Part II, Chapter 9: Of different Kinds of Compound Propositions
WE have already said that compound propositions are those which have either a double subject, or a double attribute. Now, of these there are two kinds, the one where the composition is denoted expressly and the other where it is more concealed, which logicians have, for this reason, called exponibles, since they need to be expounded or explained.
We may reduce those of the first kind to six species: Copulatives and disjunctives, conditionals and causals, relatives and discretives.
We call copulatives those which contain either several subjects, or several attributes, united by an affirmative or negative conjunction, that is to say, by and, or neither, for nor produces the same effect as and, since it signifies and, and a negation, which falls on the verb, and on the union of the two words which it joins: as, if I say, Knowledge and riches do not render a man happy, I unite knowledge to riches, in affirming of both that they do not render a man happy, as if I said—knowledge and riches render a man vain.
We may distinguish three kinds of these propositions.
1st, When they have several subjects. Mors et vita in manibus linguae. Death and life are in the power of the tongue.
2. When they have several attributes.
Auream quisquis mediocritatem Diligit, tutus, caret obsoleti Sordibus tecti, caret invidenda
Sobrius aula.
He who loves moderation, which is desirable in all things, lives neither sordidly nor superbly. Sperat infestis, metuit secundis Alteram sortem, bene praeparatum
Pectus.
A well-regulated mind hopes for prosperity in adversity, and fears adversity in prosperity.
3. When they have several subjects and a plurality of attributes.
Non domus et fundus, non aeris acervus et auri, Aegroto Domini deduxit corpore febres,
Non animo curas.
Neither houses, nor lands, nor the greatest heaps of gold and silver, can chase away fevers from the body, or cares from the mind of their possessors.
The truth of these propositions depends on the truth of both parts: thus, if I say—faith and a good life are necessary to salvation. This is true, because both are necessary; but if I said, good life and riches are necessary to salvation, this proposition would be false, since, although good life is thus necessary, riches are not.
Propositions which are considered as negative and contradictory, in relation to the copulatives, and to all the other compound ones, are not all those in which negations are found, but only those in which the negation falls on the conjunction; and this happens in different ways, as by placing the not at the top of the proposition—Non enim amas et deseris, says St Augustine,—that is to say, you must not believe you love any one when you desert him.
For it is in the same way we render a proposition contradictory, the contradictory, or copulative, by expressly denying the conjunction: as when we say—it cannot be that a thing should be, at the same time, this and that.
That we cannot be in love, and be wise.
Amare et sapere vix Deo conceditur. That love and majesty do not agree together.
Non bene conveniunt, nec in una sede morantur, Majestas et amor.
Disjunctives are of great service, and are those into which the disjunctive conjunction, aut, or, enters: —
Friendship either finds friends equal, or renders them so. Amicitia pares aut accipit, aut facit.
A woman loves or hates; there is no medium. Aut amat aut odit mulier; nihil est tertium.
He who lives in utter solitude is either a beast or an angel (says Aristotle).
Men act only through interest, or through fear.
The earth moves round the sun, or the sun round the earth.
Every deliberate action is either good or evil.
The truth of these propositions depends on the necessary opposition of the parts, which ought to admit of no medium. But as, in order to be necessarily true, they must admit of none at all, it suffices that they do not ordinarily admit of any, in order to be considered as morally true. Hence it is absolutely true that an action done deliberately is good or bad, since theologians prove that there are none which are indifferent; but when it is said that men act only through interest, or through fear, it is not absolutely true, since there are some who act from neither of these passions, but from consideration of their duty: and thus all the truth which it contains is, that these are the two motives which influence the majority of men.
The propositions which are contradictory to the disjunctives are those in which we deny the truth of the disjunction; which is done in Latin by putting the negation at the beginning, as in all the other compound propositions: Non omnis actio est bona vel mala; and in our language, It is not true that every action is either good or bad.
Conditionals are those which have two parts united by the condition if, whereof the first that contains the condition is called the antecedent, and the other the consequent. If the soul is spiritual, is the antecedent,—it is immortal, is the consequent.
This consequence is sometimes mediate, and sometimes immediate. It is mediate only when there is nothing in the terms of either part which binds them together, as when I say: —
If the earth is immoveable, the sun turns round. If God is just, sinners will be punished. These consequences are very good, since the two parts, having no common term, are connected together only by that which is in the mind, and which is not expressed; that the earth and the sun, being found continually in different situations with regard to each other, it necessarily follows, that if one is immoveable, the other moves.
When the consequence is immediate, it must generally be,
1st, Either when the two parts have the same subject: If death is a passage to a happier life, it is desirable. If you have failed to nourish the poor, you have destroyed them.
Si non pavisti, occidisti.
2. Or when they have the same attribute:
If all trials from God should be dear to us, Afflictions ought to be so.
3. Or when the attribute of the first part is the subject of the second:
If patience be a virtue, There are painful virtues.
4th, Or, lastly, when the subject of the first part is the attribute of the second, which can only be when the second part is negative:
If all true Christians live according to the Gospel, There are few true Christians.
We consider, in relation to these propositions, only the truth of the consequence; for although both parts were false, nevertheless, if the consequence of one or the other is good, the proposition, so far as it is conditional, is true.
as:
If the will of the creature is capable of preventing the absolute will of God from being accomplished, God is not almighty.
Propositions considered as negative or contradictory to the conditionals, are those only in which the condition is denied, which is accomplished in Latin by placing the negation at the beginning:
Non, si miserum fortuna Sinonem Finxit, vanum etiam mendacemque improba finget. But in our language we express these contradictions by although, and a negation:
If you eat of the forbidden fruit, you shall die.
Although you should eat of the forbidden fruit, you shall not die.
Or equally well by—It is not true, that if ye eat of the forbidden fruit ye shall die.
Causals are those which contain two propositions connected by a causal particle, quia, because,—or ut, to the end that:
Wo to the rich, because they have their comfort in this world.
The wicked are exalted, in order that, falling from a greater height, their downfal may be greater. Tolluntur in altum, Ut lapsu graviore ruant. They are able, because they believe they are able.
Possunt quia posse videntur. Such a prince was unhappy, because he was born under a certain constellation.
We may also reduce to these kinds of propositions those which are called reduplicatives: Man, as man, is reasonable. Kings, as kings, depend on God only.
For the truth of these propositions, it is necessary that one of the parts be the cause of the other, which makes it also necessary that both be true; for that which is false is not a cause, and has not a cause; but both parts may be true, and yet the causal connection false, because it is enough for this, that one of the parts be not the cause of the other. Thus a prince may have been unfortunate, and may have been born under such a constellation, while it may still be false that he was unhappy because he was born under that constellation.
Hence the contradictories of these propositions consist properly in this, that we deny the one to be the cause of the other:
Non ideo infelix, quia sub hoc natus sidere.
Relatives are those which involve comparison and some relation:
Where the treasure is, there the heart is also. As a man lives, so he dies.
Tanti es, quantum habeas.
You are valued in the world in proportion to your wealth.
The truth depends on the justness of the relation, and we contradict them by denying the relation:
It is not true, that as a man lives, so he dies. It is not true that we are valued in the world in proportion to our fortune.
Are those in which we make different judgments, denoting that difference by the particles sed, but,—tamen, nevertheless, or others like these, expressed or understood:
Fortuna opes auferre, non potest animum.
Fortune may take away wealth, but it cannot take away virtue. Et mihi res, non me rebus submittere conor.
I try to place myself above circumstances, not to be the slave of them.
Caelum non animum mutant qui trans mare currunt. They who cross the seas change only the country, not the disposition.
The truth of this sort of proposition depends on the two parts, and the separation that is made between them; for, though both the parts were true, a proposition of this kind would be ridiculous if there was no opposition between them: as, if I said —
Judas was a thief, and yet he would not suffer Magdalene to pour perfumes on Jesus Christ. A proposition of this sort may have many contradictories, as if it were said —
Happiness does not depend on riches but upon knowledge.
We may contradict this proposition in all these ways: Happiness depends on riches, and not upon knowledge. Happiness depends neither upon riches nor knowledge. Happiness depends upon riches and knowledge.
Thus we see that copulatives are the contradictories to the discretives, for these two last propositions are copulatives.