Clement of Alexandria · a new plain-English translation from the original language
Likewise, too, all men would agree that demonstration is a statement that furnishes conviction about disputed matters out of matters already agreed upon. And not demonstration and conviction and knowledge alone, but foreknowledge too is spoken of in two ways: the one scientific and secure, the other merely hopeful. Now demonstration in its most proper sense is that which implants scientific conviction in the souls of learners, while the other is opinionative — just as a man in the truest sense is the man possessed of the common faculties of a rational mind, while the other kind of man is savage and beast-like. So indeed the comic poet said: how charming a man is, so long as he is a man. And the same account holds for ox and horse and dog, according to the virtue or vice of the animal. For it is by looking to the perfection of the kind that we arrive at the most proper application of the terms in question. For instance, we conceive of a physician as one who lacks nothing of the power of medicine, and of a knower [gnostic] as one who lacks nothing of scientific knowledge.
Indication differs from syllogism in that what is indicated is itself one thing, being itself a single sign of a single fact — as we say that pregnancy is an indication that a woman is no longer a virgin — whereas what is grasped by syllogism, though it too is a single fact, follows from several premises, as, for example, that Python was betraying the Byzantines, if that in fact happened; here not one but several signs are taken together. And to draw a conclusion from things agreed upon is to reason syllogistically, while to draw a conclusion from things true is to demonstrate; so that the benefit of demonstration is in a sense composite, arising both from taking premises that are true with respect to the matters sought and from the conclusion being drawn as a consequence of them. But if either the first premise does not hold, or the second does not follow from it, one has not demonstrated, though one has reasoned syllogistically. For to bring forward the proper conclusion from the premises is merely to reason syllogistically, whereas having each of the premises be true as well is not simply reasoning syllogistically but rather achieving demonstration. And concluding means, as is plain from the word itself, arriving at an end; and the end in every argument is, of course, the very thing sought, which is indeed also called the conclusion. And no simple, single statement is called a syllogism, even if it be true, but a syllogism is at the very least composed of three such statements, two serving as premises and one as conclusion.
Either all things need demonstration, or else some things are credible of themselves.
But if the former, then by demanding a demonstration for each demonstration we shall be carried on to infinity, and thus demonstration itself will be overturned; but if the latter, then these very things credible of themselves will become the starting-points of demonstrations. For instance, the philosophers acknowledge the first principles of the universe to be undemonstrated. So that if demonstration exists at all, it is wholly necessary that something credible of itself exist prior to it — which indeed is called primary and undemonstrated. To this undemonstrated ground of conviction, then, all demonstration is ultimately referred. But there could also be other starting-points of demonstrations besides the source that comes from conviction — namely, the things that appear clearly to sense-perception and to thought. For the things that occur with respect to sense-perception are simple and indissoluble, while the things with respect to thought are simple and are the first rational truths; and the things generated out of these are composite, yet no less clear and credible and indeed more rational than the first. There is, then, a certain natural power belonging to reason itself — the power of following and of conflicting — which all of us possess by nature. If, then, some argument be found of such a kind as to be able to furnish conviction, out of things already believed, to things not yet believed, we shall say that this very thing is the essence of demonstration. And it has been said that the kind both of conviction and of demonstration is twofold: the one producing mere persuasion in the souls of the hearers, the other producing knowledge. If, then, one begins from the things clear to sense-perception and to thought, and then draws the proper conclusion, one truly demonstrates; but if one begins only from things reputable, yet not primary — that is, not clear either to sense-perception or to thought — then, if one brings forward the proper conclusion, one will indeed reason syllogistically, but will not thereby produce scientific demonstration; while if the conclusion is not proper, one will not even reason syllogistically at all.
Demonstration differs from analysis: for each of the things demonstrated is demonstrated by means of certain other things demonstrated, those in turn having been previously demonstrated by yet others, until we run back up to the things credible of themselves, or to the things clear to sense-perception and to thought — and this process is called analysis; whereas demonstration is when one proceeds from the first things to the thing sought, through all the intermediate steps. The demonstrative man, then, must take great care regarding the truth of his premises, but need not trouble himself over names, whether one wishes to call them axioms, or propositions, or premises. Likewise he must take equally great care as to what follows from what is laid down, but need not trouble himself in the least whether one wishes to call the resulting statement a conclusive argument, or a concluding one, or a syllogistic one. For I say that the demonstrative man must, in all cases, guard these two things: that he take his premises as true, and that he bring forward the conclusion as a consequence of them — which some also call the 'inference,' that is, what is carried forward upon the premises.
Concerning everything that is sought, in each individual problem, there is need of premises that are various yet proper to the matter proposed; and it is necessary that the matter proposed itself be converted into a statement, and it is fitting that this statement be one agreed upon by all. But when premises not proper to the problem are taken, it is not possible to discover anything well from it, since the whole problem — which is indeed also called the inquiry — remains, by its very nature, unknown. In all matters sought, then, there is something foreknown beforehand (which, being wholly credible of itself, is believed without demonstration), and this one must make the starting-point of the inquiry into them and the criterion for what seems to have been discovered.
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