dr. robert barnard
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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
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