The Philosophical Review/Volume 1/Summary: Voigt - Was ist Logik?
Logic is called by some the science of the laws of correct thinking. Kant regarded it as a completed science; algebraic logicians, however, view it as the meagre beginning of a science. Philosophical logicians reject the claims of the other school; for them the algebra of logic is no logic at all. But the algebra of logic aims to be logic in the full sense of the term; it claims to pursue the same ends as the older logic on safer and more exact lines. Both disciplines declare as their object the discovery of the laws or rules of correct thinking. Husserl seems to maintain that algebraic logic contains only the rules of thought and not its laws. This is not the case. Algebraic logic is not merely a calculus of logic, a mechanical method, a means of dispensing with logical thought. The logical rules applied could certainly not have been found without the recognition of the corresponding logical laws. Those who doubt the claims of algebraic logic to be a logic, we refer to its final settlement of the controversy regarding the negative judgment, the reality of the subject in the categorical judgment, etc. The algebra of logic develops laws of thought and is real logic. It is true it has hitherto neglected the elementary laws of thought, but this deficiency V. tries to make good. It is also true that this science has hitherto been, though not necessarily, a logic of extent as opposed to a logic of content. Philosophers characterize the logic of extent as an inadequate exposition of logical laws. In order to decide this question, we must determine precisely the problem of logic. If we affirm a relation between two objects, we have a judgment; if we deny it, a negation of judgment. The latter is not identical with the negative judgment of philosophy. The negation of a categorical judgment is not a negative, but a particular judgment. Now the relations between objects are two-fold: either original ones, due to synthesis, or derived from an analysis of other relations. The process of thought which in this way derives relations from given relations is deduction. Induction creates original relations. The theory of the derivation of relations forms the content of deductive sciences, of which logic is one. By means of experience or deduction we find that certain relations are true not only of particular objects, but of many such. If we hold fast one object of a relation, letting the others vary, we arrive at notions. The undetermined relation becomes the object of a new relation and is called a notion. We define a notion by giving a relation which is to be fulfilled by objects. The content of a notion is not formed by the totality of properties belonging to the objects fulfilling the notion, but the relation, which the definition demands. The totality of the objects meeting the demands 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.