Much of his work on stratified sets was developed so as to understand the notion of topologically stable maps, and to eventually prove the result that the set of topologically stable mappings between two smooth manifolds is a dense set.

It even eludes the idea a lot more even to assume the concept of " nothing " or negation was created, therefore it is seemingly impossible to conceive such a notion where it draws down to a paradox.

Since the ordinary notion of consistency involves that of contradiction, which again involves negation, and since this function does not appear in general as a primitive in generalized set of postulates a new definition must be given ".

The answer to this is that in the case of contradictory statements — A and not A — the latter is a mere negation of the former, and posits nothing ; and the negation of a notion with positive attributes, as the finite, does not extend beyond abolishing the given attributes as an object of thought.

The use of such a dialectical method can be traced back to the philosophy of Hegel, who conceived dialectic as the tendency of a notion to pass over into its own negation as the result of conflict between its inherent contradictory aspects.

Another notion Searle and Vanderveken use is that of an ' illocutionary negation '.

This leads Irenaeus to the somewhat startling notion that Adam and Eve died on the same day that they disobeyed, namely, on a Friday, as a parallel to the death of Christ on Good Friday ; ;

It had been hoped that patient adherence to antipsychotics would be higher with the atypicals, but a 2008 review found that the data have failed to substantiate the notion that novel antipsychotic drug use leads to improved medication compliance and favorable clinical outcomes.

This leads to the notion of an internal groupoid in a category.

The vagueness of the intuitionistic notion of truth often leads to misinterpretations about its meaning.

The generalization of these three properties to more abstract vector spaces leads to the notion of norm.

Russell's paradox, which shows that the notion of the set of all those sets that do not contain themselves leads to a contradiction, was instrumental in the development of modern logic and set theory.

Thus, the general notion of a statistical ensemble with nearest-neighbor interactions leads to Markov random fields, which again find broad applicability ; for example in Hopfield networks.

This leads to the notion of " genetic distance ", which is a measure of recombination frequency averaged over a ( suitably large ) sample of pedigrees.

Elliott argues that this mistaken notion of his role as king ultimately leads to Richard's failure.

4 ) Similarly, the Moore – Smith theory of convergence via nets, as supplemented by Kelley's notion of a universal net, leads to the criterion that a space is compact if and only if each universal net on the space converges.

Marston positioned that there is a male notion of freedom that is inherently anarchic and violent and an opposing female notion based on " Love Allure " that leads to an ideal state of submission to loving authority.

This is a particularly unfortunate choice as it leads to confusion with the notion of a complex structure, which often has the same coordinate expression as Ω but represents a very different structure.

This notion of one ( multiplicity ) culture to an organization leads to the classification of culture along its path of emergence into nascent, adolescent, and mature types, each of which is distinct in terms of the pattern of the three cognitive components and behavior.

Tits later reworked the foundational aspects of the theory of buildings using the notion of a chamber system, encoding the building solely in terms of adjacency properties of simplices of maximal dimension ; this leads to simplifications in both spherical and affine cases.

The further question of what is the structure of the coarse quotient space leads to the notion of a smooth stack.

Carroll disclaims the notion that Christian anti-Judaism leads inevitably to the Shoah perpetrated by National Socialism, but he argues that Church's long history of " Jew-hatred " ( his term ) laid the foundation for Hitler's crimes.

This leads to the radical notion that there is no such thing as a " doer ".

This can easily be expressed in terms of a commutative diagram, and thus leads to the notion of a medial magma object in a category with a Cartesian product.

Meanwhile, his notion that we can begin to enjoy our eternal salvation through our earthly successes leads in later generations to " a mysticism of consolation ".

This leads to the notion that the points of the stack should carry automorphisms themselves, and this in turn gives rise to the notion of a stack as a certain kind of " category fibered in groupoids ".

This leads to the questions of the relevant notion of " possibility ": is the scenario described in premise 3 possible in the sense that is suggested in premise 2?

This important remark leads to the notion of sheaf cohomology, via derived functors.

It may be a cultural notion, but has very little weight in international discourse ; very few political observers really discuss Christendom, while the Muslim World tends to comprise of a civilization in itself.

Although English largely separates tense and aspect formally, its generally recognized aspects do not correspond very closely to the traditional notion of perfective vs. imperfective aspectual distinction originally devised to classify aspect in most Classical and Slavic languages ( those languages for which the concept of aspect was first proposed in describing non-tense handling of verbal " viewpoint ").

He proposes that most commonly accepted social institutions — including the notion of State, property as a right, natural rights in general, and the very notion of society — were mere spooks in the mind.

Jesuits had brought with them various books, engravings, and paintings and, when they saw the delight Akbar held for them, sent for more and more of the same to be given to the Mughals, as they felt they were on the " verge of conversion ," a notion which proved to be very false.

However, very similar-looking alterations in the systems of long vowels in the West Germanic languages greatly postdate any possible notion of a proto-language innovation ( and cannot readily be regarded as " areal ", either, since English and continental West Germanic were not a linguistic area ).

The notion of a lexeme is very central to morphology, and thus, many other notions can be defined in terms of it.

Mass media is distinguished from local media by the notion that whilst the former aims to reach a very large market such as the entire population of a country, the latter broadcasts to a much smaller population and area, and generally focuses on regional news rather than global events.

However, also widely accepted as part of the notion of perfectly competitive market are perfect information about price distribution and very quick adjustments ( whose joint operation establish the law of one price ), to the point sometimes of identifying perfect competition with an essentially instantaneous reaching of equilibrium between supply and demand.

In fact, the very notion of finding coherence and permanence within sensory experience was so preposterous to him, that he had to postulate the notion of a God who holds all reality in HIS mind, in order to explain why the world doesn't just vanish when we stop perceiving it.

To define more exactly the Buddhist notion of the highest being, it may be convenient to borrow the term very happily coined by a modern German scholar, " panentheism ," according to which God is πᾶν καὶ ἕν ( all and one ) and more than the totality of existence.

While for piecewise smooth surfaces there is a unique natural notion of surface area, if a surface is very irregular, or rough, then it may not be possible to assign any area at all to it.

Extensions of the notion of area which partially fulfill its function and may be defined even for very badly irregular surfaces are studied in the geometric measure theory.

And — as in Magritte's case ( where there is no obvious recourse to either automatic techniques or collage )— the very notion of convulsive joining became a tool for revelation in and of itself.

Describing it as " cheap, grubby and out of control ", Mark Olsen of the Los Angeles Times declared that it " both defines and entirely supersedes the very notion of the exploitation picture ".

The notion of a theorem is very closely connected to its formal proof ( also called a " derivation ").

So that is one problem about the notion that God is a mind — namely, it is hard really to understand the very notion that a mind can create physical objects out of nothing.

But this makes the very notion of the divine mind exceedingly strange.

As the Manifesto says " Cypherpunks write code "; the notion that good ideas need to be implemented, not just discussed, is very much part of the culture of the mailing list.

Intuitionists reject the very notion of an arbitrary sequence of integers, as denoting something finished and definite as illegitimate.

He contends that the very notion of a collection of " thoughts " that exist in a privileged region of the mind such that they are in principle never accessible to conscious awareness, is incoherent.

In their speculative work on the topic of future science and artificial intelligence, authors Goertzel and Bugaj describe a very different metaphysical notion as " quantum immortality ", one they claim is applicable in all circumstances, for every " intelligent entity ", and that serves as a means of " transfer " to other universes.