bluuebunny/crossref_metadata_2025_split huggingface dataset:
Pure Proof Theory Aims, Methods and Results: Extended Version of Talks Given at Oberwolfach and Haifa
Authors: Pohlers Wolfram 
Published: May 2006

Apologies. The purpose of the following talk is to give an overview of the present state of aims, methods and results in Pure Proof Theory. Shortage of time forces me to concentrate on my very personal views. This entails that I will emphasize the work which I know best, i.e., work that has been done in the triangle Stanford, Munich and Münster. I am of course well aware that there are as important results coming from outside this triangle and I apologize for not displaying these results as well.Moreover the audience should be aware that in some points I have to oversimplify matters. Those who complain about that are invited to consult the original papers.1.1. General. Proof theory startedwithHilbert's Programme which aimed at a finitistic consistency proof for mathematics.By Gödel's Theorems, however, we know that we can neither formalize all mathematics nor even prove the consistency of formalized fragments by finitistic means. Inspite of this fact I want to give some reasons why I consider proof theory in the style of Gentzen's work still as an important and exciting field of Mathematical Logic. I will not go into applications of Gentzen's cut-elimination technique to computer science problems—this may be considered as applied proof theory—but want to concentrate on metamathematical problems and results. In this sense I am talking about Pure Proof Theory.Mathematicians are interested in structures. There is only one way to find the theorems of a structure. Start with an axiom system for the structure and deduce the theorems logically. These axiom systems are the objects of proof-theoretical research. Studying axiom systems there is a series of more or less obvious questions.
Programs, Grammars and Arguments: A Personal View of some Connections between Computation, Language and Logic
Authors: Lambek J. 
Published: May 2006

As an undergraduate I was taught to multiply two numbers with the help of log tables, using the formulaHaving graduated to teach calculus to Engineers, I learned that log tables were to be replaced by slide rules. It was then that Imade the fateful decision that there was no need for me to learn how to use this tedious device, as I could always rely on the students to perform the necessary computations. In the course of time, slide rules were replaced by pocket calculators and personal computers, but I stuck to my original decision.My computer phobia did not prevent me from taking an interest in the theoretical question: what is a computation? This question goes back to Hilbert's 10th problem (see Browder [1976]), which asks for an algorithm, or computational procedure, to decide whether any given polynomial equation is solvable in integers. It quickly leads to the related question: which numerical functionsf: ℕn→ ℕ are computable?While Hilbert's 10th problem was only resolved in 1970, this related question had some earlier answers, of which I shall single out the following three:(1)f is recursive(Gödel, Kleene),(2)f is computable on an abstract machine(Turing, Post),(3)f is definable in the untyped λ-calculus(Church, Kleene).These tentative answers were shown to be equivalent by Church [1936] and Turing [1936–7].I shall discuss here some of the more recent developments of these notions of computability and their relevance to linguistics and logic. I hope to be forgiven for dwelling on some of the work I have been involved with personally, with greater emphasis than is justified by its historical significance.
How to Compute Antiderivatives
Authors: Freiling Chris 
Published: May 2006

This isnotabout the symbolic manipulation of functions so popular these days. Rather it is about the more abstract, but infinitely less practical, problem of the primitive. Simply stated:Given a derivativef: ℝ → ℝ, how can we recover its primitive?The roots of this problem go back to the beginnings of calculus and it is even sometimes called “Newton's problem”. Historically, it has played a major role in the development of the theory of the integral. For example, it was Lebesgue's primary motivation behind his theory of measure and integration. Indeed, the Lebesgue integral solves the primitive problem for the important special case whenf(x)is bounded. Yet, as Lebesgue noted with apparent regret, there are very simple derivatives (e.g., the derivative ofF(0) = 0,F(x)=x2sin(1/x2)forx≠ 0) which cannot be inverted using his integral.The general problem of the primitive was finally solved in 1912 by A. Denjoy. But his integration process was more complicated than that of Lebesgue. Denjoy's basic idea was to first calculate the definite integralf(x) dxover as many intervals (a,b) as possible, using Lebesgue integration. Then, he showed that by using these results, the definite integral could be found over even more intervals, either by using the standard improper integral technique of Cauchy, or an extension technique developed by Lebesgue (see appendix for details).
Zermelo and the Skolem Paradox
Authors: Dalen Dirk Van , Ebbinghaus Heinz-Dieter 
Published: May 2006

On October 4, 1937, Zermelo composed a small note entitled “Der Relativismus in der Mengenlehre und der sogenannte Skolemsche Satz”(“Relativism in Set Theory and the So-Called Theorem of Skolem”) in which he gives a refutation of “Skolem's paradox”, i.e., the fact that Zermelo-Fraenkel set theory—guaranteeing the existence of uncountably many sets—has a countable model. Compared with what he wished to disprove, the argument fails. However, at a second glance, it strongly documents his view of mathematics as based on a world of objects that could only be grasped adequately by infinitary means. So the refutation might serve as a final clue to his epistemological credo.Whereas the Skolem paradox was to raise a lot of concern in the twenties and the early thirties, it seemed to have been settled by the time Zermelo wrote his paper, namely in favour of Skolem's approach, thus also accepting the noncategoricity and incompleteness of the first-order axiom systems. So the paper might be considered a late-comer in a community of logicians and set theorists who mainly followed finitary conceptions, in particular emphasizing the role of first-order logic (cf. [8]). However, Zermelo never shared this viewpoint: In his first letter to Gödel of September 21, 1931, (cf. [1]) he had written that the Skolem paradox rested on the erroneous assumption that every mathematically definable notion should be expressible by a finite combination of signs, whereas a reasonable metamathematics would only be possible after this “finitistic prejudice” would have been overcome, “a task I have made my particular duty”.
Inscriptions from Rhodes
Authors: Smith Cecil 
Published: May 2006

Mr. Albert Biliotti, the British Pro-Consul at Rhodes, who in conjunction with his brother has been carrying on excavations in that island for some years, has sent me the following eight inscriptions which he has noted from time to time and which, so far as I know, are unpublished. He has very kindly placed at my disposal his copies and, where they could be procured, paper impressions.1. On a fragment of marble, 5 inches high by 7½ inches broad, discovered in the course of excavations on the Akropolis of Kamiros: complete on the upper and left-hand sides: from a paper impression.
The Homeric Land System
Authors: Ridgeway William 
Published: May 2006

The object of the following pages, the substance of which was read before the Cambridge Branch of the Hellenic Society in 1883, is to examine into the true nature of the land-system of the Greeks of the Homeric age by means of the evidence contained in the poems themselves.On à priori grounds we might have expected, or at least should not be surprised, to find in the Iliad and Odyssey some traces of that primitive system known as the ‘Open-Field’ or ‘Common-Field’ system of agriculture, which the researches of recent years have proved to have once prevailed over a great part of the earth, and of which many survivals still exist.
Two Naucratite Vases
Authors: Gardner Ernest A. 
Published: May 2006

The two vases of which portions are reproduced upon Pl. LXXIX. may serve as representative specimens of the two most important classes of Naucratite pottery. They were both found, mixed with innumerable other fragments, amid the rubbish that covered the whole area of the temenos of Aphrodite, excavated by me in the season 1885–6. The two smaller figures represent the two sides of one fragment. These two vases are of especial interest, because they were both beyond any doubt made in Naucratis. Last year the special name of Naucratite ware was given to a class of vases covered with a fine whitish glaze, and with a polychrome decoration outside; black inside, with lotus patterns in red and white. This ware was often found by Mr. Petrie in 1884–5, and also in 1885–6, with dedicatory inscriptions painted on before baking, thus proving beyond doubt its local origin. The fragment now figured with a sphinx is one of the finest specimens of this same ware; in its treatment both inside and outside it preserves the essential characteristics that may be seen in the simpler examples.The other vase, with the lions and the stag, is one of a set of large bowls of which I found several nearly complete; in 1884–5 only a few fragments had appeared. These always have a dark glaze inside—red or black according to the firing; on this are painted concentric circles in white and purple. Their ornamentation is identical with that found on the inside of the eye-bowls; hence it would seem that these large bowls are a development of the eye-bowl type, just as the large polychrome vases are of the other Naucratite ware.
The Site and Antiquity of the Hellenic Ilion
Authors: Mahaffy J. P. 
Published: May 2006

There is an interesting question in relation to Dr. Schliemann's Trojan excavations, which seems yet unsettled; it is this: when was the historical Ilion really founded? and the answer to this question involves another of considerable interest: was the historical Ilion on the site of the mythical Troy? If its foundation be recent, and in historical times, there is room for doubt as to the identity of the sites, and accordingly the ancient inquirers who denied this identity also denied the antiquity of Ilion. I propose, therefore, to review the evidence as briefly as possible by the light of recent discussions, and beg leave for this very brevity's sake to be allowed through the following argument to call the heroic city Troy, and the historical Ilion, without further specification.Both Dr. Schliemann and I had come independently to the same conclusion on the seeond question just stated. He was led by his excavations, and I by a critical examination of the historical notices of the ancients, to assert the identity of the two sites, and we advanced from this to the further conclusion, that the alleged foundation of Ilion in historical times on a new site was not true, and that probably Ilion succeeded to the site and traditions of Troy without any considerable interruption. This was the general opinion throughout Greek history, till a very learned man, Demetrius of Scepsis, undertook to destroy the claims to a heroic ancestry of the Ilians, then rich and insolent through the favour of Lysimachus.
On the Hermes of Praxiteles
Authors: Smith A. H. 
Published: May 2006

It is well-known how, in the spring of 1877, the German explorers at Olympia had the good fortune to dig up the chief parts of a statue which had been seen by Pausanias in the same spot, and had been described by him in the following words:—χρόνῳ δὲ ὕστερον καὶ ἄλλα ἀνέθεσαν ἐς τὸ Ἡραῖον, Ἑρμῆν λίθου, Διόνυσον δὲ φέρει νήπιον, τέχνη δέ ἐστι Πραξιτέλους (Paus. v. 17, 3).The bulk of the statue is in exquisite preservation. The greater part however of the right arm of Hermes is missing. Since the whole motive of the subject depends upon the action of the arm, speculation has been busy as to the most probable restoration of this limb.With a view to the solution of this problem, Benndorf has collected together a series of types of the Hermes and Dionysos group. His list is not exhaustive, and he seems to have passed over certain instances of importance.My principal object in this paper is to attempt to show that a certain group of types contains the clue to the restoration of the missing arm, although they do not represent the arm in its true position; and on the other hand to show that certain types which have the arm in its true position, are untrustworthy guides as to the restoration of the attribute attached to it.
On the Electra and Antigone of Sophocles
Authors: Lloyd W. Watkiss 
Published: May 2006

The Electra of Sophocles betrays by the plainest indications that it is not a composition complete and rounded within itself, but only a fragment having the qualified completeness which fits it to contribute towards a larger symmetry. The action embraced falls short, it is very true but little, of full conclusion; Clytemnestra and her accomplice Aegisthus fall by the avenging sword of Orestes, and no such hints are admitted of the future troubles of the avenger, as in the treatment of the same subject by Aeschylus prepare for the concluding drama, the Eumenides. The moral dilemma, however, is neither wrought out to its complete statement nor to its most impressive solution. I find indeed in the play an illustration of a well-defined heroic nature and the eventualities of circumstance colliding with exalted character on the most critical emergencies; still we rise from the scene with sympathies in agitation—with minds eager upon interesting inquiries not pacified by adequate response.The Electra is the second of the preserved plays of Sophocles—the Antigone being another—which bears the name of a heroine for its title; there is this further and more intimate analogy between the two plays, that both the heroines are called on, or believe themselves so, to interfere between rulers of the state and their political victims in the interest of domestic piety, and in doing so exercise an influence and acquire an importance that elevate them to the dignity of the tragic stage.
Antiquities from the Island of Lipara
Authors: Murray A. S. 
Published: May 2006

The two painted vases reproduced on Pl. LXII. are part of a collection of antiquities found in some twenty tombs, which were excavated in 1879 in the island of Lipara, not far from the present town of that name. The precise locality is known as the Contrada Diana and is the property of Signor Scolarici. A road leading to it is called the Via Diana, and this name seems to have originated in the ruins of three small shrines which popular opinion has attributed to that goddess. The presence of these shrines in close proximity to the tombs has led to the conviction that this particular spot was the ancient cemetery of Lipara.The history of Lipara is briefly this. Known originally as the island Meligounis, but having no population, probably owing to its volcanic nature, it was first taken possession of by settlers from the adjoining coast of Italy, then under the legendary rule of Auson, and named after him Ausonia. The descendants of Auson continued to govern the newly-acquired island until about 580 B.C., when a colony of Rhodians and Knidians made its appearance. These colonists had started from their homes for Sicily, and had there with much disaster to themselves taken part in the war raging between the towns of Selinus and Egesta.
Inscription with a New Artist's Name, from Anaphe
Authors: Hicks E. L. 
Published: May 2006

Marble plinth from the Temple of Apollo at Anaphe. From an excellent impression of Mr. Theodore Bent. Present length of marble 20½ inches; height 5 inches.I am not aware that this dedication has been previously published. It is inscribed in beautiful letters of the best time, and can hardly be later than the fifth century. The name of the artist is otherwise unknown. The surface is beautifully preserved, and the dots of interpunction are quite clear in line 2: in line 1 there were none. The characters in line 1 are slightly larger than in the second.
A Head in the possession of Philip Nelson, Esq., M.B.
Authors: Gardner Ernest 
Published: May 2006

The head reproduced upon Pl. XI. has recently been acquired by Philip Nelson, Esq., M.B., and we are indebted to him both for his courteous permission to publish the head and for the photographs, taken by himself, from which our illustration is derived. The head is of Parian marble, and is clearly of Greek workmanship; it is also evidently derived from an original of the very highest artistic merit. It is in excellent preservation, except that the end of the nose and a part of the lips on the right side have been restored.Dr. Nelson has kindly supplied me with the following information as to the history of the head and as to its dimensions and present condition. It was acquired by him in Bath at the sale of the collection of the late Captain Maignac, who inherited it from his father-in-law, an artist named Walton, a contemporary of the painter Barker of Bath, 1769–1847. This Walton in all probability brought the head from Italy, where he is known to have travelled and collected pictures, &c.; but there seems to be no more exact record as to its origin. The head seems to have remained practically unknown to archaeologists until its acquisition by Dr. Nelson, who, appreciating its importance, sent photographs to the British Museum in July, 1897.
Mr. G. B. Grundy on Pylos and Sphacteria
Authors: Burrows Ronald M. 
Published: May 2006

It is with personal reluctance that I, like Mr. Grundy, again take up the argument. It is probably, however, better for the reader if the two sides thrash it out. The main reason why so many of the full-dress debates of archæology, on the λογєῖον for instance, or the ‘Old Temple,’ are still obscure for the non-combatant, is because the protagonists seem to get bored with each other's arguments, and pass them over in silence as self-evident fallacies. The result is endless, indecisive summarizing by those not immediately concerned.In the present number of the Journal, p. 234, Mr. Grundy expresses his astonishment that the walls on Pylos and Sphacteria, as photographed in Plates VII., IX. and X., of the preceding number present no more definite marks of date. This is surely a failure to recognize the conditions of the problem.
Some Pontic Milestones
Authors: Munro J. Arthur R. 
Published: May 2006

The following Roman milestones were copied by Mr. J. G. C. Anderson and myself in August 1899 on the direct road between Niksar (Neo-Caesarea) and the ancient bridge on the Halys near Vezir Keupru (Neo-Claudiopolis). I arrange them from East to West.1. At Zilkhor, a village near the right bank of the Lycus, about 22½ English miles from Niksar and 4½ from the bridge over the Iris at the site of Magnopolis, nearly opposite to Herek. The stone, which is of coarse marble and broken above, stands in an old cemetery outside and west of the village.
On the Tumulus of Choban Tepeh in the Troad
Authors: Calvert Frank 
Published: May 2006

I derive the materials of the present paper from some memoranda which I find amongst my archaeological notes and which relate to certain explorations to which I was not a party, made so long ago as 1887. I have thought that the particulars then obtained may be deemed sufficiently interesting to deserve a record in the history of Trojan archaeological discovery.The subject is one of the four small tumuli dotted about and near the hill of Balli-Dagh, the crest of which according to the now exploded theory of Le Chevalier (1785) was supposed to represent the Pergamos of Troy. In a memoir contributed to the Journal of the Archaeological Institute of 1864, I proved that the site in question was no other than that of the ancient city of Gergis. In the same paper I gave an account of the results of the excavation of one of the group of three tumuli on Balli-Dagh, the so-named Tomb of Priam. The other two, namely Le Chevalier's Tomb of Hector, and an unnamed hillock, were excavated respectively by Sir John Lubbock (about 1878) and Dr. Schliemann (1882) without result. The present relates to the fourth mound on the road between the villages of Bournarbashi and Arablar (as shown in the published maps), which goes by the name of Choban Tepeh (Shepherd's hillock) and the Tomb of Paris, according to Rancklin (1799).
An Inscribed Scarab
Authors: Gardner E. A. 
Published: May 2006

The above inscription appears on a very rudely formed scarab of translucent noble serpentine, which was acquired by Professor Petrie in Egypt; I publish it here with his permission; for the identification of the material I am indebted to Professor Bonney. The name Λαῖλαψ is only known as the name of a dog. It occurs as the hound of Procris in Ovid's Metamorphoses III. 771, and also among the hounds of Actaeon, ibid. III. 211, and in Hyginus Fab. 181. It is possible that this rude scarab may have been hung, as an ornament or amulet, on the neck of a hound; but perhaps such a decoration is more suitable to a pet dog; in that case the imposing name may have been given in playful irony.The ς at the end is superfluous; it may be an abbreviation of some sort; or possibly may be due to the hand of a foreigner who did not appreciate the significance of the Greek ψ. The lettering is of the late Hellenistic or of the Roman age.
Two Notes on Sophocles
Authors: Young George 
Published: May 2006

I HAVE lately spent some time in the locality in endeavouring to ascertain the true meaning of the passages concerned, which are as follows :Three commentators, a Scholiast, Col. Leake, and Sir R. C Jebb, have devoted some attention to this matter, the two latter following the first, in part or altogether, in conclusions, with which I find myself at variance. The wrong view was blindly followed by myself in my translation.I doubt if sufficient attention has been paid to the dramatic conditions of the problem to be solved. What had Sophocles in view, in planning this incident, and in writing these passages? He was proposing (1) to add interest to the action of the play by the conduct, behind the scenes, of a flight and capture along roads well known to his audience; and (2) to utilise this incident so as to bring out in Theseus the characteristic of thorough practical efficiency as a putter down of violence. Interpretations which make Theseus appear incompetent, or which militate against obvious facts of topography, should not be lightly hazarded; neither must we conclude, however we may be unable to explain the allusions, that they were not clear to an Athenian audience, or that Sophocles and his audience did not care that they should be clear.
Inscriptions from Crete
Authors: Myres John L. 
Published: May 2006

The inscriptions which follow were copied during a short tour in the west of Crete during July and August, 1893. So far as I know they are unpublished, but I trust I shall be pardoned if I have missed any previous notice of any of them. I saw and verified all those published in B.C.H. xiii. 68 ff. and that in the Syllogos at Retimo, id. 47. The type used below is selected so as to represent each individual letter as nearly as possible, without regard to the conventional printers' alphabets. The result is an apparent mixture of incongruous forms, which is however largely duo to the very irregular lettering actually in use in the remoter parts of Crete in the later Greek periods.1. On a block of fine-grained blue marble, the base of a stele: 31 cm. high, 40 broad, and 46 long: the back and left side broken: original length at least 70 cm., for the socket for the stele is 22 cm. distant from the perfect (right) side face, and is continued to the left beyond the break. The inscription consists of four elegiac couplets; the first line is cut close to the upper edge of the stone, and is consequently much effaced. The letters average 10 mm. in height and breadth, and are of the third or late fourth century.