The axiom of choice produces these intangibles ( objects that are proven to exist, but which cannot be explicitly constructed ), which may conflict with some philosophical principles.

These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.

Justice is fairness, in the sense that the fairness of the original position of choice guarantees the fairness of the principles chosen in that position.

This imagined choice justifies these principles as the principles of justice for us, because we would agree to them in a fair decision procedure.

The beauty of the style, the choice and aptness of the terminology, cannot hide the author's lack of grasp on Christian principles and his almost utter ignorance of Scripture.

Founding principles of the Canadian model of midwifery include informed choice, choice of birthplace, continuity of care from a small group of midwives and respect for the woman as the primary decision maker.

Similar choice principles are accepted for all finite types.

Rand summarizes: If chooses to live, a rational ethics will tell him what principles of action are required to implement his choice.

The first three of these characterizations can be proven equivalent in Zermelo – Fraenkel set theory without the axiom of choice, but the equivalence of the third and fourth cannot be proved without additional choice principles.

The choice of Taylor was made almost out of desperation ; he was not clearly committed to Whig principles, but he was popular for leading the war effort.

The restricted form of the Baire category theorem in which the complete metric space is also assumed to be separable is provable in ZF with no additional choice principles.

Important principles of this ideology include freedom of choice, the uniqueness of the individual and empirical inquiry grounded in objectivity.

Historian Graham Kelsey also maintains that the anarchist collectives were primarily maintained through libertarian principles of voluntary association and organization, and that the decision to join and participate was generally based on a rational and balanced choice made after the destabilization and effective absence of capitalism as a powerful factor in the region.

They are radically different, however, in the application of the cooperative principles of freedom of choice and democratic rule.

A different approach is to apply evolutionary psychology principles to economics which is argued to explain problems such as inconsistencies and biases in rational choice theory.

A different approach is to apply evolutionary psychology principles to economics which is argued to explain problems such as inconsistencies and biases in rational choice theory.

The Aniseikonia Inspector contains an aniseikonia test based on the same principles as the NAT, but the test is run on a computer screen, it is based an a forced choice method, and it can measure the size difference as a function of the size of the objects.

Rawls offers a model of a fair choice situation ( the original position with its veil of ignorance ) within which parties would hypothetically choose mutually acceptable principles of justice.

Many principles that imply the axiom of choice in their general form ( such as " Every vector space has a basis ") become provable in weak subsystems of second-order arithmetic when they are restricted.

As mentioned above, Henkin proved that the standard deductive system for first-order logic is sound, complete, and effective for second-order logic with Henkin semantics, and the deductive system with comprehension and choice principles is sound, complete, and effective for Henkin semantics using only models that satisfy these principles.

Neither had a choice other than to accept the invitation.

I do not accept that the choice is between capitulation and the certainty of nuclear war ''.

Despite these facts, most mathematicians accept the axiom of choice as a valid principle for proving new results in mathematics.

* Man has free will to respond or resist: Free will is limited by God's sovereignty, but God's sovereignty allows all men the choice to accept the Gospel of Jesus through faith, simultaneously allowing all men to resist.

The British insisted Abdur Rahman accept sovereignty over this remote region where unruly Kyrgyz held sway, he had no choice but to accept Britain's compromise.

Ecuador had no choice but to accept Peru's territorial claims and signed Peace treaty in 1942.

Successful brinksmanship convinces the other party they have no choice but to accept the offer and there is no acceptable alternative to the proposed agreement.

Christians who follow teachers such as John Calvin generally accept that God alone decides the eternal destinations of each person without regard to man's choices, so that their future actions or beliefs follow according to God's choice ( Romans 9: 14-16 ).

Classically, this view is called Arminianism, which holds that each person is able to accept or reject God's offer of salvation and hence God allows man's choice to determine salvation ( John 3: 16-18 ).

The doctrine is a tension between the divine perspective in which God saves those whom he chooses from eternity apart from human action and the human perspective in which each person is responsible for his or her choice to accept or reject God.

But to me, that was a way of life ; we had no choice but to accept what was the custom.

Thus, to propagate freedom means to present individuals with the truth and give them a choice to accept or deny it.

Prevenient grace allows those tainted by sin to nevertheless make a truly free choice to accept or reject God's salvation in Christ.

In 1939, Hitler and Mussolini agreed to give the German-speaking population of South Tyrol a choice ( the South Tyrol Option Agreement ): they could emigrate to neighbouring Germany ( including annexed Austria ) or stay in Italy and accept their complete Italianisation.

If given the choice of what money to accept, people will transact with money they believe to be of highest long-term value.

However, if not given the choice, and required to accept all money, good and bad, they will tend to keep the money of greater perceived value in their possession, and pass on the bad money to someone else.

Walpole commanded a substantial majority in Parliament and George II had little choice but to accept him or risk ministerial instability.

" He said that we cannot accept free choice as a creation of God's, and simultaneously question its logical compatibility with omnipotence.

The democratically minded Carl, aware that Norway was still debating whether to retain its monarchy or to switch to a republican system of government, was flattered by the Norwegian government's overtures, but declined to accept the offer without a referendum to show whether monarchy was truly the choice of the Norwegian people.

When he returned to Piedmont, Thomas had no choice but to accept the fait accompli, and soon after this he went to live in Paris.

When he returned to Piedmont, Thomas had no choice but to accept the fait accompli, and soon after this he went to live in Paris.

The film depicts the reaction of family and friends, and the discomfort of their parents, as all try to accept the couple's choice.

Theodosius did not readily accept this choice and according to the chronicler Theophanes the Confessor even attempted to hide in the forests near Adramyttium.