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.

Exposure to fine particulate matter in ten night clubs in Athens Greece: studying the effect of ventilation, cigarette smoking and resuspension

The aim of the present work is to study the occupants' exposure to fine particulate concentrations in ten nightclubs (NCs) in Athens, Greece. Measurements of PM1 and PM 2.5 were made in the outdoor and indoor environment of each NC. The average indoorPM1 andPM 2.5 concentrations were found to be 181.77 μgm−3 and 454.08 μg m−3 respectively, while the corresponding outdoor values were 11.04 μg m−3 and 32.19 μg m−3. Ventilation and resuspension rates were estimated through consecutive numerical experiments with an indoor air quality model and were found to be remarkably lower than the minimum values recommended by national standards. The relative effects of the ventilation and smoking on the occupants' exposures were examined using multiple regression techniques. Itwas found that given the low ventilation rates, the effect of smoking as well as the occupancy is of the highest importance. Numerical evaluations showed that if the ventilation rates were at the minimum values set by national standards, then the indoor exposures would be reduced at the 70% of the present exposure values.

Prevalence of Leptospira species among farmed and domestic animals in Greece

A total of 1527 serum samples from pigs, goats, sheep, cattle and dogs in Greece were examined by the microscopic agglutination test and 11.8 per cent of them had antibodies against one or more Leptospira serovars at titres of 1/100 or more. The predominant serovar affecting farm animal species was Bratislava, and Copenhageni was common among dogs and the second most important serovar when all animals were considered together. Another prevalent serovar was Australis, but antibodies to Pomona were detected only in goats and cattle.