Cet article est un nouvel examen des objections soulevées par Leibniz dans la controverse avec Clarke contre la théorie absolutiste de l'espace et du temps. Or la plupart de ces objections sont fondées sur le principe de raison suffisante; mais Leibniz utilise aussi le principe de l'identité des indiscernables, qu'il prétend déduire du principe de raison suffisante . Ce qui m'intéresse c'est que Leibniz présente parfois deux versions de la même objection: l'une reposant uniquement sur le principe de raison suffisante, (...) l'autre uniquement sur le principe de l'identité des indiscernables. Se pose alors la question suivante: Leibniz aurait-il pu soulever toutes les objections qu'il voulait contre la théorie absolutiste, en utilisant seulement le principe de l'identité des indiscernables? Il me semble qu'il aurait certainement pu le faire. Et de plus, je crois que si Leibniz avait suivi cette voie, son raisonnement contre la théorie absolutiste aurait été beaucoup plus convaincant. Ainsi donc, je me propose de mener l'attaque de Leibniz contre la théorie absolutiste, en isolant, reformulant, et exposant systématiquement sept arguments dont il se servait ou dont il aurait pu se servir, qui sont tous fondés sur le principe de l'identité des indiscernables. (shrink)

Femina in line 28 has nagged me subconsciously for years. I have now belatedly realized that it sabotages the poet's prudent disclaimer: it is not women in general who are in question, but only those not ruled out of bounds by stola and uittae. The repetition of the word in the following verse, where it means, as the opposition to uiri indicates, ‘the female sex’, only serves to underline its inappropriateness here. Cristante's defence of the anaphora, that it ‘ribadisce la (...) necessità dell'insegnamento, introducendone la giustificazione’ , sets up an unwanted connection: lines 25–8 are strictly parenthetic to the main argument, as indeed is signalled by the truly functional anaphora of femina in line 29, whose effect is blurred in the text as transmitted. The form of the couplet, typical of Ovid, dictates that what is wanted is a variation on nil nisi lasciui, e.g. nec or, better, non proba. The source of the intrusive femina is not far to seek, though how precisely it ousted the original reading I do not pretend to guess. (shrink)

Femina in line 28 has nagged me subconsciously for years. I have now belatedly realized that it sabotages the poet's prudent disclaimer: it is not women in general who are in question, but only those not ruled out of bounds by stola and uittae. The repetition of the word in the following verse, where it means, as the opposition to uiri indicates, ‘the female sex’, only serves to underline its inappropriateness here. Cristante's defence of the anaphora, that it ‘ribadisce la (...) necessità dell'insegnamento, introducendone la giustificazione’, sets up an unwanted connection: lines 25–8 are strictly parenthetic to the main argument, as indeed is signalled by the truly functional anaphora of femina in line 29, whose effect is blurred in the text as transmitted. The form of the couplet, typical of Ovid, dictates that what is wanted is a variation on nil nisi lasciui, e.g. nec or, better, non proba. The source of the intrusive femina is not far to seek, though how precisely it ousted the original reading I do not pretend to guess. (shrink)

SummaryWe present a systematic discussion of the structural and conceptual simplifications of proofs of standard theorems afforded by nonstandard methods and examine to what extent the resulting nonstandard proofs satisfy the informal criterion of “plausibility”. We introduce the concept of a “standard detour” and show that all nonstandard proofs considered avoid such detours. Among the proofs examined are proofs of the Intermediate Value Theorem, the Riemann Integration Theorem, the Spectral Theorem for compact Hermitian operators, and the Arzela‐Ascoli Theorem.RésuméNous discutons systématiquement (...) les simplifications structurelles et conceptuelles apportées par des méthodes non standard aux démonstrations de théorèmes standard et examinons jusQuà quel point de telles démonstrations non standard satisfont à un critère informel de plausibilityé. Nous introduisons la notion de détour standard et montrons que toutes les démonstrations non standard considérées évitent de tels détours. Parmi les démonstrations examinées: celles du théoréme de la valeur intermédiate, du théorème ?on;intégration de Riemann, du théorème spectral pour les opérateurs hermitiques compacts et du théorème ?on;Arzelà‐Arcoli.ZusammenfassungWir stellen eine systematische Betrachtung der durch die Nichtstandard‐Methoden gegebe‐nen strukturellen und begrifflichen Vereinfachungen von Beweisen von Standardsätzen an, und untersuchen, wie weit die entstandenen Nichtstandard‐Beweise das informelle Kriterium der Plausibilität erfüllen. Wir führen den Begriff eines Standard‐Umweges ein, und zeigen, dass alle betrachteten Nichtstandard‐Beweise solche Umwege vermeiden. Unter den betrachteten Beweisen befinden sich Beweise des Zwischenwertsatzes, des Riemannschen lntegralsatzes, des Spektralsatzes für kompakte, hermitische Operatoren, und des Theorems von Arzelà‐Ascoli. (shrink)

The focus of this study was to analyze the content, distribution, and comparative genome relationships of 996 chromosome bin-mapped expressed sequence tags accounting for 2266 restriction fragments on the homoeologous group 3 chromosomes of hexaploid wheat. Of these loci, 634, 884, and 748 were mapped on chromosomes 3A, 3B, and 3D, respectively. The individual chromosome bin maps revealed bins with a high density of mapped ESTs in the distal region and bins of low density in the proximal region of the (...) chromosome arms, with the exception of 3DS and 3DL. These distributions were more localized on the higher-resolution group 3 consensus map with intermediate regions of high-mapped-EST density on both chromosome arms. Gene ontology classification of mapped ESTs was not significantly different for homoeologous group 3 chromosomes compared to the other groups. A combined analysis of the individual bin maps using 537 of the mapped ESTs revealed rearrangements between the group 3 chromosomes. Approximately 232 of the consensus mapped ESTs matched sequences on rice chromosome 1 and revealed large- and small-scale differences in gene order. Of the group 3 mapped EST unigenes ∼21 and 32% matched the Arabidopsis coding regions and proteins, respectively, but no chromosome-level gene order conservation was detected. (shrink)