The tales of Cinthio and Bandello supplied them with the outlines of tragedies, leaving the poet free to exercise his analytic and imaginative powers upon the creation of character and the elaboration of motive.
The defect of deep passion and serious thought, the absence of enthusiasm, combined with rare analytic powers and an acute insight into human nature, placed Ariosto in close relation to his age.
In the theory of analytic geometry a one-to-one correspondence is assumed to exist between points on a line and numbers.
The debt which analyticgeometry owes to synthetic geometry 184.
Analytic geometry had left little to do in the way of discovery of new material, and the mathematical world was ready for the construction of the edifice.
This work was accomplished by Von Staudt,(21) who applied himself to the restatement of the theory of geometry in a form independent of analytic and metrical notions.
The parabola is thus identified with the curve of the same name studied in treatises on analytic geometry.
The debt which analytic geometry owes to synthetic geometry.
Desargues’s methods, entirely different from the analytic methods just then being developed by Descartes and Fermat, seem to have been little understood.
Thus, by means of the mechanism employed in analytic geometry, algebraic theorems are made to yield geometric ones, and vice versa.
While we may be certain that any geometrical problem may always be stated in analytic form, it does not follow that that statement will be simple or easily interpreted.
This identifies the curve with the hyperbola as defined and discussed in works onanalytic geometry.
In school-books, a great deal of noise and useless parade has been recently made about the introduction of the 'Analytic Method.
Analytic reflection often ignores the essential energy of mind, which is originally more intelligent than sensuous, more appetitive and dogmatic than aesthetic.
Sensations became the only objects of sensation, and ideas the only objects of ideas; so that the material world was rendered superfluous, and the only scientific problem was now to construct a universe in terms of analytic psychology.
Simple spontaneity of thought is manifested, but little or noanalytic reflection.
Not the higher reason, with its intuition of eternal ideas, but the analytic understanding, with its logical methods, was considered to be the ruler in the world of thought.
No answer; only, if possible, the look became more analyticthan before.
It was a questioning, analytic look, yet, unconcealed, it bore the tolerance of a strong man for a weak.
This is also the cause why I have so changed the formula of this principle, that the nature of an analytic proposition might be clearly expressed.
The comparison of two conceptions with a third, does not take from the result the character of analytic judgment, as a predicate cannot be seen in the idea of the subject, without the aid of this comparison.
Analytic affirmative judgments are those in which the union of the predicate with the subject is conceived by identity: those are called synthetic in which this union is conceived without identity.
In analytic judgments, the predicate is in the subject; nothing is added, according to Kant, it is only unfolded.
A judgment is not the less analytic because formed by the union of different conceptions; for then no judgment would be analytic.
Analytic judgments were all those formed by immediate evidence; and synthetic, those resulting from mediate evidence, whether of the purely ideal order, or in some sense depending on experience.
This condition is equally the condition sine qua non of all analytic affirmative judgments; for these disappear if that does not belong to the subject which is contained in its idea.
The proposition is then the result of the comparison of two purely analytic conceptions with a third, which is length.
Speculative truths tested by analytic process; Practical by synthetic; their work becomes their ever-growing verification.
Submitted to the analytic prism, the two elements come out at opposite poles in very decided contrast.
Invaluable per se, it will surely be found of a nature so delicate and fugitive as to escape the tests of analytic psychologists.
The analyticmethod as applied by George Eliot regards man as a social being, studies him as a member of society.
In the enlightened child of civilization the abandonment characteristic of grief is checked and varied in the subtlest manner, so as to present an interesting problem to the analytic mind.
The disadvantages of the analytic method are apparent when George Eliot is compared with Scott.
In either case, both in the synthetic and the analytic process now described, we are dealing not with the concrete but the abstract.
In other words, it is a process of analysis which we thus perform, and as all reasoning, when scientifically stated, is brought under this form, it follows that all reasoning is essentially analytic in its nature.
The divisive or analytic process remains to be considered.
The stage at which one inquirer stops is not the limit of analysis in reference to the object, but the limit of the analytic power of the individual.
This latter method, as Hamilton has shown in his New Analytic of Logical forms, is perfectly valid, though usually neglected by writers on logic.
The one is the compositive or synthetic, the other, the analytic or divisive process.
The latter may be inductive or deductive; and, as to form, analytic or synthetic, figured or unfigured.
But whence, it may still be asked, comes the general proposition which every deductive syllogism contains, whether analytic or synthetic, the proposition e.
Analytic geometry, the application of algebra to geometric relations, occupies a noteworthy position, from the point of view of method, in the science of space.
The Subjective Analytic Course leads from the self-viewing of the ego up to the vision of God; the Synthetic Course starts from the fundamental Idea, God, and deduces from this the partial Ideas, or presents the world as the revelation of God.
And, in fact, modern philosophy has a considerable amount of prose about it, is not easily impressed, accepts no limitations from feeling, and holds nothing too sacred to be attacked with the weapon of analytic thought.
All analytic judgments are a priori, all empirical or a posteriori judgments are synthetic.
The outcome of theAnalytic of Principles sounds bold enough.
Beyond these analytic truths, however, philosophy demands a law of universal synthesis.
To the former class belong the objects of mathematics, the truths of which, since they are analytic (i.
Thinkers in whom this aesthetic reverence is weaker than the analytic impulse--especially Democritus--seem half modern rather than Greek.
Cantor, and others, which look on our Euclidean space of three dimensions as a special case of the unintuitable yet thinkable analytic concept of a space of n dimensions.
In this, in turn, the analytic discovery and the synthetic adjustment of a contrariety is repeated, etc.
It is a priori inasmuch as it rests on necessary ideas, but a posteriori inasmuch as it proceeds from these ideas upwards to God in a manner which is essentially analytic and inductive.
Of the Division of Transcendental Logic into Transcendental Analytic and Dialectic.
Of the Division of General Logic into Analyticand Dialectic.
In the same way, Transcendental Analyticwas seen to be a canon of the pure understanding; for it alone is competent to enounce true a priori synthetical cognitions.
The principle of an unbroken connection between all events in the phenomenal world, in accordance with the unchangeable laws of nature, is a well-established principle of transcendental analytic which admits of no exception.
Transcendental analytic is the dissection of the whole of our a priori knowledge into the elements of the pure cognition of the understanding.
As this merely formal logic makes abstraction of all content of cognition, whether pure or empirical, and occupies itself with the mere form of thought (discursive cognition), it must contain in its analytic a canon for reason.
Emerson, Boston, read a paper entitled "The Psycho-Analytic Treatment of Hystero-Epilepsy.
Care must be taken to find the real determinants, and to set aside spurious dream material--which is not always facilitated by the psycho-analytic methods.
Jung, formerly a pupil and literal follower of Freud, is attempting to reform psycho-analytic doctrine from within the fold.
What seems to me novel and characteristic is the psycho-analytic method of working up this material into an interpretation by a process of inference.
That is why psycho-analytic method today suggests not only the free play of poetic invention, but the license of mystical speculation.
Morton Prince expressed in 1910, as to the insecurity of the psycho-analytic ideas of symbolism.
Perhaps if I had had the experience and ability to contribute the results of some original analytic investigation on specific lines, I should not then have ventured into the philosophic field.
Unquestionably, they must achieve a gratifying number of hits under the easygoing conditions of the psycho-analytic seance.
That mechanism of cure, may be stated as follows: How can one take the split off libido which results from the analytic technique and apply it to a better constructive synthesis?
In psycho-analytic work a more vague use of "dream material" is preferred and it is only by good luck that the real settings-of-ideas come into account.
From a psycho-analytic standpoint, the problem presented in Dr.
Sensations,” as the laboratory psychologist and the analytic psychologist generally studies them, are examples of just such detached things.
It is both analytic and synthetic--analytic in that it resolves each state into its constituent elements; synthetic in that it discovers the processes by which these elements combine into complex wholes and series.
In analytic observation, it is a positive object to strip off all inferential meaning so far as may be--to reduce the facts as nearly as may be to derationalized data, in order to make possible a new and better rationalization.
It is claimed for its fiction, however, that it is analytic and realistic, and that much of it has certain other qualities that make it a new school in art.
And we protest against the notion that the novel of the future is to be, or should be, merely a study of, or an essay or a series of analytic essays on, certain phases of social life.
For it is not simply that this little book of judgment is there in black and white, but that the maker of it is increasing her power of minute observation and analytic expression.
This is high praise, but by no means the highest, and when we reflect we see how immeasurably inferior, in fiction, the analytic method is to the dramatic.
The analytic method in fiction is interesting, when used by a master of dissection, but it has this fatal defect in a novel--it destroys illusion.
This concrete definition of scientific elements progressed through the use of analytic methods, by proceeding from the known to the unknown, and led to the discovery of tests for scientific assumptions and of synthetic proof.
The general use of his analytic methods by other mathematicians resulted in the solution of many scientific problems that had been handed down for centuries as insoluble.
In the last-named work, suggestions are given for the development of analytic methods.
As no one has previously gone into this matter, I have found myself obliged to coin a certain number of new terms, for the purpose at once of avoiding continuous circumlocution, and of rendering aid to the analytic inquiry.
The analytic and synthetic methods of instruction will both be found useful when judiciously employed.
Marcella was unusually endowed with analytic intelligence, but in this case she believed what she hoped.
In no part of the Critique is this so obvious as in the Analytic of Concepts.
We have still to consider the various sections in the Analytic of Principles (especially the section added in the second edition on the Refutation of Idealism) and in the Dialectic, in which Kant further develops this standpoint.
Now when proof of the specific categories does come, in the Analytic of Principles, it is manifestly based on the analysis of time-experience.
That I am identical with myself throughout the consciousness of my manifold experiences, is likewise an analytic proposition obtainable by mere analysis of the "I think.
A proposition can be accepted as true only in so far as we can at least postulate, through absence of contradiction and through sufficient reason, its analytic character.
Kant's view of analytic thinking is entirely dominated by the substance-attribute teaching of the traditional logic.
Concerning the Division of Transcendental Logic into Transcendental Analyticand Dialectic.
The implication is that analytic and synthetic thinking are co-ordinate, one and the same faculty exercising, on these two levels, the same operations.
Secondly, in the Analytic of Concepts the temporal aspect of experience falls somewhat into the background, whereas in the Analytic of Principles it is emphasised.
The unity of apperception is analytic or self-identical.
But while the Analyticof Concepts deals almost exclusively with ordinary experience, in the Analytic of Principles the physical sciences receive their due share of consideration.
He continued to ignore the fact that the analytic judgment, no less than the synthetic judgment, demands a transcendental justification.
In B 16 he himself recognises the existence of analytic mathematical judgments, but unduly minimises their number and importance.
When we determine the various forms of analytic judgment, the categories which are involved in synthetic thinking reveal themselves to consciousness.
