Strike Hard, Strike Sure - Operation Musketeer : British Military Planning during the Suez Crisis, 1956

This study analyses British military planning and actions during the Suez Crisis in 1956. It seeks to find military reasons for the change of concepts during the planning and compares these reasons with the tactical doctrines of the time. The thesis takes extensive advantage of military documents preserved in the National Archives, London. In order to expand the understanding of the exchange of views during the planning process, the private papers of high ranking military officials have also been consulted. French military documents preserved in the Service Historique de la Defence, Paris, have provided an important point of comparison. The Suez Crisis caught the British armed forces in the middle of a transition phase. The main objective of the armed forces was to establish a credible deterrence against the Soviet Union. However, due to overseas commitments the Middle East playing a paramount role because of its economic importance the armed forces were compelled to also prepare for Limited War and the Cold War. The armed forces were not fully prepared to meet this demand. The Middle Eastern garrison was being re-organised after the withdrawal from the Canal Base and the concept for a strategic reserve was unimplemented. The tactical doctrines of the time were based on experiences from the Second World War. As a result, the British view of amphibious operations and the subsequent campaigns emphasised careful planning, mastery of the sea and the air, sufficient superiority in numbers and firepower, centralised command and extensive administrative preparations. The British military had realized that Nasser could nationalise the Suez Canal and prepared an outline plan to meet this contingency. Although the plan was nothing more than a concept, it was accepted as a basis for further planning when the Canal was nationalised at the end of July. This plan was short-lived. The nominated Task Force Commanders shifted the landing site from Port Said to Alexandria because it enabled faster expansion of the bridgehead. In addition, further operations towards Cairo the hub of Nasser s power would be easier to conduct. The operational concept can be described as being traditional and was in accordance with the amphibious warfare doctrine. This plan was completely changed at the beginning of September. Apparently, General Charles Keightley, the Commander-in-Chief, and the Chairman of the Chiefs of Staff Committee developed the idea of prolonged aerial operations. The essence of the concept was to break the Egyptian will to resist by attacking the oil facilities, the transportation system and the armed forces. This victory through air concept would be supported by carefully planned psychological operations. This concept was in accordance with the Royal Air Force doctrine, which promoted a bomber offensive against selected target categories. General Keightley s plan was accepted despite suspicions at every planning level. The Joint Planning Staff and the Task Force Commanders opposed the concept from the beginning to the end because of its unpredictability. There was no information that suggested the bombing would persuade the Egyptians to submit. This problem was worsened by the fact that British intelligence was unable to provide reliable strategic information. The Task Force Commanders, who were responsible for the tactical plans, were not able to change Keightley s mind, but the concept was expanded to include a traditional amphibious assault on Port Said due to their resistance. The bombing campaign was never tested as the Royal Air Force was denied authorisation to destroy the transportation and oil targets. The Chiefs of Staff and General Keightley were too slow to realise that the execution of the plan depended on the determination of the Prime Minister. However, poor health, a lack of American and domestic support and the indecisiveness of the military had ruined Eden s resolve. In the end, a very traditional amphibious assault, which was bound to succeed at the tactical level but fail at the strategic level, was launched against Port Said.

Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

Hard Custom, Hard Dance : Social Organisation, (Un)Differentiation and Notions of Power in a Tabiteuean Community, Southern Kiribati

Hard Custom, Hard Dance: Social Organisation, (Un)Differentiation and Notions of Power in a Tabiteuean Community, Southern Kiribati is an ethnographic study of a village community. This work analyses social organisation on the island of Tabiteuea in the Micronesian state of Kiribati, examining the intertwining of hierarchical and egalitarian traits, meanwhile bringing a new perspective to scholarly discussions of social differentiation by introducing the concept of undifferentiation to describe non-hierarchical social forms and practices. Particular attention is paid to local ideas concerning symbolic power, abstractly understood as the potency for social reproduction, but also examined in one of its forms; authority understood as the right to speak. The workings of social differentiation and undifferentiation in the village are specifically studied in two contexts connected by local notions of power: the meetinghouse institution (te maneaba) and traditional dancing (te mwaie). This dissertation is based on 11 months of anthropological fieldwork in 1999‒2000 in Kiribati and Fiji, with an emphasis on participant observation and the collection of oral tradition (narratives and songs). The questions are approached through three distinct but interrelated topics: (i) A key narrative of the community ‒ the story of an ancestor without descendants ‒ is presented and discussed, along with other narratives. (ii) The Kiribati meetinghouse institution, te maneaba, is considered in terms of oral tradition as well as present-day practices and customs. (iii) Kiribati dancing (te mwaie) is examined through a discussion of competing dance groups, followed by an extended case study of four dance events. In the course of this work the community of close to four hundred inhabitants is depicted as constructed primarily of clans and households, but also of churches, work co-operatives and dance groups, but also as a significant and valued social unit in itself, and a part of the wider island district. In these partly cross-cutting and overlapping social matrices, people are alternatingly organised by the distinct values and logic of differentiation and undifferentiation. At different levels of social integration and in different modes of social and discursive practice, there are heightened moments of differentiation, followed by active undifferentiation. The central notions concerning power and authority to emerge are, firstly, that in order to be valued and utilised, power needs to be controlled. Secondly, power is not allowed to centralize in the hands of one person or group for any long period of time. Thirdly, out of the permanent reach of people, power/authority is always, on the one hand, left outside the factual community and, on the other, vested in community, the social whole. Several forms of differentiation and undifferentiation emerge, but these appear to be systematically related. Social differentiation building on typically Austronesian complementary differences (such as male:female, elder:younger, autochtonous:allotochtonous) is valued, even if eventually restricted, whereas differentiation based on non-complementary differences (such as monetary wealth or level of education) is generally resisted, and/or is subsumed by the complementary distinctions. The concomitant forms of undifferentiation are likewise hierarchically organised. On the level of the society as a whole, undifferentiation means circumscribing and ultimately withholding social hierarchy. Potential hierarchy is both based on a combination of valued complementary differences between social groups and individuals, but also limited by virtue of the undoing of these differences; for example, in the dissolution of seniority (elder-younger) and gender (male-female) into sameness. Like the suspension of hierarchy, undifferentiation as transformation requires the recognition of pre-existing difference and does not mean devaluing the difference. This form of undifferentiation is ultimately encompassed by the first one, as the processes of the differentiation, whether transformed or not, are always halted. Finally, undifferentiation can mean the prevention of non-complementary differences between social groups or individuals. This form of undifferentiation, like the differentiation it works on, takes place on a lower level of societal ideology, as both the differences and their prevention are always encompassed by the complementary differences and their undoing. It is concluded that Southern Kiribati society be seen as a combination of a severely limited and decentralised hierarchy (differentiation) and of a tightly conditional and contextual (intra-category) equality (undifferentiation), and that it is distinctly characterised by an enduring tension between these contradicting social forms and cultural notions. With reference to the local notion of hardness used to characterise custom on this particular island as well as dance in general, it is argued in this work that in this Tabiteuean community some forms of differentiation are valued though strictly delimited or even undone, whereas other forms of differentiation are a perceived as a threat to community, necessitating pre-emptive imposition of undifferentiation. Power, though sought after and displayed - particularly in dancing - must always remain controlled.

A Possible and Necessary Consistency Proof

After Gödel's incompleteness theorems and the collapse of Hilbert's programme Gerhard Gentzen continued the quest for consistency proofs of Peano arithmetic. He considered a finitistic or constructive proof still possible and necessary for the foundations of mathematics. For a proof to be meaningful, the principles relied on should be considered more reliable than the doubtful elements of the theory concerned. He worked out a total of four proofs between 1934 and 1939. This thesis examines the consistency proofs for arithmetic by Gentzen from different angles. The consistency of Heyting arithmetic is shown both in a sequent calculus notation and in natural deduction. The former proof includes a cut elimination theorem for the calculus and a syntactical study of the purely arithmetical part of the system. The latter consistency proof in standard natural deduction has been an open problem since the publication of Gentzen's proofs. The solution to this problem for an intuitionistic calculus is based on a normalization proof by Howard. The proof is performed in the manner of Gentzen, by giving a reduction procedure for derivations of falsity. In contrast to Gentzen's proof, the procedure contains a vector assignment. The reduction reduces the first component of the vector and this component can be interpreted as an ordinal less than epsilon_0, thus ordering the derivations by complexity and proving termination of the process.

The effects of organic environmental toxicants on hard tissue formation in developing tooth : An in vitro study in mice

Dioxins are organic toxicants that are known to impair tooth development, especially dental hard tissue formation. The most toxic dioxin congener is 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). Further, clinical studies suggest that maternal smoking during pregnancy can affect child s tooth development. One of the main components of tobacco smoke is the group of non-halogenated polycyclic aromatic hydrocarbons (PAHs), a representative of which is 7,12-dimethylbenz[a]anthracene (DMBA). Tributyltin (TBT), an organic tin compound, has been shown to impair bone mineralization in experimental animals. In addition to exposure to organic toxicants, a well-established cause for enamel hypomineralization is excess fluoride intake. The principal aim of this thesis project was to examine in vitro if, in addition to dioxins, other organic environmental toxicants, like PAHs and organic tin compounds, have adverse effects on tooth development, specifically on formation and mineralization of the major dental hard tissues, the dentin and the enamel. The second aim was to investigate in vitro if fluoride could intensify the manifestation of the detrimental developmental dental effects elicited by TCDD. The study was conducted by culturing mandibular first and second molar tooth germs of E18 NMRI mouse embryos in a Trowell-type organ culture and exposing them to DMBA, TBT, and sodium fluoride (NaF) and/or TCDD at various concentrations during the secretory and mineralization stages of development. Specific methods used were HE-staining for studying cell and tissue morphology, BrdU-staining for cell proliferation, TUNEL-staining for apoptosis, and QPCR, in situ hybridization and immunohistochemistry for the expressions of selected genes associated with mineralization. This thesis work showed that DMBA, TBT, TCDD and NaF interfere with dentin and enamel formation of embryonic mouse tooth in vitro, and that fluoride can potentiate the harmful effect of TCDD. The results suggested that adverse effects of TBT involve altered expression of genes associated with mineralization, and that DMBA and TBT as well as NaF and TCDD together primarily affect dentin mineralization. Since amelogenesis does not start until mineralization of dentin begins, impaired enamel matrix secretion could be a secondary effect. Dioxins, PAHs and organotins are all liposoluble and can be transferred to the infant by breast-feeding. Since doses are usually very low, developmental toxicity on most of the organs is difficult to indentify clinically. However, tooth may act as an indicator of exposure, since the major dental hard tissues, the dentin and the enamel, are not replaced once they have been formed. Thus, disturbed dental hard tissue formation raises the question of more extensive developmental toxicity.