Dilemma

4.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 antecedents (constructive dilemma), or sublates the consequents )destructive dilemma), of each of these simple conditional propositions.

CONSTRUCTIVE DILEMMA The disjunctive propositions posits the antecedent of the conditional propositions; the conclusion posits their consequents.
1.SIMPLE CONSTRUCTIVE	2.COMPLEX CONSTRUCTIVE
Either A or B But, if A, then Z; if B, then Z. Therefore Z.	Either A or B. But, if A, then X; if B, then Y. Therefore either X or Y.
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 But, either not X or not Y. Therefore not A.	If A then X; and if B, then Y. But, either not X or not Y. Therefore either not A or not B.

1. In the simple constructive dilemma, the conditional premise infers the same consequent from all the antecedents presented in the disjunctive propositions. Hence, if any antecedent is true, the consequent must be true. This form is illustrated by the reflections of a man trapped in an upper story of a burning building.

I must either jump or stay – there is no other alternative.

But if I jump, I shall die immediately from the fall.

And if I stay I shall die immediately from the fire.

Therefore I shall die immediately.

2. In the complex constructive dilemma, the conditional premise infers a different consequent from each of the antecedents presented in the disjunctive proposition. If any antecedent is true, its consequent is likewise true. But since the antecedents are posited disjunctively and, since different consequent flows from each of them, the consequents must likewise be posited disjunctively. The men who brought to Jesus the woman caught in adultery had this form of dilemma in mind.

Jesus will either urge that she be stoned to death or that she be released

without stoning.

But if he urges the first, he will make himself unpopular with the people

because of his severity.

And 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 popular with the people or get into trouble

with the Jewish authorities.

3. In the 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. This type is not distinct from a conditional syllogism in which the consequent is sublated in the minor premise and the antecedent is sublated in the conclusion. Still, on account of the disjunctive premise, it is generally called a dilemma.

If I am to pass the examination, I must do two things: I will study all night

and I must also be mentally alert as I write.

But either I will not study all night or I will not be mentally alert as I write.

Therefore I will not pass the examination.

4. In the 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.

If John were wise, he would not speak irreverently of holy things in jest;

and if he were good, he would not do so in earnest.

But he does it either in jest or in earnest.

Therefore John is either not wise or not good.

The dilemma is subject to the following rules:

Rule 1: The disjunctive must state all pertinent alternatives.

Rule 2: The consequent in the conditional proposition must flow validly

from the antecedents.

Rule 3: The dilemma must not be subject to rebuttal.

The alternatively presented in a dilemma are called horns and that a dilemma is sometimes called a syllogismus cornutus or a horned argument. If you show that the first rule us violated, you escape between the horns of the argument.

Sorites

3.Sorites – a polysyllogism consisting of a series of simple syllogisms whose conclusions, except for the last, are omitted. There are two special rules of the sorites:

Rule 1: All but the last premise must be affirmative. If a premise is negative, the conclusion must be negative.

A is B

B is C

C is D

D is (not) E

----------------

A is (not) E

Rule 2: All but the first premise must be universal. If the first premise is particular, the conclusion must be particular.

(some) A is B

B is C

C is D

D is (not) E

--------------------------------

(some) A is (not) E

The human soul is endowed with intellect and will.

What is endowed with intellect and will is spiritual.

What is spiritual is incorruptible.

What is incorruptible is immortal.

Therefore, the human soul is immortal.

Epichereme

2.Epichereme – a syllogism in which a proof is joined to one or both of the premises. The proof is often expressed by a casual clause. The premise to which a proof is annexed is an enthymeme.

major premise: If man has spiritual activities, he has a spiritual soul,

because every activity requires an adequate principle.

minor premise: But since man knows immaterial things; man has spiritual activities.

conclusion: Therefore man has a spiritual soul.

Enthymeme

1.Enthymeme – a syllogism in which one of the premises or the conclusion is

omitted. There are three orders of enthymeme:

a.first order: when the major premise is omitted – The human soul is spiritual

and therefore immortal.

b.second order: when the minor premise is omitted – What is spiritual is

immortal and for this reason the human soul is immortal.

c.third order: when the conclusion is omitted – The human soul is spiritual and

whatever is spiritual is immortal.

What is spiritual is immortal

The human soul is spiritual.

Therefore, the human soul is immortal.

Ordinary Language Arguments

Many categorical syllogisms that are not in standard form as written can be translated into standard form syllogism. The goal is to produce an argument consisting of three standard form categorical propositions that contain a total of three different terms, each of which is used twice in distinct propositions. Since this task involves not only the translation of the component statements into standard form but the adjustment of these statements one to another so that their terms occur in matched pairs, a certain amount of practice is usually required before it can be done with any facility. In reducing the terms to three matched pairs it is often helpful to identify some factor common to two or all three propositions and express this common factor through the strategic use of the parameters. Consider the following argument:

Henry must have overslept this morning because he was late for work,

and is never late for work unless he oversleeps.

All three statements are about Henry, but if the parameter “persons identical to Henry” were selected it would have to be used more than twice. The temporal adverbs in the argument “this morning” and “never,” suggest that “times” might be used. Following this suggestion, we have:

All times identical to this morning are times Henry overslept, because all times identical to this morning are times Henry is late for work, and all times Henry is late for work are times Henry overslept.

We now have a standard form categorical syllogism. If we adopt the following convention,

A = times identical to this morning

B = times Henry overslept

C = times Henry is late for work

The syllogism may then be symbolized as follows:

All C are B. All times Henry is late for work are times Henry overslept

All A are C. All times identical to this morning are times Henry is late for work.

All A are B. Therefore, all times identical to this morning are times Henry overslept.

Conjunctive Syllogism

4.Conjunctive Syllogism – A syllogism whose major premise is a conjunctive proposition, the minor premise posits one member of the major, and whose conclusion sublates the other member of the major. There is only one valid procedure: to posit one member in the minor premise and sublate the other in the conclusion.

The criminal could not be in Manila and Baguio at the same time;

But he was in Manila;

Therefore he could not be in Baguio.

[The criminal could not be in Manila and Baguio at the same time;

But he was not in Manila;

Therefore he was in Baguio.]

Disjunctive Syllogism

3.Disjunctive Syllogism – A syllogism whose major premise is a disjunctive proposition.

a.It is a strict disjunctive if only one among the alternatives enumerated in

the major premise is true. For the disjunctive syllogism in the strict sense

the following rules are applicable:

Rule 1: If the minor premise posits one or more members of the

major premise, the conclusion must sublate each of the other

members.

It is either A or B. It is either A or B or C.

But it is A. But it is A.

Therefore it is not B. Therefore it is neither B nor C.

Rule 2: If the minor premise sublates one or more of the members

of the major premise, the conclusion posits the remaining

members, one of which must be true.

It is either A or B. It is either A or B or C.

But it is not A. But it is not A.

Therefore it is B. Therefore it is either B or C.

b.It is a broad disjunctive if at least one alternative among those

enumerated in the major premise is true but more may be true. In a

disjunctive syllogism in the broad sense, the major premise is a

disjunctive proposition in the broad sense. There is only one valid

procedure: to sublate one (or more – but not all) of the members in the

minor and posit the remaining member or (members) in the conclusion.

If more than one member remains, the conclusion itself must be a

disjunctive proposition in the broad sense.

It is either A or B or C or D – at least one of them

But it is neither A nor B;

Therefore it is either C or D – at least one of them.