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, if corporations are not to run away with us, they must become quasi-governmental institutions, subject to public control and needs.

Thus Af if and only if Af.

Thus F satisfies Af if and only if F has the form Af.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus, if public pressure sets the effective limit to the price that the industry may charge, this pressure is itself a function of the wage rate.

Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.

Thus if the gyro and platform-controller combination maintains the platform with zero angular deviation about the **yf axis, the system can be rotated with an angular velocity Af if a torque is supplied to the gyro output axis Aj.

Thus, if one accelerometer is properly aligned, the other is also.

Thus, if we are to observe American folklore in the twentieth century, we will do well to establish the relationships between folklore, nationalism and imperialism at the outset.

Thus, red wine must, if possible, never be disturbed or shaken ; ;

Thus, if what is at issue is whether `` All S is P '', it is indifferent whether `` Some S is not P '' or `` No S is P '', since in either case the judgment in question is false.

Thus most Affidavits now require to be Apostilled if used for cross border issues.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

Thus throwing a rock at someone for the purpose of hitting him is a battery if the rock in fact strikes the person and is an assault if the rock misses.

Thus, a court officer taking possession of goods under a court order may use force if reasonably necessary.

Thus, there is no assault if an ox gores a man.

Thus, if P is a program in L < sub > 2 </ sub > which is a minimal description of s, then InterpretLanguage ( P ) returns the string s. The length of this description of s is the sum of

Thus, if every historian were to claim that there was a solar eclipse in the year 1600, then though we might at first naively regard that as in violation of natural laws, we'd come to accept it as a fact.

Thus, there was seen a need for a new law that would ensure the continuance of the succession following the death of the last legal heir under the Bill of Rights, being Princess Anne, guaranteeing the line of succession would continue in the Protestant line, and excluding any possible claims by the deposed James II or his son and daughter, James Francis Edward and Louisa Maria Teresa Stuart.

" Thus, even when reception was effected by a constitution, the common law was still subject to alteration by a legislature's statute.

Thus, to be valid, any law must conform to natural law and coercing people to conform to that law is morally acceptable.

Thus in Austinian terms a moral code can objectively determine what people ought to do, the law can embody whatever norms the legislature decrees to achieve social utility, but every individual remains free to choose what to do.

Thus the necessary and sufficient conditions for the truth of a proposition of law simply involved internal logic and consistency, and that the state's agents used state power with responsibility.

Thus criminal law grew out what 21st-century lawyers would call torts ; and, in real terms, many acts and omissions classified as crimes actually overlap with civil-law concepts.

Thus, the law of " interpenetrating opposites " records the inextricable interdependence of components: the " transformation of quantity to quality " defends a systems-based view of change that translates incremental inputs into alterations of state ; and the " negation of negation " describes the direction given to history because complex systems cannot revert exactly to previous states.

Thus, Egypt was by Ottoman law de jure a province of that empire, but de facto was part of the British Empire.

Thus, this law can be applied to generate a magnetic field and run an electric motor.

Thus, the total of entropy of the room plus the entropy of the environment increases, in agreement with the second law of thermodynamics.

Thus, if there is no alternate rationale for prosecuting some people more harshly for the same crime based on who the victim is, then different defendants are treated unequally under the law, which violates the United States Constitution.

Thus Jahangir was able to deliver justice to people in accordance of their beliefs, and also keep his hold on empire by unified criminal law.

Thus, law has an internal morality that goes beyond the social rules by which valid laws are made.

But this group found it increasingly difficult to prove that they were not labourers because the 1882 act defined excludables as ‘ skilled and unskilled labourers and Chinese employed in mining .’ Thus very few Chinese could enter the country under the 1882 law.

Thus the Syrian Mandate provided that the government should be based on an organic law which should take into account the rights, interests and wishes of all the inhabitants, and that measures should be enacted “ to facilitate the progressive development of Syria and the Lebanon as independent States ”.

Thus, on April 28, 2006, after the unofficial repeal of the French First Employment Contract ( CPE ), the Longjumeau ( Essonne ) conseil des prud ' hommes ( labour law court ) judged the New Employment Contract ( CNE ) contrary to international law, and therefore " illegitimate " and " without any juridical value ".

Thus in the absence of the minimum wage law unskilled workers would be paid approximately the same amount.

Thus the court accepted that a modified doctrine of tenure operated in Australia, and that the law of tenure ( as a product of the common law ) could co-exist with the law of native title ( as a product of customary laws and traditions ), though where there had been a valid grant of fee simple by the Crown the latter title would be extinguished.

Thus prosecutions have been possible of such individuals as Nazi war criminals and officials of the German Democratic Republic responsible for the Berlin Wall, even though their deeds may have been allowed or even ordered by domestic law.