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 if there is a complete negation of the theory of democratic action it is to be found in socialism.

Thus, together with negation, only one of either the universal or existential quantifier is needed to perform both tasks:

What makes a negative proposition p true is the lack of a falsemaker for it, i. e., the lack of a truthmaker for the negation of p. Thus what makes it true that there are no unicorns is the lack of a truthmaker for the proposition that there are unicorns, i. e., the lack of unicorns.

Thus, the player on move looks for a move that maximizes the negation of the value of the position resulting from the move: this successor position must by definition have been valued by the opponent.

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

Thus, an axiom is an elementary basis for a formal logic system that together with the rules of inference define a deductive system.

Thus Post in his 1936 was also discounting Kurt Gödel's suggestion to Church in 1934 – 5 that the thesis might be expressed as an axiom or set of axioms.

Thus, what the axiom is really saying is that two sets are equal if and only if they have precisely the same members.

Thus, what the axiom schema is really saying is that, given a set A and a predicate P, we can find a subset B of A whose members are precisely the members of A that satisfy P. By the axiom of extensionality this set is unique.

Thus, if one class is " small enough " to be a set, and there is a bijection from that class to a second class, the axiom states that the second class is also a set.

Thus, the essence of the axiom is that every set has a power set.

Thus the essence of the axiom is:

Thus were true prior to the assignment, by the assignment axiom, then would be true subsequent to which.

Thus this axiom guarantees the existence of an infinite tower of inaccessible cardinals ( and may occasionally be referred to as the inaccessible cardinal axiom ).

Thus a subgroup of a group is a subset on which the binary product and the unary operation of inversion satisfy the closure axiom.

Thus, Adam Smith's single axiom, broadly interpreted ... is sufficient to characterize a major portion of the human social and cultural enterprise.

Thus, allowing arbitrary sets X and Y ( rather than just Polish spaces ) would make the axiom of uniformization equivalent to AC.

Thus, central to Zoroastrianism is the emphasis on moral choice, to choose between the responsibility and duty for which one is in the mortal world, or to give up this duty and so facilitate the work of druj.

Thus Euclidean geometry corresponds to the choice of the group E ( 3 ) of distance-preserving transformations of the Euclidean space R < sup > 3 </ sup >, conformal geometry corresponds to enlarging the group to the conformal group, whereas in projective geometry one is interested in the properties invariant under the projective group.

Thus, economics Nobelist Amartya Sen sees the model of people who follow rational choice model as " rational fools.

Thus, sexual selection takes two major forms: intersexual selection ( also known as ' mate choice ' or ' female choice ') in which males compete with each other to be chosen by females ; and intrasexual selection ( also known as ' male – male competition ') in which members of the less limited sex ( typically males ) compete aggressively among themselves for access to the limiting sex.

Thus, ' sexual selection ' typically refers to the process of choice ( the limiting factor, which is typically females ) over members of the opposite sex ( the non-limited factor, typically males ).

Thus, to propagate freedom means to present individuals with the truth and give them a choice to accept or deny it.

Thus it was the preferred choice of that era for a high-speed backbone, but FDDI has since been effectively obsolesced by fast Ethernet which offered the same 100 Mbit / s speeds, but at a much lower cost and, since 1998, by Gigabit Ethernet due to its speed, and even lower cost, and ubiquity.

Thus, if each person votes to get as much cake as possible, choice 4 would be third from the top in everyone's list, and would in any direct choice lose 2 to 1 against an unequal distribution.

Thus the choice of the north as corresponding to up in the northern hemisphere, or of south in that role in the southern, is, prior to world-wide communication, anything but an arbitrary one.

Thus the long and exciting discussion touching the removal of Williams College and the location of a college in some more central town of old Hampshire County at length came to an end, and the contending parties now directed all their energies to building up the institutions of their choice.

Thus the choice among them is determined by what long filenames and Unix semantics they support and what use one wants to make of the disk volume.

Thus, suppose that ( x < sub > 1 </ sub >,..., x < sub > n </ sub >) is a choice of Cartesian coordinates, in terms of which the coordinates of the vector V are

Thus, there is sometimes a choice between imperfect outcomes, i. e. imperfect market outcomes with or without government interventions.

Thus, voters select the party of their choice, rather than any specific candidate.

Thus, a legacy switch system can be easily " converted " to allow wavelength multiplexed transport over a fiber simply by judicious choice of transceiver wavelengths, combined with an inexpensive passive optical multiplexing device.

Thus, some American countries formerly under the Spanish rule have retained the custom of calling it castellano, while others switched to calling it español at some point or the other, with many other different factors influencing the final choice.

Thus, we can interpret Boltzmann's constant as being simply the expression ( in terms of more standard physical units ) of the abstract logarithmic unit that is needed to convert the dimensionless pure-number quantity ln W ( which uses an arbitrary choice of base, namely e ) to the more fundamental pure logarithmic quantity Log ( W ), which implies no particular choice of base, and thus no particular choice of physical unit for measuring entropy.

Thus, a solution does not generally exist for an arbitrary choice of strain components.

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 since a database can be normally changed only by transactions, all the database's states are consistent.

Thus since a database can be normally changed only by transactions, all the database's states are consistent.

Thus the integration of the princely states can be viewed as one of the positive aspects of his legacy.

Thus the nomads who conquered states in the Middle East were soon forced to adapt to the local societies.

Thus, he cautiously states: " But knowing the sure number declared by Scripture, that is six hundred sixty and six, let them await, in the first place, the division of the kingdom into ten ; then, in the next place, when these kings are reigning, and beginning to set their affairs in order, and advance their kingdom, them learn to acknowledge that he who shall come claiming the kingdom for himself, and shall terrify those men of whom we have been speaking, have a name containing the aforesaid number, is truly the abomination of desolation.

Thus, the rate of transitions between two stationary states is enhanced beyond that due to spontaneous emission.

Thus, this angular arrangement sees a decrease in the net positional entropy of the approaching cylinder ( there are fewer states available to it ).

Thus if Portugal specialized in wine and England in cloth, both states would end up better off if they traded.

Thus token identity holds between colours and physical / brain states at best.

Thus, according to Wittgenstein, mental states are intimately connected to a subject's environment, especially their linguistic environment, and conceivability or imaginability arguments that claim otherwise are misguided.

Thus, the rate of transitions between two stationary states is enhanced beyond that due to spontaneous emission.

Thus, it seems that we can know, in a relatively unproblematic way, that other people are in certain mental states.

" Thus, no individual state may have its representation in the Senate adjusted without its consent unless all other states have an identical change.

" Thus, state laws purporting to nullify federal statutes or to exempt states and their citizens from federal statutes have only symbolic impact.

Thus any state which adopts the Berne Convention is penalised if it then decides to renounce it and use the UCC protections instead, since its copyrights might no longer exist in Berne Convention states.

Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.

Thus, Zurich became the fifth member of the Confederacy, which was at that time a loose confederation of de facto independent states.

Thus Lucretius states that once the vessel ( the body ) shatters ( dies ) its contents ( mind and spirit ) can no longer exist.

Thus, for example, the Great Seal of the United States, among other uses, appears on the reverse of the one-dollar bill ; and several of the seals of the U. S. states appear on their respective state flags.

Thus it concerns the interaction between the electromagnetic ( optical ) and the electrical ( electronic ) states of materials.

Thus, the current state of the law is that, while the federal government may not restrict use of peyote in ceremony, individual states do have a right to restrict its use.

Thus, despite the population of France being greater than the population of all of the German states that participated in the war, the Germans mobilized more soldiers for battle.