dedudio ad absurdum properly consists in this, that we take a false assertion which has been made as the major proposition of a syllogism, then add to it a correct minor, and arrive at a conclusion which clearly contradicts facts of experience or unquestionable truths. But by some round-about way such a refutation must be possible of every false doctrine. For the defender of this will yet certainly recognise and admit some truth or other, and then the consequences of this, and on the other hand those of the false assertion, must be followed out until we arrive at two propositions which directly contradict each other. We find many examples in Plato of this beautiful artifice of genuine dialectic.
A correct hypothesis is nothing more than the true and complete expression of the present fact, which the originator of the hypothesis has intuitively apprehended in its real nature and inner connection. For it tells us only what really takes place here.
The opposition of the analytical and synthetical methods we find already indicated by Aristotle, yet perhaps first distinctly described by Proclus, who says quite correctly: "(
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(Methodi traduntur sequentes: pulcherrima quidem ea, quæ per analysin quæsitum refert ad principium, de quo jam convenit; quam etiam Plato Laodamanti tradidisse dicitur.) "In Primum Euclidis Librum," L. iii. Certainly the analytical method consists in referring what is given to an admitted principle; the synthetical method, on the contrary, in deduction from such a principle. They are therefore analogous to the (Greek characters) and (Greek characters) explained in chapter ix.; only the latter are not used to establish propositions, but always to overthrow them. The analytical method proceeds from the facts; the particular, to the principle or rule; the universal, or from the consequents to the reasons; the other conversely. Therefore it would
