Nonsymbolic numerical magnitude comparison: reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults

The numerical ratio effect (NRE) and the Weber fraction (w) are common metrics of the precision of the approximate numbers sense (ANS), a cognitive mechanism suggested to play a role in the development of numerical and arithmetic skills. The task most commonly used to measure the precision of the ANS is the numerical comparison task. Multiple variants of this task have been employed yet it is currently unclear how these affect metrics of ANS acuity, and how these relate to arithmetic achievement. The present study investigates the reliability, validity and relationship to standardized measures of arithmetic fluency of the NRE and w elicited by three variants of the nonsymbolic number comparison task. Results reveal that the strengths of the NRE and w differ between task variants. Moreover, the reliability and validity of the reaction time NRE and the w were generally significant across task variants, although reliability was stronger for w. None of the task variants revealed a correlation between ANS metrics and arithmetic fluency in adults. These results reveal important consistencies across nonsymbolic number comparison tasks, indicating a shared cognitive foundation. However, the relationship between ANS acuity and arithmetic performance remains unclear.     

Dogs (Canis lupus familiaris) are susceptible to the Kanizsa’s triangle illusion

Animal Cognition - The ability to complete partially missing contours is widespread across the animal kingdom, but whether this extends to dogs is still unknown. To address this gap in knowledge,...     

Auf dem Bauplatz der materialistischen Dialektik

Ohne Zusammenfassung     

Dynamic and stochastic systems as a framework for metaphysics and the philosophy of science

Synthese - Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the...     

Labeled Calculi and Finite-Valued Logics

A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite-valued logic if the labels are interpreted as sets of truth values (sets-as-signs). Furthermore, it is shown that any finite-valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the number of truth values, and it is shown that this bound is tight.     

Editorial Approaches to Wittgenstein's Nachlass: Towards a Historical Appreciation

Building on the unpublished correspondence between Ludwig Wittgenstein's literary executors Rush Rhees, Elizabeth Anscombe and Georg Henrik von Wright, this paper sketches the historical development of different editorial approaches to Wittgenstein's Nachlass. Using the metaphor of a ladder, it is possible to distinguish seven significant “rungs” or “steps” in the history of editing Wittgenstein's writings. The paper focuses particularly on the first four rungs, elucidating how Rhees, Anscombe and von Wright developed different editorial approaches that resulted in significant differences in their editions. The paper sheds light on how these editorial differences are grounded in the editors' divergent understandings of their task. It is suggested that future research may investigate the development of editorial approaches to Wittgenstein's Nachlass as a human story of philosophical inheritance.