5.1 Standard Form Mood And Figure

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Course lecture I developed over section 5.1 of Patrick Hurley\'s "A Concise Introduction to Logic".

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5.1 Standard Form Mood And Figure

  1. 1. 5.1 Standard form, mood and figure
  2. 2. Categorical syllogisms <ul><li>Set of three categorical propositions </li></ul><ul><ul><li>Two premises and one conclusion </li></ul></ul><ul><li>Example: </li></ul><ul><ul><li>All P are M. </li></ul></ul><ul><ul><li>No S are M. </li></ul></ul><ul><ul><li>------------------- </li></ul></ul><ul><ul><li>Therefore, all S are P. </li></ul></ul><ul><li>Three different terms used in understanding syllogisms </li></ul><ul><ul><li>Middle term </li></ul></ul><ul><ul><ul><li>Represented as “M” </li></ul></ul></ul><ul><ul><li>Major term </li></ul></ul><ul><ul><ul><li>Predicate of the conclusion </li></ul></ul></ul><ul><ul><li>Minor term </li></ul></ul><ul><ul><ul><li>Subject of the conclusion </li></ul></ul></ul>
  3. 3. Syllogisms, continued <ul><li>Major premise </li></ul><ul><ul><li>Contains the major term </li></ul></ul><ul><li>Minor premise </li></ul><ul><ul><li>Contains the minor term </li></ul></ul><ul><li>The major premise comes first, then the minor premise, and finally the conclusion. </li></ul><ul><ul><li>All P are M. (Major premise) </li></ul></ul><ul><ul><li>No S are M. (Minor premise) </li></ul></ul><ul><ul><li>------------------- </li></ul></ul><ul><ul><li>Therefore, all S are P. (Conclusion) </li></ul></ul><ul><ul><li>Minor term comes before major term. </li></ul></ul>
  4. 4. Syllogisms, continued <ul><li>Mood </li></ul><ul><ul><li>Made up of the three letters that identify each proposition. </li></ul></ul><ul><ul><ul><li>Example: </li></ul></ul></ul><ul><ul><ul><ul><li>AAE – Two A-type premises and one E-type conclusion. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>AOE – An A-type premise, an O-type premise, and an E-type conclusion </li></ul></ul></ul></ul><ul><ul><ul><li>Major premise comes before minor premise. </li></ul></ul></ul>
  5. 5. Syllogisms, continued <ul><li>Figure </li></ul><ul><ul><li>Determined by the location of the middle term in the premises. </li></ul></ul><ul><ul><li>Identified as either 1, 2, 3 or 4. </li></ul></ul><ul><li>Example: </li></ul><ul><ul><li>All artists are happy. </li></ul></ul><ul><ul><li>All writers are artists. </li></ul></ul><ul><ul><li>---------------------- </li></ul></ul><ul><ul><li>Therefore, all writers are happy. </li></ul></ul><ul><ul><li>This is an AAA-1. </li></ul></ul><ul><ul><ul><li>Artists – Middle term </li></ul></ul></ul><ul><ul><ul><li>Writers – Minor term </li></ul></ul></ul><ul><ul><ul><li>Happy – Major term </li></ul></ul></ul>S P S P S P S P M S M S S M S M P M M P P M M P Figure 4 Figure 3 Figure 2 Figure 1
  6. 6. Syllogisms, continued <ul><li>Once a syllogism can be identified according to its mood and figure, it is possible to determine its validity. (Refer to the tables on page 240.) </li></ul><ul><ul><li>First, test it from the Boolean standpoint (see if the form appears on the table of unconditionally valid forms). </li></ul></ul><ul><ul><li>If it does, then it’s unconditionally valid. </li></ul></ul><ul><ul><li>If it does not, then test it again from the Aristotelian standpoint (refer to the table on conditionally valid forms) </li></ul></ul><ul><ul><ul><li>Different from the propositions, since now existence is extended to M and P (the middle term and the predicate term) Either S, M, or P has to exist, based on which row the form is in. </li></ul></ul></ul>
  7. 7. Syllogisms, continued <ul><li>Examples: </li></ul><ul><ul><li>(AAI-1) (Conditionally valid, if S exists) (Cats exist, so valid) </li></ul></ul><ul><ul><li>All mammals are animals. (All M are P) </li></ul></ul><ul><ul><li>All cats are mammals. (All S are M) </li></ul></ul><ul><ul><li>-------------------- </li></ul></ul><ul><ul><li>Therefore, some cats are animals. (Some S are P) </li></ul></ul><ul><ul><li>(EAO-3) (Conditionally valid, if M exists) (Superheroes do not exist, so not valid) </li></ul></ul><ul><ul><li>(Some superheroes are fast.) </li></ul></ul><ul><ul><li>(All superheroes are people.) </li></ul></ul><ul><ul><li>--------------------- </li></ul></ul><ul><ul><li>Therefore, some people are not fast. (Some S are not P) </li></ul></ul>
  8. 8. Syllogisms, continued <ul><ul><li>(AAI-4) (Conditionally valid, if P exists) (Billionaires exist, so valid) </li></ul></ul><ul><ul><li>All billionaires are happy people. (All P are M) </li></ul></ul><ul><ul><li>All happy people are movie stars. (All M are S) </li></ul></ul><ul><ul><li>----------------------- </li></ul></ul><ul><ul><li>Therefore, some movie stars are billionaires. (Some S are P) </li></ul></ul><ul><ul><li>(EAE-2) (Unconditionally valid) </li></ul></ul><ul><ul><li>No people are perfect. (No P are M) </li></ul></ul><ul><ul><li>All circles are perfect. (All S are M) </li></ul></ul><ul><ul><li>----------------------- </li></ul></ul><ul><ul><li>No circles are people. (No S are P) </li></ul></ul>

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