Chapter XII

.(23) On The Doctrine Of Science.

From the analysis of the different functions of our intellect given in the whole of the preceding chapters, it is clear that for a correct use of it, either in a theoretical or a practical reference, the following conditions are demanded: (1.) The correct apprehension through perception of the real things taken into consideration, and of all their essential properties and relations, thus of all _data_. (2.) The construction of correct conceptions out of these; thus the connotation of those properties under correct abstractions, which now become the material of the subsequent thinking. (3.) The comparison of those conceptions both with the perceived object and among themselves, and with the rest of our store of conceptions, so that correct judgments, pertinent to the matter in hand, and fully comprehending and exhausting it, may proceed from them; thus the right _estimation_ of the matter. (4.) The placing together or _combination_ of those judgments as the premisses of _syllogisms_. This may be done very differently according to the choice and arrangement of the judgments, and yet the actual _result_ of the whole operation primarily depends upon it. What is really of importance here is that from among so many possible combinations of those different judgments which have to do with the matter free deliberation should hit upon the very ones which serve the purpose and are decisive. But if in the first function, that is, in the apprehension through perception of the things and relations, any single essential point has been overlooked, the correctness of all the succeeding operations of the mind cannot prevent the result from being false; for there lie the data, the material of the whole investigation. Without the certainty that these are correctly and completely collected, one ought to abstain, in important matters, from any definite decision.

A conception is _correct_; a judgment is _true_; a body is _real_; and a relation is _evident_. A proposition of immediate certainty is an _axiom_. Only the fundamental principles of logic, and those of mathematics drawn _a priori_ from intuition or perception, and finally also the law of causality, have immediate certainty. A proposition of indirect certainty is a maxim, and that by means of which it obtains its certainty is the proof. If immediate certainty is attributed to a proposition which has no such certainty, this is a _petitio principii_. A proposition which appeals directly to the empirical perception is an _assertion_: to confront it with such perception demands judgment. Empirical perception can primarily afford us only _particular_, not universal truths. Through manifold repetition and confirmation such truths indeed obtain a certain universality also, but it is only comparative and precarious, because it is still always open to attack. But if a proposition has absolute universality, the perception to which it appeals is not empirical but _a priori_. Thus Logic and Mathematics alone are absolutely certain sciences; but they really teach us only what we already knew beforehand. For they are merely explanations of that of which we are conscious _a priori_, the forms of our own knowledge, the one being concerned with the forms of thinking, the other with those of perceiving. Therefore we spin them entirely out of ourselves. All other scientific knowledge is empirical.

A proof proves _too much_ if it extends to things or cases of which that which is to be proved clearly does not hold good; therefore it is refuted apagogically by these. The _deductio 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: “Μεθοδοι δε παραδιδονται; καλλιστη μεν ἡ δια της αναλυσεως επ᾽ αρχην ὁμολογουμενην αναγουσα το ζητουμενον; ἡν και Πλατων, ὡς φασι, Λαοδαμαντι παρεδωκεν. κ.τ.λ.” (_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 επαγωγη and απαγωγη explained in

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