(" the truth-values of our mathematical assertions depend on facts involving platonic entities that reside in a realm outside of space-time ") Whilst our knowledge of concrete, physical objects is based on our ability to perceive them, and therefore to causally interact with them, there is no parallel account of how mathematicians come to have knowledge of abstract objects.

Whilst the magnification of both the field ion and atom probe microscopes is extremely high, the exact magnification is dependant upon conditions specific to the examined specimen, so unlike for conventional electron microscopes, there is often little direct control on magnification, and furthermore, obtained images may have strongly variable magnifications due to fluctuations in the shape of the electric field at the surface.

Whilst there, the Greek army surprised and outmaneuvered Artaphernes, marching to Sardis and burning the lower city.

Whilst there, the Queen met with Bernard of Clairvaux, demanding that he have the excommunication of Petronilla and Raoul lifted through his influence on the Pope, in exchange for which King Louis would make concessions in Champagne, and recognise Pierre de la Chatre as archbishop of Bourges.

Whilst human geography is interdisciplinary, there are a number of journals with a human geography focus.

Whilst there, he staged regular Merz recitals, including a performance of Silence, his first poem in English, but was apparently seen as a somewhat pathetic irrelevant figure by other artists at the camp.

Whilst prices have reduced and availability has increased considerably since the introduction of competition, there is little sign of TPSA's market share being seriously reduced.

Whilst Anglican priests who are members of religious orders must remain celibate ( although there are exceptions, such as priests in the Anglican Order of Cistercians ), the secular clergy – ( bishops, priests, and deacons who are not members of religious orders ) – are permitted to marry before or after ordination.

Whilst on the surface the new Potsdamer Platz appears so far to have lived up to its expectations as a futuristic centre of commerce at the heart of Europe's youngest capital city, there has been much debate as to just how successful it really is.

Whilst the action of rowing and equipment used remains fairly consistent throughout the world, there are many different types of competition.

Whilst there is little evidence to invalidate the letter as a whole, both the recipient ( s ) of the letter and whether such a letter actually nominates Barbastro as the first ' crusade ' are still a matter of dispute.

Bahā ' ad-Dīn writes, " Whilst we were there they brought two Franks to the Sultan ( Saladin ) who had been made prisoners by the advance guard.

Whilst the terms spirituality and religion both relate to a search for an Absolute or God, and thus have much overlap, there are also characteristic differences in their usage.

Also in S6: E5 Whilst the boys are watching the TV there are many cans of soda with the name " ZOOP " on them.

Whilst the styles were similar, there are some notable differences between both Rococo and Baroque architecture, one of them being symmetry, since Rococo emphasised the asymmetry of forms, whilst Baroque was the opposite.

(" the truth-values of our mathematical assertions depend on facts involving platonic entities that reside in a realm outside of space-time ") Whilst our knowledge of concrete, physical objects is based on our ability to perceive them, and therefore to causally interact with them, there is no parallel account of how mathematicians come to have knowledge of abstract objects.

Whilst there his task is a simple assignment to investigate the disappearance of Commander John Strangways, the head of MI6 Station J in Kingston, Jamaica, and his secretary.

Whilst anchored in Cumberland Bay, Robinson Crusoe Island, the Dresden was trapped and forced to scuttle after fighting a battle there with the British.

Whilst there, he met the American composers George Gershwin and Irving Berlin and brought Dédé to Broadway in 1922.

Whilst this elm has little innate resistance to Dutch elm disease, it is not favoured by the vector bark beetles and thus only becomes colonized and infected when there are no other choices, a rare situation in western Europe.

Whilst there, Telemachus is again treated as an honored guest as Menelaus and Helen tell complementary, yet contradictory stories of his father's exploits at Troy.

Whilst working at the Institute, Childe took up residence at Lawn Road Flats near to Hampstead, an apartment block perhaps recommended to him by the popular crime fiction author Agatha Christie ( the wife of his colleague Max Mallowan ), who had lived there during the Second World War.

Whilst the idea that there is some objective sense in which time is flowing can be denied, the fact that conscious beings feel as though it is in some sense flowing cannot.

" Whilst there, Lumley was hailed ' Daughter of Nepal ' by the crowds of fans at the airport.

Whilst Anah has thus retained its name for forty-two centuries the site is variously described.

Whilst the uncertainty in the atomic mass computed by time-of-flight methods in atom probe is sufficiently small to allow for detection of individual isotopes within a material this uncertainty may still, in some cases, confound definitive identification of atomic species.

Whilst members of the Independent Catholic movement take seriously the issue of valid orders, it is highly significant that the relevant Vatican Congregations tend not to respond to petitions from Independent Catholic bishops and clergy who seek to be received into communion with the Holy See, hoping to continue in some sacramental role.

Whilst the population remains small, the impact of transfers will be greater, it is for that reason that the establishment of a " metapopulation management plan " occurs concurrently with conservation initiatives to enhance in-situ population growth and why this initiative is both urgent and fundamental to the future survival of mountain bongo in the wild.

Whilst distractions like background noise, poor lighting or an environment which is too hot or cold can all affect people's morale and concentration, which in turn interfere with effective communication.

Whilst the stories were shocking in their time, this affectionate portrayal of a forthright and self-assured French girl who blossoms into a charismatic adult is nowadays more likely to be regarded as chastely sensual.

Whilst Laura Mulvey's paper has a particular place in the feminist film theory, it is also important to note that her ideas regarding ways of watching the cinema ( from the voyeuristic element to the feelings of identification ) have been very important in terms of defining spectatorship from the psychoanalytical view point.

Whilst a few social scientists who draw inspiration from ' organic ' views of society have embraced Gaia philosophy as a way to explain the human-nature interconnections, most professional social scientists are more involved in reflecting upon the way Gaia philosophy is used and engaged with within sub-sections of society.

Whilst the terms are often used interchangeably, branding is more strictly related to the identifying mark or trade name for a product or service, whereas corporate identity can have a broader meaning relating to the structure and ethos of a company, as well as to the company's external image.

Whilst GATT was a set of rules agreed upon by nations, the WTO is an institutional body.

Whilst depictions of the deity vary, he is always shown with either horns or antlers upon his head, often depicted as being theriocephalic, in this way emphasizing " the union of the divine and the animal ", the latter of which includes humanity.

Whilst the Horned God is the most common depiction of masculine divinity in Wicca, he is not the only representation.

Whilst municipal law is hierarchical or vertical in its structure ( meaning that a legislature enacts binding legislation ), international law is horizontal in nature.

Whilst agreeing with ( 2 ) Searle argues that ( 1 ) is false and points out that ( 3 ) does not follow from ( 1 ) and ( 2 ).

* Whilst Alberti's treatises on painting and architecture have been hailed as the founding texts of a new form of art, breaking from the gothic past, it is impossible to know the extent of their practical impact within his lifetime.

Whilst this theory is today widely disputed and discredited by historians like Norman Cohn, Keith Thomas and Ronald Hutton, it has had a significant effect in the origins of Neopagan religions, primarily Wicca, a faith she supported.

Whilst he was thus deeply engaged at a tavern, he was called on by a grenadier, who desired his immediate attendance on his colonel ; but no entreaties could prevail on the disciple of Aesculapius to postpone his sacrifice to Bacchus.

Whilst providing no extra protection against wideband thermal noise, the frequency-hopping approach does reduce the degradation caused by narrowband interference sources.

Whilst remaining de jure UVF leader after he was jailed for murder, he no longer acted as the Chief of Staff

Whilst there are no rail services in Downpatrick, Ulsterbus provides bus services to and from the Downpatrick Bus Station.

Whilst he made no commercial recordings with the orchestra, he and the BSO toured the United States, including their debut at Carnegie Hall in April 1997.

Whilst the roads are no longer used in the reserve, pieces of them line most of the length of the pits.

Whilst historians such as Yitzhak Baer state, " the conversos and Jews were one people ", Kamen claims, " Yet if the conversos were hated by the Christians, the Jews liked them no better.

Whilst visiting Belvoir castle in the 1840s Anna Maria Russell, Duchess of Bedford found that the normal time for dinner was between 7: 00 and 8: 30 p. m. An extra meal called luncheon had been created to fill the midday gap between breakfast and dinner, but as this new meal was very light, the long afternoon with no refreshment at all left people feeling hungry.

Whilst everyone else in the programme is practical and shows no emotion or sentimentality, Granville is quite the opposite and throughout the series often reflects on life passing him by.

Whilst during this supposed séance Prodi thought the word Gradoli referred to a town on the outskirts of Rome, it probably referred to the Roman address of a Red Brigades safe house, located at no.

Whilst the British Army has the capability there is no standing UK Corps organisation, forces being allocated through a number of multi-partite arrangements to the North Atlantic Treaty Organisation ( NATO ) and European commitments, providing much of the headquarters capability and framework for the multinational Allied Rapid Reaction Corps.

Whilst the album's modest initial pressing ( which included a large batch of warped editions ) sold out, it did not enter the album charts at that time, and no singles were lifted from it.

Whilst there are no universities in Farnborough, Farnborough College of Technology provides degree-level courses, accredited by the University of Surrey.

Whilst the reduction of the peacetime strength of the German army from 780, 000 ( 1913 ) to 100, 000 actually enhanced the quality of the Reichsheer ( only the best would be permitted to join the army ) the changing face of warfare meant that the smaller army was largely helpless without mechanised and aerial support, no matter how much effort was put into modernising infantry tactics.

Whilst customers have actively dealt with a business within a particular recent period that depends from the product sold, not-customers are either past customers who are no longer customers or potential customers who choose to do business with the competition, and non-customers are people who are active in a different market segment entirely.

Whilst all seems fair at first, it is quickly discovered that the three menaces had no intent on fair play when it comes to treasure and it is revealed that Roger had in fact tied Danny's catapult to a piece of string thus yanking it away at a pinnacle moment.

Whilst Banknotes issued by the Scottish banks are legal currency, that is approved by the UK Parliament, no banknotes issued by Scottish banks, Northern Ireland banks nor the Bank of England are legal tender in Scotland.

Whilst Hoon and Byers were both banned from the House of Commons for five and two years respectively, no further action was taken against Hewitt for her part in the " Cash for Access " affair.

Whilst the former in which he appears as the Bodhisattva has no relation to his tales from the Hindu works, his role in the latter one has parallels in an important event in the Mahabharata.

Whilst there is no statistical evidence that having a commemorative plaque increases the value of a property, a Daily Mail article pointed out that it helps to make a property stand out from others, especially if there has been some publicity around it.

Whilst there may be no other accounts of the battle apart from Tacitus's account this is not unusual given the scanty nature of sources in general for this period of history.