SPECIAL TYPES OF SYLLOGISM1. ENTHEMEME – a syllogism in which one of the premises or the conclusion is omitted.The enthymeme is not a distinct form of syllogism, but an incomplete statement ofany of the forms of syllogism previously discussed.Three Orders of Enthymemes: 1st Order: The Major Premise is Omitted 2nd Order: The Minor Premise is Omitted 3rd Order: The Conclusion is Omitted
SPECIAL TYPES OF SYLLOGISM Example:Major: What is spiritual is immortal,Minor: But the human soul is spiritual,Conclusion: Therefore the human soul is immortal.1. Minor: The human soul is spiritual, Conclusion: and therefore immortal.2. Conclusion: The human soul is immortal, Minor: because it is spiritual.3. Major: What is spiritual is immortal, Conclusion: for this reason, the human soul is immortal.
SPECIAL TYPES OF SYLLOGISM Example:Major: What is spiritual is immortal,Minor: But the human soul is spiritual,Conclusion: Therefore the human soul is spiritual.4. Conclusion: The human soul is immortal, Major: since whatever is spiritual is immortal.5. Minor: The human soul is spiritual, Major: and whatever is spiritual is immortal.
SPECIAL TYPES OF SYLLOGISMEXERCISES:Directions: Using the following format, make complete syllogisms of the enthymemes givenbelow. First pick out the conclusion, expressing it if it not already given. Then fill in the othermembers, supplying those that are not expressed. Finally criticize the examples by applying tothem the various rules of inference.EXAMPLEThe open shop is good for unions because it makes them more democratic.Major: Whatever makes unions more democratic is good for unions.Minor: But the open shop (is something that) makes unions more democratic.Concl: Therefore the open shop is for unions. 1. Communism, simply because it is a godless philosophy, contains within itself the seeds its own destruction. 2. Teachers’ unions are not desirable because they take away local control of schools.
SPECIAL TYPES OF SYLLOGISM2. EPHICHIREME – a syllogism in which a proof is joined to one or both of the premises. The proof often expressed by a causal clause (“for”, “because”, “since”, etc.)Note: It is important to distinguish the main syllogism from the proofs of a premise.Example: Major: If man has spiritual activities, he has spiritual soul, because every activity requires an adequate principle. Minor: But since man knows immaterial things, man has spiritual activities. Conclusion: Therefore man has spiritual soul.
SPECIAL TYPES OF SYLLOGISM3. POLYSYLLOGISM– A polysyllogism, as the name suggest (poly is the Greek word for “many”), it is a series of syllogism connected together in which the conclusion of the preceding syllogism becomes the Major Premise of he following syllogism. Polysyllogism is also known as chain argument.Example: The more one is closed to god, the more one suffers; The more one suffers, the more one understands life; Ergo, the more one is close to God, the more one understands life. The more one understands life, the more one relates to people; Ergo, the more one is close to God, the more one relates to people. The more one relates to people, the more one understands himself; Ergo, the more one is close to God, the more one understands himself.
SPECIAL TYPES OF SYLLOGISM4. SORITES – a polysyllogism consisting of a series of simple syllogism whose conclusion, except for the last, are omitted. It is either categorical or conditional. a.) Categorical Sorites - consist of a series of simple categorical syllogisms of the first figure whose conclusions, except for the last, are omitted. It links or separates the subject and predicate of the conclusion through the intermediacy of many middle terms. Two Kinds of Categorical Sorites Aristotelian (or progressive) Sorites - the predicate of each premise is the subject of the following premise, and the subject of the first premise is the subject of the conclusion.
SPECIAL TYPES OF SYLLOGISMExample: All A is B; All B is C; All C is D; All D is E; Therefore, All A is E. All philosophers are wide readers; All wide readers are intelligent; All intelligent people are creative; All creative people are producers of great ideas; Therefore, All philosophers are producers of great ideas.
SPECIAL TYPES OF SYLLOGISMGoclenian (or regressive) Sorites - the same premises occur, but theirorder is reversed.Example: All A is B; All C is A; All D is C; All E is D; Therefore, All E is B. One who will not sacrifice truth for power is a responsible person. One who is a paragon of honesty will not sacrifice truth for power; One who is worth emulating is a paragon of honesty; A model of decency is worth emulating; Therefore, A model of decency is a responsible person.
SPECIAL TYPES OF SYLLOGISMThere is no essential difference between the Aristotelian sorites and theGoclenian sorites except in the manner of the arrangement of thepremises. To construct the Aristotelian sorites from Goclenian and vice-versa, we start with the last premise and end with the first. Theconclusion remains the same.RULES: The procedure of reducing the Sorites to its component categorical syllogism, for checking purposes, is rather lengthy and cumbersome. It does not allow for a quick checking. For the later purpose, we may rely on the following Two Rules. These rules apply to the Sorites as such, whether it is Aristotelian, or Goclenian. They are: 1. Only one premise may be particular: one that carries the Minor term. 2. Only one premise may be negative: one that carries the Major term.
SPECIAL TYPES OF SYLLOGISMb.) Conditional Sorites - is one whose premise contains a series of conditional propositions, each of which (except the first) has as its antecedent the consequent of the preceding premise. Sometimes all the premises, including the last, are conditional propositions, and then the conclusion must be conditional proposition. Sometimes the last premise is a categorical proposition, and then the conclusion must be a categorical proposition.
SPECIAL TYPES OF SYLLOGISMExample: 1.) If A, then B; If B, then C; If C, then D; If D, then E; Therefore, If A, then E. 2.) If A, then B; If B, then C; If C, then D; If D, then E; Therefore, If not E, then not A.
SPECIAL TYPES OF SYLLOGISM3.) If A, then B; If B, then C; If C, then D; If D, then E; but A: Therefore, E.4.) If A, then B; If B, then C; If C, then D; If D, then E; but not E; Therefore, If not E, then not A.
EXERCISES: 1. The human soul is endowed with intellect and will; what is endowed with intellect and will is spiritual; what is spiritual is incorruptible; and what is incorruptible is immortal; therefore the human soul is immortal. 2. The more you exercise, the hungrier you get; the hungrier you get, the more you eat; the more you eat, the fatter you get; the fatter you get, the less you move around; therefore, the more you exercise, the less you move around. 3. Peace begets prosperity; prosperity begets pride; pride begets war; war begets poverty; therefore peace begets poverty. 4. Education implies teaching; teaching implies knowledge; knowledge is truth; the truth is everywhere the same; hence, education should be everywhere the same. 5. The prudent man is temperate; the temperate man is constant; the constant man is unperturbed; buy he who is unperturbed is without sadness; and he who is without sadness is happy; therefore, the prudent man is also happy.
SPECIAL TYPES OF SYLLOGISM5. DILEMMA – a syllogism that is both conditional and disjunctive. The major premise is a compound conditional proposition consisting of two or more simple conditional propositions connected by “and” or its equivalent. The minor premise is a disjunctive proposition that alternatively posits the antecedent (constructive dilemma), of each of these simple conditional propositions. In the constructive dilemma the disjunctive proposition is commonly placed first; in the destructive dilemma, however, the conditional propositions are commonly placed first. The conclusion is either a categorical or a disjunctive proposition. If the disjunctive premise has three members, the syllogism is a trilemma; if it has many members, the syllogism is a polylemma. But the name “dilemma” is also applied to these.
SPECIAL TYPES OF SYLLOGISMa. Simple Constructive Dilemma – the conditional premise infers the same consequent from all the antecedents presented in the disjunctive proposition. Hence, if any antecedent is true, the consequent must be true. Example: I must either jump or stay – there is no other alternative. If I jump, I shall die immediately (from the fall) But If I stay, I shall die immediately, (from the fire) Therefore, I shall die immediately.
SPECIAL TYPES OF SYLLOGISMb. Complex Constructive Dilemma – the conditional premise infers a different consequent from each of the antecedents presented in the disjunctive proposition. If any of the antecedent is true, its consequent is likewise true. But since the antecedents are posited disjunctively and since a different consequent flows from each of them, the consequents must likewise be posited disjunctively.
SPECIAL TYPES OF SYLLOGISMExample: Men brought to Jesus the woman caught committing adultery Jesus will either urge that she be stoned to death or that she be released without stoning. If he urges the first, he will make himself unpopular with the people because of his severity; But If he urges the second, he will get into trouble with the Jewish authorities for disregarding the law of Moses. Therefore, he will either become unpopular with the people or get into trouble with the Jewish authorities. Jesus slipped between the horns of this dilemma by writing on the sand saying “Let him who is without sin cast the first stone.”
SPECIAL TYPES OF SYLLOGISM CONSTRUCTIVE DILEMMA (The disjunctive proposition posits the antecedents of the conditional propositions; the conclusion posits their consequence) 1. SIMPLE CONSTRUCTIVE 2. COMPLEX CONSTRUCTIVEEither A or B. Either A or B. if A, then Z. if A, then X.But But if B, then Z. if B, then Y.Therefore, Z. Therefore, either X or Y.
SPECIAL TYPES OF SYLLOGISMc. Simple Destructive Dilemma – the conditional premise infers more than one consequent from the same antecedent. If any of the consequents is false, the antecedent is false. Hence, since the disjunctive sublates the consequents alternatively, at least one of them must be false, and consequently the antecedent must also be false. Example: If I am to pass the examination, I must do two things – I must study all night and I must also be mentally alert as I write. either I will not study all night, But or I will not be mentally alert as I write. Therefore, I will not pass the examination.
SPECIAL TYPES OF SYLLOGISMd. Complex Destructive Dilemma – the conditional premise infers a different consequent from each antecedent. The disjunctive premise sublates these consequents alternatively, and the conclusion sublates their antecedents alternatively Example: If John were wise, he would not speak irreverently of holy things in jest; if he were good, he would not do so in earnest. he does it either in jest, But or in earnest. Therefore, John is either not wise or not good.
SPECIAL TYPES OF SYLLOGISM DESTRUCTIVE DILEMMA (The disjunctive proposition sublates the consequents of the conditional propositions, the conclusion sublates their antecedents) 1. SIMPLE DESTRUCTIVE 2. COMPLEX DESTRUCTIVEIf A, then X and Y. If A, then X; and if B, then Y. either not X either not XBut But or not Y or not YTherefore not A. Therefore either not A or not B.
RULES OF THE DILEMMA (ANSWERING A DILEMMA) 1.) The disjunction must state all the pertinent alternatives. 2.) The consequents in the conditional proposition must flow validly from the antecedents. 3.) The dilemma must not be subject to rebuttal.
Example for the first rule (Escape between the horn) I must either devote myself to the interest of my soul or to secular pursuits. If I devote myself to the interest of my soul, my business will fail; If I devote myself to secular pursuit, I shall lose my soul. Therefore either my business will fail, or else I shall lose my soul. There is a third alternative, to devote myself both in the interest of my soul and to secular pursuits with the proper subordination of the latter to the former. “You can be upright and at the same time rich too.”
Example for the second rule (Take the dilemma by the horn) The mother argued: If your say what is just, men will hate you; if you say what is unjust, the gods will hate you. But you must either say what is just or what is unjust. Therefore you will be hated. The son replied: If I say what is just, the gods will love me; if I say what is unjust, men will love me. But I must say either the one or the other. Therefore I will be loved.
EXERCISE: Criticize the following dilemmas. Supply the missing members of those that are stated incompletely.1. A universal skeptic (that is, one who denies that anything can be known for certain) is refuted as follows: Either you regard it as certain that nothing can be known for certain, or else you regard it as uncertain. If you regard it as a certain, you hold at least one thing as certain; if you regard it as uncertain, you also hold at least one thing as certain, namely, that you regard it. Therefore you hold it as certain.2. Tertullian criticizes the policy of the Emperors of Trajan and Marcus Aurelius in persecuting the Christians. The Christians have either committed crimes, or else they have not. If they have committed crimes, your policy is unjust in that you forbid them to be hunted out: if they have not committed crimes, your policy is unjust in that you punish those who have been brought to your attention. Therefore, your policy is unjust.