Aristotle and the Consequentia Mirabilis

1957 ◽  
Vol 77 (1) ◽  
pp. 62-66 ◽  
Author(s):  
William Kneale
Keyword(s):  
Seventeenth Century ◽  
Euclidean Geometry ◽  
Early History ◽  
Philosophical Literature ◽  
Non Euclidean Geometry ◽  
History Of ◽  
First Time

In a passage of his Protrepticus mentioned by several ancient authors Aristotle wrote: εἰ μὲνφιλοσοφητέον φιλοσοφητέον, καὶ εἰ μὴ φιλοσοφητέον φιλοσοφητέον πάντως ἄρα φιλοσοφητέον (V. Rose, Aristotelis Fragmenta, 51. Cf. R. Walzer, Aristotelis Dialogorum Fragmenta, p. 22; W. D. Ross, Select Fragments of Aristotle, p. 27). That is to say, ‘If we ought to philosophise, then we ought to philosophise; and if we ought not to philosophise, then we ought to philosophise (i.e. in order to justify this view); in any case, therefore, we ought to philosophise’. So far as I know, this is the first appearance in philosophical literature of a pattern of argument that became popular among the Jesuits of the seventeenth century under the name of the consequentia mirabilis and inspired Saccheri's work Euclides ab Omni Naevo Vindicatus, in which theorems of non-Euclidean geometry were proved for the first time. The later history has been told by G. Vailati (in his article on Saccheri's Logica Demonstrativa, ‘Di un’ opera dimenticata del P. Gerolamo Saccheri’, reprinted in his Scritti, 1911, pp. 477–84), G. B. Halsted (in the preface to his 1920 edition of Saccheri's Euclides), and J. -Łukasiewicz (in his ‘Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls’, Comptes Rendus des séances de la société des sciences et des lettres de Varsovie, Classe III, Vol. xxiii, 1930, p. 67). In this note I wish to consider only the early history of the argument and in particular a curious criticism of it which appears in Aristotle's Prior Analytics.

scholarly journals The Early History of Non-Euclidean Geometry

Nature ◽  
1910 ◽  
Vol 84 (2128) ◽  
pp. 172-172
Author(s):  
D. M. Y. SOMMERVILLE
Keyword(s):  
Euclidean Geometry ◽  
Early History ◽  
Non Euclidean Geometry ◽  
History Of

From koine to standard: the early modern origin of a key linguistic term

2021 ◽  
Vol 7 (2) ◽  
pp. 283-302
Author(s):  
Raf Van Rooy
Keyword(s):  
Seventeenth Century ◽  
Western Europe ◽  
Early History ◽  
John Dryden ◽  
Common Language ◽  
Regional Dialects ◽  
Language Studies ◽  
Linguistic Term ◽  
History Of ◽  
The Impact

Abstract In this paper, I explore the early history of the word standard as a linguistic term, arguing that it came to compete with the designation common language in the seventeenth century. The latter phrase was, in turn, formed by ideas on the Greek koine during the Renaissance and appears to have been the first widely used collocation referring to a standard language-like entity. In order to sketch this evolution, I first discuss premodern ideas on the koine. Then, I attempt to outline how the intuitive comparison of the koine with vernacular norms that were being increasingly regulated resulted in the development of the concept of common language, termed lingua communis in Latin (a calque of Greek hē koinḕ diálektos), in the sixteenth century. This phrase highlighted the communicative functionality of the vernaculars, which were being codified in grammars and dictionaries. Scholars contrasted these common languages with regional dialects, which had a limited reach in terms of communication. This distinction received a social and evaluative connotation during the seventeenth century, which created a need for terminological alternatives; an increasingly popular option competing with common language was standard, which was variously combined with language and tongue by English authors from about 1650 onwards, especially in Protestant circles, where the vernaculars tended to play a more prominent role than in Catholic areas. Of major importance for this evolution was the work and linguistic usage of the poet John Dryden (1631–1700). This essay uncovers the early history of standard as a key linguistic term, while also presenting a case study which shows the impact of the rediscovery of the Greek heritage on language studies in Western Europe, especially through the term common language.

scholarly journals Prosthesis: From Grammar to Medicine in the Earliest History of the Word

2018 ◽  
Vol 38 (4) ◽  
Author(s):  
Brandon W. Hawk
Keyword(s):  
Seventeenth Century ◽  
Disability Studies ◽  
Medical Knowledge ◽  
Early History ◽  
Archival Material ◽  
Printed Books ◽  
Study Of Medicine ◽  
History Of ◽  
Medical Treatises

This article provides an examination of the earliest history of the term prosthesis in English, re-evaluating other such histories with previously unrecognized archival material from early printed books. These sources include sixteenth- and seventeenth-century early printed books such as handbooks of grammar, English dictionaries, British Latin dictionaries, and medical treatises on surgery. Such an investigation reveals both a more nuanced trajectory of the early history of the word in English and fuller context for a shift in meaning from usages in the study of grammar and rhetoric to the study of medicine and surgery. This narrative, then, speaks to the growth of medical knowledge and discourse in the sixteenth and seventeenth centuries, as well as concepts about disability that remain part of disability studies even in the present field.

Protogeometric Vases from Amorgos in the Museum of the British School

1989 ◽  
Vol 84 ◽  
pp. 177-185
Author(s):  
R.W.V. Catling ◽  
R.E. Jones
Keyword(s):  
Chemical Analysis ◽  
Early History ◽  
The Other ◽  
The South ◽  
South West ◽  
British School ◽  
History Of ◽  
First Time

Two vases, a cup and an oinochoe, from Arkesine in south-west Amorgos are published for the first time. It is argued that both are probably Middle Protogeometric, one an import from Euboia, the other from the south-east Aegean; chemical analysis supports both attributions. Their implications for the early history of Amorgos are discussed.

Early European Sources Relating to the Kingdom of Ijebu (1500-1700): A Critical Survey

1986 ◽  
Vol 13 ◽  
pp. 245-260 ◽  
Author(s):  
Robin Law
Keyword(s):  
Seventeenth Century ◽  
Limited Range ◽  
West African ◽  
Source Material ◽  
Early History ◽  
Critical Survey ◽  
African History ◽  
The West ◽  
History Of ◽  
Original Information

The history of the Yoruba, as is well known, is very poorly documented from contemporary European sources prior to the nineteenth century, in comparison with their neighbors Benin to the east and the states of the ‘Slave Coast’ (Allada, Whydah, and Dahomey) to the west. There is, however, one Yoruba kingdom which features in contemporary European sources from quite early times, and for which at least intermittent documentation extends through the sixteenth and seventeenth centuries. This is the kingdom of Ijebu in southern Yorubaland. The availability of contemporary European documentation for the early history of Ijebu is especially valuable since the historical traditions of Ijebu itself do not appear to be very rich.Such, at least, is the impression given by published accounts of Ijebu history: although a large number of kings of Ijebu are recalled, thereby suggesting for the kingdom a considerable antiquity, and though there is some recollection locally of early contacts with the Portuguese, it does not seem that Ijebu traditions record much in the way of a detailed narrative of the kingdom's early history. At the same time, the European sources referring to Ijebu present considerable problems of interpretation, particularly with regard to establishing how far successive references to the kingdom constitute new original information rather than merely copying a limited range of early sources, and consideration of them helps to illuminate the character of early European sources for west African history in general. For these reasons, it seems a useful exercise to pull together all the available early European source material relating to Ijebu down to the late seventeenth century.

New Light on the History of Isaac Newton's Library

The Library ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 89-97
Author(s):  
Karen Thomson
Keyword(s):  
Early History ◽  
Scholarly Work ◽  
Isaac Newton ◽  
History Of ◽  
First Time ◽  
Plausible Reason

Abstract In the standard scholarly work, The Library of Isaac Newton published by CUP in 1978, John Harrison makes two significant assumptions about the library’s early history which are incorrect. This paper highlights the necessary revisions, including the unnoticed role played by Mrs Jane Musgrave, Jane Austen’s godmother, in the library’s preservation. It also proposes for the first time a plausible reason why John Huggins, Warden of the Fleet Prison, bought the library from the executors immediately after Newton’s death.

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