Undecidability and intuitionistic incompleteness

Let S be a deductive system such that S-derivability (s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and s, it follows constructively that the K-completeness of s implies MP(S), a form of Markov's Principle. If s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when s is many-one complete, MP(S) implies the usual Markov's Principle MP.An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implics MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP.These results give extensions of the theorem of Gödel and Kreisel (in [4]) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Gödel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article.     

The communication disorder in dialysis dementia: A case report

The communication disorder in dialysis dementia is an integral feature of the syndrome. This report describes the communication disorder in a 67-year-old man over a period of 4 months from his admission to the hospital to his death. In the early stage of the syndrome, the most prominent feature was a speech problem, the characteristics of which may vary among cases. In the middle stage, it was difficult to distinguish among aphemia, aphasia, or a combination of dysarthria and confusional state. The severity of the problems in these stages was temporally related to the dialysis treatments. The final stage was characterized by constant mutism and was unrelated to the dialysis treatments. Death occurred 10 months after the communication problems emerged. Communication studies of dialysis dementia patients may offer a systematic method to monitor the course of the syndrome, its response to therapeutic trials, and a clinical model for the study of communication disorders in general.     

Proto-Semantics for Positive Free Logic

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of non-existing objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth non unlike the notion of truth at world found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization).     

MORAL DELIBERATION AND OPERATIVE RIGHTS: A RESPONSE TO MARY MAGADA‐WARD AND CYNTHIA GAYMAN

Abstract: The aim of this article is to show how intimately connected Beth J. Singer's theory of operative rights is with her understanding of the deliberative process. I thus argue against Cynthia Gayman's effort to set in contrast Singer's theory of rights and Dewey's characteristic emphasis on reflective morality. Since I take the value of Singer's approach to be most evident in its relevance to the abortion debate as an ongoing deliberation, I question whether Mary Magada‐Ward sufficiently appreciates the dialogical and deliberative emphases of Singer's stance. My goal, however, is not so much to argue against either Gayman or Magada‐Ward as it is to argue for taking Singer's position even more seriously than either author does. In particular, I want to highlight the finely nuanced character of Singer's philosophical intervention in the debate regarding abortion, especially stressing certain features that Gayman and Magada‐Ward overlook.     

Two types of debunking arguments

Debunking arguments are arguments that seek to undermine a belief or doctrine by exposing its causal origins. Two prominent proponents of such arguments are the utilitarians Joshua Greene and Peter Singer. They draw on evidence from moral psychology, neuroscience, and evolutionary theory in an effort to show that there is something wrong with how deontological judgments are typically formed and with where our deontological intuitions come from. They offer debunking explanations of our emotion-driven deontological intuitions and dismiss complex deontological theories as products of confabulatory post hoc rationalization. Through my discussion of Greene and Singer’s empirically informed debunking of deontology, I introduce the distinction between two different types of debunking arguments. The first type of debunking argument operates through regular undercutting defeat, whereas the second type relies on higher-order evidence. I argue that the latter type of debunking argument, of which the argument from confabulation is an example, is objectionably sloppy and therefore inadmissible in academic discussion.     

Bentham on animal welfare

Jeremy Bentham is often thought to have set the groundwork for the modern ‘animal liberation’ movement, but in fact he wrote little on the subject. A full examination of his work reveals a less radical position than that commonly attributed to him. Bentham was the first Western philosopher to grant animals equal consideration from within a comprehensive, non-religious moral theory, and he was a staunch defender of animal welfare laws. But he also approved of killing and using animals, as long as pointless cruelty could be avoided. The nuances of his position are best brought out by comparing it to that of Peter Singer, who draws considerably more radical practical conclusions. This is not primarily explained by competing formulations of utilitarianism, however, but by different empirical background assumptions about the lives of animals.     

Stimulus and response contributions to the children's reaction-time repetition effect

Adults and 8-, 10-, 12-, and 14-year olds completed a serial reaction-time task with two stimuli mapped to each of two responses and 100-, 500-, and 1000-msec response-stimulus intervals (RSIs). Trials were classified as (1) identical (same stimulus and same response on two consecutive trials), (2) response equivalent (different stimulus but same response on two consecutive trials), or (3) different (different stimulus and different response on two consecutive trials). Identical and different trials were compared as a general indication of repetition effects. Response-equivalent minus identical reaction time identified stimulus contributions, and different minus response-equivalent reaction time identified response contributions. Adults received a repetition advantage at all RSIs and children received a repetition advantage at 500- and 1000- but not 100-msec RSIs. Stimulus contributions accounted for the repetition effect for both adults and children. At the 500- and 1000-msec RSIs, both the overall repetition effect and stimulus contribution were positive and decreased in magnitude as age increased. The response contribution was independent of RSI and was negative for 8- and 10-year-olds and near zero or positive for older performers. At the longer RSIs, positive stimulus contributions were sufficient to overcome the negative response contributions present for younger children.     

Binocular fixation in the newborn baby.

Three experiments are reported in which the newborn baby's ability to fixate binocularly was investigated, using the corneal reflection technique for measuring eye fixation position. Two criteria for consistent binocular fixation were assessed. These are (1) the two eyes will be optically more divergent when fixating more distant targets, and (2) each eye will be scored as being on-target when corrections for the expected deviations of the pupil center from the fixated stimulus are introduced.In the first experiment vertical arrays of lights were separately shown at distances of 10 and 20 in. from the subjects' eyes (with the retinal image size and luminance of the stimuli held constant). The 12 newborns who gave results at both viewing distances reliably converged to both stimuli, the optical divergence of the pupil centers of the eyes increasing with presentation of the more distant stimulus. In Expt 2 similar stimuli at 5 and 10 in. from the eyes were shown. It was again the case that the subjects reliably converged to the stimulus at 10 in. This was no so for the stimulus at 5 in., and many subjects fixated this stimulus with monocular vision. The failure to converge is probably due to an inability to accommodate to this near distance. In Expt 3 different stimuli (a vertical strip of light, an outline triangle and square, and an array of squares) were presented a constant distance (10 ± 1 in.) from the eyes. The majority of the 15 subjects binocularly fixated all three stimuli: for those subjects who failed to converge consistently to these stimuli the observed alternatives to binocular fixation were monocular fixation, divergent strabismus, and a third category of response that is most probably an indication of inattention to the stimulus. It can be concluded that the newborn baby possesses the ability to fixate binocularly an appropriately presented stimulus, and has the basic requirements for binocular vision.