Stroh assumes that every reducible seminvariant can in this way be reduced.
The clue to the discovery of transcendental conditions Kant finds in the existence of judgments, most manifest in mathematics and in the pure science of nature, which are certain, yet not trifling, necessary and yet not reducible to identities, synthetic therefore and a priori, and so accounted for neither by Locke nor by Leibnitz.
Zinc blende, however, being zinc sulphide, is not directly reducible by charcoal; but it is easy to convert it into oxide by roasting: the sulphur goes off as sulphur dioxide whilst the zinc remains in the (infusible) form of oxide, ZnO.
In recognizing, further, that the relation of an actual individual fact to its sufficient ground was not reducible to identity, he set a problem diversely treated by Kant and Herbart.
The partition method of treating symmetrical algebra is one which has been singularly successful in indicating new paths of advance in the theory of invariants; the important theorem of expressibility is, directly we exclude unity from the partitions, a theorem concerning the expressibility of covariants, and involves the theory of the reducible forms and of the syzygies.
Even in Hamilton's earlier work it was shown that all such questions were reducible to the solution of linear equations in quaternions; and he proved that this, in turn, depended on the determination of a certain operator, which could be represented for purposes of calculation by a single symbol.
On the other hand, if on the plan of Sigwart categorical universals were reducible to hypotheticals, the same inference would be a pure hypothetical syllogism, thus: If anything is a man it is mortal.
Demons, when they are regarded as spirits, may belong to either of the classes of spirits recognized by primitive animism; that is to say, they may be human, or non-human, separable souls, or discarnate spirits which have never inhabited a body; a sharp distinction is often drawn between these two classes, notably by the Melanesians, the West Africans and others; the Arab jinn, for example, are not reducible to modified human souls; at the same time these classes are frequently conceived as producing identical results, e.g.
If a fourth integral is obtainable, the solution is reducible to quadrature, but this is not possible except in a limited series of cases, investigated by H.
Logical Of course the first step was to approach the phenomena of human character and social existence with the expectation of finding them as reducible to general laws as the other phenomena of the universe, and with the hope of exploring these laws by the same instruments of observation and verification as had done such triumphant work in the case of the latter.