Word Finder - categories

definition

A group, often named or numbered, to which items are assigned based on similarity or defined criteria.

example

I wouldn't put this book in the same category as the author's first novel.

definition

A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.

example

Just as a monoid consists of an underlying set with a binary operation "on top of it" which is closed, associative and with an identity, a category consists of an underlying digraph with an arrow composition operation "on top of it" which is transitively closed, associative, and with an identity at each object. In fact, a category's composition operation, when restricted to a single one of its objects, turns that object's set of arrows (which would all be loops) into a monoid.

Then we would put the Categories into 2-3 columns.

God is incomprehensible, and the categories cannot be applied to determine his existence.

I'd be interested in reworking the place categories to make them more useful.

There is clearly a difference between these two categories.

Women vote for school committee men (categories as above, 95.18, 59.62, 76.49%).

Amazon sells millions of items in hundreds of categories.

Colors can be broken down into two categories, cool toned colors and warm toned colors.

Causality is one of the " categories " which out mind uses in building up orderly experience.

Moreover, the study of the theory of rent has had a very great influence on all branches of economics by destroying the notion that it is possible to draw sharp lines of distinction, or deal with economic conceptions as though they were entirely independent categories.

To portions of these Aristotle has been supposed to have been indebted for his doctrine of the categories and some of his chief ethical theories.

To handle these so successfully that we can discriminate defects from qualities at all, is proof of the technique of a master, even though the faults extend to whole categories of literature.

But it must remain possible that contact with new scenes and persons, and especially such controversial necessities as are exemplified in Colossians, stimulated Paul to work out more fully, under the influence of Alexandrian categories, lines of thought of which the germs and origins must be admitted to have been present in earlier epistles.

The use of Alexandrian categories is wholly governed by this interest.

Under these regulations the revenues were divided into two categories, viz.

Two categories of rent, fixed and proportional, are payable to the state by mineowners.

Compensation for the expropriated land and the categories of land to be expropriated without compensation will be determined by a special law.

A single sentence in Porphyry's Isagoge or " introduc tion " to the Categories of Aristotle furnished the i o, s text of the discussion.

In translations they had only the Categories and the De interpretatione of Aristotle in the versions of Boetius, the Timaeus of Plato in the version of Chalcidius, and Boetius's translation of Porphyry's Isagoge.

Prantl has professed to find the headstream of Nominalism also in Scotus Erigena; but beyond the fact that he discusses at considerable length the categories of thought and their mutual relations, occasionally using the term voces to express his meaning, Prantl appears to adduce no reasons for an assertion which directly contradicts Erigena's most fundamental doctrines.

His pupil Richer has left us a detailed account of his system of teaching at Reims. So far as the trivium is concerned, his text-books were Victorinus's translation of Porphyry's Isagoge, Aristotle's Categories, and Cicero's Topics with Manlius's Commentaries.

There are, however, no outward signs enabling us to distinguish conclusively between both categories of laws in the codes, nor is it possible to draw a line between permanent laws and personal ordinances of single sovereigns, as has been attempted in the case of Frankish legislation.

And as the personal element disappears in the conception of the prophetic calling, so it tends to disappear in the prophetic view of history, and the future comes to be conceived not as the organic result of the present under the divine guidance, but as mechanically determined from the beginning in the counsels of God, and arranged under artificial categories of time.

These events belonged in the main to the past, but the writer represented them as still in the future, arranged under certain artificial categories of time definitely determined from the beginning in the counsels of God and revealed by Him to His servants the prophets.

In the treatment of the spiritual categories, Croce laid special stress upon those which had been least elaborated and least studied.

The last two categories, which do not become prominent anywhere in Europe until the 12th century, had, like all gilds, a religious tinge, but their aims were primarily worldly, and their functions were mainly of an economic character.

It is true that Gentile converts carried over into the new religion many ideas and habits of cult contracted under the old; this was inevitable, for no one lightly changes his religious habits and categories.

As we advance from the logic to the metaphysics and from that to his ontology, it becomes clear that the concepts are only " categories " or predicates of a reality lying outside of them, and there is an ultimate division between the world as the object or matter of thought and the thinking or moving principle which gives its life.

The parts of the Critique of Pure Reason, more particularly the " Deduction of the Categories " in which this theory is worked out, may be said to have laid the foundation of modern idealism - " articulum stantis aut cadentis dectrinae."

The " Logic " of Hegel is merely the continuation of Kant's " Deduction " of the categories and ideas of the reason which has generally been recognized as the soberest of attempts to set forth the presuppositions which underlie all experience.

For every philosophy is scholastic whose subject-matter is imaginative and mystical, and which handles this subject-matter according to established rules in logical categories and distinctions.

The sense-organs are always situated at the margin of the unbrella and may be distinguished from the morphological point of view into two categories, according as they are, or are not, derived from modifications of tentacles; in the former case they are termed tentaculocysts.

He became secretary of the American Oriental Society and editor of its Journal, to which he contributed many valuable papers, especially on numerical and temporal categories in early Sanskrit literature.

He left some unfinished; such as the Categories, in which the main part on categories is not finished, while the last part, afterwards called postpredicaments, is probably not his, the Politics and the Poetics.

On these principles, we regard as early genuine philosophical works of Aristotle, (I) the Categories; (2) the De Interpretatione; (3) the Eudemian Ethics and Magna Moralia; (4) the Rhetoric to Alexander.

The categories then are names signifying things capable of becoming predicates in a proposition.

Having made these subdivisions of substance, he thereupon reduces secondary substances and all the rest of the categories to belongings of individual or primary substances.

On the other hand, a universal species or genus of substances is a predicate which, as well as everything else in all the other categories, always belongs to some individual substance or other as subject, and has no separate being.

In full, then, a substance is a separate individual, having universals, and things in all other categories, inseparably belonging to it.

The doctrine that all things are substances which are separate individuals, stated in the Categories, is expanded in the Metaphysics.

Both works arrive at it from the classification of categories, which is the same in both; except that in the former the categories are treated rather as a logical classification of names signifying things, in the latter rather as a metaphysical classification of things.

It follows that Aristotelianism in the Categories and in the Metaphysics is a realism both of individuals and of universals; of individual substances as real subjects, and of universals as real predicates.

Lastly, the two works agree in reducing the Categories to substance and its belongings (inrapxovra).

In brief then the common ground of the Categories and the Metaphysics is the fundamental position that all things are substances having belonging to them universals and attributes, which have no separate being as Plato falsely supposed.

This essential agreement suffices to show that the Categories and the Metaphysics are the result of one mind.

Nevertheless, there is a deep difference between them in detail, which may be expressed by saying that the Categories is nearer to Platonism.

We have now to see that, in writing the Categories, on the one hand he carried his differences from his master further than he had done in his early criticisms by insisting that individual substances are not only real, but are the very things which sustain the universal; but on the other hand, he clung to further relics of the Platonic theory, and it is those which differentiate the Categories and the Metaphysics.

In the first place, in the Categories the belonging of things in other categories to individual substances in the first category is not so well developed.

But even so the Categories concludes that everything is either a predicate of, or inherent in, a substance; and the view that this colour belongs to this substance only in the sense of being in it, not of it, leaves the impression that, like a Platonic form, it is an entity rather in than of an individual substance, though even in the Categories Aristotle is careful to deny its separability.

The first difference then between the Categories and the Metaphysics is in the nature of an attribute; and the theory of inherence in the Categories is nearer to Plato and more rudimentary than the theory of predication in the Metaphysics.

For though both works rest on the reality of individual substances, the Categories (chap. 5) admits that universal species and genera can be called substances, whereas the Metaphysics (Z 13) denies that a universal can be a substance at all.