Complete inferential rigour is achieved by breaking down arguments into steps that are as small as possible: inferential ‘atoms’. For example, a mathematical or philosophical argument may be made completely inferentially rigorous by decomposing its inferential steps into the type of step found in a natural deduction system. It is commonly thought that atomization, paradigmatically in mathematics but also more generally, is pro tanto epistemically valuable. The paper considers some plausible candidates for the epistemic value arising from atomization and finds (...) that none of them fits the bill. In particular, atomized arguments do not ground the correctness of their unatomized counterparts; they are typically not credence-preserving; and they need not reveal the source of inferential disagreement. The moral this suggests is that complete rigour is not even a defeasible epistemic ideal. (shrink)

Purpose: Explore public attitudes towards the trade-offs between justice and medical outcome inherent in organ allocation decisions.Background: The US Task Force on Organ Transplantation recommended that considerations of justice, autonomy and medical outcome be part of all organ allocation decisions. Justice in this context may be modeled as a function of three types of need, related to age, clinical urgency, and quality of life.Methods: A web-based survey was conducted in which respondents were asked to choose between two hypothetical patients who (...) differed in clinical urgency , age, pretransplant and post-transplant quality of life, and life expectancy.Results: A pool of 1600 people were notified via email about the survey; 623 responded. Respondents preferred giving organs to younger people up to an age difference of <15.4 years and more clinically urgent people up to a difference in urgency of <2.54 months . Priority varied with the quality of life of the worst-off patient and the relative status of the patients. If both had worse than average quality of life, respondents preferred the better-off patient. When both had better than average quality of life, they preferred the worse-off patient. In analysis according to age versus clinical urgency, the older the patient, the more urgency needed to receive priority. In quality of life versus clinical urgency, the better the control’s quality of life, the more urgency the competing patient required. The worse the patient’s post-transplant outcome, the more urgency needed to receive priority.Conclusions: It appears that clinical urgency is only one of many factors influencing attitudes about allocation decisions and that respondents may invoke different principles of fairness depending the relative clinical status of patients. (shrink)

A mathematical matrix is usually defined as a two-dimensional array of scalars. And yet, as I explain, matrices are not in fact two-dimensional arrays. So are we to conclude that matrices do not exist? I show how to resolve the puzzle, for both contemporary and older mathematics. The solution generalises to the interpretation of all mathematical discourse. The paper as a whole attempts to reinforce mathematical structuralism by reflecting on how best to interpret mathematics.

Examines the role played by the Aristotelian logic in Neoplatonic philosophers. To start with, it is remarked that Aristotelian Organon was regarded not only as a corpus of logical texts but also as an introduction to philosophy. Focuses on several Neoplatonic Aristotelian commentators, from Alexander of Aphrodisias to Byzantine thinkers, presenting both the characteristics of their works and their lack of interest in discussing their own philosophical view. Finally, it is observed that, although not original, these commentaries provide a rather (...) reliable and correct investigation of Aristotle. (shrink)

Devoted to the key Neoplatonic concepts of procession and emanation. The two terms are taken to express the same idea, although procession is preferred as more neutral. Points out how procession can be explained in Aristotelian terms. More specifically, it is demonstrated how Plotinus’ notion of procession uses the Aristotelian theory of the actualization of an activity by a potency in order to explain how a higher activity can actualize a lower one. Finally, considers the doctrine of Proclus who expresses (...) the procession, involving the theory of causal relation, in a way opposite to Plotinus. (shrink)

Focuses on Porphyry's semantic and more specifically on his theory of ‘imposition of names’, i.e. how names are related to things. Examines Porphyry's treatment of genus and species and also of individual, singular, and general terms to emphasize his peculiarity in Neoplatonic philosophy. Infers that Porphyry's attitude is not to develop a metaphysical and a logical semantics, but only a metaphysical one. Finally, considers how Porphyry's metaphysical approach towards semantics was maintained by eleventh and twelfth century Byzantine Neoplatonists.

The core of the third chapter is the study of the P‐series. This theory is presented after a detailed discussion of the relationship of individuals to species and genus. A P‐series is a sequence of terms classified according to priority and posteriority starting from the most universal one. This theory is the result of the evolution of the Aristotelian doctrine of pros en done in order to fit with the not strictly Aristotelian notion of ‘genus’ of some Neoplatonic philosophers.

The purpose of Ch. 6 is to outline the role played by the P‐series theory in Neoplatonic epistemology. To start with, it is explained that knowledge of a P‐series consists in an order of priority and posteriority of the terms: intellect, scientific knowledge, belief, presentation, and perception. In second place, some peculiar Neoplatonic epistemological issues, e.g. how can the divine possibly know temporal truths, are carefully examined. To conclude, some particular Neoplatonic rules, which allow higher entities to have knowledge of (...) lower ones, are investigated. (shrink)

In line 1171 of Aeschylus' Agamemnon the MSS. read μ The remainder of the sentence, after μ, is much disputed, but I am not concerned with finding the true reading of it. The whole sentence runs, in the MSS., as follows: κος δ' οδν πρκεσαντ μ πλιν μν σπερ ον χει παθεν: which appears in Thomson's Oresteia as:… πρκεσεν τ μ ok χειν πλιν μν σπερ ον χει. It is the note on this passage in Thomson to which I wish (...) to draw attention. It is from Headlam, and says, in justification of reading μ οκ, that in such phrases the scribes, finding μο, constantly omitted ο as περιττν. It adds that ο should always be restored, at any rate where there is any trace of it. (shrink)