Critical Thinking CRIT 1101
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This 3 page Class Notes was uploaded by Destini Hermann on Monday October 5, 2015. The Class Notes belongs to CRIT 1101 at Clayton State University taught by Elliott McElroy in Fall. Since its upload, it has received 38 views. For similar materials see /class/219548/crit-1101-clayton-state-university in Critical Thinking at Clayton State University.
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Date Created: 10/05/15
NOTES ON 52 USING VENN DIAGRAMS TO TEST THE VALIDITY OF CATEGORICAL SYLLOGISMS In Chapter 4 we used Venn diagrams to represent the content of categorical propositions There we needed only two overlapping circles 0 one for the subject term and 0 one for the predicate term Here we need three overlapping circles 0 one for the subject term 0 one for the predicate term and 0 one for the middle term V9 Always follow the convention of having the subject term represented by the lower left circle the predicate term by the lower right circle and the middle term by the upper center circle Begin numbering the sections at the top and drop down moving from left to right REMEMBER On the Boolean interpretation universal propositions 1A amp E do not imply the existence of any member of the subject categogy They only serve to limit the possibilities of the members of the subject category if it should happen that any members do in fact exist For example 0 The statement All humans are animals states nothing more than No humans if any humans actually exist are outside of the category of animals 0 The statement All leprechauns are little people States nothing more than No leprechauns if any leprechauns actually exist are outside of the category of little people 0 The statement No human beings are sh States nothing more than All human beings if any human beings actually exist are outside of the category of sh 0 The statement No leprechauns are purple people simply states that All leprechauns if any leprechauns actually exist are outside of the category of purple people In developing a Venn diagram of these universal categorical propositions we shade the part of the overlapping circles that the propositions exclude REMEMBER On the Boolean interpretation particular categorical propositions I and O which begin with the word Some assert that at least one member of the category designated by the subject exists and is included in or excluded from the predicate category In developing a Venn diagram for these categorical propositions we place an X in the part ofthe subject circle that is inside or outside of the predicate circle The following rules apply 1 Place marks on the diagram shadings or Xs to represent only the premises DO NOT EVER ADD ANY MARKS T0 DIAGRAM THE CONCLUSION If the argument contains a universal premise and a particular premise enter the markings for the universal premise rst This will make it clear where the X goes if the other premise is a particular proposition If there are two universal premises or two particular premises it does not matter which you diagram first 3 When shading an area shade all of the area that is designated See the right and wrong diagrams for 5 on page 253 245 4 When diagramming a particular premise place an X in the area designated by the subject That area will be divided into two parts If part ofthe area is shaded place the X in the unshaded part If neither part is shaded place the X on the line between the two parts See the right and wrong diagrams for 6 on pages 253 245 and 254 246 N To test for validity of a categorical syllogism diagram the two premises and then inspect the diagram to see if the conclusion is also diagrammed If it is the syllogism is valid the premises necessarily imply the conclusion If diagramming the premises does not result in the conclusion s also being diagrammed the syllogism in invalid the premises do not necessarily imply the conclusion
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