Passages similar to: Stromata (Miscellanies) — Chapter III: Demonstration Defined.
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Christian Mysticism
Stromata (Miscellanies)
Chapter III: Demonstration Defined. (14)
Now demonstration differs from analysis. For each one of the points demonstrated, is demonstrated by means of points that are demonstrated; those having been previously demonstrated by others; till we get back to those which are self-evident, or to those evident to sense and to understanding; which is called Analysis. But demonstration is, when the point in question reaches us through all the intermediate steps. The man, then, who practises demonstration, ought to give great attention to the truth, while he disregards the terms of the premisses, whether you call them axioms, or premisses, or assumptions.
Dear Glaucon, I said, you will not be able to follow me here, though I would do my best, and you should behold not an image only but the absolute...
(533) Dear Glaucon, I said, you will not be able to follow me here, though I would do my best, and you should behold not an image only but the absolute truth, according to my notion. Whether what I told you would or would not have been a reality I cannot venture to say; but you would have seen something like reality; of that I am confident. Doubtless, he replied. But I must also remind you, that the power of dialectic alone can reveal this, and only to one who is a disciple of the previous sciences. Of that assertion you may be as confident as of the last. And assuredly no one will argue that there is any other method of comprehending by any regular process all true existence or of ascertaining what each thing is in its own nature; for the arts in general are concerned with the desires or opinions of men, or are cultivated with a view to production and construction, or for the preservation of such productions and constructions; and as to the mathematical sciences which, as we were saying, have some apprehension of true being—geometry and the like—they only dream about being, but never can they behold the waking reality so long as they leave the hypotheses which they use unexamined, and are unable to give an account of them. For when a man knows not his own first principle, and when the conclusion and intermediate steps are also constructed out of he knows not what, how can he imagine that such a fabric of convention can ever become science? Impossible, he said. Then dialectic, and dialectic alone, goes directly to the first principle and is the only science which does away with hypotheses in order to make her ground secure; the eye of
5. “Whoever, therefore, is able to analyze all the genera which are contained under one and the same principle, and again to compose and con-numerate...
(7) 5. “Whoever, therefore, is able to analyze all the genera which are contained under one and the same principle, and again to compose and con-numerate them, he appears to me to be the wisest of men, and to possess the most perfect veracity. Farther still, he will also have discovered a beautiful place of survey, from which it will be possible to behold divinity, and all things that are in co-ordination with, and successive to him, subsisting separately, or distinct from each other. Having likewise entered this most ample road, being impelled in a right direction by intellect, and having arrived at the end of his course, he will have conjoined beginnings with ends, and will know that God is the principle, middle, and end, of all things which are accomplished according to justice and right reason.”
Assuredly not, he said; I have hardly ever known a mathematician who was capable of reasoning. But do you imagine that men who are unable to give and ...
(531) regard the skilled mathematician as a dialectician? Assuredly not, he said; I have hardly ever known a mathematician who was capable of reasoning. But do you imagine that men who are unable to give and take a reason will have the knowledge which we require of them? Neither can this be supposed. And so, Glaucon, I said, we have at last arrived at the hymn of dialectic. This is that strain which is of the intellect only, but which the faculty of sight will nevertheless be found to imitate; for sight, as you may remember, was imagined by us after a while to behold the real animals and stars, and last of all the sun himself. And so with dialectic; when a person starts on the discovery of the absolute by the light of reason only, and without any assistance of sense, and perseveres until by pure intelligence he arrives at the perception of the absolute good, he at last finds himself at the end of the intellectual world, as in the case of sight at the end of the visible. Exactly, he said. Then this is the progress which you call dialectic? True. But the release of the prisoners from chains, and their translation from the shadows to the images and to the light, and the ascent from the underground den to the sun, while in his presence they are vainly trying to look on animals and plants and the light of the sun, but are able to perceive