5.5 ENTHYMEMES

ENTHYMEMESIts all up here. UB TaglineA. DefinitionEnthymeme An argument that is stated incompletely, the unstated part of it being taken for granted. (Introduction to Logic by Copi and Cohen 14th Edition)An informal syllogism relying on unstated assumptions that are omitted because they are already well-known or agreed upon. (Wikipedia.org)Example 1:Jacobson McArthur Labatiti is a son of a Filipino citizen.Therefore, Jacobson McArthur Labatiti is a Natural-born citizen.Standard Syllogistic FormAll sons of Filipino citizens are natural-born citizens.Jacobson McArthur Labatiti is a son of a Filipino citizen.Therefore Jacobson McArthur Labatiti is a natural-born citizen.The unstated part is understood or only in the mind.Example 2:"Socratesis mortal because he's human."The completeformalsyllogism would be the classic:All humans are mortal. (major premise - assumed)Socrates is human. (minor premise- stated)Therefore, Socrates is mortal. (conclusion - stated)B. Orders of EnthymemeB.1. First-order enthymemeAn incompletely stated syllogism in which the proposition that is taken for granted but not stated is the major premise.Example 1:Abe is a great lawyer because he is a UC lawyer.All UC lawyers are great lawyers.(ASSUMED)Abe is a UC lawyer.(STATED)Therefore, Abe is a great lawyer.(STATED)AAA-1Example 2:Transgenic animals are manmade and as such are patentable.The premise understood but not stated here is that whatever is manmade is patentable.Standard form translation:All manmade things are patentable things.All transgenic animals are manmade things.Therefore, all transgenic animals are patentable things.AAA-1Example 3:Productivity is desirable because it betters the condition of the vast majority of the people.The premise understood but not stated here is that whatever betters the condition of the vast majority of people is desirable.Standard form translation:All states that better the condition of the vast majority of people are desirable.Productivity is a state that betters the condition of the vast majority of the people.Therefore, productivity is desirable.AAA-1B.2. Second-order enthymemeAn incompletely stated syllogism in which the proposition that is taken for granted but not stated is the minor premise.Example 1:Abe is a great lawyer because all UC layers are great lawyers. All UC lawyers are great lawyers.(STATED)Abe is a UC lawyer.(ASSUMED)Therefore, Abe is a great lawyer.(STATED)Example 2:No enthymemes are complete, so this argument is incomplete.The premise understood but not stated here is that this argument is an enthymeme.Standard form translation:All enthymemes are incomplete.This argument is an enthymeme.Therefore, this argument is incomplete.AAA-1

Example 3:Some of the boys in SS1B are handsome so there are people who are handsome yet arrogant.The premise understood but not stated here is that All SS1B boys are arrogant.Standard form translation:Some SS1B boys are handsome.All SS1B boys are arrogant people.Some arrogant people are handsome.IAI-3B.3. Third-order EnthymemeAn incompletely stated syllogism in which the proposition that is taken for granted but not stated is the conclusion.Example 1:Abe is a UC lawyer and all UC layers are great lawyers.All UC lawyers are great lawyers.(STATED)Abe is a UC lawyer.(STATED)Therefore, Abe is a great lawyer.(ASSUMED)Example 2:Who controls the past controls the future. Who controls the present controls the past.The premise understood but not stated here is that who controls the present controls the future.Standard form translation:A person who controls the past is a person who controls the future.A person who controls the present is a person who controls the past.A person who controls the present is a person who controls the future. (Barbara)Example 3:A nation without conscience is a nation without a soul. A nation without a soul is a nation that cannot live.The premise understood but not stated here is that a nation without conscience is a nation that cannot live.Standard form translation:A nation without a soul is a nation that cannot live.A nation without conscience is a nation without a soul.Therefore, a nation without conscience is a nation that cannot live. (Barbara)More Examples:As a matter of fact, man, like woman, is flesh, therefore passive, theplaything of his hormones and of the species, the restless prey of hisdesires.Simone de Beauvoir, The Second Sex, 1949

More Examples:As a matter of fact, man, like woman, is flesh, therefore passive, theplaything of his hormones and of the species, the restless prey of hisdesires.Simone de Beauvoir, The Second Sex, 1949

TRANSLATION:

All men are matters made of flesh.:. All men are passive matters.

More Examples:As a matter of fact, man, like woman, is flesh, therefore passive, theplaything of his hormones and of the species, the restless prey of hisdesires.Simone de Beauvoir, The Second Sex, 1949

TRANSLATION:

*All matters made of flesh are passive matters.All men are matters made of flesh.:. All men are passive matters.

(Barbara)An enthymeme on its first order, the major premise being the one assumed.SoritesLoaf Bread Magkabilang Dulo lang natitiraA. DefinitionSorites An argument whose conclusion is inferred from its premises by a chain of syllogistic inferences in which the conclusion of each inference serves as a premise for the next, and the conclusion of the last syllogism is the conclusion of the entire argument.An argument in this form is not a syllogism but a chain of syllogisms, connected by the conclusion of the first, which is a premise to the second. Example 1:All depressed persons are suicidal persons.No happy persons are suicidal persons.No happy persons are depressed person.Some stressed persons are happy persons.Some stressed persons are not depressed persons.Example 1:All depressed persons are suicidal persons.No happy persons are suicidal persons.No happy persons are depressed person.Some stressed persons are happy persons.Some stressed persons are not depressed persons.Example 1:All depressed persons are suicidal persons.No happy persons are suicidal persons.No happy persons are depressed person.(AEE-2)Some stressed persons are happy persons.Some stressed persons are not depressed persons.Example 1:All depressed persons are suicidal persons.No happy persons are suicidal persons.No happy persons are depressed person.(AEE-2)Some stressed persons are happy persons.Some stressed persons are not depressed persons.Example 1:All depressed persons are suicidal persons.No happy persons are suicidal persons.No happy persons are depressed person.(AEE-2)Some stressed persons are happy persons. Some stressed persons are not depressed persons.(EIO-1)*Where an argument is expressed enthymematically, with only the premises and the final conclusion stated, it is called a sorites.

(Introduction to Logic, Copi and Cohen, 14th Edition)Example 2:All musicians are artists.Some lawyer are musicians.All lawyers are people who conform to law.Therefore some people who conform to law are artists.Example 2:All musicians are artists.Some lawyer are musicians.(Therefore some lawyers are artists.)All lawyers are people who conform to law.Therefore some people who conform to law are artists.Example 2:All musicians are artists.Some lawyer are musicians.(Therefore some lawyers are artists.)All lawyers are people who conform to law.Therefore some people who conform to law are artists.Example 2:All musicians are artists.Some lawyer are musicians.(Therefore some lawyers are artists.)All lawyers are people who conform to law.Therefore some people who conform to law are artists.An argument of this type is valid if, and only if, all of its constituent syllogisms are valid.B. GOCLENIAN and ARISTOTELIAN SORITESA sorites is a chain argument. It involves the connection of several propositions into one long argument.A sorites that begins with a major premise (the top one) is called a Goclenian sorites.If it begins with a minor premise (the bottom one), its called an Aristotelian sorites.

(Logical Arithmetic by Vern Crisler, Copyright 1999; 2005, 2011)Goclenian SoritesAll Z is P (MP)All Y is ZAll X is YAll S is X:. All S is PGoclenian SoritesAll Z is P (MP)All Y is ZAll X is YAll S is X:. All S is PSince some of the middle terms are suppressed or hidden, we will not say that we can cancel the middle terms of the above argument, but rather that we can cancel the linking terms. The terms that we can cancel are obviously the ones that are polarized which means having a positive term operator and a negative term operator. To do this we will have to perform inferences.Goclenian SoritesAll Z is P (MP)All Y is ZAll X is YAll S is X:. All S is PZaP+YaZ+XaY+SaX = SaPZe~P + Ye~Z + Xe~Y + Se~X = Se~PGoclenian SoritesAll Z is P (MP)ZaP-Ze~PNo Z is non-PAll Y is ZYaZ-Ye~ZNo Y is non-ZAll X is YXaY-Xe~YNo X is non-YAll S is XSaX-Se~XNo S is non-X:. All S is PSaP-Se~PNo S is non-P Goclenian SoritesAll Z is P (MP)All Y is ZAll X is YAll S is X:. All S is P1) All Z is P 2) All Y is P 3) All X is P All Y is Z All X is Y All S is X All Y is P All X is P :.All S is P Barbara Barbara BarbaraAristotelian SoritesAll A is B (mP)All B is CAll C is DAll D is E:. All A is EAristotelian SoritesAll A is B (mP)All B is CAll C is DAll D is E:. All A is EAaB + BaC + CaD + DaE = AaEAe~B + Be~C + Ce~D + De~E = Ae~E Aristotelian SoritesAll A is B (mP)All B is CAll C is DAll D is E:. All A is ECompare this Aristotelian equation with the previous Goclenian equation and take note of the placement of the cancelled terms with reference to the + sign. The cancelled terms in the Aristotelian sorites are next to the plus sign, while the cancelled terms of the Goclenian sorites are away from the plus sign.To help the memory, here is a silly mnemonic:Go clean away.This mnemonic expresses that the Goclenian linking terms are away from the plus sign in deriving the conclusion. B. GOCLENIAN and ARISTOTELIAN SORITESZaP+YaZ+XaY+SaX = SaPZe~P +Ye~Z + Xe~Y + Se~X = Se~P

AaB + BaC + CaD + DaE= AaEAe~B + Be~C + Ce~D + De~E = Ae~E

Aristotelian SoritesAll A is B (mP)AaB-Ae~BNo A is non-BAll B is CBaC-Be~CNo B is non-CAll C is DCaD-Ce~DNo C is non-DAll D is EDaE-De~ENo D is non-E:. All A is EAaE-Ae~ENo A is non-EAristotelian SoritesAll A is B (mP)All B is CAll C is DAll D is E:. All A is E1)All A is B 2)All A is C 3)All A is D All B is C All C is D All D is E ??? All B is C All C is D All D is E All A is B All A is C All A is D All A is C All A is D :.All A is E BarbaraBarbara Barbara B.1.1 GoclenianHeres an example of a Goclenian sorites from Parry and Hacker:(1) All dogs are mammals.(2) No reptiles are mammals.(3) All snakes are reptiles.(4) All cobras are snakes.Therefore, no dogs are cobras.Lets Check for Validity!All dogs are mammalsNo reptiles are dogsNo reptiles are mammalsAll snakes are reptiles:. No reptiles are dogs:. No snakes are dogs(AEE-2, Camestres)(EAE-1, Celarent)

No snakes are dogsAll cobras are snakes:. No cobras are dogs or No dogs are cobras (Conversion)(EAE-1, Celarent)B.2.2 Aristotelian(1)Babies are illogical.(2)Nobody is despised who can manage a crocodile.(3)Illogical persons are despised.Therefore babies cannot manage crocodiles.(1)All babies are illogical persons.(2)All illogical persons are despised persons.(3)No persons who can manage crocodiles are despised persons.Therefore, no babies are persons who can manage crocodiles.Lets test the validity, yet again!All illogical persons are despised persons.All babies are illogical persons.:. All babies are despised persons.(Barbara)No persons who can manage crocodiles are despised persons.All babies are despised persons.:. No babies are persons who can manage crocodiles.(Cesare)More Examples:(1) Only profound scholars can be dons at Oxford.(2) No insensitive souls are great lovers of music.(3) No one whose soul is not sensitive can be a Don Juan.(4) There are no profound scholars who are not great lovers of music.Therefore all Oxford dons are Don Juans.More Examples:(1) Only profound scholars can be dons at Oxford.(2) No insensitive souls are great lovers of music.(3) No one whose soul is not sensitive can be a Don Juan.(4) There are no profound scholars who are not great lovers of music.Therefore all Oxford dons are Don Juans.STANDARD FORM TRANSLATION:

(1) All Oxford dons are profound scholars.(2) No insensitive souls are great lovers of music.(3) No insensitive souls are Don Juans.

(4) No profound scholars are non-great lover of music.Therefore all Oxford dons are Don JuansMore Examples:STANDARD FORM TRANSLATION:

(1) All Oxford dons are profound scholars.(2) No insensitive souls are great lovers of music.(3) No insensitive souls are Don Juans.(4) No profound scholars are non-great lovers of music.Therefore all Oxford dons are Don JuansCREATE BALANCE:

(1) All Oxford dons are profound scholars.(2) No insensitive souls are great lovers of music.(3) No insensitive souls are Don Juans.(4) All profound scholars are great lovers of music.

Therefore all Oxford dons are Don JuansMore Examples:STANDARD FORM TRANSLATION:

(1) All Oxford dons are profound scholars.(2) No insensitive souls are great lovers of music.(3) No insensitive souls are Don Juans.(4) All profound scholars are great lovers of music.

Therefore all Oxford dons are Don JuansARRANGE THE PREMISES:

(4) All profound scholars are great lovers of music.(1) All Oxford dons are profound scholars.(2) No insensitive souls are great lovers of music.(3) No insensitive souls are Don Juans.

Therefore all Oxford dons are Don JuansMore Examples:STANDARD FORM TRANSLATION (Goclenian):

(4) All profound scholars are great lovers of music.(1) All Oxford dons are profound scholars.(2) No insensitive souls are great lovers of music.(3) No insensitive souls are Don Juans.

Therefore all Oxford dons are Don Juans.VALIDITY CHECK:

(4) All profound scholars are great lovers of music.(1) All Oxford dons are profound scholars. All Oxford dons are great lovers of music. AAA-1(2) No insensitive souls are great lovers of music. No insensitive souls are Oxford Dons. AEE-2(3) No insensitive souls are Don Juans.

Therefore all Oxford dons are Don Juans.

INVALID ARGUMENT!*A sorites may have three, four, or any number of premises. (Introduction to Logic, Copi and Cohen, 14th Edition)The human soul is a thing whose activity is thinking. A thing whose activity is thinking is one whose activity is immediately apprehended, and without any representation of parts therein. A thing whose activity is immediately apprehended, and without any representation of parts therein is a thing whose activity does not contain parts. A thing whose activity does not contain parts is one whose activity is not in motion. A thing whose activity is not in motion is not a body. What is not a body is not in space. What is not in space is insusceptible of motion. What is insusceptible of motion is indissoluble (for dissolution of movement of parts). What is indissoluble is incorruptible. What is incorruptible is immortal. Therefore the human soul is immortal.Thanks to the following sponsors:

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