Their policy ran counter to the traditional idea that a good fighter was usually a libertine, and that in sex affairs `` God-given passion '' was a proof of manliness.

The basic idea of his proof is that a proposition that holds of x if x = n for some natural number n can be called a definition for n, and that the set

Although Kronecker had conceded, Hilbert would later respond to others ' similar criticisms that " many different constructions are subsumed under one fundamental idea " — in other words ( to quote Reid ): " Through a proof of existence, Hilbert had been able to obtain a construction "; " the proof " ( i. e. the symbols on the page ) was " the object ".

If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.

Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann.

However, this idea can be understood as a basis for the following proof of the Lemma.

The proof of ✸ 2. 1 is roughly as follows: " primitive idea " 1. 08 defines p → q

By establishing a pattern, sometimes with the use of a powerful computer, mathematicians may have an idea of what to prove, and in some cases even a plan for how to set about doing the proof.

In the De Praescriptione he develops as its fundamental idea that, in a dispute between the Church and a separating party, the whole burden of proof lies with the latter, as the Church, in possession of the unbroken tradition, is by its very existence a guarantee of its truth.

Rather than focus on narrow debates about the true nature of mathematical truth, or even on practices unique to mathematicians such as the proof, a growing movement from the 1960s to the 1990s began to question the idea of seeking foundations or finding any one right answer to why mathematics works.

Hofstadter points to Bach's Canon per Tonos, M. C. Escher's drawings Waterfall, Drawing Hands, Ascending and Descending, and the liar paradox as examples that illustrate the idea of strange loops, which is expressed fully in the proof of Gödel's incompleteness theorem.

Ancient Greek mathematics contributed many important developments to the field of mathematics, including the basic rules of geometry, the idea of formal mathematical proof, and discoveries in number theory, mathematical analysis, applied mathematics, and approached close to establishing integral calculus.

The seeds, cork and coins would suggest trade to and from the Iberian peninsula and the presence of Merino sheep wool in the caulking material supports this idea ; but is not conclusive proof.

He intended to seek proof of this idea to satisfy those who did not believe him, or that broadcasting 9-1-1 calls hurt investigations.

But no one today appears to have a clear idea of what a finitistic proof would be like that is not capable of formulation within arithmetic.

He is also credited for categorizing logic into two separate groups, the first being " idea " and the second being " proof ".

Proof theory is important in philosophical logic, where the primary interest is in the idea of a proof-theoretic semantics, an idea which depends upon technical ideas in structural proof theory to be feasible.

In response to this Stanisław Jaśkowski ( 1929 ) and Gerhard Gentzen ( 1934 ) independently provided such systems, called calculi of natural deduction, with Gentzen's approach introducing the idea of symmetry between the grounds for asserting propositions, expressed in introduction rules, and the consequences of accepting propositions in the elimination rules, an idea that has proved very important in proof theory.

Gentzen ( 1934 ) further introduced the idea of the sequent calculus, a calculus advanced in a similar spirit that better expressed the duality of the logical connectives, and went on to make fundamental advances in the formalisation of intuitionistic logic, and provide the first combinatorial proof of the consistency of Peano arithmetic.

The general acceptance of the idea of governmental ( i.e., societal ) responsibility for the economic well-being of the American people is surely one of the two most significant watersheds in American constitutional history.

The dweller at p is last to hear about a new cure, the slowest to announce to his neighbors his urgent distresses, the one who goes the farthest to trade, and the one with the greatest difficulty of all in putting over an idea or getting people to join him in a cooperative effort.

And it is clearly argued by Lord Percy of Newcastle, in his remarkable long essay, The Heresy Of Democracy, and in a more general way by Voegelin, in his New Science Of Politics, that this same Rousseauan idea, descending through European democracy, is the source of Marx's theory of the dictatorship of the proletariat.

As a Humanist, Dr. Huxley interests himself in the possibilities of human development, and one thing we can say about this suggestion, which comes from a leading zoologist, is that, so far as he is concerned, the scientific outlook places no rigid limitation upon the idea of future human evolution.

The idea here is one of discharge but this must stand in opposition to a second view, Plato's notion of the arousal of emotion.

A third idea is that artistic literature serves to reduce emotional conflicts, giving a sense of serenity and calm to individuals.

It is possible that the idea of enrichment of emotion is a fifth idea.

It is true that this distinction between style and idea often approaches the arbitrary since in the end we must admit that style and content frequently influence or interpenetrate one another and sometimes appear as expressions of the same insight.

At this point a working definition of idea is in order, although our first definition will have to be qualified somewhat as we proceed.

Outstanding among these is the idea of human nature itself, including the many definitions that have been advanced over the centuries ; ;

An idea, of the sort that we have in mind, although of necessity readily available to imagination, is more general in connotation than most poetic or literary images, especially those appearing in lyric poems that seek to capture a moment of personal experience.

Finally we may note that the idea appears in educational theory where its influence is at present widespread.

namely, is the idea that there were Saxon mercenaries in England at all reasonable??

And to do this requires first of all the kind of information about people which is provided by the scientists in industrial anthropology and consumer research, who, for example, tell Courtenay that three days is the `` optimum priming period for a closed social circuit to be triggered with a catalytic cue-phrase '' -- which means that an effective propaganda technique is to send an idea into circulation and then three days later reinforce or undermine it.

He mentions the beats only once '', when he refers to their having revived through mere power and abandonment and the unwillingness to, commit death in life some idea of a decent equivalent between verbal expression and actual experience,, but the entire narrative, is written in the tiresome vocabulary `` of '' that lost `` and '' dying cause, `` and in the '' `` sprung syntax that is supposed to supplant, our mother, tongue.

The trouble is that at first glance the idea looks like such a good one.

Although Mr. Brown was not himself its inventor ( it was a French idea ), it is typical that his intuition first conceived the importance of mass producing this basic tool for general use.

He had no idea how much time Budd would give him.

`` It was Brenner's idea '', Jess mumbled, dabbing at his nose.

He had no idea which was up and which was down.

She had hated the whole idea before they started.

At first it had been just a romantic dream of his, the same as the idea of finishing Oxford after the war.

`` You are a big muscle-bound ape and you got this idea about setting a record.

Beyond the two basic tasks mentioned above, no attention was paid by statesman or scholar to an idea of state responsibility, either internally or externally.

The idea of national responsibility thus has become a common feature of the nations of the non-Soviet world.

However, for convenience we will stick to the idea that information can be classified according to Table 1.

Yet, after Rousseau had given the social contract a new twist with his notion of the General Will, the same philosophy, it may be said, became the idea source of the French Revolution also.

Demagogues of this sort found communist bogeys lurking behind any new idea that would run counter to stereotyped notions.

They give strict interpretation to William James' statement that `` Every idea that enters the mind tends to express itself ''.

Seemingly, with an unrestricted flow of ideas, all will be well, and we are even assured that `` an idea a day will keep the sheriff away ''.

Despite the clarity of his presentation, his idea was not of Einsteinian calibre.

In this phase of change, no idea has social acceptance and so none has ontological status in the community.

`` I arrived in the United States with the idea of establishing myself there more or less permanently and finding inspiration for new compositions ''.

The pamphlets are about law, the corporation, forms of government, the idea of freedom, the defense of liberty, the various lethargies which overtake our major institutions, the gap between traditional social ideals and the working mechanisms that have been set in motion for their realization.

So when textbooks, like that of Baker set out drawings of the ' Ptolemaic System ', complete with earth in the center and the seven heavenly bodies epicyclically arranged on their several deferents, we have nothing but a misleading 20th-century idea of what never existed historically.

Another contrast stressed when discussing Ptolemaic vs. Copernican astronomy, turns on the idea of simplicity.

To get an idea of the embarrassment and chagrin that was heaped upon Wright and Olgivanna, we should bear in mind that the raids were sometimes led by Miriam in person.

As he made plans for the new Taliesin, Wright also got on paper his conception of a cathedral of steel and glass to house a congregation of all faiths, and the idea for a planetarium with a sloping ramp.