Philosophy 103 Linguistics 103 Yet still Even further
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![Philosophy 103 Linguistics 103 Yet, still, Even further More and yet more, ad infinitum, Philosophy 103 Linguistics 103 Yet, still, Even further More and yet more, ad infinitum,](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-2.jpg)
![Last Time: • Introduction to Categorical Logic • Categorical Propositions – Parts and Characteristics Last Time: • Introduction to Categorical Logic • Categorical Propositions – Parts and Characteristics](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-3.jpg)
![Plan for Today • Venn Diagrams for Propositions • Existential Import in Diagramming • Plan for Today • Venn Diagrams for Propositions • Existential Import in Diagramming •](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-4.jpg)
![REVIEW: THE 4 TYPES of CATEGORICAL PROPOSITION UNIVERSAL PARTICULAR AFFIRMATIVE ALL S is P REVIEW: THE 4 TYPES of CATEGORICAL PROPOSITION UNIVERSAL PARTICULAR AFFIRMATIVE ALL S is P](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-5.jpg)
![REVIEW: TERM Proposition Form A, E, I, and O Quantity Quality A ALL S REVIEW: TERM Proposition Form A, E, I, and O Quantity Quality A ALL S](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-6.jpg)
![Diagramming Propositions… Diagramming is a tool that can be used to make explicit information Diagramming Propositions… Diagramming is a tool that can be used to make explicit information](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-7.jpg)
![…is FUN!!! We can also diagram CATEGORICAL PROPOSITIONS. They describe a relationship between the …is FUN!!! We can also diagram CATEGORICAL PROPOSITIONS. They describe a relationship between the](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-8.jpg)
![Focus on Standard Diagrams • Since there are 4 basic standard form categorical propositions, Focus on Standard Diagrams • Since there are 4 basic standard form categorical propositions,](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-9.jpg)
![Euler Diagrams (not Standard) A ALL S is P E NO S is P Euler Diagrams (not Standard) A ALL S is P E NO S is P](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-10.jpg)
![Pro and Cons: Pro: Euler Diagrams are very intuitive Con: Euler Diagrams can represent Pro and Cons: Pro: Euler Diagrams are very intuitive Con: Euler Diagrams can represent](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-11.jpg)
![Alternative: Venn Diagrams • Venn Diagrams are less intuitive to some people than Euler Alternative: Venn Diagrams • Venn Diagrams are less intuitive to some people than Euler](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-12.jpg)
![The Basic VENN Diagram SUBJECT CIRCLE PREDICATE CIRCLE X LABEL S RULE 1: SHADING The Basic VENN Diagram SUBJECT CIRCLE PREDICATE CIRCLE X LABEL S RULE 1: SHADING](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-13.jpg)
![Questions? Questions?](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-14.jpg)
![THE UNIVERSAL AFFIRMATIVE TYPE A : ALL S is P Conceptual Claim THE UNIVERSAL AFFIRMATIVE TYPE A : ALL S is P Conceptual Claim](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-15.jpg)
![THE UNIVERSAL NEGATIVE TYPE E : No S is P Conceptual Claim THE UNIVERSAL NEGATIVE TYPE E : No S is P Conceptual Claim](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-16.jpg)
![THE PARTICULAR AFFIRMATIVE TYPE I: Some S is P At least one thing X THE PARTICULAR AFFIRMATIVE TYPE I: Some S is P At least one thing X](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-17.jpg)
![THE PARTICULAR NEGATIVE TYPE O: Some S is not P At least one thing THE PARTICULAR NEGATIVE TYPE O: Some S is not P At least one thing](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-18.jpg)
![EXISTENTIAL IMPORT ONLY a proposition with EXISTENTIAL IMPORT requires that there be an instance EXISTENTIAL IMPORT ONLY a proposition with EXISTENTIAL IMPORT requires that there be an instance](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-19.jpg)
![PROPOSITIONS ABOUT INDIVIDUALS In CATEGORICAL LOGIC a proper name denotes a class with one PROPOSITIONS ABOUT INDIVIDUALS In CATEGORICAL LOGIC a proper name denotes a class with one](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-20.jpg)
![The Traditional Square of How are the 4 standard CPs related? Opposition The Traditional Square of How are the 4 standard CPs related? Opposition](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-21.jpg)
![Contraries The A Proposition is related to the E proposition as a CONTRARY X Contraries The A Proposition is related to the E proposition as a CONTRARY X](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-22.jpg)
![Contraries: Not Both True A E If both are TRUE then S is all Contraries: Not Both True A E If both are TRUE then S is all](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-23.jpg)
![The Traditional Square of Opposition The Traditional Square of Opposition](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-24.jpg)
![Sub-Contraries The SUBCONTRARY RELATION holds between the IProposition and the O-Proposition. Sub-Contrary = Not Sub-Contraries The SUBCONTRARY RELATION holds between the IProposition and the O-Proposition. Sub-Contrary = Not](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-25.jpg)
![Sub-Contrary: Not Both False I IF both are FALSE, then there is no PARTYICULAR Sub-Contrary: Not Both False I IF both are FALSE, then there is no PARTYICULAR](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-26.jpg)
![The Traditional Square of Opposition The Traditional Square of Opposition](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-27.jpg)
![Contradictories Contradictory Propositions ALWAYS take opposite TRUTH VALUES • A and O are Contradictories Contradictories Contradictory Propositions ALWAYS take opposite TRUTH VALUES • A and O are Contradictories](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-28.jpg)
![A – O Contradiction If BOTH are True then the Non-P region of S A – O Contradiction If BOTH are True then the Non-P region of S](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-29.jpg)
![E – I Contradictories • If Both are TRUE, then the overlap Region is E – I Contradictories • If Both are TRUE, then the overlap Region is](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-30.jpg)
![The Traditional Square of Opposition The Traditional Square of Opposition](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-31.jpg)
![Subalternation What is the relation between the UNIVERSAL and the PARTICULAR? • If All Subalternation What is the relation between the UNIVERSAL and the PARTICULAR? • If All](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-32.jpg)
![Some Subalternations: • If All dogs are Brown, then Some dogs are brown. • Some Subalternations: • If All dogs are Brown, then Some dogs are brown. •](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-33.jpg)
![The TRADITIONAL Interpretation The TRADITIONAL or ARISTOTELIAN interpretation allows SUBALTERNATION Because FOR ARISTOTLE all The TRADITIONAL Interpretation The TRADITIONAL or ARISTOTELIAN interpretation allows SUBALTERNATION Because FOR ARISTOTLE all](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-34.jpg)
![TRADITIONAL A and E When we want to clearly indicate a TRADITIONAL ARISTOTELIAN interpretation TRADITIONAL A and E When we want to clearly indicate a TRADITIONAL ARISTOTELIAN interpretation](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-35.jpg)
![The Traditional Square of Opposition The Traditional Square of Opposition](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-36.jpg)
![Questions? Questions?](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-37.jpg)
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- Slides: 39
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![Philosophy 103 Linguistics 103 Yet still Even further More and yet more ad infinitum Philosophy 103 Linguistics 103 Yet, still, Even further More and yet more, ad infinitum,](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-2.jpg)
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 Last Time: • Introduction to Categorical Logic • Categorical Propositions – Parts and Characteristics](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-3.jpg)
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 Plan for Today • Venn Diagrams for Propositions • Existential Import in Diagramming •](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-4.jpg)
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 REVIEW: THE 4 TYPES of CATEGORICAL PROPOSITION UNIVERSAL PARTICULAR AFFIRMATIVE ALL S is P](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-5.jpg)
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
![REVIEW TERM Proposition Form A E I and O Quantity Quality A ALL S REVIEW: TERM Proposition Form A, E, I, and O Quantity Quality A ALL S](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-6.jpg)
REVIEW: TERM 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 Diagramming Propositions… Diagramming is a tool that can be used to make explicit information](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-7.jpg)
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 …is FUN!!! We can also diagram CATEGORICAL PROPOSITIONS. They describe a relationship between the](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-8.jpg)
…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 Focus on Standard Diagrams • Since there are 4 basic standard form categorical propositions,](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-9.jpg)
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 Euler Diagrams (not Standard) A ALL S is P E NO S is P](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-10.jpg)
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 X X
![Pro and Cons Pro Euler Diagrams are very intuitive Con Euler Diagrams can represent Pro and Cons: Pro: Euler Diagrams are very intuitive Con: Euler Diagrams can represent](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-11.jpg)
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 Alternative: Venn Diagrams • Venn Diagrams are less intuitive to some people than Euler](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-12.jpg)
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 S RULE 1 SHADING The Basic VENN Diagram SUBJECT CIRCLE PREDICATE CIRCLE X LABEL S RULE 1: SHADING](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-13.jpg)
The Basic VENN Diagram SUBJECT CIRCLE PREDICATE CIRCLE X LABEL S RULE 1: SHADING = EMPTY P RULE 2: X in a Circle = at least one thing here!
![Questions Questions?](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-14.jpg)
Questions?
![THE UNIVERSAL AFFIRMATIVE TYPE A ALL S is P Conceptual Claim THE UNIVERSAL AFFIRMATIVE TYPE A : ALL S is P Conceptual Claim](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-15.jpg)
THE UNIVERSAL AFFIRMATIVE TYPE A : ALL S is P Conceptual Claim
![THE UNIVERSAL NEGATIVE TYPE E No S is P Conceptual Claim THE UNIVERSAL NEGATIVE TYPE E : No S is P Conceptual Claim](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-16.jpg)
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 THE PARTICULAR AFFIRMATIVE TYPE I: Some S is P At least one thing X](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-17.jpg)
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 THE PARTICULAR NEGATIVE TYPE O: Some S is not P At least one thing](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-18.jpg)
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 EXISTENTIAL IMPORT ONLY a proposition with EXISTENTIAL IMPORT requires that there be an instance](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-19.jpg)
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 PROPOSITIONS ABOUT INDIVIDUALS In CATEGORICAL LOGIC a proper name denotes a class with one](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-20.jpg)
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 the 4 standard CPs related Opposition The Traditional Square of How are the 4 standard CPs related? Opposition](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-21.jpg)
The Traditional Square of How are the 4 standard CPs related? Opposition
![Contraries The A Proposition is related to the E proposition as a CONTRARY X Contraries The A Proposition is related to the E proposition as a CONTRARY X](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-22.jpg)
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 Contraries: Not Both True A E If both are TRUE then S is all](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-23.jpg)
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 The Traditional Square of Opposition](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-24.jpg)
The Traditional Square of Opposition
![SubContraries The SUBCONTRARY RELATION holds between the IProposition and the OProposition SubContrary Not Sub-Contraries The SUBCONTRARY RELATION holds between the IProposition and the O-Proposition. Sub-Contrary = Not](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-25.jpg)
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
![SubContrary Not Both False I IF both are FALSE then there is no PARTYICULAR Sub-Contrary: Not Both False I IF both are FALSE, then there is no PARTYICULAR](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-26.jpg)
Sub-Contrary: Not Both False I IF both are FALSE, then there is no PARTYICULAR Proposition asserted!!! O
![The Traditional Square of Opposition The Traditional Square of Opposition](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-27.jpg)
The Traditional Square of Opposition
![Contradictories Contradictory Propositions ALWAYS take opposite TRUTH VALUES A and O are Contradictories Contradictories Contradictory Propositions ALWAYS take opposite TRUTH VALUES • A and O are Contradictories](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-28.jpg)
Contradictories Contradictory Propositions ALWAYS take opposite TRUTH VALUES • A and O are Contradictories • E and I are Contradictories
![A O Contradiction If BOTH are True then the NonP region of S A – O Contradiction If BOTH are True then the Non-P region of S](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-29.jpg)
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 E – I Contradictories • If Both are TRUE, then the overlap Region is](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-30.jpg)
E – I Contradictories • If Both are TRUE, then the overlap Region is EMPTY and contains an object. E I
![The Traditional Square of Opposition The Traditional Square of Opposition](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-31.jpg)
The Traditional Square of Opposition
![Subalternation What is the relation between the UNIVERSAL and the PARTICULAR If All Subalternation What is the relation between the UNIVERSAL and the PARTICULAR? • If All](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-32.jpg)
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 Some Subalternations: • If All dogs are Brown, then Some dogs are brown. •](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-33.jpg)
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 The TRADITIONAL Interpretation The TRADITIONAL or ARISTOTELIAN interpretation allows SUBALTERNATION Because FOR ARISTOTLE all](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-34.jpg)
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 TRADITIONAL A and E When we want to clearly indicate a TRADITIONAL ARISTOTELIAN interpretation](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-35.jpg)
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 The Traditional Square of Opposition](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-36.jpg)
The Traditional Square of Opposition
![Questions Questions?](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-37.jpg)
Questions?
![](https://slidetodoc.com/presentation_image_h/dedb600271fb11bd22048ef116f132e8/image-38.jpg)
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Still not there yet
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