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.

Inertia in Japanese organizations: knowledge management routines and failure to innovate

This paper argues that features of Japanese organizations, previously held to be the foundations of innovation, change and flexibility, can equally be significant barriers to change, innovation and adaptation in turbulent economic environments. This paper draws on two in-depth case studies of Japanese organizations. It shows how, in both cases, these firms displayed specific weaknesses in the ways in which they integrate and bundle knowledge, in particular around their research and development (R&D) functions. Despite the adoption of strategies of technological innovation and internationalization, the data suggest that the pursuit of both strategies is beset by barriers of inertia. Embedded internal network connections and knowledge-sharing routines between central R&D and other divisions are inappropriate for the revised strategy. Existing external connections, with preferred suppliers and customers within keiretsu structures, and close relationships with existing R&D partners retard these firms' strategic flexibility. With a limited variety of latent routines, knowledge, capabilities and agency to draw on when needed, these firms have limited organizational responsiveness and high levels of path-dependency.

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.