However, it seems axiomatic that the government has an obligation `` to exercise its mandate reasonably, equitably and with full regard for the disruptions which it inevitably causes ''.

In the late 1990s Wilfried Sieg analyzed Turing's and Gandy's notions of " effective calculability " with the intent of " sharpening the informal notion, formulating its general features axiomatically, and investigating the axiomatic framework ".

Some axiomatic set theories assure that the empty set exists by including an axiom of empty set ; in other theories, its existence can be deduced.

They expanded the range of geometry to many new kinds of figures, curves, surfaces, and solids ; they changed its methodology from trial-and-error to logical deduction ; they recognized that geometry studies " eternal forms ", or abstractions, of which physical objects are only approximations ; and they developed the idea of the " axiomatic method ", still in use today.

In several axiomatic derivations of logic, this is effectively resolved by showing that ( P ∨ ¬ P ) and its negation are constants, and simply defining TRUE as ( P ∨ ¬ P ) and FALSE as ¬( P ∨ ¬ P ), without taking a position as to the principle of bivalence or the law of excluded middle.

Where it differs from a " true " axiomatic set theory book is its character: there are no long-winded discussions of axiomatic minutiae, and there is next to nothing about advanced topics like large cardinals.

It has its origins in correspondence discussing the mathematics of games of chance between Blaise Pascal and Pierre de Fermat in the seventeenth century, and was formalized and rendered axiomatic as a distinct branch of mathematics by Andrey Kolmogorov in the twentieth century.

When an axiomatic system begins with its axioms, the primitive notions may not be explicitly stated.

As discussed below, the definition given above turned out to be inadequate for formal mathematics ; instead, the notion of a " set " is taken as an undefined primitive in axiomatic set theory, and its properties are defined by the Zermelo – Fraenkel axioms.

In the Axioms Scholium of his Principia Newton said its axiomatic three laws of motion were already accepted by mathematicians such as Huygens ( 1629 – 1695 ), Wallace, Wren and others, and also in memos in his draft preparations of the second edition of the Principia he attributed its first law of motion and its law of gravity to a range of historical figures.

From this perspective, geometry is equivalent to an axiomatic algebra, replacing its elements by symbols.

A Consistency proof requires ( i ) an axiomatic system ( ii ) a demonstration that it is not the case that both the formula p and its negation ~ p can derived in the system.

The court of Louis XIV was seen as the center of this form of classicism, with its references to the gods of Olympus as a symbolic prop for absolutism, its adherence to axiomatic and deductive reasoning, and its love of order and predictability.

A mathematical theory consists of an axiomatic system and all its derived theorems.

An axiomatic system is said to be consistent if it lacks contradiction, i. e. the ability to derive both a statement and its negation from the system's axioms.

An axiomatic system will be called complete if for every statement, either itself or its negation is derivable.

Further, its logical axiomatic approach and rigorous proofs remain the cornerstone of mathematics.

The Fundamental Theorem of Poker is simply expressed and appears axiomatic, yet its proper application to the countless varieties of circumstances that a poker player may face requires a great deal of knowledge, skill, and experience.

These are completely equivalent and either treatment has as its starting point the axiomatic version of the geometries under consideration.

`` We the people of the Confederate States, each state acting in its sovereign and independent character, in order to form a permanent federal government, establish justice, insure domestic tranquility, and secure the blessings of liberty to ourselves and our posterity -- invoking the favor and the guidance of Almighty God -- do ordain and establish this Constitution for the Confederate States of America ''.

But the highroad, according to the description of its traffic, belongs to life as it is lived in unawareness of death, while the way to the churchyard belongs to some other sort of life: a suffering form, an existence wholly comprised in the awareness of death.

And if I have gone into so much detail about so small a work, that is because it is also so typical a work, representing the germinal form of a conflict which remains essential in Mann's writing: the crude sketch of Piepsam contains, in its critical, destructive and self-destructive tendencies, much that is enlarged and illuminated in the figures of, for instance, Naphta and Leverkuhn.

All such imitations of negative quality have given rise to a compensatory response in the form of a heroic and highly individualistic humanism: if man can neither know nor love reality as it is, he can at least invent an artistic `` reality '' which is its own world and which can speak to man of purely personal and subjective qualities capable of being known and worthy of being loved.

Whitehead contends that the human way of understanding existence as a unity of interlocking and interdependent processes which constitute each other and which cause each other to be and not to be is possible only because the basic form of such an understanding, for all its vagueness and tendency to mistake the detail, is initially given in the way man feels the world.

But while the corporation has all the disadvantages of the socialist form of organization ( so cumbersome it cannot constructively do much of anything not compatible with its need to perpetuate itself and maintain its status quo ), unluckily it does not have the desirable aspect of socialism, the motivation to operate for the benefit of society as a whole.

The second involves something deeper, but its characteristic form focuses on a shift in policy for the community, not in the truth on which the community rests.

Its ontological status is itself most tenuous because apart from individual men, who are its `` matter '', tradition, the `` form '' of society exists only as a shared perception of truth.

Moreover its posture of stubborn but simple resistance is doomed to failure because of the metaphysical weakness of the existent form of order, once the activation of change has reached visible proportions.

In its dynamic form, it visualizes the community as the embodiment of an ontological force -- the race, for instance, which unfolds in history.

we accord it its place there, and in Lawrence's treatment we are given the innocent fantasy of a child, in fact, the form in which oedipal love is expressed in childhood.

But as he remarks in his preface to The Walnut Trees, `` a novel can hardly ever be rewritten '', and `` when this one appears in its final form, the form of the first part will no doubt be radically changed ''.

Even in its present form, however, the first part of Malraux's unrecoverable novel is among the greatest works of mid-twentieth century literature ; ;

This magnificent but greatly underestimated book, which bodies forth the very form and pressure of its time as no other comparable creation, has suffered severely from having been written about an historical event -- the Spanish Civil War -- that is still capable of fanning the smoldering fires of old political feuds.

Krim came to believe that `` the novel as a form had outlived its vital meaning ''.

Our comment was that this was `` featherbedding '' in its ultimate form and that sympathy for the railroad was misplaced since it had entered into such an agreement.

In presenting it to other governments and to the United Nations, we could propose that every nation consider the formation of its own peace corps and that the United Nations sponsor the idea and form an international coordinating committee.

It stood in its original form until 1882.

`` When working from one of my sketches I square it up and project its linear form freehand to the watercolor sheet with charcoal.

Or, equally often, a concretistic-seeming, particularistic-seeming statement may consist, with its mundane exterior, in a form of poetry -- may be full of meaning and emotion when interpreted as a figurative expression: a metaphor, a smile, an allegory, or some other symbolic mode of speaking.

Hence, when the address Af is computed from Af, the cell Af and all Y-cells in its chain must be inspected to determine whether Af is already in the form list or whether it should be added to the form list and the chain.

Applying the techniques developed at Harvard for generating a paradigm from a representative form and its classification, we can add all forms of a word to the dictionary at once.