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�����tre 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.

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.