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Diagram for Categorical Syllogism 1.pptx
- 2. Areas/Regions/Quadrants and Term Relation 3 overlapping circles (one for each of the 3 terms) 7 areas (area 8 is outsidewe wont use that).What does each one mean? 2 TERMS (CIRCLES) DONE AT A TIME. ONE PREMISE AT A TIME. SHADE EMPTY AREAS: SHADING MEANS EMPTY EXAMPLE: No A are B. All C are A. So, no C are B. In No A are B, terms A and B: There are no As in B. SHADE THE AREAS WHERE 2 TERMS COME TOGETHER. No problem if the shading extends into C, or, in the case of C and A (in the All C are A premise), into B.
- 3. Diagramming Steps Initials: Minor (S of conclusion), major (P of conclusion), and middle (M) Three overlapping circles: lower left for subject (minor), lower right for predicate (major), and middle for the middle term. Diagram premises only, universal statements 1stbefore particular ones. Shading for universal statements, if overlapping area is empty. X for particular statements, if there are some (at least one) of one term in another. If a circle line runs through the area where the x should go, place the x on the line. For the Aristotelian (but not for the hypothetical) standpoint, add x in an unshaded area next to a shaded one (to show existence)
- 4. Last Step of Diagramming After diagramming the premises, inspect the diagram. If the content of the conclusion is represented in the diagram, the argument is valid (the premises guarantee the conclusion). If the content of the conclusion is not represented in the diagram, the argument is invalid (the premises do not guarantee the conclusion). Venn diagramming is a visual test of validity. It shows whether or not the premises guarantee the conclusion. We do not diagram the conclusion. The diagram has to tell us whether the argument is valid or not.
- 5. Can You Diagram this? Some warriors are Spartans All Spartans are Greeks Some Greeks are warriors (FYI: IAI-4) Head start: S= G P=W M=S
- 7. Lower left: G: Greeks (Subject of conclusion-minor term) Lower right: W: Warriors (Predicate of the conclusion-Major term) Top one: S: Spartans (Middle term) 1st: Diagram the universal premise: All Spartans are Greeks: Top and left circles: Shade 1 and 4 2nd: Diagram the particular premise: Some warriors are Spartans: Left and top circles: Place an x in area 3 Last: After diagramming the premises, can you see the conclusion (Some Greeks are warriors? If the conclusion is represented, the argument is valid. Shading: 1, 4 X: 3 Validity: V
- 8. UNIVERSAL STATEMENTS NOTE: In the examples below, the copula should be are, not is.
- 9. Syllogisms with a Particular Premise VALID: First example INVALID: 2nd and 3dr examplesmore than one area for X. All these syllogisms will be invalid. Something exists but it is not shown exactly wherethe premises do not guarantee the conclusion. SHOW INVALIDITY: An x may be placed in each area along with a line connecting them, as shown in 2nd. BUT USE THIS METHOD INSTEAD: Place the x on the line, as shown in ex. 3
- 10. AGAIN: The X Symbol for Particular Premises and to show the Reality of the Subject Term X for particular premises: If not clear which one of two areas, place it on the line separating the two areas P and M Some To show reality: In the case of the Aristotelian standpoint, for the subject terms of the premises (if we can assume existence): If there is only one region unshaded an unshaped area next to a shaded one--(either or both circles), place an X there
- 11. NOTE With most syllogisms, whether or not you presuppose that things exist in the three categories doesnt matter in assessing validity. But in a few cases all involving syllogisms with two universal premises and a particular conclusion it does. If you have a syllogism with two universal premises and a particular conclusion it will be counted invalid using the hypothetical viewpoint. To tell whether it is valid assuming the existence of things in at least one of your categories, after representing the premises, represent the key assumption you want to make about existence and see whether the conclusion is then represented. For instance: Invalid from hypothetical viewpoint: Valid from existential viewpoint, assuming the existence of Ss
- 12. How to Report VD of Categorical Syllogisms on Exam III FIRST BOX--Shading: Identify the number/s of the region/s--just the number/s. If more than one section (more than one number), separate the numbers with commas. Do not use the word and (before the last number), just commas. Sample: 1, 4, 7. If no shading, write the word none. SECOND BOX--X: Identify the number/s of the region/s--just the numbers. If more than one section (more than one number), separate the numbers with commas. Do not use the word and (before the last number), just commas. Sample: 1, 4, 7. If you have to place the x on the line, write "on the line between(number of first area) and (number of second area)" Sample: on the line between 5 and 6 If an x on the line appears twice, separate the two instances with a comma: Sample: on the line between 4 and 6, on the line between 5 and 6 Note: When diagramming from the existential viewpoint and the x goes on the line, skip it; do not add an existential x on the line.) If no X, write word none. THIRD BOX--Valid or Invalid: Write the letter V for valid--not the word valid; or the letter I for invalid--not the word invalid.