Mastering Venn Diagrams: Validity in Categorical Syllogisms
School
Nanjing University**We aren't endorsed by this school
Course
CHINE 209
Subject
Philosophy
Date
Dec 12, 2024
Pages
20
Uploaded by EarlSummer15691
10/13/2022“Some” Statements: Example, 3Some Baptists are coffee lovers•Since part of the area that represents the overlap of Baptists and coffee lovers is already shaded, we place the “X” in the unshaded part of that overlapAll Baptists are ProtestantsJump to “Some” Statements: Example, 3, Appendix© 2019 McGraw-Hill Companies. All Rights Reserved. 9-21“Some” Statements: Example, 4Some Baptists are coffee loversAll Baptists are ProtestantsSo, some Protestants are coffee lovers•Since the conclusion suggests that there is at least one individual within the overlap of Protestants and
coffee lovers, and the first two Jump to “Some” Statements: Example, 4, Appendixpremises place an “X” in that area, the argument is valid © 2019 McGraw-Hill Companies. All Rights Reserved. 9-2211
10/13/2022Diagramming When an Argument is Invalid: Example, 1•All painters are artists•Some magicians are artists •So, some magicians are paintersJump to Diagramming When an Argument is Invalid: Example, 1, Appendix © 2019 McGraw-Hill Companies. All Rights Reserved. 9-23Diagramming When an Argument is Invalid: Example, 2All painters are artists•Notice we start with the first premise because it is an “all” statement and thus requires shadingJump to Diagramming When an Argument is Invalid: Example, 2, Appendix © 2019 McGraw-Hill Companies. All Rights Reserved. 9-24
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10/13/2022Diagramming When an Argument is Invalid: Example, 3All painters are artistsSome magicians are artists•We place an X in that portion of the Magicians circle that overlaps with the Artists circle to represent the claim•The area is divided into two parts (“1” and “2”)•We have no information thatwarrants Jump to Diagramming When an Argument is Invalid: Example, 3, Appendix placing the X in one of these areas rather than the other. In such cases, we place the X precisely on the line between the two sections.© 2019 McGraw-Hill Companies. All Rights Reserved. 9-25Diagramming When an Argument is Invalid: Example, 4All painters are artistsSome magicians are artistsSo, some magicians are painters
•There is an X in the Magicians circle, but it dangles on the line between the Artists circle and the Painters circle. We don’t know whether it is inside or outside the Painters circle. © 2019 McGraw-Hill Companies. All Rights Reserved. 9-2613
10/13/2022Using Venn Diagrams to Test the Validity of Categorical Syllogisms, 1Step 1: Translate all statements in the argument (if necessary) into standard-form categorical statementsStep 2: Draw and label three overlapping circles •One for each term (class name) in the argument, with the two circles for the conclusion at the bottomStep 3: Use shading to represent the information in all or no statements and use X’s to represent the information in “some” statements© 2019 McGraw-Hill Companies. All Rights Reserved. 9-27Using Venn Diagrams to Test the Validity of Categorical Syllogisms, 2Step 4: Diagram the two premises•No marks should be entered for the conclusionStep 5: When placing an X in a two-part area, if one part of the area has been shaded, place the X in the unshaded part
•If neither part of the area has been shaded, place the X precisely on the line separating the two parts© 2019 McGraw-Hill Companies. All Rights Reserved. 9-2814
10/13/2022Using Venn Diagrams to Test the Validity of Categorical Syllogisms, 3Step 6: Look to see if the diagram contains all the information presented in the conclusion•If it does, the argument is 9-29•If it doesn’t, the argument is invalid© 2019 McGraw-Hill Companies. AllRights Reserved.Practice:1. No sharks are pets, since no barracuda are pets, and no sharks are barracuda2. Some bankers are vegetarians.No anarchists are bankers.So, some anarchists are not vegetarians.3. No poker players are early-risers.Some firefighters are early-risers.So, some firefighters are not poker players
© 2019 McGraw-Hill Companies. All Rights Reserved. 9-3015
10/13/2022Midterm exam preparation40 multiple choices questions (90 min)-10 for chapter 1,2(20 points)-10 for chapter 3 (20 points)-10 for chapter 9(30 points)-10 for chapter 10(30 points)Practice the examples in reference book for these chapters© 2019 McGraw-Hill Companies. All Rights Reserved. 9-31Appendices
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10/13/2022Standard-Form Examples, 1, Appendix 1The Venn diagram contains two partially overlapping circles. The circle on the left islabeled S and is shaded. The circle on the right is labeled P.Jump back to Standard-Form Examples, 1© 2019 McGraw-Hill Companies. All Rights Reserved. 9-33Standard-Form Examples, 1, Appendix 2The Venn diagram contains two partially overlapping circles. The circle on the left is labeled S, and the circle on the right is labeled P. The area where the circles overlap is shaded.
Jump back to Standard-Form Examples, 1© 2019 McGraw-Hill Companies. All Rights Reserved. 9-3417
10/13/2022Standard-Form Examples, 2, Appendix 1The Venn diagram contains two partially overlapping circles. The circle on the left is labeled S, and the circle on the right is labeled P. The area where the circles overlap contains an X.Jump back to Standard-Form Examples, 2© 2019 McGraw-Hill Companies. All Rights Reserved. 9-35Standard-Form Examples, 2, Appendix 2The Venn diagram contains two partially overlapping circles. The circle on the left is labeled S, and the circle on the right is labeled P. The circle on the left contains an X.
Jump back to Standard-Form Examples, 2© 2019 McGraw-Hill Companies. All Rights Reserved. 9-3618
10/13/2022Using Venn Diagrams to Test Validity, 1, AppendixThe Venn diagram represents the statements “No doctors are professional wrestlers. All cardiologists are doctors. So,no cardiologists are professional wrestlers.” The diagram contains three partially overlapping circles. In a clockwisedirection, the first circle is labeled doctors,the second circle is labeled professional wrestlers, and the third circle is labeled cardiologists. Jump back to Using Venn Diagrams to Test Validity, 1© 2019 McGraw-Hill Companies. All Rights Reserved. 9-37Using Venn Diagrams to Test Validity, 2, AppendixThe Venn diagram represents the statements “No doctors are professional wrestlers. All cardiologists are doctors. So, no cardiologists are professional wrestlers.” The diagram contains three partially overlapping circles. In a clockwise direction, the first circle is labeled doctors, the second circle is labeled professionalwrestlers, and the third circle is labeled cardiologists. The circles labeled doctors and
professional wrestlers and the area where the three circles overlap are shaded.Jump back to Using Venn Diagrams to Test Validity, 2© 2019 McGraw-Hill Companies. All Rights Reserved. 9-3819
10/13/2022Using Venn Diagrams to Test Validity, 3, AppendixThe Venn diagram represents the statements “No doctors are professional wrestlers. All cardiologists are doctors. So, no cardiologists are professional wrestlers.” The diagram contains three partially overlapping circles. In clockwise direction, the first circle is labeled doctors, the second circle is labeled professional wrestlers, andthe third circle is labeled cardiologists. The circles labeled doctors and professional wrestlers and the area where the three circles overlap are shaded to represent the premise “No doctors are professional wrestlers.” To represent the premise “All cardiologistsare doctors,” the part of the Cardiologists circle that does not overlap with the Doctors circle is shaded using lines.Jump back to Using Venn Diagrams to Test Validity, 3© 2019 McGraw-Hill Companies. All Rights Reserved. 9-39“Some” Statements: Example, 1, AppendixThe Venn diagram represents the statements “Some Baptists are coffee lovers. All Baptists are Protestants. So, some Protestants are coffee lovers.” The diagram contains three
partially overlapping circles. In a clockwise direction, the first circle is labeled Baptists, the second circle is labeled coffee lovers, and the third circle is labeled Protestants. Jump back to “Some” Statements: Example, 1© 2019 McGraw-Hill Companies. All Rights Reserved. 9-4020