On a Spector ultrapower of the Solovay model

We prove that a Spector--like ultrapower extension \gN of a countable Solovay model \gM (where all sets of reals are Lebesgue measurable) is equal to the set of all sets constructible from reals in a generic extension \gM[\al] where \al is a random real over \gM. The proof involves an almost everywhere uniformization theorem in the Solovay model

Formal foundations for semantic theories of nominalisation

This paper develops the formal foundations of semantic theories dealing with various kinds of nominalisations. It introduces a combination of an event-calculus with a type-free theory which allows a compositional description to be given of such phenomena like Vendler's distinction between perfect and imperfect nominals, iteration of gerunds and Cresswell's notorious non-urrival of'the train examples. Moreover, the approach argued for in this paper allows a semantic explanation to be given for a wide range of grammatical observations such as the behaviour of certain tpes of nominals with respect to their verbal contexts or the distribution of negation in nominals

The logic and topology of Kant's temporal continuum

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory of rest and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises

Blended Support of Undergraduate Interdisciplinary Research

This paper discusses blended support for undergraduate students to perform interdisciplinary research in teams. Interdisciplinary research is a complex process that consists of multiple steps and requires collaboration with people from different backgrounds. This paper presents research done at Liberal Arts and Sciences, Utrecht University (LAS), where as part of the core curriculum, students learn to do interdisciplinary research. Considering the complex process of doing interdisciplinary research, it is important that students are guided in this process. Blended support that provides technology-mediated guidance while at the same time encouraging face-to-face meetings would be of use to help students become more independent interdisciplinary researchers. This paper explores preferences in blended support, based on a survey and interviews with second and third year students and with undergraduate research supervisors at LAS, UU. Results indicate that there are different activities during the interdisciplinary research process where technology-mediated support would be of value. However, students and supervisors especially value meeting face-to-face when doing interdisciplinary integration. This should be taken into account when designing a blended framework for support of undergraduate interdisciplinary research.Van Lambalgen, R. (2020). Blended Support of Undergraduate Interdisciplinary Research. En 6th International Conference on Higher Education Advances (HEAd'20). Editorial Universitat Politècnica de València. (30-05-2020):437-445. https://doi.org/10.4995/HEAd20.2020.11083OCS43744530-05-202

A formalization of kant’s transcendental logic

Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kantgeneralformaltranscendental logics is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kants logic is after all a distinguished subsystem of first-order logic, namely what is known as geometric logi