Castaneda ’ s accounts are largely dismissed as being fiction, largely because the Toltec reality map is an uncompromising contradiction of conventional spiritual and secular beliefs.

Structuralism was developed in post-war Paris as a response to the perceived contradiction between the free subject of philosophy and the determined subject of the human sciences ; and drew on the systematic linguistics of ( Saussure ) for a view of language and culture as a conventional system of signs preceding the individual subject's entry into them.

This was in contradiction to Ernst Haeckel's theory that the complete phylogeny of a species would be repeated during embryonic development, including generation of the first nucleated cell from a " Monerula ", a structureless mass of primordial mucus (" Urschleim ").

For Adorno and Horkheimer state intervention in the economy had effectively abolished the tension in capitalism between the " relations of production " and " material productive forces of society ," a tension which, according to traditional critical theory, constituted the primary contradiction within capitalism.

" For Adorno and Horkheimer, this posed the problem of how to account for the apparent persistence of domination in the absence of the very contradiction that, according to traditional critical theory, was the source of domination itself.

The phrase " Cogito ergo sum " ( I think, therefore I am ) is also commonly associated with Descartes ' theory, because in his own methodological doubt, doubting everything he previously knew in order to start from a blank slate, the first thing that he could not logically bring himself to doubt was his own existence: " I do not exist " would be a contradiction in terms ; the act of saying that one does not exist assumes that someone must be making the statement in the first place.

An anomaly that arose in the late 19th century involved a contradiction between the wave theory of light and measurements of the electromagnetic spectrum emitted by thermal radiators, or so-called black bodies.

At first glance, the first paper seemed to point out a contradiction between the electrodynamic theory and the relativistic one concerning the calculation of the electromagnetic masses.

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.

Gosse believed that he had discovered a theory that might neatly resolve the seeming contradiction in the age of the earth between the evidence of God's Word and the evidence of His creation as expounded by such contemporary geologists as Charles Lyell.

In simultaneous equilibrium systems, phenomena that are in apparent contradiction to Le Chatelier principle can occur ; these can be resolved by the theory of response reactions.

In the foundations of mathematics, Russell's paradox ( also known as Russell's antinomy ), discovered by Bertrand Russell in 1901, showed that the naive set theory created by Georg Cantor leads to a contradiction.

* challenge ( or even refute ) a prevailing theory, often involving the device known as reductio ad absurdum, ( as in Galileo's original argument, a proof by contradiction ),

In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that naïvely constructing " the set of all ordinal numbers " leads to a contradiction and therefore shows an antinomy in a system that allows its construction.

For a hidden variable theory, if Bell's conditions are correct, then the results which are in agreement with quantum mechanical theory appear to evidence superluminal effects, in contradiction to the principle of locality.

The formal proof reveals exactly the hypotheses required for the theory T in order for the self-contradictory nature of G to lead to a genuine contradiction.

For most of the last century, it was recognized that Fourier equation is in contradiction with the theory of relativity because it admits an infinite speed of propagation of heat signals.

In logic, a consistent theory is one that does not contain a contradiction.

When Emil Post in his 1921 Introduction to a general theory of elementary propositions extended his proof of the consistency of the propositional calculus ( i. e. the logic ) beyond that of Principia Mathematica ( PM ) he observed that with respect to a generalized set of postulates ( i. e. axioms ) he would no longer be able to automatically invoke the notion of " contradiction " – such a notion might not be contained in the postulates:

According to Marxist theory, such a contradiction can be found, for example, in the fact that:

Behavioral economics and quantitative analysis use many of the same tools of technical analysis, which, being an aspect of active management, stands in contradiction to much of modern portfolio theory.

A contradiction in a formal theory is a formal proof of an absurdity inside the theory ( such as 2 + 2 = 5 ), showing that this theory is inconsistent and must be rejected.

But a paradox may either refer to a surprising but true result in a given formal theory, or to an informal argument leading to a contradiction, so that a candidate theory where a formalization of the argument might be attempted must disallow at least one of its steps ; in this case the problem is to find a satisfying theory without contradiction.

It is the gradual unfolding and deepening of this contradiction which creates the inner dialectic of the evolution of the mystery story.

It is the growing contradiction between individualism and public service in the mystery story which creates this fatal dilemma.

Dealers that sponsor infomercials on shortwave radio are notorious for such sales pitches, most notably Discount Gold & Silver Trading on WWCR, which proclaims graded coins, in direct contradiction to their pricing history, as having appreciated more than non-graded coins, or as not likewise being " opinion coins.

Later ancient commentators such as Proclus ( 410 – 485 CE ) treated many questions about infinity as issues demanding proof and, e. g., Proclus claimed to prove the infinite divisibility of a line, based on a proof by contradiction in which he considered the cases of even and odd numbers of points constituting it.

Euclid frequently used the method of proof by contradiction, and therefore the traditional presentation of Euclidean geometry assumes classical logic, in which every proposition is either true or false, i. e., for any proposition P, the proposition " P or not P " is automatically true.

That is why expert systems using variable facts, which are more understandable to developers creating such systems and hence more common, are less easy to develop, less clear to users, less reliable, and why they don't produce explanations of their reasoning, or contradiction detection.

These " politically neutral " groups tend to avoid global conflicts and view the settlement of inter-human conflict as separate from regard for nature-in direct contradiction to the ecology movement and peace movement which have increasingly close links: While Green Parties and Greenpeace, and groups like the ACTivist Magazine for example, regard ecology, biodiversity and an end to non-human extinction as absolutely basic to peace, the local groups may not, and may see a high degree of global competition and conflict as justifiable if it lets them preserve their own local uniqueness.

Falwell repeatedly denounced certain teachings in public schools and secular education in general, calling them breeding grounds for atheism, secularism, and humanism, which he claimed to be in contradiction with Christian morality.

Then ( E2 ) is false, which means ( E3 ) is true, and hence ( E1 ) is false, leading to a contradiction.

Chief among these is that since dialetheism recognizes the liar paradox, an intrinsic contradiction, as being true, it must discard the long-recognized principle of ex falso quodlibet, which asserts that any proposition can be deduced from a contradiction, unless the dialetheist is willing to accept trivialism-the view that all propositions are true.

There are theories which have developed a concept called human capital ( referring to the skills that workers possess, not necessarily their actual work ), although there are also counter posing macro-economic system theories that think human capital is a contradiction in terms.

Faced with a contradiction between two equally authentic texts of the statute, the court considered which interpretation better served the objects and purposes of the statute, and hence found that they are binding.

#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

In more extreme cases paradox can cause Quiet ( madness that may leak into reality ), Paradox Spirits ( nebulous, often powerful beings which purposefully set about resolving the contradiction, usually by directly punishing the mage ), or even the removal of the Mage to a paradox realm, a pocket dimension from which it may be difficult to escape.

And in fact, Cantor's diagonal argument is constructive, in the sense that given a bijection between the real numbers and natural numbers, one constructs a real number which doesn't fit, and thereby proves a contradiction.

Instead of using " that which promotes my ( human ) life " as his standard of value, he mistakes " that which I ( mindlessly happen to ) value " for a standard of value, in contradiction of the fact that, existentially, he is a human and therefore rational organism.

Necessary being is that which cannot but be, since its non-being entails a contradiction.

If − 1 is positive, then (− 1 )(− 1 ) = 1 is positive, which is a contradiction )

There are also examples in which terms that are superficially contradictory are juxtaposed in such a way that there is no contradiction.

In response to questions of a deity performing impossibilities ( such as making square circles ) Aquinas says that " Nothing which implies contradiction falls under the omnipotence of God.