Article history: Received 1 September 2013 Available online xxxx

IN HER brief portrait of Mrs. Catherine Gladstone in 1956, Mrs. Georgina Battiscombe wrote that Mrs. Gladstone's efforts 'to be of some use in the [Crimean] war troubles' brought her into 'a most unfortunate collision' with Florence Nightingale when, under the influence of Mrs. Elizabeth Herbert, Mrs. Gladstone 'threw herself heart and soul ... into the good work of providing nurses for the mil...

In work culminating in Know How (2009), Jason Stanley argues, against Gilbert Ryle, that knowledge-how is a species of knowledge-that. In How Propaganda Works (2015), Stanley portrays this work as undermining a “flawed ideology” supporting elitist valuations of intellectual work and workers. However, the link between Stanley’s two philosophical projects is weak. Ryle’s distinction between knowl...

In this paper, we study the Stanley depth for the partially ordered set (poset) of nonempty submultisets of a multiset. We find the Stanley depth explicitly for any multiset with at most five distinct elements and provide an upper bound for the general case. On the other hand, the elements of a product of chains corresponds to the submultisets of a multiset. We prove that the Stanley depth of t...

Let K be a field, R = K[X1, . . . ,Xn] be the polynomial ring and J ( I two monomial ideals in R. In this paper we show that sdepth I/J− depth I/J = sdepth I /J p − depth I /J , where sdepth I/J denotes the Stanley depth and I p denotes the polarization. This solves a conjecture by Herzog [Her13] and reduces the famous Stanley conjecture (for modules of the form I/J) to the squarefree case. As ...

Let P be a graded poset with 0 and 1 and rank at least 3. Assume that every rank 3 interval is a distributive lattice and that, for every interval of rank at least 4, the interval minus its endpoints is connected. It is shown that P is a distributive lattice, thus resolving an issue raised by Stanley. Similar theorems are proven for semimodular, modular, and complemented modular lattices. As a ...