Proposition necessary & contingent.
10. Fifthly, propositions are distinguished into necessary, that is, necessarily true; and true, but not necessarily, which they call contingent. A necessary proposition is when nothing can at any time be conceived or feigned, whereof the subject is the name, but the predicate also is the name of the same thing; as man is a living creature is a necessary proposition, because at what time soever we suppose the name man agrees with any thing, at that time the name living-creature also agrees with the same. But a contingent proposition is that, which at one time may be true, at another time false; as every crow is black; which may perhaps be true now, but false hereafter. Again, in every necessary proposition, the predicate is either equivalent to the subject, as in this, man is a rational living creature; or part of an equivalent name, as in this, man is a living creature, for the name rational-living-creature, or man, is compounded of these two, rational and living-creature. But in a contingent proposition this cannot be; for though this were true, every man is a liar, yet because the word liar is no part of a compounded name equivalent to the name man, that proposition is not to be called necessary, but contingent, though it should happen to be true always. And therefore those propositions only are necessary, which are of sempiternal truth, that is, true at all times. From hence also it is manifest, that truth adheres not to things, but to speech only, for some truths are eternal; for it will be eternally true, if man, then living-creature; but that any man, or living-creature, should exist eternally, is not necessary.
Categorical & hypothetical.
11. A sixth distinction of propositions is into categorical and hypothetical. A categorical proposition is that which is simply or absolutely pronounced, as every man is a living-creature, no man is a tree; and hypothetical is that which is pronounced conditionally, as, if any thing be a man, the same is also a living-creature, if anything be a man, the same is also not-a-stone.
A categorical proposition, and an hypothetical answering it, do both signify the same, if the propositions be necessary; but not if they be contingent. For example, if this, every man is a living-creature, be true, this also will be true, if any thing be a man, the same is also a living-creature; but in contingent propositions, though this be true, every crow is black, yet this, if any thing be a crow, the same is black, is false. But an hypothetical proposition is then rightly said to be true, when the consequence is true, as every man is a living-creature, is rightly said to be a true proposition, because of whatsoever it is truly said that is a man, it cannot but be truly said also, the same is a living creature. And therefore whensoever an hypothetical proposition is true, the categorical answering it, is not only true, but also necessary; which I thought worth the noting, as an argument, that philosophers may in most things reason more solidly by hypothetical than categorical propositions.
The same proposition diversely pronounced.
12. But seeing every proposition may be, and uses to be, pronounced and written in many forms, and we are obliged to speak in the same manner as most men speak, yet they that learn philosophy from masters, had need to take heed they be not deceived by the variety of expressions. And therefore, whensoever they meet with any obscure proposition, they ought to reduce it to its most simple and categorical form; in which the copulative word is must be expressed by itself, and not mingled in any manner either with the subject or predicate, both which must be separated and clearly distinguished one from another. For example, if this proposition, man can not sin, be compared with this, man cannot sin, their difference will easily appear if they be reduced to these, man is able not to sin, and, man is not able to sin, where the predicates are manifestly different. But they ought to do this silently by themselves, or betwixt them and their masters only; for it will be thought both ridiculous and absurd, for a man to use such language publicly. Being therefore to speak of equipollent propositions, I put in the first place all those for equipollent, that may be reduced purely to one and the same categorical proposition.
Propositions that may be reduced to the same categorical proposition, are equipollent.
13. Secondly, that which is categorical and necessary, is equipollent to its hypothetical proposition; as this categorical, a right-lined triangle has its three angles equal to two right angles, to this hypothetical, if any figure be a right-lined triangle, the three angles of it are equal to two right angles.
Universal propositions converted by contradictory names, are equipollent.