development of the Topic of the Animal Kingdom, and it is the aim of Definition and Division, as combined in the single process of Classification, to indicate precisely the nature and position of this stage in relation to the whole Topic. Where class distinctions are understood in this way, the use of the term 'abstract' is unnecessary and uncalled for. It is simpler to say that there are degrees of determinacy or indeterminacy among concepts, and to interpret this statement in the way above suggested. Logicians are accustomed to raise the question as to whether abstract terms are connotative or not. The question is legitimate, but should include the question whether abstract terms are denotative or not. There seems to be no reason for dealing differently in this matter with concrete and with abstract terms. For the concreteness or abstractness concerns the objective reference only, and in no way the conceptual interrelations of any system of meanings, whether these be abstract or concrete, whereas it is precisely with these interrelations within a conceptual system that the distinctions of connotation and denotation are concerned. If by 'connotation' we mean the product of definition per genus et differentiam, then in a system of abstract concepts the summum genus, relatively to the system, will be non-connotative; the infimæ species-e.g., mathematical equality-will be non-denotative; all the other abstract concepts will be both connotative and denotative. Thus the term 'Insanity,' abstractly used, might have a connotation 'morbid mental state,' and a denotation 'mania, or monomonia, or melancholia, or dementia, or amentia.' So the connotation of 'Roundness,' abstractly used, might be 'spatial form having a curved surface or outline,' and this connotation admits of being differentiated after the ordinary manner of denotation. There are at least two main kinds of roundness: roundness of line and roundness of surface. To the former type belong circularity, the roundness of the oval, of the cycloid, of the catenary, etc.; to the latter all the varieties of three-dimensional roundness-the roundness of the sphere, the ellipsoid, etc. III. THE LOGICAL PROPOSITION. (i.) The Judgment or Proposition. Introductory Statement (ch. ix.). (ii.) The Laws of Thought (ch. x.). (a) The Law of Logical Identity in its relation to the Proposition. (b) The Laws of Non-contradiction and Excluded Middle. (c) The Inviolability of the Laws of Thought. CHAPTER IX. III. (i.) THE JUDGMENT OR PROPOSITION. A JUDGMENT, in the simplest logical sense of the word, is a meaning which admits of being characterized as true or false, or at least as self-consistent. Where such characterization is out of place, the expression cannot rank as a judgment. Thus, optatives, imperatives, and ejaculations fall, as such, outside the sphere of logical judgments. An optative expresses a wish, and we cannot say of mere wishes that they are either true or false; they are merely reasonable or unreasonable. Similarly imperatives call, not for belief, but for obedience; they announce commands, but do not communicate truths. The relation of Proposition to Judgment or Assertion may be defined by saying that the proposition is the judgment in a purposively fixed form. It is the judgment in that form in which it first becomes available for logical purposes. The proposition is not to be understood as a mere drapery of words which the judgment, as a synthetic act of thought, can put on or put off as it pleases. It is quite true that we can think without words. It is not at all essential that the sensory assistance so indispensable to thought should take the form of a conventional verbal sign. But whatever the sensory symbolism may be, it is only as a purposive fixation of meaning that it has any logical significance. The grammatical, or, to speak more correctly, the philological and phonetic interest in verbal structure as such is non-logical. In Logic we are interested in words only as the visible or audible forms in which thought fixes and controls its own meaning. The proposition, qua logically serviceable, is therefore indistinguishable from the judgment. As in Definition the distinction between verbal and conceptual definition was found, on closer inspection, to have no logical raison d'être, so, in the matter of assertion generally, the distinction between proposition and judgment, so far as logical interest is concerned, is a distinction without a difference. The terms 'proposition' and 'judgment' are logically interchangeable. On the other hand, we must distinguish between proposition and sentence. Every proposition is a sentence, but not every sentence a proposition. For the sentence is the unit of speech generally. Any |