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

Last Time: Introduction to Categorical Logic Categorical Propositions Parts and Characteristics Conditional and Conjunctive Equivalents

Existential Import Plan for Today Venn Diagrams for Propositions Existential Import in Diagramming Traditional Square of Opposition REVIEW: 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

TERM REVIEW: Proposition Form A, E, I, and O

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 Diagramming Propositions Diagramming is a tool that can be used to make explicit information that is both descriptive and relational. Geometric Diagrams

Blueprints Road Maps Flow Charts is FUN!!! We can also diagram CATEGORICAL PROPOSITIONS.

They describe a relationship between the subject term (class) and the predicate term (class). Focus on Standard Diagrams Since there are 4 basic standard form categorical propositions, this means that there are exactly 4 standard diagrams for

Categorical Propositions. BUT there are two flavors of diagrams we might use! Euler Diagrams (not Standard) A ALL S is P

E NO S is P I SOME S is P

O Some S is not P P

S P S X

X Pro and Cons: Pro: Euler Diagrams are very intuitive Con: Euler Diagrams can represent single propositions but are difficult to combine and apply to syllogisms. Con: Euler Diagrams Cannot capture Existential

Import in both the Aristotelian AND Modern modes. (more later) Alternative: Venn Diagrams Venn Diagrams are less intuitive to some people than Euler Diagrams Venn Diagrams Can easily be combined and used in Syllogisms.

Venn Diagrams CAN represent alternative modes of Existential Import. The Basic VENN Diagram SUBJECT CIRCLE PREDICATE CIRCLE

X LABEL LABEL S RULE 1: SHADING = EMPTY

P RULE 2: X in a Circle = at least one thing here! Questions? THE UNIVERSAL AFFIRMATIVE TYPE A : ALL S is P

Conceptual Claim THE UNIVERSAL NEGATIVE TYPE E : No S is P Conceptual Claim

THE PARTICULAR AFFIRMATIVE TYPE I: Some S is P At least one thing X is Both S and P Existential Claim THE PARTICULAR NEGATIVE TYPE O: Some S is not P

At least one thing X is S and not P Existential Claim 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. Diagrams with an X indicate EXISTENTIAL IMPORT. PROPOSITIONS ABOUT INDIVIDUALS In CATEGORICAL LOGIC a proper name denotes a class with one member. Fred Rodgers is Beloved by Millions Fred

Beloved The Traditional Square of How are theOpposition 4 standard CPs related? Contraries

The A Proposition is related to the E proposition as a CONTRARY X is CONTRARY to Y = X and Y cannot both be true at the same time. Thus if A is true: E is False If E is True: A is False If A is False: E is UNDETERMINED

Contraries: Not Both True A E If both are TRUE then S is all EMPTY and there is no UNIVERSAL Proposition asserted!!!!

The Traditional Square of Opposition Sub-Contraries The SUBCONTRARY RELATION holds between the IProposition and the O-Proposition. Sub-Contrary = Not both False at the same time If I is False then O is true If O is False then I is true If O (or I) is True, then I (or O) is undetermined

Sub-Contrary: Not Both False I IF both are FALSE, then there is no PARTYICULAR Proposition asserted!!! O

A O Contradiction If BOTH are True then the Non-P region of S is BOTH empty and contains an object! A O E I Contradictories

If Both are TRUE, then the overlap Region is EMPTY and contains an object. E I The Traditional Square of Opposition

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.

Some Subalternations: If All dogs are Brown, then Some dogs are brown. If All Fish have Gills, then Some Fish have Gills. If All Greeks are Brave, then Some Greeks are Brave The TRADITIONAL Interpretation

The TRADITIONAL or ARISTOTELIAN interpretation allows SUBALTERNATION Because FOR ARISTOTLE all category terms denote REAL objects. -- Every name picks out something in the world. TRADITIONAL A and E When we want to clearly indicate a TRADITIONAL ARISTOTELIAN interpretation we need to adapt

the A and E Diagrams! E A X X

The Traditional Square of Opposition Questions?