EXERCISES ON CHAPTER XII

1. Make your own example of the constructive and destructive hypothetical syllogism.

2. Reduce each example to categorical form, showing the mood and figure.

3. Take the examples made in answer to Exercise 1, deny the antecedent and affirm the consequent, reduce to the categorical form, and demonstrate the fallacy.

4. Make an example of each form of disjunctive syllogism. 5. Take the example of the simple constructive dilemma given in the text, analyze it, and adapt it to the symbolic formulation. 6. Do as directed in Exercise 5 in the case of the complex constructive dilemma cited in the text.

7. Do as directed in Exercise 5 in the case of the destructive dilemma cited in the text.

CHAPTER XIII.-IRREGULAR SYLLOGISTIC

FORMS

81. THE ENTHYMEME.-Oftentimes one of the propositions forming the premises of a syllogism is a truism, that is, too obvious to any intelligent person to require expression in words. Or it may be that even the conclusion is so plain that it is tedious to put it in verbal form. A syllogism in which a proposition is thus left to be supplied by the mind is called an enthymeme (Greek, év, in, and Ovuós, mind). Most arguments met with in daily speech or reading are enthymemes. It is rare to find a fully expressed syllogism. Indeed, it would sound strange and pedantic to express the reasoning in the standard form. But whenever words like therefore, and so, because, for, since, inasmuch as, consequently occur, a deductive inference has taken place, and the argument, if valid, could be couched in the form of a fully expressed syllogism. It is usually the major premise which has the widest generality, and hence expresses the most obvious truth. Consequently it is this premise that is most frequently left to be supplied by the mind of the person who is following the reasoning. A syllogism whose major premise is suppressed is known as an enthymeme of the first order. Less often it is the minor premise which is not given. Under these circumstances we have an enthymeme of the second order. Occasionally even the conclusion is

not put into words. Epigrams and witty sayings are often expressed by using this device of a suppressed conclusion. This gives rise to enthymemes of the third order. The following are examples of the three orders of enthymemes:

It is understood that the enthymeme, since it is a regular syllogism with a proposition unexpressed, may be any valid mood in any figure in which it is valid.

82. PROSYLLOGISMS AND EPISYLLOGISMS.-Any conclusion, since it is a proposition, may become a premise of another syllogism. A syllogism whose conclusion is so used is called a prosyllogism. The syllogism, one of whose premises is the conclusion of another syllogism, is called an episyllogism. These terms are therefore relatives.

PROSYLLOGISM AND EPISYLLOGISM

No Republicans believe in free-trade;

The members of the present administration are Republicans; Therefore the members of the present administration do not believe in free-trade;

The members of the present administration do not believe in freetrade;

The statesmen, Messrs. B. and C., believe in free-trade;

Therefore the statesmen, Messrs. B. and C., are not members of the present administration.

It is seen that the conclusion reached by E A E, first figure, in the first of the two syllogisms, is used as the major premise of the second syllogism in E A E, second figure. It is to be understood that prosyllogisms and episyllogisms may be in any valid mood.

83. THE EPICHEIREMA.—This name is given to an episyllogism either or both of whose premises is the conclusion of an enthymeme; if the latter, it is a double epicheirema, as in the example here added:

EPICHEIREMA

All beetles have external skeletons, for they are insects;
All fireflies are beetles, for they have hardened fore-wings;
Therefore all fireflies have external skeletons.

The syllogism itself (independent of the expressed premise of each enthymeme) is A A A in the first figure. When the enthymemes that furnish its premises are fully expressed, they also happen to fall into the mood A A A, as follows:

FIRST ENTHYMEME

(All insects have external skeletons;)
All beetles are insects;

Therefore all beetles have external skeletons.

SECOND ENTHYMEME

(All insects with hardened fore-wings are beetles;)
All fireflies have hardened fore-wings;
Therefore all fireflies are beetles.

Each of these enthymemes is of the first order. 84. THE SORITES.-A sorites is a series of premises whose conclusions excepting the last are not expressed. In other words, it is a series of prosyllogisms and episyllogisms suppressing all conclusions except the last. The word's derivation-from the Greek σwpós, heap-indicates quite graphically what is the type of argument. It is as though our thinking rushed on at such a headlong pace that there was no time to pause for a conclusion until the end of the process-the special conclusion wanted-is reached. The form of the sorites most usually met with is as follows:

All A is B;

All B is C;

All C is D;

Therefore all A is D.

Upon analysis this resolves itself into the following syllogisms:

FIRST SYLLOGISM

All B is C;

All A is B;
Therefore all A is C.

SECOND SYLLOGISM

All C is D;

All A is C;

Therefore all A is D.

An inspection of these syllogisms shows us that no premise but the first may be particular. For if B, which is the middle term in the first syllogism above, and also in the first two premises of the sorites, were in a particular premise in the case where it has the position of subject