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Three Circle Venn Diagrams and Validity

by: Alexis Kreusch

Three Circle Venn Diagrams and Validity PHL

Marketplace > Wright State University > PHL > Three Circle Venn Diagrams and Validity
Alexis Kreusch

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About this Document

Learning how to graph an argument when using three circles and determining if the argument is valid at the end.
Critical Thinking
Jacob N. Bauer
Class Notes
critical, thinking, philosophy, Venn, diagram, validity, Chapter, 9, Syllogisms, Jacob, Bauer, PHL3000-05
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This 5 page Class Notes was uploaded by Alexis Kreusch on Thursday October 6, 2016. The Class Notes belongs to PHL at Wright State University taught by Jacob N. Bauer in Fall 2016. Since its upload, it has received 4 views.


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Date Created: 10/06/16
10­4­16 and 10­6­16 ­Diagramming with 3 Circles  These statements will always have 2 premises and 1 conclusion o In total three statements           o Ex. All P are T (A)          No H  (E)        No P are H (E)   Only diagram the premises  Use the conclusion to determine the order of labeling the circles o Using the statements form above o Therefore, the first circle is P and the second H o Leaving the middle term (the one stated in both premises) as the bottom one T P H P/H P H P/H/n P/ H/ TT T T  In diagramming, always do the universal statements (A and E) first  o Meaning always shade in first  Take one step at a time o First All P are T (shade exactly as before acting as if the third bubble is not there)  Shade in wherever P is not touching the T circle P H T  The Shade where No H are T imagining the P bubble is not there o That finishes this statement   Now we can check for validity o Premise True the conclusion must be true, necessarily speaking o If yes = valid o If no, or not for certain = Invalid (for sure anytime the X is on a line)  One way to tell if valid to to graph the conclusion to see if it matches the premises o If so valid, if not invalid  The example given above would be valid because it would match the conclusion  P H Particular Claims (I and O)  When having particular claims with universal it is important to always o DO universal (A and E) first – Shade first o Then the Xs can be added (I and O) o Ex. Some P are not T (O)       All M are T (A) Some P are not M (O)  The second statement, All M are T, would be graphed first  Then the first, one has to decide if the x goes on the a line or in the  bubbles. This is done by looking at what is around it   Since we know All M are T is shaded we know nothing can go  in those areas.   Some P are not T we would graph an X were it would fit.  Seeing as there is only one spot open were the P and T circles  intersect it must go there.  P M T  Particular claims are trickier due to this reasoning o If not shaded it would have been on the line from the M circle in the P bubble  because that is the letter we are given  Now we can trick for Validity by graphing the conclusion  P H  The graphs match so it is a Valid argument  o Ex. All P are T (A)  Some M are   (I) Some P are M (I)  State with graphing the A statement  The see if the I term will go into a bubble or sit on a line  Some M are T has two open spaces on the diagram so therefore we do not know which one it should go in. Meaning it will be  on the line between them instead P M T  Now the last step, Validity P M  The conclusion does not match the first diagram making the argument invalid


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