Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

Thus while his theory or technique may not be oversubscribed, it is commonplace for bullish and bearish positions to become temporarily over-subscribed.

Thus, theory and doctrine applicable among the great nations and the smaller European states did not really comfortably fit less developed and less powerful societies elsewhere.

Thus, while altruistic persons may under some circumstances be outcompeted by less altruistic persons at the individual level, according to group selection theory the opposite may occur at the group level where groups consisting of the more altruistic persons may outcompete groups consisting of the less altruistic persons.

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

Thus the axiom of choice is not generally available in constructive set theory.

Thus aesthetic judgments might be seen to be based on the senses, emotions, intellectual opinions, will, desires, culture, preferences, values, subconscious behavior, conscious decision, training, instinct, sociological institutions, or some complex combination of these, depending on exactly which theory one employs.

Thus, the theory asserts that the apple is no more than the collection of its properties.

Thus, the Big Bang theory cannot and does not provide any explanation for such an initial condition ; rather, it describes and explains the general evolution of the universe going forward from that point on.

Thus, while Nozick's side-constraints are absolute restrictions on behavior, Amartya Sen proposes a theory that recognizes the importance of certain rules, but these rules are not absolute.

Thus, in an agent-neutral theory, an actor's personal goals do not count any more than anyone else's goals in evaluating what action the actor should take.

Thus literary criticism became highly theoretical and some of those practicing it began referring to the theoretical dimension of their work as " critical theory "-a philosophically inspired theory of literary criticism.

Thus, theory has its roots in the materiality of social existence.

Thus, though knowledge requires justification, truth, and belief, the word " knowledge " can't be, according to Williamson's theory, accurately regarded as simply shorthand for " justified true belief.

Thus, Gibbs ' theory becomes

Thus Fermi saw the theory published in Italian and in German before it was published in English.

Thus the aqua cations behave as acids in terms of Brønsted-Lowry acid-base theory.

" Thus irreal works such as Italo Calvino's Cosmicomics and Jorge Luis Borges ' Ficciones can be seen as an attempt to find a new allegorical language to explain our changed perceptions of the world that have been brought about by our scientific and technical culture, especially concepts such as quantum physics or the theory of relativity.

Thus, according to Keynesian theory, some individually-rational microeconomic-level actions such as not investing savings in the goods and services produced by the economy, if taken collectively by a large proportion of individuals and firms, can lead to outcomes, wherein the economy operates below its potential output and growth rate.

Thus three major themes in 19th century mathematics were combined by Lie in creating his new theory: the idea of symmetry, as exemplified by Galois through the algebraic notion of a group ; geometric theory and the explicit solutions of differential equations of mechanics, worked out by Poisson and Jacobi ; and the new understanding of geometry that emerged in the works of Plücker, Möbius, Grassmann and others, and culminated in Riemann's revolutionary vision of the subject.

Thus for a theory " T ", " G " is true, but not provable in " T ".

Thus, both the statement " Murder is bad " and the statement " Murder is good " are false, according to an error theory.

Thus in theory, if law enforcement officials decline to offer a Miranda warning to an individual in their custody, they may still interrogate that person and act upon the knowledge gained, but may not use that person's statements to incriminate him or her in a criminal trial.

Thus lubricant burning takes place in specialized facilities that have incorporated special scrubbers to remove airborne pollutants and have access to landfill sites with permits to handle the toxic ash.

Thus as there is no fixed meaning in things, but they draw their meaning in a referential difference to other things, the wind objection can be incorporated into Theaetetus's claim that " Knowledge is sense perception ".

Thus, with the help of a powerful local ally, the town was incorporated on May 14, 1852, and renamed Marion in honor of Revolutionary War hero Francis Marion.

Thus in the same year, the towns of Pelham and Holles were incorporated, and named after the duke.

Thus were born dedicated hydrographic organizations for the collection, organization, publication and distribution of hydrography incorporated into charts and sailing directions.

Thus, in formal writing, the interjection will be incorporated into a larger sentence clause.

Thus COGIC became the first legally chartered Pentecostal body incorporated in the United States.

Thus, a dummy variable can be defined as a qualitative representative variable incorporated into a regression, such that it assumes the value 1 whenever the category it represents occurs, and 0 otherwise.

Thus, on July 19, 1990, the Konkan Railway Corporation Limited ( KRCL ) was incorporated as a public limited company under the Companies Act, 1956, with its headquarters at CBD Belapur in Navi Mumbai and E. Sreedharan, a senior railway official, as its first Chairman and Managing Director.

Thus the Kingdom of the Two Sicilies ceased to exist and its territory was incorporated into that of the Kingdom of Sardinia ( soon renamed the Kingdom of Italy ), and Francis II was deposed.

Thus the revolution was accomplished without a drop of blood being shed, and after a period of provisional government Tuscany was incorporated in the kingdom of Italy.

Thus in order to make house music more appealing to the Singapore crowd, it introduced a blend of music which incorporated pop hits from the 70s and 80s with house music which were to be played every Wednesday night.

Thus, property in land is only a form of invested capital, a quantity of labour or the fruits of labour permanently incorporated with the soil.

Thus Muhammad II incorporated nearly the whole of Transoxania and what is now Afghanistan into his empire, which after further conquests in western Persia ( by 1217 ) stretched from the Syr Darya to the Zagros Mountains, and from the Indus Valley to the Caspian Sea.

" Thus, the states were allowed to reject the Sixth Amendment, for example, while ratifying all of the other amendments including the Due Process Clause ; in that case, the rights in the Sixth Amendment would not have been incorporated against the federal government.

Thus, the Citizenship Clause in the Fourteenth Amendment parallels citizenship language in the Civil Rights Act of 1866, and likewise the Equal Protection Clause parallels nondiscrimination language in the 1866 Act ; the extent to which other clauses in the Fourteenth Amendment may have incorporated elements of the Civil Rights Act of 1866 is a matter of continuing debate.

Thus the Lusignans ' diplomatic rebellion led directly to the loss of half of England's French territory, which was soon incorporated into France by Philip Augustus ( The other " half ", Aquitaine, was the possession of Eleanor, who was still alive ).

Thus, procedurally, only a jury can convict a defendant of a serious crime, since the Sixth Amendment jury-trial right has been incorporated against the states ; substantively, for example, states must recognize the First Amendment prohibition against a state-established religion, regardless of whether state laws and constitutions offer such a prohibition.

Thus, Bigorre was incorporated into the estates of the House of Foix-Grailly, which included the county of Foix, Béarn, and Nébouzan.

Thus, if an incorporated town became a city of the same name, it is not listed here as extinct or lost.

Thus, in his commentary upon Torath Kohanim ( pp. 41a, 71b ), we find the caustic observation that many obscure passages in rabbinical literature owe their obscurity to the fact that occasional explanatory or marginal notes not tending to elucidate the text have been incorporated.

Thus, the pioneer parishes of New Orleans and Louisiana were incorporated into the Diocese of Louisiana and the Two Floridas when it was erected on April 25, 1793.

Thus, the Military Police incorporated an agile, efficient and effective equipment for combating criminality: the helicopter " Eagle Uno ", which had the mission to support the PM in all its activities.

Thus whilst the other Saxon-Thuringian principalities were later incorporated into the German Democratic Republic after World War II, Coburg became part of West Germany.