LOGISTIC is not a special branch of logic for it is the reali zation of the ideal of logic, the exhibition of form. The word "logistic" is an old name revived with a new meaning to denote what has been variously referred to as "symbolic logic," "algebra of logic," "mathematical logic" and "algorithmic logic." These different terms are, however, not exact synonyms. Symbolic logic is the study of the various types of deductions; it is distinguished from the special branches of pure mathematics by its generality. It uses symbols, but this is not its distinctive characteristic, for other sciences use symbols. The generality of symbolic logic is due to the fact that it is based upon a few fundamental, undefined concepts, called "primitives," and upon one or more fundamental postulates, called "primitive propositions" from which everything asserted is deduced. An "algebra of logic" denotes a special set of postulates and primitive concepts, so that there are various algebras differing with respect to the fundamental notions em ployed. "Mathematical logic" is concerned with the logistic devel opment of mathematics from the fewest possible number of prim itive concepts and primitive propositions. In the widest sense of the term, Logistic may be said to be the science of the most general principles of deduction, expressed in ideographic symbols, and developed so as to exhibit the interconnection of these principles.
merely to abbreviate the writing of ordinary words, but the utility of such symbols is slight. The S,M,P, used in expositions of the traditional syllogism were probably at the outset mere shorthand devices. Nevertheless, even these symbols suggest the importance for logic of form as such, since there is abstraction from the particular meanings for which S,M, or P, might stand. Abstraction is necessary in order to secure generality; hence, the importance of this device.
A satisfactory logical symbolism must satisfy two different kinds of conditions. First, the symbols must be as concise as possible, so that they can be easily comprehended at a glance; secondly, the symbols must be such as to facilitate the deduction of conclusions according to a mechanical process in which thinking is reduced to a minimum. The symbols must, in other words, provide a calculus of reasoning, i.e., an instrument for economizing thought, so that difficult operations can be performed without the trouble of thinking about them. The importance of good sym bolism is revealed in the development of mathematics which has, throughout, been conditioned by the adequacy of the symbols it employs. An adequate set of symbols both presupposes analysis of the fundamental ideas and, aids further analysis. Ideograms, which directly represent concepts, are better fitted than phono grams to fulfil these requirements. Although conciseness is in practice indispensable, all that is logically necessary is that the symbols should be exact and unique. The purpose of these ideo graphic symbols is not to translate words already in use, but to denote unambiguously explicit concepts, involving no reference to any special subject-matter. Their use, therefore, marks the achievement of the ideal of form, which it is the purpose of logic to exhibit.