The concept, the universal, considered abstractly in itself, is _inexpressible._ No word is proper to it. So true is this, that the logical concept remains always the same, notwithstanding the variation of verbal forms. In respect to the concept, expression is a simple _sign_ or _indication._ There must be an expression, it cannot be absent; but what it is to be, this or that, is determined by the historical and psychological conditions of the individual who is speaking. The quality of the expression is not deducible from the nature of the concept. There does not exist a true (logical) sense of words. The true sense of words is that which is conferred upon them on each occasion by the person forming a concept.
[Sidenote: _Distinction between logical and non-logical judgements._]
This being so, the only truly logical (that is, æsthetico-logical) propositions, the only rigorously logical judgements, must be those whose proper and sole content is the determination of a concept. These propositions or judgements are _definitions._ Science itself is nothing but a collection of definitions, unified in a supreme definition; a system of concepts, or highest concept.
It is therefore necessary (at least as a preliminary) to exclude from Logic all those propositions which do not affirm universals. Narrative judgements, not less than those termed non-enunciative by Aristotle, such as the expression of desires, are not properly logical judgements. They are either purely æsthetic propositions or historical propositions. "Peter is passing; it is raining to-day; I am sleepy; I want to read": these and an infinity of propositions of the same kind are nothing but either a mere enclosing in words the impression of the fact that Peter is passing, of the falling rain, of my organism inclining to sleep, and of my will directed to reading, or an existential affirmation concerning those facts. They are expressions of the real or of the unreal, historical-imaginative or pure-imaginative; they are certainly not definitions of universals.
This exclusion cannot meet with great difficulties. It is already almost an accomplished fact, and the only thing required is to render it explicit, decisive and coherent. But what is to be done with all that part of human thought called _syllogistic,_ consisting of judgements and reasonings based upon concepts? What is syllogistic? Is it to be looked down upon with contempt, as something useless, as has so often been done by the humanists in their reaction against scholasticism, by absolute idealism, by the enthusiastic admiration of our times for the methods of observation and experiment of the natural sciences?--Syllogistic, reasonings _forma,_ is not the discovery of truth; it is the art of expounding, debating, disputing with oneself and others. Proceeding from concepts already formed, from facts already observed, and appealing to the persistence of the true or of thought (such is the meaning of the laws of identity and contradiction), it infers consequences from those data, that is, it re-states what has already been discovered. Therefore, if it be an _idem per idem_ from the point of view of invention, it is most efficacious in teaching and in exposition. To reduce affirmations to a syllogistic form is a way of controlling one's own thought and of criticizing the thought of others. It is easy to laugh at syllogizers, but, if syllogistic has been born and persists, it must have good reasons of its own. Satire on it can concern only its abuses, such as the attempt to prove syllogistically questions of fact, observation and intuition, or the neglect of profound meditation and unprejudiced investigation of problems, in favour of syllogistic externality. And if so-called _mathematical Logic_ can sometimes aid us in our attempt to remember with ease, rapidly to control the results of our own thought, let us welcome this form of syllogistic also, anticipated by Leibnitz among others and again attempted by some in our own days.