Denominator

“ In its abstract terms a Judgment is expressible in the proposition: 'The individual is the universal.' These are the terms under which the subject and the predicate first confront each other, when the functions of the notion are taken in their immediate character or first abstraction. [Propositions such as, 'The particular is the universal,' and 'The individual is the particular,' belong to the further specialisation of the judgment.] ”

“ Either there is a distinction, or else there is not a distinction, between connotation that is receptual, and connotation that is conceptual. If there is no distinction, all argument is at an end: the brute and the man are one in kind. But I allow that there is a distinction, and I acknowledge that the distinction resides where it is alleged to reside by my opponents—namely, in the presence or absence of self-consciousness on the part of a mind which bestows a name. Or, to revert to my own terminology, it is the distinction between denotation and denomination. ”

“ If we analyse a judgment, every word in which it is expressed, whether it is a noun or a verb or a preposition or a conjunction, conveys a distinct meaning, indicates a term or a relation, each of which can be made a distinct object to the mind, and all of which are combined in the single meaning the judgment expresses. It is in this complexity that the possibility of error lies, and the possibility increases as the complexity increases. ”

“ The distinction between nominal and real definitions, between definitions of words and what are called definitions of things, though conformable to the ideas of most of the Aristotelian logicians, can not, as it appears to us, be maintained. ”

“ Whatever is the half of anything is less than that of which it is the half:
A is half of B:
A is less than B. The subject of such a proposition is separated into two terms, a “subject nominative” and an “object accusative.”
In an argument, the premisses form a representation of the conclusion, because they indicate the interpretant of the argument, or representation representing it to represent its object. The premisses may afford a likeness, index, or symbol of the conclusion. ”

“ And so in all cases, the general propositions, whether called definitions, axioms, or laws of nature, which we lay down at the beginning of our reasonings, are merely abridged statements, in a kind of short-hand, of the particular facts, which, as occasion arises, we either think we may proceed on as proved, or intend to assume. In any one demonstration it is enough if we assume for a particular case suitably selected, what by the statement of the definition or principle we announce that we intend to assume in all cases which may arise. ”

“ Deductive Reasoning.+—When once a general principle has been established, we may demonstrate the truth of a specific proposition by showing that the general principle applies to it. We see a gold ring and say, "This ring is valuable," because we believe the general proposition, "All articles made of gold are valuable." ”

“ As we judge by comparing- concepts with other concepts or with impressions, one judgment by a faculty is associated with other judgments by the same faculty, and as one property is concomitant with all the others, one property becomes a symbol of all the others, so that there is association by comparison of concepts and association by symbolism. ”

“ Now there are propositions, in which one or both of the terms are common nouns, as standing for what is abstract, general, and non-existing, such as “Man is an animal, some men are learned, an Apostle is a creation of Christianity, a line is length without breadth, to err is human, to forgive divine.” These I shall call notional propositions, and the apprehension with which we infer or assent to them, notional. ”

“ From this it is already evident, why the question respecting the definition of an abstract name is often one of so much difficulty. The question, What is justice? is, in other words, What is the attribute which mankind mean to predicate when they call an action just? ”

“ This realised particularity of the notion is the Judgment.
The ordinary classification of notions, as clear, distinct and adequate, is no part of the notion; it belongs to psychology. Notions, in fact, are here synonymous with mental representations; a clear notion is an abstract simple representation: a distinct notion is one where, in addition to the simplicity, there is one 'mark' or character emphasised as a sign for subjective cognition. ”

“ It remains to note that such phrases as 'Being and Nothing are the same,' or 'The unity of Being and Nothing'—like all other such unities, that of subject and object, and others—give rise to reasonable objection. ”

“ The judgment or proposition, which is the characteristic form in which the result of reflection finds its expression, consists, in its most rudimentary shape, of the embodiment of this distinction in the separation of predicate from subject, and the subsequent affirmation of the first about the second. The work of thought or knowledge in making our world more intelligible to us essentially consists in the progressive analysis of a content or what, considered in abstraction from the this to which it belongs. ”

“ Each category, or determination, is a general principle by which we seek to make experience a consistent whole and render it a concrete universal; and each has its own way of relating the two root factors, viz., unity and difference. ”

“ The interpretation of the judgment, according to which it is assumed to be merely subjective, as if we ascribed a predicate to a subject, is contradicted by the decidedly objective expression of the judgment. The rose is red; Gold is a metal. It is not by us that something is first ascribed to them.—A judgment is however distinguished from a proposition. ”

“ But when we say that definition is unfolding the intension of terms, it must not be imagined that we are bound in defining to unfold completely the intension of terms. This would be a tedious, and often an endless, task. A term may mean, or convey to the mind, a good many more attributes than those which are stated in its definition. There is no limit indeed to the meaning which a term may legitimately convey, except the common attributes of the things denoted by it. ”

“ We must not, however, conclude that the generality of the principle is merely verbal; it will be found on inspection to be no vague or unmeaning assertion, but a most important and really fundamental truth. ”

“ Now when we say 'John is a man' or 'This table is oblong,' the proposition is quite as universal, in the sense of the predicate applying to the whole of the subject, as when we say 'All men are mortal.' For since a singular term applies only to one thing, we cannot avoid using it in its whole extent, if we use it at all. ”

“ Whether, therefore, we conform to the practice of those who have made the subject their particular study, or to that of popular writers and common discourse, the province of logic will include several operations of the intellect not usually considered to fall within the meaning of the terms Reasoning and Argumentation. ”

“ A primary judgment is a judgment that a sensible thing is determined as existing; but later judgments are concerned with either existing things, or with ideas, or with words, and signify that they are determined in all sorts of ways. (5) When a judgment is expressed by a proposition, the proposition expresses the results of the division by two terms, subject and predicate, and by the copula that what is signified by the subject is what is signified by the predicate; and the proposition is a combination of the two terms; e.g. border war is evil. ”

“ The second principle I shall take notice of is that of comparison, or the variation of our judgments concerning objects, according to the proportion they bear to those with which we compare them. We judge more of objects by comparison than by their intrinsic worth and value; and regard every thing as mean, when set in opposition to what is superior of the same kind. ”

“ We find the inner ground for this systematisation of judgments in the circumstance that when the Notion, which is the unity of Being and Essence in a comprehensive thought, unfolds, as it does in the judgment, it must reproduce these two stages in a transformation proper to the notion. ”

“ Hence possibility, relation, and distinction are to be looked upon as entities having only a conventional reality, from which their denomination of “real” has been desumed. Let us therefore inquire what are the principles on which these nominal realities depend.
Principles of possible being. It has been proved, in one of our preceding articles, that every created being is constituted of an act, of a potential term, and of their formal complement. ”

“ As an art logic may be called the navigation of the sea of thought.
§ 25. The laws of thought are all reducible to the three following axioms, which are known as The Three Fundamental Laws of Thought.
(1) The Law of Identity—
Whatever is, is;
or, in a more precise form,
Every A is A.
(2) The Law of Contradiction—
Nothing can both be and not be;
Nothing can be A and not A.
(3) The Law of Excluded Middle—
Everything must either be or not be;
Everything is either A or not A.
§ 26. ”

“ Every proposition is given empirically as a spoken or written sentence, a complex of physical signs, which is itself a fact in the real world: comparing a proposition with the state of affairs it expresses is, therefore, nothing but a comparison of two facts. ”

“ It will simplify matters to bear in mind that the intension of a term is the same thing as its meaning. To take an example, the term 'man' applies to certain things, namely, all the members of the human race that have been, are, or ever will be: this is its quantity in extension. But the term 'man' has also a certain meaning, and implies certain attributes—rationality, animality, and a definite bodily shape: the sum of these attributes constitutes its quantity in intension. ”

“ It was natural enough that the originators of conceptual logic, seeing that judgments can be expressed by propositions, and conceptions by terms, should fall into the error of supposing that, as propositions consist of terms, so judgments consist of conceptions, and that there is a triple mental order—conception, judgment, reasoning—parallel to the triple linguistic order—term, proposition, discourse. ”

“ In a word, as we understand by the measure of celestial bodies the relation resulting from the comparison of these bodies with each other, so, by the measure of values, we must understand the relation which results from their comparison. ”

“ The general principle of right arrangement in sentences, which we have traced in its application to the leading divisions of them, equally determines the proper order of their minor divisions. In every sentence of any complexity the complement to the subject contains several clauses, and that to the predicate several others ”

“ Beginning with definitions, they find that the definitions themselves need defining; and just at the triumphant moment when the structure of argument seems complete and logic-proof, some lynx-eyed adversary detects an inaccuracy or a contradiction in the use of some keystone term, and the whole magnificent pile, so painfully reared, tumbles into ruins. ”

“ Why rob one to feed the other?
“If you adopt, as absolute, a standard of evenness which is so only relatively, your results will not be absolutely even. If you adopt, as absolute, a criterion of right which is so only relatively, your results will not be absolutely right. ”

“ 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. ”

“ What has been said can be expressed in a formal manner by saying that the nature of judgment or the proposition in general, which involves the distinction of subject and predicate, is subverted and destroyed by the speculative judgment ”

“ Thus the explanation of the term 'Centaur' would be a nominal, that of 'horse' a real definition.
It is useless to assert, as is often done, that a nominal definition explains the meaning of a term and a real definition the nature of a thing; for, as we have seen already, the meaning of a term is whatever we know of the nature of a thing. ”

“ All cases, then, tend to show that deduction involves generalization from an observed case on a single axiom; the axioms, therefore, of induction are the axioms of reasoning, and the generalization of particulars is the work of reason. ”

“ The Materialist, admitting all this, may say that a judgment is only the proximate meaning of a proposition, and that the ultimate meaning, the meaning of the judgment itself, is always some matter-of-fact; that the other schools have not hitherto been eager to recognise the unity of Deduction and Induction or to investigate the conditions of trustworthy experiments and observations within the limits of human understanding ”

“ When we can suppose that A loves B, we "understand the proposition" A loves B. Thus we often understand a proposition in cases where we have not enough knowledge to make a judgment. Supposing, like judging, is a many-term relation, of which a mind is one term. The other terms of the relation are called the constituents of the proposition supposed. ”

“ We found that whatever be the form of the proposition, and whatever its nominal subject or predicate, the real subject of every proposition is some one or more facts or phenomena of consciousness, or some one or more of the hidden causes or powers to which we ascribe those facts ”