The variety of consequence,according to Bolzano

Contemporary historians of logic tend to credit Bernard Bolzano with the invention of the semantic notion, of consequence, a full century before Tarski. Nevertheless, Bolzano's work played no significant rôle in the genesis of modern logical semantics. The purpose of this paper is to point out three highly original, and still quite relevant themes in Bolzano's work, being a systematic study of possible types of inference, of consistency, as well as their meta-theory. There are certain analogies with Tarski's concerns here, although the main thrust seems to be different, both philosophically and technically. Thus, if only obliquely, we also provide some additional historical perspective on Tarski's achievement.     

The prevalence of specific learning disorder in mathematics and comorbidity with other developmental disorders in primary school-age children

Mathematics difficulties are common in both children and adults, and they can have a great impact on people's lives. A specific learning disorder in mathematics (SLDM or developmental dyscalculia) is a special case of persistent mathematics difficulties, where the problems with maths cannot be attributed to environmental factors, intellectual disability, or mental, neurological or physical disorders. The aim of the current study was to estimate the prevalence rate of SLDM, any gender differences in SLDM, and the most common comorbid conditions. The DSM-5 provides details regarding these only for specific learning disorders in general, but not specifically for SLDM. We also compared the prevalence rates obtained on the basis of the DSM-IV and DSM-5 criteria. We investigated the performance of 2,421 primary school children on standardized tests of mathematics, English, and IQ, and several demographic factors over the primary school years. We applied the DSM-5 diagnostic criteria to identify children with a potential diagnosis of SLDM. Six per cent of our sample had persistent, severe difficulties with mathematics, and, after applying the exclusion criteria, 5.7% were identified as having an SLDM profile. Both persistent maths difficulties and consistently exceptionally high performance in maths were equally common in males and females. About half of the children with an SLDM profile had some form of language or communication difficulty. Some of these children also had a diagnosis of autism, social, emotional, and behavioural difficulties or attention deficit and hyperactivity disorder. Our findings have important implications for research and intervention purposes, which we discuss in the study.