Logical reflection and formalism

1958 ◽  
Vol 23 (3) ◽  
pp. 241-249 ◽  
Author(s):  
P. Lorenzen
Keyword(s):  
Nineteenth Century ◽  
Seventeenth Century ◽  
Set Theory ◽  
Basic Concept ◽  
Special Class ◽  
Formal System ◽  
One Step ◽  
Greek Mathematics ◽  
Axiomatic Set Theory ◽  
Modern Mathematics

A “foundational crisis” occurred already in Greek mathematics, brought about by the Pythagorean discovery of incommensurable quantities. It was Eudoxos who provided new foundations, and since then Greek mathematics has been unshakeable. If one reads modern mathematical textbooks, one is normally told that something very similar occurred in modern mathematics. The calculus invented in the seventeenth century had to go through a crisis caused by the use of divergent series. One is told that by the achievements of the nineteenth century from Cauchy to Cantor this crisis has definitely been overcome. It is well known, but it is nevertheless very often not taken seriously into account, that this is an illusion. The so-called ε-δ-definitions of the limit concepts are an admirable achievement, but they are only one step towards the goal of a final foundation of analysis. The nineteenth century solution of the problem of foundations consists of recognizing, in addition to the concept of natural number as the basis of arithmetic, another basic concept for analysis, namely the concept of set. By the inventors of set theory it was strongly held that these sets are self-evident to our intuition; but very soon the belief in their self-evidence was destroyed by the set-theoretic paradoxes. After that, about 1908, the period of axiomatic set theory began. In analogy to geometry there was put forward an uninterpreted system of axioms, a formal system. This, of course, is quite possible. A formal system contains strings of marks; and a special class of these strings, the class of the so-called “theorems”, is inductively defined.

scholarly journals A Formal System of Axiomatic Set Theory in Coq

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 21510-21523 ◽  
Author(s):  
Tianyu Sun ◽  
Wensheng Yu
Keyword(s):  
Set Theory ◽  
Formal System ◽  
Axiomatic Set Theory

Interrelationship of Jatharagni and Dhatvagni in context to Dhatvagni Pradoshaj Vikaras.

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Kishor G. Satani ◽  
Hemang Raghvani ◽  
Kunjal Bhatt
Keyword(s):  
Basic Concept ◽  
Functional Relationship ◽  
Structural Relationship ◽  
The Other ◽  
Proper Function ◽  
One Step ◽  
Material Form

The concept of Agni is basic concept of Ayurveda. Agni is believed to be the agency for any kind of transformation. Maharshi Vagbhatta says that each of the Dosha, Dhatu, Mala etc. have their own Agni. This is how the number of Agni cannot be limited. Though each and every Agni has its own importance, Dehagni or Jatharagni is the most important one as all other Agnis are depended upon Dehagni. Acharya Vagbhatta says that proper function of every Dhatvagni is depended on the Jatharagni. Increase or decrease of Jatharagni directly affects the function of Dhatvagni. Thus, Maharshi Charaka established functional relationship among Jatharagni and other Agnis. Maharshi Vagbhattta goes one step ahead of Maharshi Charaka by using word “Amsha” means; moieties of Kayagni, located to in its own place, are distributed to and permeate to all the Dhatus. A decrease of it (below the normal) makes for an increase of the Dhatus, while an increase of it (above the normal) makes for a decrease of a Dhatus. This shows structural relationship too, between Jatharagni and Dhatvagni as “Amsha” always indicates Murtatva or material form. Further more all these Agnis are connected with each other and due to this relationship, vitiation of Jatharagni results in vitiation of all the other Agnis.

Hymnody and Liturgy

2019 ◽  
pp. 491-506
Author(s):  
Jonathan Hehn
Keyword(s):  
Nineteenth Century ◽  
Seventeenth Century ◽  
Sixteenth Century ◽  
North American ◽  
John Calvin ◽  
Church Of Scotland ◽  
Metrical Psalmody ◽  
History Of ◽  
The Church

This chapter outlines the history of Presbyterian worship practice from the sixteenth century to the present, with a focus on North American Presbyterians. Tracing both their hymnody and their liturgy ultimately to John Calvin, Presbyterian communions have a distinct heritage of worship inherited from the Church of Scotland via seventeenth-century Puritans. Long marked by metrical psalmody and guided by the Westminster Directory, Presbyterian worship underwent substantial changes in the nineteenth century. Evangelical and liturgical movements led Presbyterians away from a Puritan visual aesthetic, into the use of nonscriptural hymnody, and toward a recovery of liturgical books. Mainline North American and Scottish Presbyterians solidified these trends in the twentieth and twenty-first centuries; however, conservative North American denominations and some other denominations globally continue to rely heavily on the use of a worship directory and metrical psalmody.

PAWNSHIP, DEBT, AND ‘FREEDOM’ IN ATLANTIC AFRICA DURING THE ERA OF THE SLAVE TRADE: A REASSESSMENT

2014 ◽  
Vol 55 (1) ◽  
pp. 55-78 ◽  
Author(s):  
Paul E. Lovejoy
Keyword(s):  
Nineteenth Century ◽  
Seventeenth Century ◽  
Slave Trade ◽  
Gold Coast ◽  
Guinea Coast ◽  
Congo River

AbstractA reassessment of the institution of pawnship in Africa for the period from the seventeenth century to the nineteenth century tightens the reference to situations in which individuals were held as collateral for debts that had been incurred by others, usually relatives. Contrary to the assumptions of some scholars, pawnship was not related to poverty and enslavement for debt but rather to commercial liquidity and the mechanisms by which funds were acquired to promote trade or to cover the expenses of funerals, weddings, and religious obligations. A distinction is made, therefore, between enslavement for debt and pawnship. It is demonstrated that pawnship characterized trade with European and American ships in many parts of Atlantic Africa, but not everywhere. While pawnship was common north of the Congo River, at Gabon, Cameroon, Calabar, the interior of the Bights of Biafra and Benin, the Gold Coast, and the upper Guinea coast, it was illegal in most of Muslim Africa and the Portuguese colony of Angola, while it was not used in commercial dealings with Europeans at Bonny, Ouidah, and other places.

Firearms in Southern Africa: A survey

1971 ◽  
Vol 12 (4) ◽  
pp. 517-530 ◽  
Author(s):  
Shula Marks ◽  
Anthony Atmore
Keyword(s):  
Nineteenth Century ◽  
Seventeenth Century ◽  
Southern Africa ◽  
Sub Saharan Africa ◽  
Black And White ◽  
Sub Saharan ◽  
Settler Population ◽  
White Settlement

The relationships of the peoples of southern Africa after the establishment and expansion of the white settlement in the mid-seventeenth century can be seen in terms of both conflict and interdependence, both resistance and collaboration. The conflict often split over into warfare, not only between black and white, but also within both groups. As time passed, firearms came to be used by ever-widening circles of the combatants, often as much the result of the increased collaboration and interdependence between peoples as of the increased conflict. As Inez Sutton has pointed out, ‘in contrast to most of the rest of [sub-Saharan] Africa, the presence of a settler population ensured that the supply of arms was the most modern rather than the most obsolete’, and on the whole non-whites were acutely aware of changes in the manufacture of firearms in the nineteenth century.

TRANSFORMING THE CHARACTER OF THE UPPER MISSISSIPPI RIVER

2021 ◽  
Vol 40 (1) ◽  
pp. 102-129
Author(s):  
KRISTAN COCKERILL
Keyword(s):  
Nineteenth Century ◽  
Seventeenth Century ◽  
Mississippi River ◽  
River Management ◽  
Late Nineteenth Century ◽  
Upper Mississippi River ◽  
Flow Rates ◽  
Specific Language ◽  
Late Nineteenth ◽  
Over Time

ABSTRACT Despite the long-understood variability in the Mississippi River, the upper portions of the river have historically received less attention than the lower reach and this culminated in the lower river dominating twentieth century river management efforts. Since the seventeenth century, there have been multiple tendencies in how the upper river was characterized, including relatively spare notes about basic conditions such as channel width and flow rates which shifted to an emphasis on romantic descriptions of the riparian scenery by the mid-nineteenth century. Finally, by the late nineteenth century the upper river was routinely portrayed as a flawed entity requiring human intervention to fix it. While the tone and specific language changed over time, there remained a consistent emphasis that whatever was being reported about the river was scientifically accurate.

Invisible Architectures

2000 ◽  
Vol 13 (1) ◽  
pp. 121-136 ◽  
Author(s):  
Hans-Jörg Rheinberger
Keyword(s):  
Nineteenth Century ◽  
Seventeenth Century ◽  
Historical Development ◽  
Basic Problem ◽  
Life Sciences ◽  
The Other ◽  
Modern Life ◽  
Historical Process ◽  
Strategy I ◽  
The Invisible

The ArgumentIn this essay I will sketch a few instances of how, and a few forms in which, the “invisible” became an epistemic category in the development of the life sciences from the seventeenth century through the end of the nineteenth century. In contrast to most of the other papers in this issue, I do not so much focus on the visualization of various little entities, and the tools and contexts in which a visual representation of these things was realized. I will be more concerned with the basic problem of introducing entities or structures that cannot be seen, as elements of an explanatory strategy. I will try to review the ways in which the invisibility of such entities moved from the unproblematic status of just being too small to be accessible to the naked or even the armed eye, to the problematic status of being invisible in principle and yet being indispensable within a given explanatory framework. The epistemological concern of the paper is thus to sketch the historical process of how the “unseen” became a problem in the modern life sciences. The coming into being of the invisible as a space full of paradoxes is itself the product of a historical development that still awaits proper reconstruction.

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