Formal Ontology and Mathematics. A Case Study on the Identity of Proofs

We propose a novel, ontological approach to studying mathematical propositions and proofs. By “ontological approach” we refer to the study of the categories of beings or concepts that, in their practice, mathematicians isolate as fruitful for the advancement of their scientific activity (like discovering and proving theorems, formulating conjectures, and providing explanations). We do so by developing what we call a “formal ontology” of proofs using semantic modeling tools (like RDF and OWL) developed by the computer science community. In this article, (i) we describe this new approach and, (ii) to provide an example, we apply it to the problem of the identity of proofs. We also describe open issues and further applications of this approach (for example, the study of purity of methods). We lay some foundations to investigate rigorously and at large scale intellectual moves and attitudes that underpin the advancement of mathematics through cognitive means (carving out investigationally valuable concepts and techniques) and social means (like communication, collaboration, revision, and criticism of specific categories, inferential patterns, and levels of analysis). Our approach complements other types of analysis of proofs such as reconstruction in a deductive system and examination through a proof-assistant.

     

Associations between financial strain and the diurnal salivary cortisol secretion of long-term unemployed individuals

Objective: The study investigated the associations between self-rated financial strain and overall diurnal salivary cortisol levels, as well as secretory patterns among long-term unemployed individuals.Methods: Psychosocial and life-style variables were assessed by means of questionnaires among 85 participants (mean age 42±9 years; 56% females). Salivary cortisol was sampled on four occasions during a 24-hour period and data was analysed separately for men and women.Results: Among females, high financial strain was related to higher overall cortisol levels, and to elevated levels in the evening. These associations did not reach significance among men. Multivariate analyses showed that evening levels of cortisol were positively associated with financial strain, but largely unrelated to life-style variables and psychological distress.Conclusions: The results suggest that high financial strain influences the diurnal cortisol secretion of unemployed individuals in terms of elevated cortisol levels in the evening. The mediating mechanisms are in need of further investigation.     

Rudimental numerical competence in 5-day-old domestic chicks (Gallus gallus): identification of ordinal position

Numerical competencies were investigated for the 1st time in very young nonhuman animals. Chicks (Gallus gallus) learned to identify the 3rd, 4th, or 6th positions in a series of 10 identical positions (Experiment 1). Use of spatial information (i.e., distances) was ruled out in Experiment 2 (chicks generalized the reinforced response to an array of stimuli rotated by 90 degrees as compared with training) and Experiment 3 (chicks generalized their response to a series in which distances between the single positions had been manipulated). Chicks found the correct position even when both identity and distance of each position changed from trial to trial (Experiment 4). Overall, young chicks seemed to use ordinality when required to identify a target by its numerical serial position.     

Persistent autobiographical amnesia: a case report

We describe a 47-year-old man who referred to the Emergency Department for sudden global amnesia and left mild motor impairment in the setting of increased arterial blood pressure. The acute episode resolved within 24 hours. Despite general recovery and the apparent transitory nature of the event, a persistent selective impairment in recollecting events from some specific topics of his personal life became apparent. Complete neuropsychological tests one week after the acute onset and 2 months later demonstrated a clear retrograde memory deficit contrasting with the preservation of anterograde memory and learning abilities. One year later, the autobiographical memory deficit was unmodified, except for what had been re-learnt. Brain MRI was normal while H20 brain PET scans demonstrated hypometabolism in the right globus pallidus and putamen after 2 weeks from onset, which was no longer present one year later. The absence of a clear pathomechanism underlying focal amnesia lead us to consider this case as an example of functional retrograde amnesia.     

Does the Survey Mode Affect the Association Between Subjective Well-being and its Determinants? An Experimental Comparison Between Face-to-Face and Web Mode

Journal of Happiness Studies - Subjective well-being research increasingly uses web surveys to understand how subjective well-being indicators are related to other concepts of interest. Although we...     

Cornerstones: You’d better believe them

Crispin Wright??s ??Unified Strategy?? for addressing some familiar sceptical paradoxes exploits a subtle distinction between two different ways in which we can be related to a proposition: (full-blown) belief and (mere) acceptance. The importance of the distinction for his strategy stems from his conviction that we cannot acquire any kind of evidence, either empirical or a priori, for the ??cornerstones?? of our cognitive projects, i.e., for those basic presuppositions of our inquiries that we must be warranted to endorse if we are to claim warrant for any of the beliefs formed as a result of such inquiries: regarding the idea of a non-evidential warrant to believe a proposition as a kind of ??conceptual solecism??, he doesn??t set himself the task of showing that we are evidentially warranted to believe such presuppositions, but only that of showing that we are non-evidentially warranted to accept them. In the present paper, I argue that such choice involves a fatal departure from a basic principle governing doxastic commitment??a principle that requires that we regard cornerstones propositions as propositions we are rationally committed to believe, not just entitled to accept. I press the point by presenting the Acceptance Argument, a sceptical paradox whose consideration leads to the conclusion that the Unified Strategy is caught between the Scylla of incoherently invoking a rather dubious form of epistemic alchemy and the Charybdis of placing an unexpected and apparently ad hoc restriction on the doxastic commitments we undertake by believing the things we believe. My final suggestion is that the Unified Strategy might be spared this dilemma only by undergoing a rather radical revision??a revision that would require setting aside the distinction between belief and acceptance to re-conceptualise its goal unabashedly in terms of (non-evidentially) warranted belief.     

A Case of Partial Biotinidase Deficiency Associated With Autism

We report the case of a child with partial biotinidase deficiency and autistic developmental disorder. We arrived at the diagnosis of biotinidase deficiency when the child was almost 4 years of age. Consequently, he began cofactor biotin treatment (10 mg daily) which did not resolve his autistic behavior. His younger brother was affected by partial biotinidase deficiency diagnosed at birth through our neonatal screening program. He was precociously treated with cofactor biotin therapy (10 mg daily) and did not show any behavioral abnormality or developmental delay. Since the brain is quite vulnerable to biotin deficiency, delayed biotin therapy could result in neurological damage. Our patient is the first case of partial biotinidase deficiency associated with autism. We hypothesize that the low biotinidase activity could have caused biotin deficiency in his brain and cerebrospinal fluids and consequently serious neurological problems, such as stereotyped and autistic behaviors, which were irreversible in spite of biotin supplementation.     

The cradle of causal reasoning: newborns’ preference for physical causality

Perception of mechanical (i.e. physical) causality, in terms of a cause–effect relationship between two motion events, appears to be a powerful mechanism in our daily experience. In spite of a growing interest in the earliest causal representations, the role of experience in the origin of this sensitivity is still a matter of dispute. Here, we asked the question about the innate origin of causal perception, never tested before at birth. Three experiments were carried out to investigate sensitivity at birth to some visual spatiotemporal cues present in a launching event. Newborn babies, only a few hours old, showed that they significantly preferred a physical causality event (i.e. Michotte's Launching effect) when matched to a delay event (i.e. a delayed launching; Experiment 1) or to a non‐causal event completely identical to the causal one except for the order of the displacements of the two objects involved which was swapped temporally (Experiment 3). This preference for the launching event, moreover, also depended on the continuity of the trajectory between the objects involved in the event (Experiment 2). These results support the hypothesis that the human system possesses an early available, possibly innate basic mechanism to compute causality, such a mechanism being sensitive to the additive effect of certain well‐defined spatiotemporal cues present in the causal event independently of any prior visual experience.