Category (logic)

“ This turning of Conditionals into Categoricals is called a Change of Relation; and the process may be reversed: All the wise are virtuous may be written, If any man is wise he is virtuous; or, again, Either a man is not-wise or he is virtuous. But the categorical form is usually the simplest.
If, then, as substitutes for the corresponding conditionals, categoricals are formally adequate, though sometimes inelegant, it may be urged that Logic has nothing to do with elegance ”

“ In the foregoing categorical propositions the quantity signs are respectively, every, all and no. In any case the quantity sign is always attached to the subject and indicates its breadth or extension. For example, in the two propositions, “All men are mortal” and “Some men are wise,” the quantity sign all makes the term man much broader than does the quantity sign some.
The logical subject of a categorical proposition is the term of which something is affirmed or denied, whereas the logical predicate of a categorical proposition is the term which is affirmed or denied of the subject. ”

“ Classification thus considered, differs from classification in the wider sense, in having reference to real objects exclusively, and not to all that are imaginable: its object being the due co-ordination in our minds of those things only, with the properties of which we have actually occasion to make ourselves acquainted. But, on the other hand, it embraces all really existing objects. We can not constitute any one class properly, except in reference to a general division of the whole of nature ”

“ The only remaining class of Namable Things is Attributes; and these are of three kinds, Quality, Relation, and Quantity. Qualities, like substances, are known to us no otherwise than by the sensations or other states of consciousness which they excite: and while, in compliance with common usage, we have continued to speak of them as a distinct class of Things, we showed that in predicating them no one means to predicate any thing but those sensations or states of consciousness, on which they may be said to be grounded, and by which alone they can be defined or described. ”

“ 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. ”

“ What we usually do is first to frame some system of concepts mentally classified, serialized, or connected in some intellectual way, and then to use this as a tally by which we 'keep tab' on the impressions that present themselves. When each is referred to some possible place in the conceptual system, it is thereby 'understood.' This notion of parallel 'manifolds' with their elements standing reciprocally in 'one-to-one relations,' is proving so convenient nowadays in mathematics and logic as to supersede more and more the older classificatory conceptions. ”

“ The second kind of imperfect definition, therefore, in which the name of a class is defined by any of its accidents,—that is, by attributes which are not included in its connotation,—has been rejected from the rank of genuine Definition by all logicians, and has been termed Description. ”

“ Since the common properties of a true Kind, and consequently the general assertions which can be made respecting it, or which are certain to be made hereafter as our knowledge extends, are indefinite and inexhaustible; and since the very first principle of natural classification is that of forming the classes so that the objects composing each may have the greatest number of properties in common; this principle prescribes that every such classification shall recognize and adopt into itself all distinctions of Kind, which exist among the objects it professes to classify. ”

“ If the minor premise asserted nothing more than that something belongs to a class, and if the major premise asserted nothing of that class except that it is included in another class, the conclusion would only be that what was included in the lower class is included in the higher, and the result, therefore, nothing except that the classification is consistent with itself. ”

“ But we have seen that it is no sufficient account of the meaning of a proposition, to say that it refers something to, or excludes something from, a class. Every proposition which conveys real information asserts a matter of fact, dependent on the laws of nature, and not on classification. It asserts that a given object does or does not possess a given attribute ”

“ An attribute, therefore, is necessarily either an existence, a co-existence, a causation, a sequence, or a resemblance. When a proposition consists of a subject and predicate which are abstract terms, it consists of terms which must necessarily signify one or other of these things. ”

“ It is a fundamental principle in logic, that the power of framing classes is unlimited, as long as there is any (even the smallest) difference to found a distinction upon. Take any attribute whatever, and if some things have it, and others have not, we may ground on the attribute a division of all things into two classes; and we actually do so, the moment we create a name which connotes the attribute. ”

“ A categorical proposition is one in which the assertion is made unconditionally. An hypothetical proposition is one in which the assertion depends upon a condition. A disjunctive proposition is one which asserts an alternative. ”

“ Nor can there be any real difficulty in representing, by an enumeration of characters, the nature and degree of the resemblance which is strictly sufficient to include any object [pg 505] in the class. There are always some properties common to all things which are included. Others there often are, to which some things, which are nevertheless included, are exceptions. But the objects which are exceptions to one character are not exceptions to another; the resemblance which fails in some particulars must be made up for in others. ”

“ On the other hand, the concepts of the Philosophy of nature are categories, which as such present themselves in their emptiness as intuitions, and intuitions, which in their blindness present themselves as categories. ”

“ The requisites of a classification intended to facilitate the study of a particular phenomenon, are, first to bring into one class all Kinds of things which exhibit that phenomenon, in whatever variety of forms or degrees ”

“ There is no impropriety in saying that, of these two classifications, the one answers to a much more radical distinction in the things themselves, than the other does. And if any one even chooses to say that the one classification is made by nature, the other by us for our convenience, he will be right ”

“ When the syllogism is resolved, by all who treat of it, into an inference that what is true of a class is true of all things whatever that belong to the class; and when this is laid down by almost all professed logicians as the ultimate principle to which all reasoning owes its validity; it is clear that in the general estimation of logicians, the propositions of which reasonings are composed can be the expression of nothing but the process of dividing things into classes, and referring every thing to its proper class. ”

“ The ends of scientific classification are best answered, when the objects are formed into groups respecting which a greater number of general propositions can be made, and those propositions more important, than could be made respecting any other groups into which the same things could be distributed. The properties, therefore, according to which objects are classified, should, if possible, be those which are causes of many other properties ”

“ In reality, however, particular and universal judgments are too closely connected to have such different imports. In opposition, a categorical particular is the contradictory of a universal, which is also categorical, not hypothetical, e.g., “not all M is P” is the contradictory of “all M is P,” not of “if anything is M it is P.” In inference, a particular is an example of a universal which in its turn may become a particular example of a higher universal. ”

“ This shows, more strongly than ever, how extensive a knowledge of the properties of objects is necessary for making a good classification of them. And as it is one of the uses of such a classification that by drawing attention to the properties on which it is founded, and which, if the classification be good, are marks of many others, it facilitates the discovery of those others; we see in what manner our knowledge of things, and our classification of them, tend mutually and indefinitely to the improvement of each other. ”

“ With respect to general propositions of this class, that is, which affirm the bare fact of existence, they have a peculiarity which renders the logical treatment of them a very easy matter; they are generalizations which are sufficiently proved by a single instance. ”

“ There is no property of objects which may not be taken, if we please, as the foundation for a classification or mental grouping of those objects; and in our first attempts we are likely to select for that purpose properties which are simple, easily conceived, and perceptible on a first view, without any previous process of thought. ”

“ The primary condition implied in having this clear idea, is that the class be really a class; that it correspond to a real distinction; that the things it includes really do agree with one another in certain particulars, and differ, in those same particulars, from all other things. A person without clear ideas is one who habitually classes together, under the same general names, things which have no common properties, or none which are not possessed also by other things ”

“ But we shall have to follow here the guidance of the categories,—only, as in the present case a thing, "I," as thinking being, is at first given, we shall—not indeed change the order of the categories as it stands in the table,—but begin at the category of substance, by which at the a thing a thing is represented and proceeds backwards through the series. ”

“ We can not ascertain general truths, that is, truths applicable to classes, unless we have formed the classes in such a manner that general truths can be affirmed of them. In the formation of any class, there is involved a conception of it as a class, that is, a conception of certain circumstances as being those which characterize the class, and distinguish the objects composing it from all other things. ”

“ Now, as we have already seen, what is signified by the subject may be existing or not, and in either case a judgment remains categorical so long as it is a belief without conditions. Thus, “Some existing men are poets,” “All existing men are mortal,” “Some conceivable centaurs are human in their forequarters,” “All conceivable centaurs are equine in their hindquarters,” are all categorical judgments, while the two first are also categorical judgments of existence. ”

“ Determine the figure and mood by using symbols.
(3) Apply the rules for negatives and particulars.
(4) Indicate the distribution by underscoring the terms distributed.
(5) Apply the rules for distribution.
(6) Name fallacies, if any, giving reasons.
We recall that to be strictly logical any categorical argument must take this form: first, major premise; second, minor premise; third, conclusion. Often in common conversation either the minor premise or conclusion is given first. Illustrations of this: (1) “He cannot be a gentleman (conclusion) ”

“ Whatever proposition we like to take may be read either in extension or in intension, according as we fix our minds on the fact of inclusion in a class or the fact of the possession of attributes.
§ 333. It will be seen that the term 'species,' as it appears in the scheme, has a wholly different meaning from the current acceptation in which it was defined above. Species, in its now accepted meaning, signifies the relation of a smaller class to a larger one: as it was originally intended in the heads of predicables it signifies a class in reference to individuals. ”

“ Again, things are classed according to their resemblances and differences: that is to say, those that most closely resemble one another are classed together on that ground; and those that differ from one another in important ways, are distributed into other classes. ”

“ To these are added, as a sort of appendix, such other species, generally in small number, as possess nearly all the properties selected; wanting some of them one property, some another, and which, while they agree with the rest almost as much as these agree with one another, do not resemble in an equal degree any other group. Our conception of the class continues to be grounded on the characters; and the class might be defined, those things which either possess that set of characters, or resemble the things that do so, more than they resemble any thing else. ”

“ Willing and knowing are indeed categories. If the test, by which we recognize the categories, consists in that they are valid, not only for certain objects, but for all, and in that they should express the universal nature of things, it is not difficult to see in what a profoundly significant way knowing and willing emerge triumphantly from such a test. ”

“ Some modes of classing things are more valuable than others for human uses, whether of speculation or of practice; and our classifications are not well made, unless the things which they bring together not only agree with each other in something [pg 463] which distinguishes them from all other things, but agree with each other and differ from other things in the very circumstances which are of primary importance for the purpose (theoretical or practical) which we have in view, and which constitutes the problem before us. ”