A number of arguments, including (Whittle 2004), (Field 2008), (Shapiro 2012), and (Beall & Murzi 2012), have been put forward for the claim that logical validity is plagued by a paradox (or paradoxes) similar to the more well-known paradoxes that afflict notions such as truth, knowledge, or set. These claims are incorrect. As I will show here, there is no paradox of logical validity. In additi...

Development and assessment of safety critical software is governed by many standards. Given the growing dependence on software in a range of industries, one might expect to see these standards reflecting a growing maturity in processes for development and assessment of safety critical software, and an international consensus on best practise. In reality, whilst there are commonalities in the st...

Much work has gone into the construction of quasicontinuum energies that reduce the coupling error along the interface between atomistic and continuum regions. The largest consistency errors are typically pointwise O( 1 ε ) errors, and in some cases this has been reduced to pointwise O(1) errors. In this paper we show that one cannot create a coupling method using a finite-range coupling interf...

Sepsis is a systemic inflammatory response syndrome in the presence of suspected or proven infection, and it may progress to or encompass organ failure (severe sepsis) and hypotension (septic shock). Clinicians possess an arsenal of supportive measures to combat severe sepsis and septic shock, and some success, albeit controversial, has been achieved by using low doses of corticosteroids or rec...

We prove that there is no degree invariant solution to Post’s problem that always gives an intermediate degree. In fact, assuming definable determinacy, if W is any definable operator on degrees such that a <W (a) < a′ on a cone then W is low2 or high2 on a cone of degrees, i.e., there is a degree c such that W (a)′′ = a′′ for every a ≥ c or W (a)′′ = a′′′ for every a ≥ c. A striking phenomenon...