Categorical Syllogisms Definition Three categorical propositions Three terms: each used twice Two Premises One Conclusion All Men are Mortal Socrates is a man/ All people identical with Socrates are Men Socrates is mortal/ All people identical with Socrates are people who are mortal Symbolized All M are P All S are M All S are P Terms Major Term: Predicate of the conclusion Symbolized by “P” Minor Term: Subject of the conclusion Symbolized by “S” Premises Standard Form Major Premise listed first Minor Premise listed second Example All M are P Major Premise All S are M Minor Premise All S are P Standard Form Same terms Same Sense (no equivocation) Major premise first Minor premise second Mood Three letter phrase which corresponds to the 3 proposition types in the syllogism Example: All Great Danes are dogs No cats are dogs Therefore: No Cats are Great Danes Mood AEE ( Figure: 2 Unconditionally Valid) Figure 1 M are P S are M S are P Left Right Figure 2 P are M S are M S are P Left Right Figure 3 M are P M are S S are P Left Right Figure 4 P are M M are S S are P Left Right Venn Diagrams Marks/ Shading for premises only Universals shaded first Particulars: That one thing exists That it belongs or is excluded from some class Venn Diagrams Continued Shade areas completely “x” goes in unshaded region “x” on the line when there is insufficient information Not on the intersection of two lines Boolean/ Aristotelian: does the subject denote existent things? Examples EAE- 2 (Valid) M No P are M All S are M No S are P S P Example AEE- 4 (Valid) M All P are M No M are S No S are P S P AOO- 2 (Valid) All P are M M Some S are not M Some S are not P X S P AOO- 1 Invalid All M are P M M Some S are not M Some S are not P X S P OIO-1 (Invalid) Some M are not P M Some S are M X Some S are not P X S P Rules Method Rules and Fallacies Rules: The Middle term must be distributed in at least one premise If not: undistributed middle If a term is distributed in the conclusion then it must be distributed in the premise in which occurs If not: illicit Major/ Minor Rules and Fallacies Continued If there is a negative premise then there must be a negative conclusion There can not be more than 2 negative propositions in the argument Existential Fallacy .