In the case of solid figures a more difficult geometrical abstraction is involved.
The abstraction keeps moving forward, and the technology races to keep up.
This, again, is a process of abstraction, the attainment of abstract ideas which, apart from the concrete individuals, are conceived as having a substantive existence.
Berkeley, though at length the notions of spirits, acts and relations 6 give him pause, prefers the formula which Hume expresses in the phrase that " some ideas are particular in their nature but general in their representation," 7 and the afterhistory of " abstraction " is a discussion of the conditions under which one idea " stands for " a group. Not from those for whom general ideas mean schematic concepts, not imageable.
By this theory, Hume is freed from all the problems of abstraction and judgment.
There is a permissible abstraction, and in general they practise this, and although they narrow its range unduly, it is legitimately to be applied to certain characters of thinking.
Princess Mary roused him from his abstraction by drawing his attention to her nephew who had entered the room.
Adherents of the Yoga philosophy and the system of ascetic practices enjoined by it with the view of mental abstraction and the supposed attainment of superhuman powers - practices which, when not merely pretended, but rigidly carried out, are only too apt to produce vacuity of mind and wild fits of frenzy.
In the Odyssey, where they are represented as bringing round the seasons in regular order, they are an abstraction rather than a concrete personification.
Our mistake lies in abstraction of the one from the other, which, as always, ends in confusion of the one with the other.
It is Wundt's own statement of his solution of the epistemological problem " that on the one hand the whole outer world exists for us only in our ideas, and that on the other hand a consciousness without objects of idea is an empty abstraction which possesses no actuality " (System, 212 -213).
The workings in Great Britain represent the annual abstraction of rather more than a mass of rock equal to a foot in thickness spread over a square mile.
The "psychologicm" thus introduced into logic amounts to a systematic protest against the notion of a dehumanized thought and the study of logic in abstraction from actual psychic process.
The fundamental thought is with him the unsatisfactoriness of abstraction or one-sidedness.
It follows that for the prposes of such description as is possible some process of abstraction is inevitable if our statements are to be simple and definite.
In the Positive state, inherent volition or external volition and inherent force or abstraction personified have both disappeared from men's minds, and the explanation of a phenomenon means a reference of it, by way of succession or resemblance, to some other phenomenon, - means the establishment of a relation between the given fact and some more general fact.
In isolation from its object the will is as much an abstraction as though apart from the world of precepts, memories and associations which give it content and stability.
Metaphosphoric acid, HP0 3, is a monobasic acid which may be regarded as derived from orthophosphoric acid by the abstraction of one molecule of water, thus H 3 PO 4 - H 2 O = HP0 3; its constitution is therefore (HO)P0 2.
4, 22) an attribute (o - vy13E 1 377KOs) is said to be only by being the substance possessing it, and any separation of an attribute from a substance is held to be entirely a work of human abstraction (acPaip€ n).
Many of its most distinguished exponents are Flemings by birth, and their writings reflect the characteristic Flemish scenery; they have the sensuousness, the colour and the realism of Flemish art; and on the other hand the tendency to mysticism, to abstraction, is far removed from the lucidity and definiteness associated with French literature properly so-called.
So he explains " concepts or general notions " 1 by an abstraction which he represents as a sort of alt-relief operated by attention and fixed by naming, association with the name giving to a set of attributes a unity they otherwise lack.
He spoke throughout, however, as if form and content were mutually indifferent, so that the abstraction of form from content implied nothing of falsification or mutilation.
The reserve, therefore, that it was abstraction and not a decomposing that was in question remained to the admirers of his logic quite nugatory.
Of the formal-symbolic logic all that falls to be said here is, that from the point of view of logic as a whole, it is to be regarded as a legitimate praxis as long as it shows itself aware of the sense in which alone form is susceptible of abstraction, and is aware that in itself it offers no solution of the logical problem.
While Anu, with whom there was associated as a pale reflection a consort Antum, assigned to him under the influence of the widely prevalent view among the early Semites which conceived of gods always in pairs, remained more or less of an abstraction during the various periods of the Babylonian-Assyrian religion and taking little part in the active cult of the temples, his unique position as the chief god of the highest heavens was always recognized in the theological system developed by the priests, which found an expression in making him the first figure of a triad, consisting of Anu, Bel and Ea, among whom the priests divided the three divisions of the universe, the heavens, the earth with the atmosphere above it, and the watery expanse respectively.
The last supposed syllogism, namely, that having two affirmative premises and entailing an undistributed middle in the second figure, is accepted by Wundt under the title "Inference by Comparison" (Vergleichungsschluss), and is supposed by him to be useful for abstraction and subsidiary to induction, and by Bosanquet to be useful for analogy.
When we take into account relative matter, however, and traces of a conception of abstraction as admitting of degree, 6 the question is not free from difficulty.
The critic from this side has little difficulty in showing that abstraction of the kind alleged still leave the residuum particular this redness, e.g.
Reason has three stages, in the highest of which the mind is able, by abstraction from earthly things, to rise to contemplatio or the vision of the divine.
These qualities are required all the more because, in order to make any further progress with such an inquiry as we have suggested, we have deliberately to make use of abstraction as an instrument of investigation.
His genius was one of generalization and abstraction; and the aspirations of the time towards unity and perfection received, by his serene labours, an embodiment denied to them in the troubled world of politics.
The simplest member of the series is acrolein, C 3 H 4 0 or CH 2: CHï¿½CHO, which can be prepared by the oxidation of allyl alcohol, or by the abstraction of the elements of water from glycerin by heating it with anhydrous potassium bisulphate.
From one abstraction they are led to another, to solve the difficulties which are created by the realization of the first.
As has been said, a large proportion of water enters into the composition of all living matter; a certain amount of drying arrests vital activity, and the complete abstraction The properties of living matter are intimately related to temperature.
Not only so, but the physician, thus fascinated by "types," and impressed by the silent monumentsof the pathological museum, was led to localize disease too much, to isolate the acts of nature, and to forget not only the continuity of the phases which lead up to the exemplary forms, or link them together, but to forget also that even between the types themselves relations of affinity must exist - and these oftentimes none the less intimate for apparent diversities of form, for types of widely different form may be, and indeed often are, more closely allied than types which have more superficial resemblance - and to forget, moreover, how largely negative is the process of abstraction by which types are imagined.
Finally, the substance is reconverted into the first state at the temperature 0", completing the cycle by the abstraction of a quantity of heat By the application of the first law, the difference of the quantities of heat absorbed and evolved in the cycle must be equal to the work represented by the area of the cycle, which is equal to (p' - p") (v" - v') in the limit when the difference of pressure is small.
All units of thought) are (1) analysable only by abstraction, and (2) are compound of deduction and induction, i.e.
Deliverance from the pantheistic conception of the universe comes through the recognition of the central place occupied by thought and purpose in the actual world, and, as a consequence of this, of the illegitimacy of the abstraction whereby material energy is taken for the ultimate reality.
(2) The process of abstraction takes an important place both in psychological and metaphysical speculation.
Abstraction differs from Analysis, inasmuch as its object is to select a particular quality for consideration in itself as it is found in all the objects to which it belongs, whereas analysis considers all the qualities which belong to a single object.
Its nitrile (prussic acid) has an acid character, a property not possessed by the nitriles of the other members of the series; and, by the abstraction of the elements of water from the acid,.
Their aperient action is dependent upon the minimum of irritation of the bowel, and is exercised by their abstraction from the blood of water, which passes into the bowel to act as a diluent of the salt.
On this false abstraction Sigwart has made an excellent criticism in an appendix at the end of his Logic, where he remarks that we cannot isolate events from the substances of which they are attributes.
If knowledge is experience of ideas distinguished by inner will of apperception into subject and object in inseparable connexion, if the starting-point is ideas, if judgment is analysis of an aggregate idea, if inference is a mediate reference of the members of an aggregate of ideas to one another, then, as Wundt says, all we can know, and all reason can logically infer from such data, is in our ideas, and consciousness without an object of idea is an abstraction; so that reason, in transcending experience, can show the necessity of ideas and " ideals," but infer no corresponding reality beyond, whether in nature, or in Man, or in God.
Though, for simplicity and universality of thought, even in science, we must use the abstraction of attributes, and, by the necessity and weakness of language, must signify what are not substances by nouns substantive, we must guard against the over-abstraction of believing that a thing exists as we abstract it.
When a variable quantity is at a minimum a slight change in the system does not affect its value, and therefore, when a solution is saturated, the increase in the available energy of the liquid phase produced by dissolving in it some of the solid must be equal to the decrease in the available energy of the solid phase, caused by the abstraction from the bulk of that part dissolved.
Thus a mixture of ice, salt and the saturated solution has a constant freezing point, and the composition of the solution is constant and the same as that of the mixed solids which freeze out on the abstraction of heat.
Again, starting from 0, by the abstraction of heat we can remove all the liquid and travel along the curve OD of equilibrium between the two solids (salt and ice) and the vapour.
He lays special stress on the point that abstract ideas when held in their abstraction are almost interchangeable with their opposites - that extremes meet, and that in every true and concrete idea there is a coincidence of opposites.
In the sphere of abstract form, mathematics, the like may be allowed, abstraction being treated as an elimination of matter from the cn voXov by one act.
By this way of abstraction they are made capable of representing more individuals than one."
It is, however, of the sorts constituted by the representation which his abstraction makes possible that definition is given, either by enumeration of the simple ideas combined in the significance of the sortal name, or " to save the labour of enumerating," and " for quickness and despatch sake," by giving the next wider general name and the proximate difference.
Upon abstraction from all particular methods of thought these rules were to be discerned a priori or without dependence on experience by reflection solely upon the use of the understanding in general.
Even in his " logic " Kant speaks of abstraction from all particular objects of thought rather than of a resolution of concrete thinking into thought and its " other " as separable co-operating factors in a joint product.
To allow, however, that abstraction admits of degrees, and that it never obliterates all reference to that from which it is abstracted, is to take a step forward in the direction of the correlation of logical forms with the concrete processes of actual thinking.
A judgment is practical, and not to be divorced without improper abstraction from the purpose and will that informs it.
Nicholas glanced at her and, wishing to appear not to notice her abstraction, made some remark to Mademoiselle Bourienne and then again looked at the princess.
They failed to realize that permissible abstraction from specific contents or methods of knowledge does not obliterate reference to matter or content.
Abstraction proves to be synthesis with compensatory universal marks in the place of the particular marks abstracted from.
Finally, by abstraction from the individual things of sense, the mind is able to contemplate the universal apart from its accompaniments (animal sine homine, asino, et aliis speciebus); these subjective existences are the universalia post rem of the Nominalists and Conceptualists.
They take thought and " the given " as self-contained units which, if not in fact separable, are at any rate susceptible of an abstraction the one from the other so decisive as to constitute an ideal separation.