of the notion we call its extent. Former theories of notions erroneously identify ideation and knowing, whereas the idea is but a means of knowledge and not even an indispensable one. We know many things of which we have no idea, e.g., chemical processes. The notion is not a complexus of ideas, but a judgment which holds for a series of objects. We may also form judgments whose objects are judgments and notions. Deductive logic is the science of the relations between judgments and notions. This definition embraces everything that philosophical logic claims, and at the same time rejects much that algebraic logic incorporates. Between judgments there are two kinds of relations: a) a judgment is derived from one or more others; it is the consequent. The judgments from which we deduce are the grounds of the deduction. b) The relation of 'conditionedness' according to which the second judgment is true if the first is true. The logic of judgments is concerned with deductions drawn from such conditioned propositions. Since all sciences consist of judgments, logic is applicable to all. The last-named propositions may be divided into Gelegenheitsurtheil and feste Sätze. V. gives a logic of these latter in the formulae of algebraic logic and derives successively the principles of identity, syllogism, contradiction, excluded middle, distribution, conversion. Logic of notions: If every object which fulfils the notion A also fulfils the notion B, then A and B are categorically related. Every A is a B. The categorical relation of notions conditions a relation of the extent of notions, called subsumption. A logic of categorical relations must show a complete parallelism with the logic of subsumption. A science claiming to embrace the whole of logic can afford to neglect neither of these two. V. gives the algebraic formulae for a logic of notions, and concludes that the algebraic method consists not only in the substitution of symbols for words, but in a strict definition of the notions and relations introduced.
PSYCHOLOGICAL.
In higher stages of hypnotism the phenomena observed are, the so-called 'automatism of command,' suggested hallucinations, insensibility of the skin to otherwise painful impressions, and post-hypnotic effects. The explanation of these facts has thus far proved unsatisfactory. As a rule, the physiological explanations use known psychological data and construct from them unknown and hypothetical physiological processes.
