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.

Geoarchaeology and taphonomy of plant remains in early urban environments in the Ancient Near East

A number of recent articles emphasize the fundamental importance of taphonomy and formation processes to interpretation of plant remains assemblages, as well as the value of interdisciplinary approaches to studies of environmental change and ecological and social practices. This paper examines ways in which micromorphology can contribute to integrating geoarchaeology and archaeobotany in analysis of the taphonomy and context of plant remains and ecological and social practices. Micromorphology enables simultaneous in situ study of diverse plant materials and thereby traces of a range of depositional pathways and histories. In addition to charred plant remains, also often preserved in semi-arid environments are plant impressions, phytoliths and calcitic ashes. These diverse plant remains are often routinely separated and extracted from their depositional context or lost using other analytical techniques, thereby losing crucial evidence on taphonomy, formation processes and contextual associations, which are fundamental to all subsequent interpretations. Although micromorphological samples are small in comparison to bulk flotation samples of charred plant remains, their size is similar to phytolith and pollen samples. In this paper, key taphonomic issues are examined in the study of: fuel; animal dung, animal management and penning; building materials; and specific activities, including food storage and preparation and ritual, using selected case-studies from early urban settlements in the Ancient Near East. Microarchaeological residues and experimental archaeology are also briefly examined.

The domestication of water: water management in the ancient world and its prehistoric origins in the Jordan Valley

The ancient civilizations were dependent upon sophisticated systems of water management. The hydraulic engineering works found in ancient Angkor (ninth to thirteenth century AD), the Aztec city of Tenochtitlan (thirteenth to fifteenth century AD), Byzantine Constantinople (fourth to sixth century AD) and Nabatean Petra (sixth century BC to AD 106) are particularly striking because each of these is in localities of the world that are once again facing a water crisis. Without water management, such ancient cities would never have emerged, nor would the urban communities and towns from which they developed. Indeed, the ‘domestication’ of water marked a key turning point in the cultural trajectory of each region of the world where state societies developed. This is illustrated by examining the prehistory of water management in the Jordan Valley, identifying the later Neolithic (approx. 8300–6500 years ago) as a key period when significant investment in water management occurred, laying the foundation for the development of the first urban communities of the Early Bronze Age.

'Youth language' in ancient Rome

This article presents some of the findings of a UROP project, collecting the evidence for youth language phenomena in the ancient world (with a focus on the Roman Empire).

On collective intentions: collective action in economics and philosophy

Philosophers and economists write about collective action from distinct but related points of view. This paper aims to bridge these perspectives. Economists have been concerned with rationality in a strategic context. There, problems posed by “coordination games” seem to point to a form of rational action, “team thinking,” which is not individualistic. Philosophers’ analyses of collective intention, however, sometimes reduce collective action to a set of individually instrumental actions. They do not, therefore, capture the first person plural perspective characteristic of team thinking. Other analyses, problematically, depict intentions ranging over others’ actions. I offer an analysis of collective intention which avoids these problems. A collective intention aims only at causing an individual action, but its propositional content stipulates its mirroring in other minds.