37,910 research outputs found
Animal Cognition, Species Invariantism, and Mathematical Realism
What can we infer from numerical cognition about mathematical realism? In this paper, I will consider one aspect of numerical cognition that has received little attention in the literature: the remarkable similarities of numerical cognitive capacities across many animal species. This Invariantism in Numerical Cognition (INC) indicates that mathematics and morality are disanalogous in an important respect: proto-moral beliefs differ substantially between animal species, whereas proto-mathematical beliefs (at least in the animals studied) seem to show more similarities. This makes moral beliefs more susceptible to a contingency challenge from evolution compared to mathematical beliefs, and indicates that mathematical beliefs might be less vulnerable to evolutionary debunking arguments. I will then examine to what extent INC can be used to flesh out a positive case for mathematical realism. Finally, I will review two forms of mathematical realism that are promising in the light of the evolutionary evidence about numerical cognition, ante rem structuralism and Millean empiricism
State-of-Science review: learning difficulties: SR-D4: Dyscalculia
Low numeracy skills in general and developmental dyscalculia (DD) in particular constitute
a severe handicap. This review examines the causes and behavioural manifestations of
numeracy deficits, their neuropsychological correlates and the limits to our understanding of
these conditions. It then goes on to describe a validated test for diagnosing DD ā a specific
impairment in the capacity to learn arithmetic. The challenges in educating DD children and
analysing their particular intervention needs are described. Reference is also made to the
impact of dyscalculia on mental health (and ill-health) and individual wellbeing
Founding quantum theory on the basis of consciousness
In the present work, quantum theory is founded on the framework of
consciousness, in contrast to earlier suggestions that consciousness might be
understood starting from quantum theory. The notion of streams of
consciousness, usually restricted to conscious beings, is extended to the
notion of a Universal/Global stream of conscious flow of ordered events. The
streams of conscious events which we experience constitute sub-streams of the
Universal stream. Our postulated ontological character of consciousness also
consists of an operator which acts on a state of potential consciousness to
create or modify the likelihoods for later events to occur and become part of
the Universal conscious flow. A generalized process of measurement-perception
is introduced, where the operation of consciousness brings into existence, from
a state of potentiality, the event in consciousness. This is mathematically
represented by (a) an operator acting on the state of potential-consciousness
before an actual event arises in consciousness and (b) the reflecting of the
result of this operation back onto the state of potential-consciousness for
comparison in order for the event to arise in consciousness. Beginning from our
postulated ontology that consciousness is primary and from the most elementary
conscious contents, such as perception of periodic change and motion, quantum
theory follows naturally as the description of the conscious experience.Comment: 41 pages, 3 figures. To be published in Foundations of Physics, Vol
36 (6) (June 2006), published online at
http://dx.doi.org/10.1007/s10701-006-9049-
An emergentist perspective on the origin of number sense
open2noopenZorzi, Marco; Testolin, AlbertoZorzi, Marco; Testolin, Albert
Why do spatial abilities predict mathematical performance?
Spatial ability predicts performance in mathematics and eventual expertise in science, technology and engineering. Spatial skills have also been shown to rely on neuronal networks partially shared with mathematics. Understanding the nature of this association can inform educational practices and intervention for mathematical underperformance. Using data on two aspects of spatial ability and three domains of mathematical ability from 4174 pairs of 12-year-old twins, we examined the relative genetic and environmental contributions to variation in spatial ability and to its relationship with different aspects of mathematics. Environmental effects explained most of the variation in spatial ability (~70%) and in mathematical ability (~60%) at this age, and the effects were the same for boys and girls. Genetic factors explained about 60% of the observed relationship between spatial ability and mathematics, with a substantial portion of the relationship explained by common environmental influences (26% and 14% by shared and non-shared environments respectively). These findings call for further research aimed at identifying specific environmental mediators of the spatialāmathematics relationship
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