The individual substances, of which the universe is composed, fall into three great irreducible kinds: nature, God, man.
There remains too the consequence that there are different substances, separate from but related to one another; and these substances of three irreducible kinds, natural, supernatural, human.
Indeed, if thought admits irreducible units, what can unite?
an irreducible element of indetermination, e.g.
On British railways the duty of the companies to provide all practicable safeguards and to educate and caution the servants may be said to have been faithfully performed, and the accident totals must be taken as being somewhat near the " irreducible minimum" - unless some of the infirmities of the human mind can be cured.
Thus in the true idea of things there is no irreducible residuum of matter: mind is the Alpha and Omega, at once the initial postulate and the final truth of reality.
The peace of Bromsebro was the first of the long series of treaties, extending down to our own days, which mark the progressive shrinkage of Danish territory into an irreducible minimum.
Or again, within the latter in his admission of a duality of thought and " the given " in knowledge, which within knowledge was apparently irreducible, concurrently with hints as to the possibility, upon a wider view, of the sublation of their disparateness at least hypothetically and speculatively.
It is true matter can never be completely resolved into motion, but the irreducible remainder may be treated like the 7rpc.)T fl van of Aristotle as an abstraction which we asymptotically approach but never reach.
In the place of Maura he found a more pliant minister for the colonies, Seor Abarzuza, who framed a Cuban Reform Bill so much short of what his predecessor had thought an irreducible minimum of concessions, that it was censured in Havana by all the colonial Liberals and home rulers, and by their representatives in Madrid.
In respect to them, the final result was found in a series of irreducible notions or categories, the prima possibilia, the analysis and elucidation of which was specifically the business of philosophy or metaphysics.
But if it is an error to treat the unity of the world as its only real aspect, it is equally an error to treat its differences as something ultimately irreducible.
It may be said summarily that Kant holds the antithesis between thought and " the given " to be unresolved and within the limits of theory of knowledge irreducible.
He believes that the irreducible complexity of cellular structures point firmly to them having been designed.
This is why Moore's own view of goodness as sui generis and irreducible is supposed to avoid the naturalistic fallacy.
irreducible numerical semigroups containing it.
irreducible polynomial over the field S.
irreducible subgroups of GL(n, q) arise in that way.
irreducible complexity, the entire ensemble of proteins is not needed.
irreducible characters of G q, too.
The result was a contradiction which was absolutely irreducible within the limits of formal democracy.
For [computationally irreducible] complex systems there is no other way to predict their evolution than by tracking it.
The framework was designed to capture the irreducible minimum of teacher-student activities needed to ensure that learning takes place.
A finite group G is called monomial (or M -group) if each ordinary irreducible character of G is monomial.
It can be an integer or an irreducible polynomial over the field S.
The first difficulty to be overcome was the algebraical solution of cubic equations, the " irreducible case" (see Equation).
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.
irreducible representations are unknown in general.
If there are any absorbing states, the chain is not irreducible.
The aim of the project is to study various constructions of the " minimal " representations of the classical groups, called irreducible.
Clearer ideas of imaginary quantities and the " irreducible case " were subsequently published by Bombelli, in a work of which the dedication is dated 1572, though the book was not published until 1579.
It follows from them that the relation of a real ground to that which is thereby posited or denied cannot be expressed by a judgment but only by means of a notion, which by analysis may certainly be reduced to yet simpler notions of real grounds, but yet in such a way that the final resort of all our cognition in this regard must be found in simple and irreducible notions of real grounds, the relation of which to their consequents cannot be made clear."
In his previous essays, Kant, while likewise maintaining that such pure, irreducible notions existed, had asserted in general terms that they applied to experience, and that their applicability or justification rested on experience itself, but had not raised the question as to the ground of such justification.
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