Purpose: One of my goals in the paper is to investigate why realists reject radical constructivism (RC) as well as social constructivism (SC) out of hand. I shall do this by means of commenting on Peter Slezak’s critical paper, Radical Constructivism: Epistemology, Education and Dynamite. My other goal is to explore why realists condemn the use of RC and SC in science and mathematics education for no stated reason, again by means of commenting on Slezak’s paper. Method: I restrict my (...) comments to Slezak’s paper and leave it to the reader to judge which, if any, of the reasons that I advance for these two states of affairs are not specific to Slezak’s paper. Other readers might not agree with my interpretations of Slezak’s paper, including Slezak himself, but I offer them after having worked with von Glasersfeld in interdisciplinary research in mathematics education for over 25 years. Findings: My findings are that Slezak: (1) rejects RC and SC on the basis of unjustified criticisms, (2) does not explore basic tenets of RC nor of SC beyond the unjustified criticisms, (3) rejects how SC and RC have been used in science and mathematics education, based at least in part on the unjustified criticisms, (3) dislikes how SC has been used in science and mathematics education, a dislike that fuels his rejection of any constructivism, and (4) doesn’t explore how RC has been used in scientific investigations in mathematics education. On the basis of these findings, I conclude that how epistemological models of knowing might be used in science or mathematics education would be better left to the educators who use them in interdisciplinary work. (shrink)

THOUGHT .—THE BITTER CRY OF THE PLAIN MAN AN APPEAL TO PHILOSOPHERS " The best philosopher is the man who can think most imply. ...

---- t. 6. O nachalakh : opyt khristīanskoĭ metafiziki. [no.] 1. Bog i tvarnyi mīr. [no.] 2-3. Bog i mīr, v Bogochelovi︠e︡ki︠e︡ vi︠e︡chnyĭ ad pobi︠e︡zhdai︠u︡shchīĭ.

The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective geometry of the weakly modular orthocomplemented lattice of propositions may be imbedded in a complex Hilbert space; this is the structure which has traditionally been used. This paper reviews some work which has been devoted to generalizing the target space of this imbedding to Hilbert modules of a (...) more general type. In particular, detailed discussion is given of the simplest generalization of the complex Hilbert space, that of the quaternion Hilbert module. (shrink)

The fragmentary columns of the Fourth Book of Philodemus' περ μονσικς were the first-fruits of Herculaneum, published in 1793, with venturesome reconstructions and learned notes, by the Academici of Naples. Fragments of the other books occur in four volumes of the Collectio Altera of 1862–5. A. Teubner Text by J. Kemke, a pupil of Bücheler, appeared in 1884, upon which Gomperz made a number of improvements in a pamphlet published in the following year. Otherwise, save for a few pages in (...) H. Abert's Die Lehre vom Ethos in der griechischen Musik published in 1899, the work has attracted very little attention; which is scarcely surprising in view of the state of the text and the peculiar awkwardness of Philodemus' Greek. (shrink)

It has been pointed out to me that in my article on ‘The Augustan Rules for Dactylic Verse’ I misrepresented an observation of Maas as reported by Wilamowitz in his Griechische Verskunst, p. 53. Wilamowitz' words are: ‘Wenn Tibull und Ovid den Pentameter so bauen, dass die vorletzte Silbe betont wird, tun sie das nach dem Vorgange gleichzeitiger griechischer Epigrammatiker.’ This means, of course, that the Greek writers mentioned ended with a paroxytone word, not necessarily with a disyllable, as I (...) assumed it to mean, and I apologize for the oversight. (shrink)

In C.Q. xliii , p. 39, Mr. J. H. Quincey quotes the opening lines of Catalepton 5 as, Ite hinc,-inanes, ite, rhetorum ampullae, inflata rhoso* non Achaico verba, and adds, ‘the second line is corrupt and no satisfactory emendation has been proposed’. The MS. readings are: rhorso B, roso Mu, om. in lacuna Ar. In face of these voces nihili many have fallen back on the rore of the Aldine edition of 1517. But this does not really help, for one (...) does not inflate with dew: orators are not dew-bags, but wind-bags. It occurred to me some years ago that what is needed is some word meaning breath or wind to go with inflata, and that in view of the rh in rhorso it was probably a Greek word which a scribe had failed to recognize. I conjectured οζ, and found subsequently that this had been proposed by K. Münscher in Hermes, xlvii , pp. 153–4. οȋζος used of any rushing sound, is applied to speech by Philostratus , and by Pollux . It is easy to see how rhoezo could degenerate into rhoeso-rhoso-roso. (shrink)