Analytic Sentence Examples
Analytic This is the analytical expression of the projective Geometry.
Justification by faith is a " synthetic " judgment - the sinner is righteous; it is not an " analytic " judgment - the believer is righteous.
They afford yet another great advantage in that the derivation of the results requires only the analytic operations of the infinitesimal calculus.
The power and spirit of the analytic method will be appreciated by showing how it expresses the relations of motion as they were conceived geometrically by Newton and Kepler.
The analytic method sought to express the moon's motion by integrating the differential equations of the dynamical theory.Advertisement
He holds that the true method of research is the analytic, rising from lower to higher notions; yet he sees clearly, and admits, that inductive reasoning, as conceived by Bacon, rests on a general proposition not itself proved by induction.
The book is also interesting as having appeared on the borderland between the medieval and the modern school of natural history, avoiding the uncritical blundering of the old Encyclopaedists, without entering on the technical and analytic character of the opening age of separate monographs.
The encyclopaedic interest in nature, although in White's day culminating in the monumental synthesis of Buffon, was also disappearing before the analytic specialism inaugurated by Linnaeus; yet the catholic interests of the simple naturalist of Selborne fully reappear a century later in the greater naturalist of Down, Charles Darwin.
The tract on the False Subtlety of the Four Syllogistic Figures, in which the view of thought or reason as analytic is clearly expressed, closes with the significant division of judgments into those which rest upon the logical axioms of identity and contradiction and those for which no logical ground can be shown.
It was impossible that the question regarding their nature and legitimacy and their distinction from analytic judgments should not present itself to him.Advertisement
Now synthesis was explicable neither by reference to pure thought, the logical or elaborative faculty, which in Kant's view remained analytic in function, nor by reference to the effects of external real things upon our faculties of cognition.
Longer term costs and consequences will be explored using decision analytic modeling.
What it is, is empathetic, not analytic or academic.
The respondents were found to be very analytic in their approach and were aware of the historical developments that had led to these events.
And yet, in spite of every critically analytic bone in our body, we do of course absolutely love this game to pieces.Advertisement
The former values mental lucidity while the latter is highly analytic and intended to sharpen awareness.
Like Richardson, very little analytic text will be presented here.
Informatics seeks to understand and to construct (or reconstruct) such systems, using analytic, experimental and engineering methodologies.
To develop analytic, communication and management skills to enable you to work effectively in a business environment.
I am by early training and inclination an analytic rather than a historical bibliographer.Advertisement
Very few analytic models require that these links be defined as biological links, as is required to legitimately calculate inbreeding coefficients.
Examples of regular functions defined by series or integrals and their analytic continuations.
I would normally use either golden ratio or simplex optimization for functions where analytic derivatives are not available.
It uses a formal logic to express issues about agent design, giving the impression that the subject is an analytic one.
Based on these three analytic inverses, three formulae were developed for computing the inverse numerically.Advertisement
Cancer bioinformatics aims to integrate molecular, biological and clinical knowledge about cancer with analytic methods from bioinformatics.
The first part of the paper brings in the analytic concept of the unconscious followed by a more detailed account of unconscious phantasy.
Does the free marriage owe anything to the analytic philosophy?
In other words, analytic phonics is stressed at the expense of synthetic phonics.
Dynamo models of our Galaxy as a flattened spheroid have been investigated, using asymptotic analytic methods and high resolution numerical techniques.
The Polar Nature of Thinking There are two fundamental gestures of thinking, one of which is analytic, and the other synthetic.
We make use of the convolution theorems for the Mellin transforms to produce analytic structures for part of the calculation.
They were, according to his analysis, personal will, primitive instincts, voluntary movement, natural and artificial signs, sensibility and the faculties of intellect; on this analytic he founded his scheme of the universe.
Among the revisions may be adduced some addition to our knowledge of dyspepsia, attained by analytic investigations into the contents of the stomach at various stages of digestion, and by examining the passage of opaque substances through the primae vine by the RÃ¶ntgen rays.
It was in seeking to close up the fissure in his system represented by this dualism that his successors succeeded only in adding weakness to weakness by reducing the principle of sufficient reason to that of formal identity (see Wolff) and representing all thought as in essence analytic. From this it immediately followed that, so far as the connexion of our experiences of the external world does not show itself irreducible to that of formal identity, it must remain unintelligible.
Thereupon the Newtonian analysis which preceded this synthesis, became forgotten; until at last Mill in his Logic, neglecting the Principia, had the temerity to distort Newton's discovery, which was really a pure example of analytic deduction, into a mere hypothetical deduction; as if the author of the saying " Hypotheses non lingo" started from the hypothesis of a centripetal force to the sun, and thence deductively explained the facts of planetary motion, which reciprocally verified the hypothesis.
In analytic we work with an ethos different from that of dialectic. We presume truth and not probability or concession, but a true conclusion can follow from false premises, and it is only in the attempt to derive the premises in turn from their grounds that we unmask the deception.
If we set aside such transcendental conditions as belong to sensibility or to the receptive phase of mind and are the presuppositions of juxtaposition of parts, the remainder are ascribable to spontaneity or understanding, to thought with its unifying, organizing or focussing function, and their elucidation is the problem of transcendental analytic. It is still logic, indeed, when we are occupied with the transcendent objects of the discursive faculty as it is employed beyond the limits of experience where it cannot validate its ideas.
Cousin was observational and generalizing rather than analytic and discriminating.
This was a philosophical treatise on universal science that included a 100-page appendix on geometry, containing his fundamental contributions to analytic geometry.
Prahl et al  derived an analytic theory for the interpretation of photothermal signals detected in turbid media.
When teachers use analytic phonics, they teach students to analyze whole phonemes for sound meaning.
Many whole language programs use analytic phonics.
Netdraw is also a free program, which was created by Steve Borgatti of Analytic Technologies.
The application of "common sense" to the problem of substance supplied a more satisfactory analytic for him than the scepticism of Hume which reached him through a study of Kant.
But analytic thinking is victorious in morals, where the test of formal self-consistency distinguishes virtue from vice.
Among the revisions may be adduced some addition to our knowledge of dyspepsia, attained by analytic investigations into the contents of the stomach at various stages of digestion, and by examining the passage of opaque substances through the primae vine by the Rntgen rays.
More particularly by the confusion in which he left the relation between the two logical principles of identity and of sufficient reason underlying respectively analytic and synthetic, deductive and inductive thought, he may be said to have undermined in another way the idealism he strove to establish.
The systematic Introduction is a characteristic production of Germany and has done excellent service in its day, though there are signs that the analytic method hitherto mainly practised is beginning to give place to something more synthetic or constructive.
Not by any means an argument to be despised, but stopping short of the truth through an inadequate analytic of knowledge."
The merit of Hegel is to have indicated and to a large extent displayed the filiation and mutual limitation of our forms of thought; to have arranged them in the order of their comparative capacity to give a satisfactory expression to truth in the totality of its relations; and to have broken down the partition which in Kant separated the formal logic from the transcendental analytic, as well as the general disruption between logic and metaphysic. It must at the same time be admitted that much of the work of weaving the terms of thought, the categories, into a system has a hypothetical and tentative character, and that Hegel has rather pointed out the path which logic must follow, viz.
In this way the Presocratics and Sophists, and still more Socrates and Plato, threw out hints on sense and reason, on inferential processes and scientific methods which may be called anticipations of logic. But Aristotle was the first to conceive of reasoning itself as a definite subject of a special science, which he called analytics or analytic science, specially designed to analyse syllogism and especially demonstrative syllogism, or science, and to be in fact a science of sciences.
Much of the Principia consists of synthetical deductions from definitions and axioms. But the discovery of the centripetal force of the planets to the sun is an analytic deduction from the facts of their motion discovered by Kepler to their real ground, and is so stated by Newton in the first regressive order of Aristotle - P-M, S-P, S-M.
This done, as the major is convertible, the analytic order - P-M, S-P, S-M - was easily inverted into the synthetic order - M-P, S-M, S-P; and in this progressive order the deduction as now taught begins with the centripetal force of the sun as real ground, and deduces the facts of planetary motion as consequences.
Worse still, Jevons proceeded to confuse analytic deduction from consequence to ground with hypothetical deduction from ground to conseguence under the common term "inverse deduction."
It is noticeable that Wundt quotes Newton's discovery of the centripetal force of the planets to the sun as an instance of this supposed hypothetical, analytic, inductive method; as if Newton's analysis were a hypothesis of the centripetal force to the sun, a deduction of the given facts of planetary motion, and a verification of the hypothesis by the given facts, and as if such a process of hypothetical deduction could be identical with either analysis or induction.
As the example shows, that analytic process starts from the scientific knowledge of a universal and convertible law (every M is P, and every P is M), e.g.
Really, we first experience that particular causes have particular effects; then induce that causes similar to those have effects similar to these; finally, deduce that when a particular cause of the kind occurs it has a particular effect of the kind by synthetic deduction, and that when a particular effect of the kind occurs it has a particular cause of the kind by analytic deduction with a convertible premise, as when Newton from planetary motions, like terrestrial motions, analytically deduced a centripetal force to the sun like centripetal forces to the earth.
In the course of inquiry into the formal consequences from probable premises, the principle of mediation or linking was so laid bare that the advance to the analytic determination of the species and varieties of syllogism was natural.
In analytic we work with an ethos different from that of dialectic.
In transcendental analytic on the other hand we concern ourselves only with the transcendental " deduction " or vindication of the conditions of experience, and we have a logic of cognition in which we may establish our epistemological categories with complete validity.
They cannot go beyond the limits of formal consistency or analytic correctness.
Hamilton's significance for the history of logic lies in the stimulus that he gave to the development of symbolic logic in England by his new analytic based upon his discovery or adoption of the principle of the quantification of the predicate.
In this he was an innovator against the excessively analytic tendency of Cambridge mathematicians.
He had no sympathy with the tendency represented by George Eliot, or with any attempt to be analytic in art.
He held art to be essentially synthetic, creative and manifesting, not analytic, destructive or questioning.
If we adopted the counting method, we should proceed in a different way, our method being analytic.
The first step in the process shows in a striking way the perfection of the analytic method.
In the analytic process these specific data, called elements of the distance.
General logic has also to deal with the union of representations, though its unity is analytic merely, not synthetic. But the same intellectual function which serves to give unity in the analytic judgments of formal logic serves to give unity to the synthetic combinations of real perception.
With respect to his attacks on the critical philosophy in the Metakritik (1799), it is easy to understand how his concrete mind, ever alive to the unity of things, instinctively rebelled against that analytic separation of the mental processes which Kant attempted.
This resolution or analysis into simple, because clear and distinct, elements may be brought to a standstill again and again by obscurity and indistinctness, but patient and repeated revision of all that is included in the problem should bring the analytic process to fruition.
Chief among these encumbering presuppositions was that of a fundamental distinction between perception and conception and consequent upon it between the synthetic and the analytic use of thought.
His mental qualities were - a quick analytic perception, strong logical powers, a tenacious memory, a liberal estimate and tolerance of the opinions of others, ready intuition of human nature; and perhaps his most valuable faculty was rare ability to divest himself of all feeling or passion in weighing motives of persons or problems of state.
More important were his Dialogues on Eloquence, wherein he entered an eloquent plea for greater simplicity and naturalness in the pulpit, and urged preachers to take the scriptural, natural style of Bossuet as their model, rather than the coldly analytic eloquence of his great rival, Bourdaloue.
But he maintained that the procedure of philosophy must be analytic, rising from the particular facts to the universal in which we find them explained.