1. SPECIAL TYPES OF SYLLOGISM
1. 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 of
any 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

2. 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.

3. 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.

4. SPECIAL TYPES OF SYLLOGISM
EXERCISES:
Directions: Using the following format, make complete syllogisms of the enthymemes given
below. First pick out the conclusion, expressing it if it not already given. Then fill in the other
members, supplying those that are not expressed. Finally criticize the examples by applying to
them the various rules of inference.
EXAMPLE
The 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.

5. SPECIAL TYPES OF SYLLOGISM
2. 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.

6. SPECIAL TYPES OF SYLLOGISM
3. 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.

7. SPECIAL TYPES OF SYLLOGISM
4. 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.

8. SPECIAL TYPES OF SYLLOGISM
Example:
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.

9. SPECIAL TYPES OF SYLLOGISM
Goclenian (or regressive) Sorites - the same premises occur, but their
order 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.

10. SPECIAL TYPES OF SYLLOGISM
There is no essential difference between the Aristotelian sorites and the
Goclenian sorites except in the manner of the arrangement of the
premises. To construct the Aristotelian sorites from Goclenian and vice-
versa, we start with the last premise and end with the first. The
conclusion 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.

11. SPECIAL TYPES OF SYLLOGISM
b.) 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.

12. SPECIAL TYPES OF SYLLOGISM
Example: 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.

13. SPECIAL TYPES OF SYLLOGISM
3.) 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.

14. 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.

15. SPECIAL TYPES OF SYLLOGISM
5. 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.

16. SPECIAL TYPES OF SYLLOGISM
a. 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.

17. SPECIAL TYPES OF SYLLOGISM
b. 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.

18. SPECIAL TYPES OF SYLLOGISM
Example: 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.”

19. 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 CONSTRUCTIVE
Either 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.

20. SPECIAL TYPES OF SYLLOGISM
c. 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.

21. SPECIAL TYPES OF SYLLOGISM
d. 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.

22. 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 DESTRUCTIVE
If A, then X and Y. If A, then X; and if B, then Y.
either not X either not X
But But
or not Y or not Y
Therefore not A. Therefore either not A or not B.

23. 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.

24. 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.”

25. 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.

26. 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.