::“ involves our saying, for instance, that a world in which absolutely nothing except pleasure existed — no knowledge, no love, no enjoyment of beauty, no moral qualities — must yet be intrinsically better — better worth creating — provided only the total quantity of pleasure in it were the least bit greater, than one in which all these things existed as well as pleasure .”

::“ It is much better to kill only such you want, without wasting your powder and lead, then to be firing into God ’ s creatures in such a wicked manner .” ( Natty to Judge Marmeduke ) – Chapter III, The Slaughter of Pigeons

::“ Suppose that a ruler controls a weapon capable of instantly and painlessly destroying the human race.

::“ One ought to abide by the general principles whose general inculcation is for the best ; harm is more likely to come, in actual moral situations, from questioning these rules than from sticking to them, unless the situations are very extra-ordinary ; the results of sophisticated felicific calculations are not likely, human nature and human ignorance being what they are, to lead to the greatest utility .”

::“ In the traditional view, it is assumed that there exists a reality in space-time and that this reality is a given thing, all of whose aspects can be viewed or articulated at any given moment.

::“ happiness, private happiness, is the proper or ultimate end of all our actions … each particular action may be said to have its proper and peculiar end …( but )….

::“ Now it is evident from the nature of God, viz.

::“ It is true there are cases in which, if we confine ourselves to the effects of the first order, the good will have an incontestable preponderance over the evil.

::“ It is quite compatible with the principle of utility to recognise the fact, that some kinds of pleasure are more desirable and more valuable than others.

::“ It is truly a whimsical supposition that, if mankind were agreed in considering utility to be the test of morality, they would remain without any agreement as to what is useful, and would take no measures for having their notions on the subject taught to the young, and enforced by law and opinion … to consider the rules of morality as improvable, is one thing ; to pass over the intermediate generalisations entirely, and endeavour to test each individual action directly by the first principle, is another … The proposition that happiness is the end and aim of morality, does not mean that no road ought to be laid down to that goal … Nobody argues that the art of navigation is not founded on astronomy, because sailors cannot wait to calculate the Nautical Almanack.

::“ I agree with you that the right way of testing actions by their consequences, is to test them by the natural consequences of the particular action, and not by those which would follow if everyone did the same.

::“ there is, from the ethical point of view, no symmetry between suffering and happiness, or between pain and pleasure … In my opinion human suffering makes a direct moral appeal, namely, the appeal for help, while there is no similar call to increase the happiness of a man who is doing well anyway.

::“ Surely the utilitarian must admit that whatever the facts of the matter may be, it is logically possible that an ‘ unjust ’ system of punishment — e. g. a system involving collective punishments, retroactive laws and punishments, or punishments of parents and relations of the offender — may be more useful than a ‘ just ’ system of punishment ?”

::“ We certainly cannot hope directly to compare their effects except within a limited future ; and all the arguments, which have ever been used in Ethics, and upon which we commonly act in common life, directed to shewing that one course is superior to another, are ( apart from theological dogmas ) confined to pointing out such probable immediate advantages …

::“ It is the beginningless round of rebirths that is called the ’ Wheel of the round of rebirths ’ ( saṃsāracakka ).

::“ They ’ re supposed to say, ‘ I got this student, her attendance is good, her GPA is all right — can you interview this person ?’ They ’ re not doing that ,” she said.

::“ For all those people who have lost or misplaced something that was dear to them, as I have, never give up the dream of searching – never let go of the hope that you ’ ll find it because after all these many years, at last, my Oscar has been returned to me .”

::“ For all those people who have lost or misplaced something that was dear to them, as I have, never give up the dream of searching – never let go of the hope that you ’ ll find it because after all these many years, at last, my Oscar has been returned to me .”

::“ Arguments for and against God's just judgment resemble those found in Plutarch's De sera numinis vindicta ” the delays of divine vengeance “ as well as in the targumic midrash about Cain and Abel in Gen ” “ 4.

::“ Nature has placed mankind under the governance of two sovereign masters, pain and pleasure.

::“ Utilitarian ethics makes all of us members of the same moral community.

::“ Tanizaki wrote clear, rational sentences ,” Mr. Seidensticker wrote.

::“ He would dutifully scrutinize the passage, and answer: ‘ Yes ,’ ” Mr. Seidensticker wrote.

::“ I am going to ask you a rather strange question.

::“ If we consider ‘ The will ’ by Kamel Selim in 1939 the beginning of Egyptian realism in cinema, so we have to admit that ‘ House-Boat No. 70 ’ by Khairy Beshara, 1982, is the start of the new realism ”

::“ Her Majesty is now Queen of Canada but she is the Queen of Canada because she is Queen of the United Kingdom.

After his arrest, Popitz told the Gestapo ::“ As somebody who was very familiar with conditions in the System period the Weimar Republic, my view of the Jewish question was that the Jews ought to disappear from the life of the state and the economy.

Attorneys for the eight other defendants said only that there was no proof of their clients' guilt.

The proof of the independence result also shows that a wide class of mathematical statements, including all statements that can be phrased in the language of Peano arithmetic, are provable in ZF if and only if they are provable in ZFC.

When one attempts to solve problems in this class, it makes no difference whether ZF or ZFC is employed if the only question is the existence of a proof.

That was so because it not only was proof of excessive pride, but also resulted in violent acts by or to those involved.

For the frequent case of propositional logic, the problem is decidable but Co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.

It was at this time that ` Abdu ' l-Bahá, in order to provide proof of the falsity of the accusations leveled against him, in tablets to the West, stated that he was to be known as "` Abdu ' l-Bahá " an Arabic phrase meaning the Servant of Bahá to make it clear that he was not a Manifestation of God, and that his station was only servitude.

In this case, if a proof uses this statement, researchers will often look for a new proof that doesn't require the hypothesis ( in the same way that it is desirable that statements in Euclidean geometry be proved using only the axioms of neutral geometry, i. e. no parallel postulate.

Note that the validity of a conditional proof does not require that the CPA is actually true, only that if it is true it leads to the consequent.

Convictions can only be made when proof beyond a reasonable doubt is achieved.

The burden of proof for civil contempt, however, is a preponderance of the evidence, and theoretically punitive sanctions ( punishment ) can only be imposed after due process but the due process is unpublished.

In the Education ( Scotland ) Act, it is only necessary to produce a register as proof of lack of attendance.

( For groups of low 2-rank the proof of this breaks down, because theorems such as the signalizer functor theorem only work for groups with elementary abelian subgroups of rank at least 3.

In this reality, the only proof that Charles Xavier ever existed is a secret monument in Magneto's palace garden, with the engraved message " He died so Genosha could live ".

If we insert vertices in random order, it turns out ( by a somewhat intricate proof ) that each insertion will flip, on average, only O ( 1 ) triangles – although sometimes it will flip many more.

For example, the proof that the column rank of a matrix over a field equals its row rank yields for matrices over division rings only that the left column rank equals its right row rank: it does not make sense to speak about the rank of a matrix over a division ring.

This new proof is similar to Appel and Haken's but more efficient because it reduced the complexity of the problem and required checking only 633 reducible configurations.

More precisely, all known FFT algorithms require Θ ( N log N ) operations ( technically, O only denotes an upper bound ), although there is no known proof that better complexity is impossible.

Moore argued that once arguments based on the naturalistic fallacy had been discarded, questions of intrinsic goodness could only be settled by appeal to what he ( following Sidgwick ) called " moral intuitions :" self-evident propositions which recommend themselves to moral reflection, but which are not susceptible to either direct proof or disproof ( PE § 45 ).

A simpler proof considering only 633 configurations was given twenty years later by Robertson, Seymour, Sanders and Thomas.

In August 1970, Gödel told Oskar Morgenstern that he was " satisfied " with the proof, but Morgenstern recorded in his diary entry for 29 August 1970, that Gödel would not publish because he was afraid that others might think " that he actually believes in God, whereas he is only engaged in a logical investigation ( that is, in showing that such a proof with classical assumptions ( completeness, etc.

From these hypotheses, it is also possible to prove that there is only one God in each world by Leibniz's law, the identity of indiscernibles: two or more objects are identical ( are one and the same ) if they have all their properties in common, and so, there would only be one object in each world that possesses property G. Gödel did not attempt to do so however, as he purposely limited his proof to the issue of existence, rather than uniqueness.

This uniqueness proof will only work if one supposes that the positiveness of a property is independent of the object to which it is applied, a claim which some have considered to be suspect.