Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.

Military doctrine, command philosophy and the generation of fighting power: genesis and theory

Military doctrine is one of the conceptual components of war. Its raison d’être is that of a force multiplier. It enables a smaller force to take on and defeat a larger force in battle. This article’s departure point is the aphorism of Sir Julian Corbett, who described doctrine as ‘the soul of warfare’. The second dimension to creating a force multiplier effect is forging doctrine with an appropriate command philosophy. The challenge for commanders is how, in unique circumstances, to formulate, disseminate and apply an appropriate doctrine and combine it with a relevant command philosophy. This can only be achieved by policy-makers and senior commanders successfully answering the Clausewitzian question: what kind of conflict are they involved in? Once an answer has been provided, a synthesis of these two factors can be developed and applied. Doctrine has implications for all three levels of war. Tactically, doctrine does two things: first, it helps to create a tempo of operations; second, it develops a transitory quality that will produce operational effect, and ultimately facilitate the pursuit of strategic objectives. Its function is to provide both training and instruction. At the operational level instruction and understanding are critical functions. Third, at the strategic level it provides understanding and direction. Using John Gooch’s six components of doctrine, it will be argued that there is a lacunae in the theory of doctrine as these components can manifest themselves in very different ways at the three levels of war. They can in turn affect the transitory quality of tactical operations. Doctrine is pivotal to success in war. Without doctrine and the appropriate command philosophy military operations cannot be successfully concluded against an active and determined foe.

The zooarchaeology of medieval Christendom: ideology, the treatment of animals and the making of medieval Europe

The formation of Christendom – of Europe – was associated with a standardized worldview expressing dominion over the natural world. While some sections of medieval society, specifically monasteries and the aristocratic class, appear to have developed this paradigm, there is also evidence for heterogeneity in practice and belief. Zooarchaeologists have accumulated vast quantities of data from medieval contexts which has enabled the ecological signatures of specific social groups to be identified, and how these developed from the latter centuries of the first millennium ad. It is possible from this to consider whether trends in animal exploitation can be associated with the Christian world view of dominion, and with the very idea of what it meant to be Christian. This may enable zooarchaeologists to situate the ecological trends of the Middle Ages within the context of Europeanization, and the consolidation of a Christian society.

Support for global climate reorganization during the "Medieval Climate Anomaly"

Widely distributed proxy records indicate that the Medieval Climate Anomaly (MCA; *900–1350 AD) was characterized by coherent shifts in large-scale Northern Hemisphere atmospheric circulation patterns. Although cooler sea surface temperatures in the central and eastern equatorial Pacific can explain some aspects of medieval circulation changes, they are not sufficient to account for other notable features, including widespread aridity through the Eurasian sub-tropics, stronger winter westerlies across the North Atlantic and Western Europe, and shifts in monsoon rainfall patterns across Africa and South Asia. We present results from a full-physics coupled climate model showing that a slight warming of the tropical Indian and western Pacific Oceans relative to the other tropical ocean basins can induce a broad range of the medieval circulation and climate changes indicated by proxy data, including many of those not explained by a cooler tropical Pacific alone. Important aspects of the results resemble those from previous simulations examining the climatic response to the rapid Indian Ocean warming during the late twentieth century, and to results from climate warming simulations—especially in indicating an expansion of the Northern Hemisphere Hadley circulation. Notably, the pattern of tropical Indo-Pacific sea surface temperature (SST) change responsible for producing the proxy-model similarity in our results agrees well with MCA-LIA SST differences obtained in a recent proxy-based climate field reconstruction. Though much remains unclear, our results indicate that the MCA was characterized by an enhanced zonal Indo-Pacific SST gradient with resulting changes in Northern Hemisphere tropical and extra-tropical circulation patterns and hydroclimate regimes, linkages that may explain the coherent regional climate shifts indicated by proxy records from across the planet. The findings provide new perspectives on the nature and possible causes of the MCA—a remarkable, yet incompletely understood episode of Late Holocene climatic change.

Mesolithic to Neolithic and medieval coastal environmental change: intertidal survey at Woolaston, Gloucestershire

At Woolaston on the western shores of the middle Severn Estuary c. 7 km upstream of Chepstow intertidal Holocene sediment exposures have been surveyed and the stratigraphic sequence established by coring and limited excavation. There are two main peats each with a submerged forest. An existing dendrochronological sequence for the Upper Submerged Forest has been extended and the preliminary results of pollen analysis from the peat sequence are summarised. A few flint flakes were found but were not stratified in the mid-Holocene sequence. There is evidence for late Mesolithic / early Neolithic burning episodes which may relate to human activity. Evidence is reported for Medieval activity and the extensive modification of drainage in this period is suggested.