The proposition on which the truth of the other depends, is called the Antecedent: that which follows on its admission, is called the Consequent.

Thus in the proposition, 'If the shepherd be negligent, the sheep go astray,' the antecedent is ' If the shepherd be negligent ' ; the consequent is 'the sheep go astray.'

It will be seen that neither part of the proposition is independently asserted as true. We do not affirm that 'the shepherd is negligent,' nor yet that ' the sheep go astray.' It is the nexus between the two, the dependence of consequent on antecedent, which is affirmed.

There are two forms in which the hypothetical sentence may be expressed. These are (1) If A is B, C is D, and (2) If S is M, it is P. Judgments constructed according to the first formula, may usually by a little manipulation be expressed in the second form also. But it is incorrect to say that the latter is a more fundamental type than the former.

Hypotheticals of the second form, can be expressed categorically, by substituting in the place of 'If S is M, it is P,' the form 'All S that is M is P,' or 'All SM is P.' Similarly for the categorical 'All S is P,' we may write, ' If anything is S. it is P.'

Some writers on Logic have maintained that the categorical and hypothetical propositions are in fact equivalent. There can be no doubt that this opinion is erroneous. In the categorical we state unconditionally that S is P. In the hypothetical we state that S is P, if certain conditions are fulfilled. The constituent parts of the categorical are related as subject and attribute: the parts of a hypothetical are related as reason and consequent.

Nor is it only the mental forms that are different. The fact to be expressed positively demands one form to the exclusion of the other. Such propositions as 'Gold is yellow,' and 'If the King comes, a salute will be fired,' are distorted when they are expressed as 'If anything is gold, it is yellow,' and 'The case of the King's arrival is a case of firing a salute.'

In regard to the employment of the one form in place of the other, Professor Case has well said: "Taking the carelessly expressed propositions of ordinary life logicians do not perceive that similar propositions are often differently expressed, e.g. ''I being a man am mortal,' and 'If I am a man I am mortal': and conversely that different judgments are often similarly expressed. In ordinary life we may say 'All men are mortal, . 'All candidates arriving five minutes late are fined.'

But of these universal propositions, the first expresses a categorical belief . . . the other is a slipshod expression of the 'hypothetical belief, 'If any candidates arrive late, they are 'fined.'" Encycl. Brit. (10th ed.), vol. 30, p. 333, Art. Logic.

Quantity and Quality of Hypotheticals. All hypothetical propositions are affirmative. If we desire to meet a hypothetical with its negation, we must deny what it affirms. That is to say we must deny the nexus between the antecedent and consequent. This is done by the form 'Although S is M, it need not be P.' The negative of ‘If he is poor, he is uneducated,' is 'Although he is poor, he may not be uneducated.' These negative forms, however, are not themselves hypotheticals: for they do not assert the dependence of consequent on antecedent.

There can be no differences of quantity in hypotheticals, because there is no question of extension. The affirmation, as we have seen, relates solely to the nexus between the two members of the proposition.

Hence every hypothetical is singular.

Disjunctives like Hypotheticals are of two forms

(i) Either A is B, or C is D; and (2) S is either P or Q, e.g. 'Either the general was incompetent or his subordinates were disobedient,' 'Religions are either false or true.'

It has been much disputed whether the alternatives in a disjunctive are mutually exclusive or not in other words, whether we not only know that one must be true, but also that if the one is true, the other is certainly false. Thus supposing we are aware that 'S is either P or Q,' and are then informed that 'S is P,' can we conclude that S is not Q? We shall consider this point later.¹

The Disjunctive can be expressed by means of Hypothetical propositions. If it be maintained that the disjunction is exclusive, we need two hypothetical propositions to represent a disjunctive, viz., (1) If S is P, it is not Q. (2) If S is not P, it is Q.

If the mutual exclusiveness be denied, a single hypothetical will suffice. viz., ' If S is not P, it is Q.'

Quantity and Quality of Disjunctives. By virtue of their form all disjunctives are affirmative. The alternative is necessarily asserted. However, a difference in quantity is possible. The proposition may be of the form 'All S are P or Q'; or it may be particular, as, 'Some S are P or

A form of proposition termed by the Scholastics Conjunctive gives us what is practically the negative form of the Disjunctive.

Its formula is 'S is not both P and Q,' 'The King is not both at London and Windsor.'

The whole terminology of Conditionals is in confusion. We have followed that preferred by Hamilton (Logic, I. 236) and subsequently by several other authors. Some logicians make hypothetical the genus, and give the name conditional to those we have called hypothetical. This division is found in Whately and is accepted by Mill (I. 91). Perhaps the most satisfactory division is that of Boethius. He terms the genus conditionalis or hypothetica indifferently, and calls the species respectively conjuncta (connexa) and disjuncta.