Interpolation in 16-Valued Trilattice Logics

In a recent paper we have defined an analytic tableau calculus \({{\mathbf {\mathsf{{PL}}}}}_{\mathbf {16}}\) for a functionally complete extension of Shramko and Wansing’s logic based on the trilattice \({SIXTEEN}_3\). This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic—such as the relations Open image in new window , Open image in new window , and Open image in new window that each correspond to a lattice order in \({SIXTEEN}_3\); and Open image in new window , the intersection of Open image in new window and Open image in new window . It turns out that our method of characterising these semantic relations—as intersections of auxiliary relations that can be captured with the help of a single calculus—lends itself well to proving interpolation. All entailment relations just mentioned have the interpolation property, not only when they are defined with respect to a functionally complete language, but also in a range of cases where less expressive languages are considered. For example, we will show that Open image in new window , when restricted to \(\mathcal {L}_{tf}\), the language originally considered by Shramko and Wansing, enjoys interpolation. This answers a question that was recently posed by M. Takano.     

形而上学及其当代命运——A.F.科赫教授访谈

A.F.科赫教授因其对康德与德国观念论(尤其是黑格尔)的深入研究而著名,此外他非常熟悉分析哲学与实用主义的当代成果。这使他能够以一种不同于其前辈诠释者的方式来理解德国哲学,并以一种完全不同于布兰顿和麦克道威尔这两位当代著名的分析哲学家的方式对大西洋两岸的两种不同的哲学传统进行让人瞩目的融合。从科赫教授身上我们可以看到,一个在欧陆哲学传统中成长起来的哲学家如何吸收和消化分析哲学的成果并尝试建立起一种新的思想方式。     

Ernest Gellner's Words and Things: A Case Study of Empirical Philosophy

This article considers how Ernest Gellner used sociology and anthropology to attack ordinary language philosophy in Words and Things. It argues that this attack can be seen as a part of the movement to make philosophy more empirical or “naturalized,” something that has not been generally noted. It also discusses what general lessons to draw from Words and Things regarding how empirical knowledge should be used in philosophy. Among other things, the article argues that one important lesson is that empirical philosophers should make more use of “soft” social sciences, such as sociology and anthropology, and not focus exclusively on “harder” disciplines, such as physics and experimental psychology. Another upshot of the discussion is that philosophers should draw on empirical knowledge not only when they solve problems but also when they formulate them.     

The impact of concurrent visual feedback on coding of on-line and pre-planned movement sequences

The purpose of this study was to determine the extent to which participants could effectively switch from on-line (OL) to pre-planned (PP) control (or vice versa) depending on previous practice conditions and whether concurrent visual feedback was available during transfer testing. The task was to reproduce a 2000 ms spatial–temporal pattern of a sequence of elbow flexions and extensions. Participants were randomly assigned to one of two practice conditions termed OL or PP. In the OL condition the criterion waveform and the cursor were provided during movement production while this information was withheld during movement production for the PP condition. A retention test and two effector transfer tests were administered to half of the participants in each acquisition conditions under OL conditions and the other half under PP conditions. The mirror effector transfer test required the same pattern of muscle activation and limb joint angles as required during acquisition. The non-mirror transfer test required movements to the same visual–spatial locations as experienced during acquisition. The results indicated that when visual information was available during the transfer tests performers could switch from PP to OL. When visual information was withdrawn, they shifted from the OL to the PP-control mode. This finding suggests that performers adopt a mode of control consistent with the feedback conditions provided during testing.