This book makes a significant contribution to the standard decision theory, that is, the theory of choice built around the principle of maximizing expected utility, both to its causal version and to the more traditional noncausal approach. The author’s success in clarifying the foundations of the standard decision theory in general, and causal decision theory in particular, also makes the book uniquely suitable for a person whose research in philosophy has led her to want to learn about contemporary decision theory. (...) The book presupposes some mathematical sophistication, and it contains more philosophical and mathematical argumentation per page than may be suitable for an undergraduate level course; but it stands out as an ideal textbook for a graduate-level course focused on the foundations of the standard decision theory. (shrink)

The system R, or more precisely the pure implicational fragment R›, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R› yields the pure implicational fragment RM› of the system? As concerns the weak systems there are at least two (...) approaches to the problem. First of all, it is possible to restrict a validity of some theorems. In another approach we can investigate even weaker logics which have no theorems and are characterized only by rules of deducibility. (shrink)

Piero della Francesca is best known as a painter but he was also a mathematician. His treatise De prospectiva pingendi is a superb example of a union between the fne arts and mathemati‑ cal sciences of arithmetic and geometry. In this paper, I explain some reasons why his paint‑ ing is considered as a part of perspective and, therefore, can be identifed with a branch of geometry.

Artykuł ten powstał w wyniku realizacji projektu badawczego nr 2012/07/B/HS1/01986.

Postural instability in Parkinson’s disease (PD) is characterized by impaired postural responses to transient perturbations, increased postural sway in stance and difficulty transitioning between tasks. In addition, some studies suggest that loss of dopamine in the basal ganglia due to PD results in difficulty using proprioceptive information for motor control. Here, we quantify the ability of subjects with PD and age-matched control subjects to use and re-weight sensory information for postural control during steady-state conditions of continuous rotations of the stance (...) surface or visual surround. We measure the postural sway of subjects in response to a pseudorandom, surface-tilt stimulus with eyes closed, and in response to a pseudorandom, visual-tilt stimulus. We use a feedback control model of the postural control system to interpret our results, focusing on sensory weighting as a function of stimulus amplitude. We find that subjects with PD can re-weight their dependence upon sensory information in response to changes in surface- or visual-stimulus amplitude. Specifically, subjects with PD behaved like age-matched control subjects by decreasing proprioceptive contribution to stance control with increasing surface-tilt amplitude, and decreasing visual contribution with increasing visual-tilt amplitude. However, subjects with PD do not decrease their reliance on proprioception as much as age-matched controls for small increases in surface-stimulus amplitudes. Levodopa medication did not affect sensory re-weighting behaviors for postural control. The impairment in PD subject’s ability to respond differently to small changes in surface rotation amplitudes is consistent with an increased threshold for perceiving proprioceptive signals, which may result from decreased signal-to-noise in the dopaminergic pathways associated with sensory processing and/or sensory integration. (shrink)