For if (1) be violated, you will find when you expand your sorites into its full form that you have a particular major in the first figure (contrary to canon), and if (2) be violated you will find in the same way that you have a negative minor in the first figure (contrary to canon).

[If asked (as possibly you might be) what is the regressive or Goclenian Sorites, remember it is the reverse of the above. Begin with the last premiss and write the train from last to first, and keep the old conclusion, e.g.,

All D is E,

All C is D,

All B is C,

All A is B,

... All A is E.

'The rules are reversed, too; only one premiss particular, the last; only one negative, the first (the same propositions being negative and particular as before, you observe)].'

Would it be enough,' asked I, if you were asked about the Goclenian Sorites to give a full description of the ordinary Sorites, and then finish up by saying, "Such is Sorites; and the Goclenian. is not this, but the reverse," leaving the examiners. to draw upon their imaginations for your meaning.'

'It would be a great deal better than leaving the question out altogether,' he replied with a laugh.

=

As yet our propositions have been only simple or categorical. There are propositions which link together a couple of simple propositions as simple propositions link together a couple of terms. These are called "complex or hypothetical propositions." "Hypothetical" means "with something put under or supposed" (vπò тíoŋμi = sub-pono suppose), or "with a condition." Your father says, "I'll give you a horse," that's one thing; but it is quite another thing if he says, "I'll give you a horse IF you pass your examination." The universal dislike of IF's is proverbial, for they make all the difference being the signs of "conditions." Now simple propositions may be linked together in two ways: first, where the truth of the consequent depends upon the truth of the antecedent (antecedent and consequent are the names of the two simple propositions when linked together; the first, the antecedent; the second, the consequent); and secondly, where the truth of the consequent depends upon the falsity of the antecedent. The first kind are called "conjunctive," e.g., "If the weather is rainy my sponge is

damp" (their sign is "if"). The second kind are called disjunctive, e.g., " Either Logic is deep or I an dull" (their sign is "either-or"). Hence we may divide propositions in the following manner :

Complex or hypothetical

PROPOSITIONS

Simple or categorical (of which we have already spoken).

Conjunctive

Disjunctive.

We

'Now syllogisms are composed of these hypothetical propositions, and so borrow their names. have conjunctive and disjunctive hypothetical syllogisms, i.e. syllogisms composed of such premisses. Cases where both premisses are hypothetical we shall discuss under "dilemma." For the present we shall consider cases where one premiss is hypothetical and one simple.

I. Conjunctive Hypothetical Syllogisms. These admit of two valid conclusions out of the four possible ones you get by affirming and denying the antecedent and consequent.

(a) If the weather is rainy, my sponge is damp. The weather is rainy,

.. my sponge is damp.

Affirming the antecedent for a minor premiss.

(b) If the weather is rainy, my sponge is damp. The weather is not rainy.

No conclusion.

Denying the antecedent for a minor premiss.'

Surely,' said I, it follows that "my sponge is not damp.""

'No,' said he, 'for it may have fallen into the bath. Suppose I say "If the Brighteyes' are going, I shall enjoy the ball;" it does not follow that if they do not go, I shall not enjoy the ball, for I may meet the "Lighttoes.""

(c) If the weather is rainy, my sponge is damp. My sponge is damp.

No conclusion.

Affirming the consequent for a minor premiss. For though it follows that my sponge is damp if the weather is wet, it does not follow that the weather is wet because my sponge is damp. If the wife weeps because the husband is condemned to death, does it follow that the husband is condemned to death because the wife weeps?

(d) If the weather is rainy, my sponge is damp. My sponge is not damp.

... the weather is not rainy.

Denying the consequent for the minor premiss. Thus the conjunctive hypothetical syllogism admits of two conclusions-where you affirm the antecedent called "constructive," and where you deny the consequent called "destructive."

II. Disjunctive Hypothetical Syllogisms admit of four conclusions, for you may affirm or deny antecedent and consequent.

e.g., (1) Either Logic is deep, or I am dull.

Logic is deep.

... I am not dull.

(2) Either Logic is deep, or I am dull.
Logic is not deep.

... I am dull.

(3) Either Logic is deep, or I am dull.
I am dull.

.. Logic is not deep.

(4) Either Logic is deep, or I am dull.
I am not dull.

.. Logic is deep.

'The dilemma is a combination of conjunctive and disjunctive premisses. As it is a difficult matter to understand, I should advise you to remember the three forms of it by their examples, and after your examination go more deeply into the theory of it as expounded in the books on Logic. There are:

(i.) The simple constructive Instance: "Science."
(ii.) The complex dilemma
iii.) The destructive dilemma.

Instance: "Politician."

Instance: "Jesting at Scripture."

(i) The Simple Constructive Dilemma is of this form:

If science lightens labour, it should be cultivated; and if science invigorates the faculties, it should be cultivated;

But science does one, or the other;

Therefore science should be cultivated.