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

Slides:



Advertisements
Similar presentations
Reason and Argument Chapter 7 (1/2).
Advertisements

Venn Diagram Technique for testing syllogisms
Test the validity of this argument: Some lawyers are judges. Some judges are politicians. Therefore, some lawyers are politicians. A. Valid B. Invalid.
Part 2 Module 3 Arguments and deductive reasoning Logic is a formal study of the process of reasoning, or using common sense. Deductive reasoning involves.
Test the validity of this argument: Some lawyers are judges. Some judges are politicians. Therefore, some lawyers are politicians. A. Valid B. Invalid.
An overview Lecture prepared for MODULE-13 (Western Logic) BY- MINAKSHI PRAMANICK Guest Lecturer, Dept. Of Philosophy.
Deductive Arguments: Categorical Logic
Categorical Arguments, Claims, and Venn Diagrams Sign In! Review Group Abstractions! Categorical Arguments Types of Categorical Claims Diagramming the.
Part 2 Module 3 Arguments and deductive reasoning Logic is a formal study of the process of reasoning, or using common sense. Deductive reasoning involves.
Deduction: the categorical syllogism - 1 Logic: evaluating deductive arguments - the syllogism 4 A 5th pattern of deductive argument –the categorical syllogism.
Today’s Topics Introduction to Predicate Logic Venn Diagrams Categorical Syllogisms Venn Diagram tests for validity Rule tests for validity.
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.
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.
Copyright © Cengage Learning. All rights reserved.
Critical Thinking: A User’s Manual
Categorical Syllogisms
1.1 Sets and Logic Set – a collection of objects. Set brackets {} are used to enclose the elements of a set. Example: {1, 2, 5, 9} Elements – objects inside.

CATEGORICAL PROPOSITIONS, CHP. 8 DEDUCTIVE LOGIC VS INDUCTIVE LOGIC ONE CENTRAL PURPOSE: UNDERSTANDING CATEGORICAL SYLLOGISMS AS THE BUILDING BLOCKS OF.
Chapter 1 Logic Section 1-1 Statements Open your book to page 1 and read the section titled “To the Student” Now turn to page 3 where we will read the.
The Science of Good Reasons
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.
Critical Thinking Lecture 8 An introduction to Categorical Logic By David Kelsey.
Question of the Day!  We shared a lot of examples of illogical arguments!  But how do you make a LOGICAL argument? What does your argument need? What.
Chapter 15: Rules for Judging Validity. Distribution (p. 152) Several of the rules use the notion of distribution. A term is distributed if it refers.
Deductive Reasoning Rules for Valid Syllogisms. Rules for a valid categorical syllogism 1.A valid syllogism must possess three, and only three, unambiguous.
Chapter 18: Conversion, Obversion, and Squares of Opposition
4 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.
Logic – Basic Terms Logic: the study of how to reason well. Validity: Valid thinking is thinking in conformity with the rules. If the premises are true.
LOGICAL REASONING FOR CAT 2009.
CATEGORICAL SYLLOGISMS
Critical Thinking Lecture 8 An introduction to Categorical Logic
Critical Thinking Lecture 9 The Square of Opposition
Chapter 17: Missing Premises and Conclusions. Enthymemes (p. 168) An enthymeme is an argument with an unstated premise or conclusion. There are systematic.
Invitation to Critical Thinking Chapter 6
DEDUCTIVE ARGUMENTS The aim of this tutorial is to help you learn to recognize, analyze, and evaluate deductive arguments.
Chapter 6 Evaluating Deductive Arguments 1: Categorical Logic Invitation to Critical Thinking First Canadian Edition.
Critical Thinking: A User’s Manual
Critical Thinking Lecture 10 The Syllogism By David Kelsey.
Critical Thinking Lecture 8 An introduction to Categorical Logic By David Kelsey.
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
Logic.
Testing Validity With Venn Diagrams
Deductive Logic, Categorical Syllogism
5 Categorical Syllogisms
Today’s Topics Introduction to Predicate Logic Venn Diagrams
5.1 Standard Form, Mood, and Figure
5 Categorical Syllogisms
Chapter 3 Philosophy: Questions and theories
4.1 The Components of Categorical Propositions
Categorical Propositions
Philosophy 1100 Class #8 Title: Critical Reasoning
Critical Thinking Lecture 9 The Square of Opposition
Philosophy 1100 Title: Critical Reasoning Instructor: Paul Dickey
“Only,” Categorical Relationships, logical operators
5 Categorical Syllogisms
Chapter 6 Categorical Syllogisms
Reason and Argument Chapter 7 (2/2).
Philosophy 1100 Class #9 Title: Critical Reasoning
Philosophy 1100 Class #7 Title: Critical Reasoning
TODAY’S OBJECTIVE: Standard: MM1G2
TODAY’S OBJECTIVE: Standard: MM1G2
Presentation transcript:

1 Philosophy 1100 Title:Critical Reasoning Instructor:Paul Dickey Website: Today: “Nail that Claim” Exercise! Exercises 8-1 & 8-2 Next week: Reading Assignment: Chapter 8, pp Exercise 8-4 (odd numbered problems) Exercise 8-11, problems #1-5

COURSE EVALUATION Electronic/Online Course/Instructor Feedback 13/WI Availability until February 20, Instruction Sheet will be on Quia site.

3 Final Editorial Analysis. 10% of your total grade. 40 Points. The paper MUST be 3 to 5 pages. The article that you select will need to be approved by instructor by class next week. The article must be at least 7 paragraphs or 500 words in length. I recommend that you select your editorials or “articles” carefully from one of these sources ) As before, there are five steps to the required analysis. Each step must be discussed appropriately.

New Quia Activity for Categorical Logic (Chapter 8) "Dude, Sink the H.M.S. Invalid to the Bottom of the Sea!" & NOW …. PRESENTS FOR EVERYBODY!

Chapter Eight D eductive Arguments: Categorical Logic

Categorical Logic Consider the following claims: 1. Everybody who is ineligible for Physics 1A must take Physical Science 1. 2) No students who are required to take Physical Sciences 1 are eligible for Physics 1A. Are these different claims or the same claim? Categorical logic is important because it gives us a tool to work through the confusion with a technique to answer that question clearly. Such is done through the use of standard logic forms.

Categorical Logic Categorical Logic is logic based on the relations of inclusion and exclusion among classes. That is, categorical logic is about things being in and out of groups and what it means to be in or out of one group by being in or out of another group.

Four Basic Kinds of Claims in Categorical Logic (Standard Forms) A: All _________ are _________. (Ex. All Presbyterians are Christians. E: No ________ are _________. (Ex. No Muslims are Christians. ___________________________________ I: Some ________ are _________. (Ex. Some Arabs are Christians. O: Some ________ are not _________. (Ex. Some Muslims are not Sunnis.

Four Basic Kinds of Claims in Categorical Logic What goes in the blanks are terms. In the first blank, the term is the subject. In the second blank goes the predicate term. A: All ____S_____ are ____P_____. (Ex. All Presbyterians are Christians.

Venn Diagrams

(See page 256 in textbook.) Categorical Logic The Four Basic Kinds of Claims in Categorical Logic can be represented using Venn Diagrams. The two claims that include one class or part of a class within another are the affirmative claims (I.e. the A-claims & the I-Claims. The two claims that exclude one class or part of a class from another are the negative claims (I.e. the E-claims and the O-claims.

The Bottom Line? Translating Claims into Standard Form for Analysis Two claims are equivalent claims if, and only if, they would be true in all and exactly the same circumstances. Equivalent claims, in this sense, say the same thing. Equivalent claims will have the same Venn Diagram.

1.The word “only” used by itself, introduces the predicate term of an A-claim, e.g. “Only Matinees are half-price shows” is to be translated as “All half-price shows are matinees” 2.The phrase “the only” introduces the subject term of an A-claim, e.g Matinees are the only half-price shows” also translates to “All half-price shows are matinees.” 3.Claims about single individuals should be treated as A-claims or E-claims, e.g. “Aristotle is left-handed” translates to either “Everybody who is Aristotle is left handed” or “No person who is Aristotle is not left- handed.” Some Tips

Class Workshop: Exercise 8-1 and 8-2

1.Conversion – The converse of a claim is the claim with the subject and predicate switched, e.g. The converse of “No Norwegians are Swedes” is “No Swedes are Norwegians.” 2.Obversion – The obverse of a claim is to switch the claim between affirmative and negative (A -> E, E -> A, I -> O, and O -> I and replace the predicate term with the complementary (or contradictory) term, e.g. The obverse of “All Presbyterians are Christians” is “No Presbyterians are non-Christians.” 3.Contrapositive – The contrapositive of a claim is the cliam with the subject and predicate switched and replacing both terms with complementary terms (or contradictory terms), e.g. The contrapositive of “Some citizens are not voters” is “Some non-voters are not noncitiizens. Three Categorical Operations

By understanding these concepts, you can apply the three rules of validity for deductive arguments: Conversion – The converses of all E- and I- claims, but not A- and O- claims are equivalent to the original claim. Obversion – The obverses of all four types of claims are equivalent to their original claims. 3.Contrapositive – The contrapositives of all A- and O- claims, but not E- and I- claims are equivalent to the original claim. OK, So where is the beef?

Class Workshop: Exercise 8-5

Categorical Syllogisms A syllogism is a deductive argument that has two premises -- and, of course, one conclusion (claim). A categorical syllogism is a syllogism in which: 1.each of these three statements is a standard form, and 2.there are three terms which occur twice, once each in two of the statements.

Three Terms of a Categorical Syllogism For example, the following is a categorical syllogism: (Premise 1) No Muppets are Patriots. (Premise 2) Some Muppets do not support themselves financially. (Conclusion) Some puppets that do not support themselves are not Patriots.. The three terms of a categorical syllogism are: 1) the major term (P) – the predicate term of the conclusion (e.g. Patriots). 2) the minor term (S) – the subject term of the conclusion (e.g. Self-supporters) 3) the middle term (M) – the term that occurs in both premises but not in the conclusion (e.g. Muppets).

USING VENN DIAGRAMS TO TEST ARGUMENT VALIDITY 1.Identify the classes referenced in the argument (if there are more than three, something is wrong). When identifying subject and predicate classes in the different claims, be on the watch for statements of “not” and for classes that are in common. Make sure that you don’t have separate classes for a term and it’s complement. 2. Assign letters to each classes as variables. 3. Given the passage containing the argument, rewrite the argument in standard form using the variables. No M are P. Some M are S. ____________________ Therefore, Some S are not P. M = “ xxxx “ S = “ yyyy “ P = “ zzzz “

4.Draw a Venn Diagram of three intersecting circles. 5.Look at the conclusion of the argument and identify the subject and predicate classes. Therefore, Some S are not P. 6.Label the left circle of the Venn diagram with the name of the subject class found in the conclusion. (10 A.M.) 7.Label the right circle of the Venn diagram with the name of the predicate class found in the conclusion. 8.Label the bottom circle of the Venn diagram with the middle term.

9.Diagram each premise according the standard Venn diagrams for each standard type of categorical claim (A,E, I, and O). If the premises contain both universal (A & E- claims) and particular statements (I & O-claims), ALWAYS diagram the universal statement first (shading). When diagramming particular statements, be sure to put the X on the line between two areas when necessary. 10. Evaluate the Venn diagram to whether the drawing of the conclusion "Some S are not P" has already been drawn. If so, the argument is VALID. Otherwise it is INVALID. No M are P. Some M are S.

Class Workshop: Exercise 8-11, #6

Power of Logic Exercises: ANOTHER GOOD SOURCE: