNo S is P

Some S is PSome S is not P

Questions?

Questions?

Week -

• Categorical Propositions• Conditional and Conjunctive equivalents• Existential Import• Traditional Square of Opposition• Modern Square of Opposition• Existential Fallacy• Venn Diagrams for Propositions

Week-

• Immediate Inferences• Conversion• Contraposition• Obversion

Week-

• Syllogistic Logic• Form- Mood- Figure• Medieval Logic• Venn Diagrams for Syllogisms (Modern)

Week -

• Venn Diagrams for Syllogisms (traditional)• Limits of Syllogistic Logic• Review of Counter-Example Method

Week -

• Logic of Propositions• Decision Problem for Propositional Logic• Symbolization and Definition• Translation Basics

Week -

• Truth Tables for Propositions• Tautology• Contingency• Self-Contradiction

Week -

• Truth Tables for Propositions II• Consistency• Inconsistency• Equivalence

Week -

• Truth Table for Arguments• Validity / Invalidity• Soundness

Week -

• Indirect Truth Tables• Formal Construction of Counter-Examples

Week -

• Logical Truths• Necessity • Possibility• Impossibility