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, a nonlinear system is one whose behavior can't be expressed as a sum of the behaviors of its parts ( or of their multiples ).

Thus, public property can't be used to establish a waqf, the property must be the founder's own.

Thus, one " can't grasp anything more easily or plainly than mind.

When I want to think of a chiliagon, I understand that it is a figure with a thousand sides as well as I understand that a triangle is a figure with three, but I can't imagine its sides or " look " at them as though they were present (...) Thus I observe that a special effort of mind is necessary to the act of imagination, which is not required to conceiving or understanding ( ad intelligendum ); and this special exertion of mind clearly shows the difference between imagination and pure intellection ( imaginatio et intellectio pura ).

Thus, this gives a competitive edge against a batter who can't hit well off the movement of a left-hander's curveball, and they may often face a left-hander in a late inning situation.

Thus, a Markov network can represent certain dependencies that a Bayesian network cannot ( such as cyclic dependencies ); on the other hand, it can't represent certain dependencies that a Bayesian network can ( such as induced dependencies ).

Thus, Dominic formed an important aspect of his philosophy of life, which was, in his words, " I can't do big things but I want everything to be for the glory of God.

Thus, it is doubtful that one can define telic expressions by means of properties of the events or states that they refer to ( a very similar problem arises with the notion that mass nouns refer to things that can't be counted ).

Thus, by doing this, a player can stop a tank from harassing him, while creating a " dead zone " that he can't move in without getting attacked.

Thus, despite the obvious analogy to planets revolving around the Sun, electrons cannot be described as solid particles.

Thus, small minority parties cannot easily enter the Bundestag and prevent the formation of stable majority governments as they could under the Weimar constitution.

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, for example, controversies in physics are limited to subject-areas where experiments cannot be carried out yet, whereas Benford's Law implies that controversy is inherent to politics, where communities must frequently decide on courses of action based on insufficient information.

Thus perceptions must already come parcelled into distinct " bundles " before they can be associated according to the relations of similarity and causality: in other words, the mind must already possess a unity that cannot be generated, or constituted, by these relations alone.

Thus we cannot define being, unity and similar concepts.

Thus, encountering something which evokes the implicit associations of an experience or sensation that cannot be remembered may lead to déjà vu.

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, the meaning of sentences containing the word " good " cannot be explained entirely in terms of sentences not containing the word " good.

Thus the function cannot access memory out-of-bounds.

Thus cannot be too little, less than some constant.

Thus, as a simple instance posed by Hume, we cannot know with certainty by inductive reasoning that the sun will continue to rise in the East, but instead come to expect it to do so because it has repeatedly done so in the past.

Thus, higher hormone concentration alone cannot trigger the negative feedback mechanism.

Thus, one cannot expect to find a clear origin.

Thus the 32-bit integer and 32-bit floating-point objects can simply use the value directly ; whereas the 64-bit integer and 64-bit floating-point cannot use this method.

Thus, any real object cannot remain the same, also because of movement of its physical parts ( even much bigger than molecules ).

Thus, the main lesson from the argument is not that one risks big losses, but merely that one cannot always win.

If a statement P is provable, then it is certainly impossible to prove that there is no proof of P. But even if it can be shown that no disproof of P is possible, we cannot conclude from this absence that there is a proof of P. Thus P is a stronger statement than not-not-P.

Thus, the eventually attainable perfection and complexity of manufactured products, while they can be calculated in theory, cannot be predicted with confidence.

Thus, these cells cannot survive for long ' as they cannot exchange sufficient material to maintain active metabolism.

Thus, the statement " there are no contradictions in the Principia system " cannot be proven in the Principia system unless there are contradictions in the system ( in which case it can be proven both true and false ).

Thus, people cannot see or otherwise come into sensory contact with universals, but in order to conceive of universals, one must be able to conceive of these abstract forms.

Thus over-provisioning cannot be blindly assumed on the Internet.

Thus ' b ' and'd ' can rhyme ( both being ' voiced plosives '), as can ' bh ' and ' l ' ( which are both ' voiced continuants ') but ' l ', a ' voiced continuant ', cannot rhyme with ' ph ', a ' voiceless continuant '.

Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus the fictional detective is much more than a simple businessman.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus in both types attention is focused on the community itself, and its phenomenological life.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

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

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

Thus there is a clearer division of authority, administrative and legislative.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus technical efficiency is achieved at the expense of actual experience.

Thus, there is an added incentive to stay on the job.

Thus, the Span of its ossification was shortened and the center's ability to `` catch up '' in ossification is demonstrated.

Thus T is not diagonalizable.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

Thus we do not score the number of bull's-eyes, and the random variable is not the number of successes.

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 Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.