A system of natural deduction is presented whose set of theses is identical with that of the systemE of entailment. For that system a decision procedure is described proving the decidability ofE.

Context: The idea for this article sprang from a desire to revive a conversation with the late Ernst von Glasersfeld on the heuristic function - and epistemological status - of forms of ideations that resist linguistic or empirical scrutiny. A close look into the uses of humor seemed a thread worth pursuing, albeit tenuous, to further explore some of the controversies surrounding the evocative power of the imaginal and other oblique forms of knowing characteristic of creative individuals. Problem: People generally (...) respond to humor, i.e., they are inclined to smile at things they find funny. People like to crack jokes, make puns, and, starting at age two, human infants engage in pretense or fantasy play. Research on creativity, on the other hand, has mostly scorned the trickster within. Cognitivists in particular are quick to relegate wit, whimsy, and even playfulness to the ranks of artful or poetic frivolities. Method: We use the emblems of the craftsman, the trickster, and the poet to highlight some of the oblique ways of knowing by which creative thinkers bring forth new insights. Each epitomizes dimensions intrinsic to the art of “possibilizing.” Taken together, they help us better understand what it means to be playful beyond curious, rigorous beyond reasonable, and why this should matter, even to constructivists! Results: The musings characteristic of creative individuals speak to intelligent beings’ ability to use glitches intentionally or serendipitously as a means to open up possibilities; to hold on to a thought before spelling it out; and to resist treating words or images as conventional and arbitrary signs regardless of their evocative power. To fall into nominalism, Bachelard insisted, is a poet’s nightmare! Implications: Psyche is image, said Jung, and when we feel alive we rely on the imaginal to guide our reason. Note that image is not here to be understood as a picture in the head or a photographic snapshot of the world. The imaginal does not represent, it brings forth what we understand beyond words. It does not lock us into a single mode. Instead, it is a call to be mindful, in Ellen Langer’s sense: in the present, mentally alert, and on the outlook for our psyche’s own surprising wisdom (sagacity. Constructivist content: Debates on the heuristic function and epistemological status of oblique ways of knowing have long occupied constructivist scholars. I can only guess whether my uses of Jung’s imaginal or Bachelard’s anti-nominalism would have amused or exasperated Ernst! I do know that, on occasion, Ernst the connoisseur, bricoleur, and translator allowed the rationalist-within to include the poet’s power to evoke as a legitimate form of rationality. He himself has written about oblique knowing as legit! (shrink)

Upshot: In view of Kenny’s clinical insights, Hug’s notes on the intricacies of rational vs. a-rational “knowing” in the design sciences, and Chronaki & Kynigos’s notice of mathematics teachers’ meta-communication on experiences of change, this response reframes the heuristic power of bisociation and suspension of disbelief in the light of Kelly’s notion of “as-if-ism” (constructive alternativism. Doing as-if and playing what-if, I reiterate, are critical to mitigating intra-and inter-personal relations, or meta-communicating. Their epistemic status within the radical constructivist framework is (...) cast in the context of mutually enriching conversational techniques, or language-games, inspired by Maturana’s concepts of “objectivity in parenthesis” and the multiverse. (shrink)

In this article, an ethical analysis of an educational programme on renal replacement therapy options for patients and their social network is presented. The two main spearheads of this approach are: (1) offering an educational programme on all renal replacement therapy options ahead of treatment requirement and (2) a home-based approach involving the family and friends of the patient. Arguments are offered for the ethical justification of this approach by considering the viewpoint of the various stakeholders involved. Finally, reflecting on (...) these ethical considerations, essential conditions for carrying out such a programme are outlined. The goal is to develop an ethically justified and responsible educational programme. (shrink)

Gow and Page are of the opinion that Planudes’ àένναος in the fifth line of this epigram may be not his conjecture but the true reading, and reject Jacobs' commonly received emendation àєί λáνος, with κηρο in the following line. But I have no doubt that for the two words μέν àλανóς we should read μєμαλαγαγμένος for ó μєμαλαγαγμένος κηρóς is the regular gloss1 on the waxy substance called μàλθα or μàλθα which was used in Athens—at the time of Sophocles (...) himself2—particularly for spreading on wooden writing-tablets. It was surmised by Schwabe that μàλθη had been the word glossed in Ael. Dion.Two entries in Pollux are especially important for establishing the use ofmaltha. In 10. 58–9, describing it as ό ένών т πινακίδί κηρϳς, he quotes passages from Herodotus, Cratinus, and Aristophanes referring to the soft wax which could easily be scraped from writing-tablets to erase writing. In 8. 16 he says it is the wax spread on the dicasts’ πινáκιον тιμηтικóν, from scratching on which the ‘long line’ of condemnation it will be remembered that Athenian philheliasts got wax under their finger-nails. (shrink)

The study of syntax is fundamental to linguistics and language study, but it is often taught solely within the framework of transformational grammar. This book is unique in several respects: it introduces the basic concepts used in the description of syntax, independently of any single model of grammar. Most grammatical models fail to deal adequately with one aspect of syntax or another, and the authors argue that an understanding of the concepts used in any full description of language is crucial (...) for assessing the strengths and weaknesses of formal grammars. Formal approaches to some of these concepts are critically examined. This book will train students, of either linguistics or language, to understand and make the best use of any grammar they encounter. Secondly, the book deals with the whole of syntax from immediate constituents and relations between sentences. It also examines concepts like subject and object, agent and patient, topic, comment and theme. Thirdly, there is a section on morphology, and a discussion of the relationship between syntax and morphology. As a book which explains, in a lucid and approachable way, why linguists have adopted certain solutions to problems and not others, this will be an invaluable introductory text. It is profusely illustrated with diagrams, and there are sets of exercises for every chapter which can be used in class, or by students working independently. This second edition has been extensively revised to take account of recent developments in syntactic studies. (shrink)

In an article1 entitled Lucrèce et les éléphants, Professor Ernout has referred to recent archaeological evidence that in palaeolithic times the skeletons of mammoths were used in the construction of primitive habitations, and observes that the well-known lines of Lucretius. 532 ff. about India being so prolific inelephants that the whole land ‘milibus e multis vallo munitur eburno’ mayrefer not to anything legendary, nor to themilitary use of elephants in large numbers for frontier defence, but to a recognitionof the fact (...) that even in later times ‘les Indiens avaient pu conserver leurmode de vie et utiliser avec ses défenses d'éléphant le système de protectioninvente par leurs ancêtres, ou simplement conserver ces gigantesques os demammouths’, etc. (shrink)

Bowra, referring to the image of the, and to the striking impression, states ‘Pindar seems to fuse two unusually disparate images into a single result… While the sheddingof leaves implies that he would have grown old without winning any wide renown, the cock means that such renown as he would have got would have beenof little account in the Greek world at large.’ Gildersleeve's comment ad loc, ‘The thus becomes a flower’, implies a similar assumption, that the secondimage is entirely (...) unconnected with the first. (shrink)

In a recent article I drew attention to the fact that the well-known fable of the improvident cicada and the industrious ant has a close resemblance to the story of the twin brothers Amphion and Zethus and their classic debate on the respective merits of the artistic and practical life in Euripides' Antiope, which is reflected not only in the argument of Callicles and Socrates in the Gorgias and Horace, Ep. i. 18.

This second visit to the place of Virgil's birth was made partly in actuality—for my wife and I, before taking part in the Virgilian Cruise of last summer, spent two delightful days at Pietole with our hosts, the Signori Prati, and our guest and friend Bruno Nardi—and partly in a renewed pondering of the arguments presented by my friend Professor Conway both in his earlier article and in his recent review of the question, to which, as he says, I had (...) urged him to return. I promised him at the time that if he should not speak the last word on the subject, I would still further defend the view commonly accepted until he bestowed an extraordinary publicity on Calvisano and Carpenedolo. He declares that I maintain the traditional site at Pietole, ‘though not perhaps with very great confidence.’ He further implies that I ‘do not want to accept the evidence of Probus because “I prefer” to believe a mediaeval tradition.’ Let me assure him and the reader that I do not regard a mediaeval tradition per se as better proof than the certain statement of an ancient authority. I have been led, by studies in various fields, to respect tradition in general until it is disproved, and to lay the burden of the argument on those who would disprove it. But the mere sight of something hoary and mediaeval does not prompt me to exclaim, ‘Media Aetas locuta est; causa finita est’ I relish the attempts of an iconoclast to destroy rigid error, and accept his destruction if it is accomplished. In the present case, however, I have ‘very great confidence’ that Conway's assault on the tradition has come to naught. Possibly some new and unexpected evidence may yet be discovered, showing that Virgil was born at Calvisano, or Carpenedolo, or at some other site than Pietole—but nobody has presented it yet. (shrink)

We may now consider this ancient evidence that Andes lay three miles away from Mantua in connection with Conway's remaining arguments and with Virgil's ‘own statement’ in his Bucolics.In the matter of the inscriptions, Conway's ‘impenitence’ does nothing to strengthen his case. All the points that he raises in an apparent refutation had been met by me. I had distinguished between public and private inscriptions, as Conway had not done in his earlier article, where he declared the period of the (...) two monuments to be ‘Virgil's own,’ the inscriptions being ‘cut in the style which marks the best work between 50 B.C. and A.D. 50.’ I had not, as he asserts, failed to notice the point that caps the climax of his recent article, that ‘the P. Magius who wrote the inscription of Casalpoglio … was related to Virgil's mother.’ I was inclined to date both inscriptions, with the approval of Professor Egbert, somewhere in the third quarter of the first century of our era, but ‘even allowing for them both a date as early as the end of the first century B.C.,’ which is apparently as far back as Conway means to stretch their date, I clamored for an inscription of the time of Virgil's birth if it were to serve as evidence for his birthplace. This point is not met by Conway. If Virgil was born at Pietole, his fame and his family could certainly have extended as far north as Casalpoglio and Calvisano at the time of his death in 19 B.C. Supposing that we knew on other evidence that he was born at Calvisano, the presence of an inscription with the name of Magius or Vergilius would corroborate that evidence. (shrink)