In turn, when B is replaced with a list of attached atoms, A itself is excluded in accordance with the general principle of not doubling back along a bond that has just been followed, but a ghost atom for A is included so that the double bond is properly represented from both ends.

For Cuvier, this was related to another principle of his, the conditions of existence, which excluded the possibility of transmutation of species.

In several axiomatic derivations of logic, this is effectively resolved by showing that ( P ∨ ¬ P ) and its negation are constants, and simply defining TRUE as ( P ∨ ¬ P ) and FALSE as ¬( P ∨ ¬ P ), without taking a position as to the principle of bivalence or the law of excluded middle.

In logic, the law of excluded middle ( or the principle of excluded middle ) is the third of the three classic laws of thought.

The law is also known as the law ( or principle ) of the excluded third ( or of the excluded middle ), or, in Latin, principium tertii exclusi.

The principle of contradiction is merely an expression of the mutually exclusive aspect of that dichotomy, and the principle of excluded middle is an expression of its jointly exhaustive aspect.

This response to the paradox is, in effect, the rejection of the claim that every statement has to be either true or false, also known as the principle of bivalence, a concept related to the law of the excluded middle.

In particular, the law of excluded middle, " A or not A ", is not accepted as a valid principle.

These views were forcefully expressed by David Hilbert in 1928, when he wrote in < cite > Die Grundlagen der Mathematik </ cite >, " Taking the principle of excluded middle from the mathematician would be the same, say, as proscribing the telescope to the astronomer or to the boxer the use of his fists ".

The principle of bivalence is related to the law of excluded middle though the latter is a syntactic expression of the language of a logic of the form " P ∨ ¬ P ".

Constructivism and intuitionism are realistic about objects that can be explicitly constructed, but reject the use of the principle of the excluded middle to prove existence by reductio ad absurdum.

If a principle is presented as a generalization, the gemara clarifies how much is included ; if an exception, how much is excluded.

Also in 1925, he published his famous work in intuitionistic logic — On the principle of the excluded middle, in which he proved that under a certain interpretation, all statements of classical formal logic can be formulated as those of intuitionistic logic.

" On the principle of the excluded middle " in Jean van Heijenoort, 1967.

No women ever acquired citizenship in ancient Athens, and therefore women were excluded in principle and practice from ancient Athenian democracy.

L. E. J. Brouwer: " On the significance of the principle of excluded middle in mathematics, especially in function theory.

A. N. Kolmogorov: " On the principle of excluded middle ", pp. 414 – 437.

Section 601This section states the general principle that no person in the United States shall be excluded from participation in or otherwise discriminated against on the ground of race, color, or national origin under any program or activity receiving Federal financial assistance.

Consumers ' expenditure abroad is usually excluded ; visitors ' expenditure within the country may be excluded in principle if not in practice ; the rural population may or may not be included ; certain groups such as the very rich or the very poor may be excluded.

The middle ear couples sound from air to the fluid via the oval window, using the principle of " mechanical advantage " in the form of the " hydraulic principle " and the " lever principle ".

The Dilbert principle refers to a 1990s satirical observation by Dilbert cartoonist Scott Adams stating that companies tend to systematically promote their least-competent employees to management ( generally middle management ), in order to limit the amount of damage they are capable of doing.

' When earlier developmental stages have gone astray, however, then, on the principle that ' if you miss a stage, you can always go through it later ,' some middle children ' come to school for another purpose ... to learn but to find a home from home ... a stable emotional situation in which they can exercise their own emotional liability, a group of which they can gradually become a part.

As he declared in his last great public speech, at the Grey Festival organized in his honour at Edinburgh in September 1834, its purpose was to strengthen and preserve the established constitution, to make it more acceptable to the people at large, and especially the middle classes, who had been the principal beneficiaries of the Reform Act, and to establish the principle that future changes would be gradual, " according to the increased intelligence of the people, and the necessities of the times ".

Since p ⇒ q and ~ q ⇒ ~ p are equivalent by the principle of transposition ( see law of excluded middle ), p ⇒ q is indirectly proved.

Carmichael saw nonviolence as a tactic as opposed to a principle, which separated him from moderate civil rights leaders like Martin Luther King, Jr .. Carmichael became critical of civil rights leaders who simply called for the integration of African Americans into existing institutions of the middle class mainstream.

He thought innovatively about traditional propositional logic, the principle of non-contradiction and the law of excluded middle.

The principle of Schwerpunkt enabled the attacker to win numerical superiority at the point of the main effort, which in turn gave the attacker tactical and operational superiority even though the attacker may be numerically and strategically inferior along the entire front.

This uncompromising principle, along with their reputation for courage, excellent training, and heavy armament, made the Templars one of the most feared combat forces in medieval times.

A crude diagram of the LORAN principle — the difference between the time of reception of synchronized signals from radio stations A and B is constant along each hyperbolic curve ; when demarcated on a map, such curves are known as " TD lines "

In this case, the polarization along one plane is intrinsically tied to the polarization along the other, and by Heisenberg ’ s principle, there is a limit to the certainty with which both states can be known.

Hooke remained bitter about Newton claiming the invention of this principle, even though Newton ’ s “ Principia ” acknowledged that Hooke, along with Wren and Halley, had separately appreciated the inverse square law in the solar system, as well as giving some credit to Bullialdus.

Hooke clearly postulated mutual attractions between the Sun and planets, in a way that increased with nearness to the attracting body, along with a principle of linear inertia.

James I and Charles I of England tried to import this principle ; fears that Charles I was attempting to establish absolutist government along European lines were a major cause of the English Civil War.

An explicit statement of this, along with the further principle that nothing can pass away into nothing, is found in Empedocles ( ca.

During the Mandate of Iraq ( 1920 – 32 ), the British advisors in Iraq were able to keep the waterway binational under the presitful principle that worked in Europe ( see Danube River ): the dividing line was a line drawn between the deepest points along the stream bed.

A self-anchored suspension bridge has some similarity in principle to the cable-stayed type in that tension forces that prevent the deck from dropping are converted into compression forces vertically in the tower and horizontally along the deck structure.

For example, Bernoulli's principle, which describes the relationship between pressure and velocity in an inviscid fluid, is derived for locations along a streamline.

Albert Einstein seemed to view Mach's principle as something along the lines of:

Modern jets are based on the turbojet principle, but Campini's jet was nevertheless a true jet, since it was the reactive force of the burning exhaust gases that pushed the plane along.

After a year-long trip with her husband, Dennis Meadows, from England to Sri Lanka and back, she became, along with him, a research fellow at MIT as a member of a team in the department created by Jay Forrester, the inventor of system dynamics as well as the principle of magnetic data storage for computers.

The operating principle of a parabolic antenna is that a point source of radio waves at the focal point in front of a paraboloidal reflector of conductive material will be reflected into a collimated plane wave beam along the axis of the reflector.

When the group is the entire nation, the same principle is in effect whether the property is small ( e. g. picnic rest stops along highways ) or large such as national parks, highways, ports, and publicly owned buildings.

The title is bestowed along the same automatic principle as the dukedom of Cornwall ( see above ).

In the 17th century Pierre de Fermat postulated that " light travels between two given points along the path of shortest time ," which is known as the principle of least time or Fermat's principle.

Then, using an interpretive principle known as the day-year principle, Miller, along with others, interpreted a prophetic " day " to read not as a 24-hour period, but rather as a calendar year.

The kings under this principle will build temples to glorify the reign of himself along with the spread of Hinduism.