PHIL 1102 PHILOSOPHY AND LOGIC CATEGORICAL SYLLOGISM STUDY GUIDE Categorical syllogisms consist of three categorical propositions In a standard categorical syllogism there are a total of 3 terms The major term the minor term and the middle term Each of them appear twice in the syllogism All Soldiers are Patriots No Traitors are Patriots No Traitors are Soldiers The major term is always the predicate of the conclusion Therefore in the example above the major term is Soldier It also always appears in the first premise The minor term is always the subject of the conclusion Therefore in the example above the minor term is Traitor It also always appears in the second premise The middle term does not appear in the conclusion but is repeated in the premises Therefore in the example above the middle term is Patriot Mood and Figure The figure of a syllogism is determined by the arrangement of the middle term in the premises In the first figure the middle term is the subject of the first premise and the predicate of the second In the second figure the middle term is the predicate of both premises In the third figure the middle term is the subject of both premises In the fourth figure the middle term is the predicate of the first premise and the subject of the second Figure 1 M P S M S P Figure 2 P M S M S P Figure 3 Figure 4 M P M S S P P M M S S P The mood of a syllogism is a three letter mnemonic using the Letters assigned to the four kinds of categorical propositions A E I and O Therefore All Soldiers are Patriots No Traitors are Patriots No Traitors are Soldiers has a mood of AEE Additionally since the middle term Patriot appears as the predicate of both premises we know that it uses Figure 2 Due to the differences in how the Aristotelian and Boolean viewpoints view existential import an argument may be valid from the Aristotelian standpoint even if it s not valid from the Boolean standpoint However if it s valid from the Boolean standpoint it s also valid from the Aristotelian standpoint From this we can say that the earlier example is valid from the Boolean standpoint because it has the form AEE 2 which is valid Boolean Standpoint Valid Syllogistic Forms AAA EAE AII EIO EAE AEE EIO AOO IAI AII OAO EIO AEE IAI EIO AAI EAO AEO EAO AAI EAO AAI EAO AEO Aristotelian Standpoint Figure Valid Syllogistic Forms Figure 1 2 3 4 1 2 3 4 Rules and Fallacies In addition to these forms there are 5 rules that can be used to test categorical syllogisms based on the rules of distribution in the categorical proposition section If a syllogism satisfies all of these rules then it is valid from the Boolean standpoint and thus the Aristotelian standpoint as well The middle term must be distributed at least once If this rule is broken the syllogism commits the fallacy of Undistributed Middle If a term is distributed in the conclusion then it must be distributed in the premise If this rule is broken the syllogism commits the fallacy of Illicit Major or Illicit Minor depending on A syllogism cannot have two negative premises If this rule is broken the syllogism commits A syllogism cannot have an negative premise and an affirmative conclusion or a negative the term in question the fallacy of Exclusive Premises conclusion with no negative premises From the Boolean standpoint if both premises are universal then the conclusion cannot be particular If this rule is broken the syllogism commits the Existential Fallacy However from the Aristotelian standpoint this may be perfectly valid as long as all terms in the syllogism are things that exist in the real world Study Tips The EAO mood is valid from the Aristotelian standpoint no matter the figure Watch out for syllogisms that use fantasy characters or paradoxes as their terms Aristotelian existential import doesn t extend to things that do not exist in the material world Also remember that the Existential fallacy only extends to syllogisms with universal premises and a particular conclusion For example No headless horsemen are keen sighted riders Therefore no keen sighted riders are headless horsemen is still valid Venn Diagrams Venn diagrams can be used to assess the validity of a syllogism Based on the what is contained in a 3 variable venn diagram it can be determined whether the premises logically imply the conclusion or not In boolean logic A propositions are represented by shading the entirety of the circle representing the subject except for it s intersection with the predicate while E propositions are represented by shading only the intersection of the subject and the predicate Aristotelian logic differs by placing a circled X in the non shaded area of universal propositions as existential import is taken into account for all things that exist in the material world I propositions are represented by placing an X in the intersection of the subject and the predicate while O propositions are represented by placing an X in the circle representing the subject outside of the intersection Sorites A sorites is a chain of syllogisms that leaves the intermediate conclusions out If a single one of the component syllogisms is invalid then the whole sorites is invalid In order to test a sorites you need to rearrange the premises so that it is in standard form To do that you first need to find which term is the predicate of the conclusion and find that term in one of the premises Some M are H All G are Q All S are G No H are Q Some M are not S Some M are not S All S are G Once you have found the premise write it first on the line Then use the other term in that premise find it in one of the premises and write that premise second on the line Do this for every premise and the write the conclusion at the bottom All S are G All G are Q No H are Q Some M are H Some M are not S Now that it is in standard form you need to derive the intermediate conclusions either through use of venn diagrams or your knowledge of valid syllogistic forms For Example the premises All S are G and All G are Q imply the conclusion All S are Q This conclusion is now written on another line as a premise and paired with the next premise in the sorites If this can be done all the way through to the conclusion the sorites is valid All S are G All S are Q All G are Q No S are H No H are Q No H are Q Some M are not S Some M are H Some M are H Some M are not S