We offer a formal account of the English past tenses. We see the perfect as having reference time at speech time and the preterite as having reference time at event time. We formalize four constraints on reference time, which we bundle together under the term ‘perspective’. Once these constraints are satisfied at the different reference times of the perfect and preterite, the contrasting functions of these tenses are explained. Thus we can account formally for the ‘definiteness effect’ and the ‘lifetime (...) effect’ of the perfect, for the fact that the perfect seems to ‘explain’ something about the present, and that the perfect cannot presuppose a past time point. We explain why perfect and preterite can sometimes be interchangeable, and we offer a solution to the ’present perfect puzzle’. We explain the unacceptability of notorious examples of the perfect such as * Gutenberg has discovered the art of printing . We give greater definition to the familiar notions of ‘current relevance’ and ‘extended now’. (shrink)

Recently, a class of $\mathcal{P}\mathcal{T}$ -invariant scalar quantum field theories described by the non-Hermitian Lagrangian $\mathcal{L}$ = $ \frac{1}{2} $ (∂ϕ) 2 +gϕ 2 (iϕ)ε was studied. It was found that there are two regions of ε. For ε<0 the $\mathcal{P}\mathcal{T}$ -invariance of the Lagrangian is spontaneously broken, and as a consequence, all but the lowest-lying energy levels are complex. For ε≥0 the $\mathcal{P}\mathcal{T}$ -invariance of the Lagrangian is unbroken, and the entire energy spectrum is real and positive. The subtle (...) transition at ε=0 is not well understood. In this paper we initiate an investigation of this transition by carrying out a detailed numerical study of the effective potential V eff (ϕc) in zero-dimensional spacetime. Although this numerical work reveals some differences between the ε<0 and the ε>0 regimes, we cannot yet see convincing evidence of the transition at ε=0 in the structure of the effective potential for $\mathcal{P}\mathcal{T}$ -symmetric quantum field theories. (shrink)