The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized $J$-$J'$ model interpolating between both systems by varying $J'/J$ from $J'/J=0$ (bounce limit) to $J'/J=1$ (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the "pure" bounce ($J'/J=0$) and maple-leaf ($J'/J=1$) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range $0 \le J'/J \lesssim J'_c/J$ and that the magnetic order parameter varies only weakly with $J'/J$. At $J'_c \approx 1.45 J$ a direct first-order transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place. The orthogonal-dimer state is the exact ground state in this large-$J'$ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We a find a 1/3 magnetization plateau for $J'/J \gtrsim 1.07$ and another one at 2/3 of saturation emerging only at large $J'/J \gtrsim 3$.Comment: 9 pages, 10 figure

The open future, bivalence and assertion

It is highly intuitive that the future is open and the past is closed—whereas it is unsettled whether there will be a fourth world war, it is settled that there was a first. Recently, it has become increasingly popular to claim that the intuitive openness of the future implies that contingent statements about the future, such as ‘there will be a sea battle tomorrow,’ are non-bivalent (neither true nor false). In this paper, we argue that the non-bivalence of future contingents is at odds with our pre-theoretic intuitions about the openness of the future. These are revealed by our pragmatic judgments concerning the correctness and incorrectness of assertions of future contingents. We argue that the pragmatic data together with a plausible account of assertion shows that in many cases we take future contingents to be true (or to be false), though we take the future to be open in relevant respects. It follows that appeals to intuition to support the non-bivalence of future contingents is untenable. Intuition favours bivalence

Third-person knowledge ascriptions: a crucial experiment for contextualism

In the past few years there has been a turn towards evaluating the empirical foundation of epistemic contextualism using formal (rather than armchair) experimental methods. By-and-large, the results of these experiments have not supported the original motivation for epistemic contextualism. That is partly because experiments have only uncovered effects of changing context on knowledge ascriptions in limited experimental circumstances (when contrast is present, for example), and partly because existing experiments have not been designed to distinguish between contextualism and one of its main competing theories, subject-sensitive invariantism. In this paper, we discuss how a particular, “third-person”, experimental design is needed to provide evidence that would support contextualism over subject-sensitive invariantism. In spite of the theoretical significance of third-person knowledge ascriptions for debates surrounding contextualism, no formal experiments evaluating such ascriptions that assess contextualist claims have previously been conducted. In this paper, we conduct an experiment specifically designed to examine that central gap in contextualism’s empirical foundation. The results of our experiment provide crucial support for epistemic contextualism over subject-sensitive invariantism

On the Epistemology of the Precautionary Principle: Reply to Steglich-Petersen

In a recent paper in this journal, we proposed two novel puzzles associated with the precautionary principle. Both are puzzles that materialise, we argue, once we investigate the principle through an epistemological lens, and each constitutes a philosophical hurdle for any proponent of a plausible version of the precautionary principle. Steglich-Petersen claims, also in this journal, that he has resolved our puzzles. In this short note, we explain why we remain skeptica