“The space is bounded by three straight lines, therefore it is triangular.”
In each of these three propositions, there are two predications; the one of which is dependent on the other. The dependence is that of necessary consequence. The triangularity is the consequence of being bounded by three straight lines.
In order to have names for two Predications thus related, we may call the one the conditioning, the other the conditioned. In the above instances, “The space is bounded by three straight lines,” is the conditioning 216 predication; “The space is triangular,” is the conditioned.
There are two states of the conditioning predication; one, in which it is contingent; another, in which it is positive. Observe, now, the simple contrivance for marking the dependence of the conditioned upon the conditioning predication, in all the above cases.
In the first of the examples, “The space is triangular, if it is bounded by three straight lines,” the conditioning predication is contingent. The word if, which is equivalent to give,[64] prefixed to the conditioning predication, marks it both as the conditioning predication, and as contingent.
[64] That if has no connection with give, is manifest from the cognate forms; Goth. jabai, Frisic jef, Ang. Sax. gif, Old Ger. ibu, Lettish ja, all meaning primarily “in which or in that case, or supposition.” “Jabai—from which the other Germanic forms are descended—appears to have originally been a dative or instrumental case of ja, analogous to tubya = Latin tibi: compare ibi, ubi, Gr. βίῃφι, Slavonic tebje = tibi.”—Garnett.—F.
In the second of the examples, “The space is triangular, because it is bounded by three straight lines,” the conditioning predication is positive; the word because (having the meaning of, cause be, or cause is)[65] prefixed to it, marks it as at once the conditioning predication, and also positive. If for had been the 217 mark instead of because, the artifice would have been still the same, as for has the meaning of cause.
[65] The syllable be, in “because,” “before,” &c., is the simple preposition by, Sans. abhi, Gr. επὶ, “near,” “close to.” Therefore is for that; in which for is a preposition, meaning primarily “position in front,” and thence, by metaphor, the relation of motive or cause.—F.
In the third of the examples, “The space is bounded by three straight lines, therefore it is triangular;” the order of the predications is inverted, the conditioning being put first. In this case, therefore, we need a mark to show that the last predication is conditioned, and conditioned by the preceding. This is done by prefixing to it the compound word, therefore, of which the first part there is equivalent to that, and fore or for means cause. The expression in its elementary form being, “The space is bounded by three straight lines; for that, or cause that, the space is triangular.”
In these cases we have examples of what are called, the Suppositive, the Causal, and the Illative conjunctions.