4 Categorical Propositions

Slides:

Advertisements

Similar presentations

Venn Diagram Technique for testing syllogisms

Advertisements

Test the validity of this argument: Some lawyers are judges. Some judges are politicians. Therefore, some lawyers are politicians. A. Valid B. Invalid.

Test the validity of this argument: Some lawyers are judges. Some judges are politicians. Therefore, some lawyers are politicians. A. Valid B. Invalid.

Four Rules of Aristotelian Logic 1. Rule of Identity: A is A 2. Rule of Non-Contradiction: A is not (-A) 3. Rule of Excluded Middle: Either A or (-A)

An overview Lecture prepared for MODULE-13 (Western Logic) BY- MINAKSHI PRAMANICK Guest Lecturer, Dept. Of Philosophy.

Deductive Arguments: Categorical Logic

Operations (Transformations) On Categorical Sentences

1 Philosophy 1100 Title:Critical Reasoning Instructor:Paul Dickey Website:

Contrapositive and Inverse

Critical Thinking Lecture 9 The Square of Opposition By David Kelsey.

Philosophy 1100 Today: Hand Back “Nail that Claim” Exercise! & Discuss

Categorical Syllogisms Always have two premises Consist entirely of categorical claims May be presented with unstated premise or conclusion May be stated.

Syllogistic Logic 1. C Categorical Propositions 2. V Venn Diagram 3. The Square of Opposition: Tradition / Modern 4. C Conversion, Obversion, Contraposition.

Immediate Inference Three Categorical Operations

Chapter 9 Categorical Logic w07

Chapter 16: Venn Diagrams. Venn Diagrams (pp ) Venn diagrams represent the relationships between classes of objects by way of the relationships.

Introduction to Venn Diagrams SP This is a Venn diagram for two terms. We can conceive of every element of S as being within the boundary of the S circle.

Categorical Propositions To help us make sense of our experience, we humans constantly group things into classes or categories. These classifications are.

CATEGORICAL PROPOSITIONS, CHP. 8 DEDUCTIVE LOGIC VS INDUCTIVE LOGIC ONE CENTRAL PURPOSE: UNDERSTANDING CATEGORICAL SYLLOGISMS AS THE BUILDING BLOCKS OF.

Testing Validity With Venn Diagrams

Philosophy 148 Chapter 7. AffirmativeNegative UniversalA: All S are PE: No S is P ParticularI: Some S is PO: Some S is not P.

Venn Diagrams and Categorical Syllogisms

Chapter 18: Conversion, Obversion, and Squares of Opposition

Strict Logical Entailments of Categorical Propositions

MLS 570 Critical Thinking Reading Notes for Fogelin: Categorical Syllogisms We will go over diagramming Arguments in class. Fall Term 2006 North Central.

Related Conditional Statements 2-1B What are the three related conditional statements? How are the three related conditional statements made?

 Outside across from the word: › write the symbol for conditional: p -> q  INSIDE: › How to write the statement : If p, then q. › Example : If an angle.

CATEGORICAL SYLLOGISMS

Set Operations Chapter 2 Sec 3. Union What does the word mean to you? What does it mean in mathematics?

Venn Diagrams Truth Sets & Valid Arguments Truth Sets & Valid Arguments Truth Tables Implications Truth Tables Implications Truth Tables Converse, Inverse,

Critical Thinking Lecture 9 The Square of Opposition

Relationships of Equivalences February Observe Relationship How two things relate to each other Mathematical A=A or ~A=~A Logically A=A, E=E,

Midterm Practice Famous Fallacies, TFTD, Hurley

Practice Quiz 3 Hurley 4.3 – 4.6.

Chapter 17: Missing Premises and Conclusions. Enthymemes (p. 168) An enthymeme is an argument with an unstated premise or conclusion. There are systematic.

Chapter 19: Living in the Real World. Introductory Remarks (p. 190) The joy and misery of ordinary English is that you can say the same thing in many.

GEOMETRY HELP Identify the hypothesis and the conclusion: If two lines are parallel, then the lines are coplanar. In a conditional statement, the clause.

Chapter 14: Categorical Syllogisms. Elements of a Categorical Syllogism (pp ) Categorical syllogisms are deductive arguments. Categorical syllogisms.

The Traditional Square of Opposition

Get one of these Think about *linear pairs *degrees in a triangle *degrees in a quadrilateral.

Midterm Practice Famous Fallacies, TFTD, Hurley

McGraw-Hill ©2004 by The McGraw-Hill Companies, Inc. All rights reserved. Testing Validity With Venn Diagrams The aim of this tutorial is to help you learn.

Categorical Propositions Chapter 5. Deductive Argument A deductive argument is one whose premises are claimed to provide conclusive grounds for the truth.

Venn Diagram Technique for testing syllogisms

VENNS DIAGRAM METHOD FOR TESTING CATEGORICAL SYLLOGISM

PHIL 151 Week 8.

Testing Validity With Venn Diagrams

Deductive Logic, Categorical Syllogism

5 Categorical Syllogisms

Venn Diagrams 1= s that are not p; 2= s that are p; 3= p that are not s S P.

Today’s Topics Introduction to Predicate Logic Venn Diagrams

5.1 Standard Form, Mood, and Figure

Famous Fallacies, TFTD, Hurley

5 Categorical Syllogisms

Practice Quiz 3 Hurley

Rules and fallacies Formal fallacies.

Famous Fallacies, TFTD, Hurley

4.1 The Components of Categorical Propositions

Categorical Propositions

Philosophy 1100 Class #8 Title: Critical Reasoning

Critical Thinking Lecture 9 The Square of Opposition

Diagramming Universal-Particular arguments

Philosophy 1100 Title: Critical Reasoning Instructor: Paul Dickey

4 Categorical Propositions

4 Categorical Propositions

5 Categorical Syllogisms

Chapter 6 Categorical Syllogisms

Logic and Reasoning.

4 Categorical Propositions

Practice Quiz 3 Hurley 4.3 – 4.6.

Presentation transcript:

4 Categorical Propositions 4.4. Conversion, Obversion, and Contraposition

Conversion, Obversion, and Contraposition These are 3 operations that can be used to change standard form statements or change a statement into standard form. Conversion is the simplest: simply switch the subject and predicate terms. No S are P -----conversion----> No P are S

Conversion Compare the Venn Diagrams of each statement: No S are P No P are S S S P P For E propositions, there is no change in diagram, and so no change in truth value.

Conversion Compare the Venn Diagrams of each statement: All S are P All P are S S P S P For A propositions, there IS a change in diagram, and so a change in truth value.

Conversion Compare the Venn Diagrams of each statement: Some S are P Some P are S X X S S P P For I propositions, there is no change in diagram, and so no change in truth value.

Conversion Compare the Venn Diagrams of each statement: Some S are not P Some P are not S S P X X S P For O propositions, there IS a change in diagram, and so a change in truth value.

Conversion So, what do we know? Immediate inferences (inferences with one premise and one conclusion) are valid for the converses of E and I propositions, but not for A and O propositions. All puppies are evil. Therefore, all evil things are puppies. Since this is conversion of an A proposition, it is an illicit inference … an illicit conversion. Some puppies are evil. Therefore, some evil things are puppies. No problem.

Obversion Obversion (2 steps): Change the quality Replace Predicate term with its complement All S are P ------- obversion----->____________? No S are P -------obversion ------> _____________? Some S are P ----- obversion -----> _______________? Some S are not P ----obversion---> _____________?

Obversion No S are non-P All S are P S P S P All S are non-P No S are P S P P S Some S are P Some S are not non-P S P X S P X Some S are not P Some S are non-P S P X S P X

Contraposition Contraposition (2 steps): Switch Subject and Predicate terms Replace both Subject and Predicate terms with their complements All S are P ------- contraposition----->____________? No S are P -------contraposition ------> _____________? Some S are P ----- contraposition -----> _______________? Some S are not P ----contraposition---> _____________?

Contraposition S P All S are P All non-P are non-S No S are P No non-P are non-S S P S P X Some S are P Some non-P are non-S S P X Some S are not P Some non-P are not non-S

Method to Drawing Venn Diagrams Place an X in each distinct area of subject class Remove Xs based on what the proposition says using shading for universal propositions and eraser for particular ones Remove Xs based on Boolean interpretation using your eraser

Helpful Wording All non-P are non-S Every single non-P is also a non-S If there were any Xs inside the left part of the S circle, the statement would allow a non-P that was an S, which is denied in the statement. If there are any Xs, they would be outside the two circles (they don’t appear because this is the Boolean interpretation) S P

Helpful Wording No non-P are non-S Not even one of the non-Ps is also a non-S (an X outside both circles says, here is a non-P that is also a non-S) So, to prohibit allowing an X outside those circles, that area must be shaded. P S