19th Century Logic Between Philosophy and Mathematics

1999 ◽  
Vol 5 (4) ◽  
pp. 433-450 ◽  
Author(s):  
Volker Peckhaus

AbstractThe history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole's The Mathematical Analysis of Logic of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical development of logic, although logic is evidently one of the basic disciplines of philosophy. One needs only to recall some of the standard 19th century definitions of logic as, e.g., the art and science of reasoning (Whateley) or as giving the normative rules of correct reasoning (Herbart).In the paper the relationship between the philosophical and the mathematical development of logic will be discussed. Answers to the following questions will be provided:1. What were the reasons for the philosophers' lack of interest in formal logic?2. What were the reasons for the mathematicians' interest in logic?3. What did “logic reform” mean in the 19th century? Were the systems of mathematical logic initially regarded as contributions to a reform of logic?4. Was mathematical logic regarded as art, as science or as both?


Author(s):  
Doron Swade

The principles on which all modern computing machines are based were enunciated more than a hundred years ago by a Cambridge mathematician named Charles Babbage.’ So declared Vivian Bowden—in charge of sales of the Ferranti Mark I computer— in 1953.1 This chapter is about historical origins. It identifies core ideas in Turing’s work on computing, embodied in the realisation of the modern computer. These ideas are traced back to their emergence in the 19th century where they are explicit in the work of Babbage and Ada Lovelace. Mechanical process, algorithms, computation as systematic method, and the relationship between halting and solvability are part of an unexpected congruence between the pre-history of electronic computing and the modern age. The chapter concludes with a consideration of whether Turing was aware of these origins and, if so, the extent—if any—to which he may have been influenced by them. Computing is widely seen as a gift of the modern age. The huge growth in computing coincided with, and was fuelled by, developments in electronics, a phenomenon decidedly of our own times. Alan Turing’s earliest work on automatic computation coincided with the dawn of the electronic age, the late 1930s, and his name is an inseparable part of the narrative of the pioneering era of automatic computing that unfolded. Identifying computing with the electronic age has had the effect of eradicating pre-history. It is as though the modern era with its rampant achievements stands alone and separate from the computational devices and aids that pre-date it. In the 18th century lex continui in natura proclaimed that nature had no discontinuities, and we tend to view historical causation in the same way. Discontinuities in history are uncomfortable: they offend against gradualism, or at least against the idea of the irreducible interconnectedness of events. The central assertion of this chapter is that core ideas evidenced in modern computing, ideas with which Turing is closely associated, emerged explicitly in the 19th century, a hundred years earlier than is commonly credited.



1999 ◽  
Vol 5 (1) ◽  
pp. 1-44 ◽  
Author(s):  
Wilfried Sieg

AbstractHilbert's finitist program was not created at the beginning of the twenties solely to counteract Brouwer's intuitionism, but rather emerged out of broad philosophical reflections on the foundations of mathematics and out of detailed logical work; that is evident from notes of lecture courses that were given by Hilbert and prepared in collaboration with Bernays during the period from 1917 to 1922. These notes reveal a dialectic progression from a critical logicism through a radical constructivism toward finitism; the progression has to be seen against the background of the stunning presentation of mathematical logic in the lectures given during the winter term 1917/18. In this paper, I sketch the connection of Hilbert's considerations to issues in the foundations of mathematics during the second half of the 19th century, describe the work that laid the basis of modern mathematical logic, and analyze the first steps in the new subject of proof theory. A revision of the standard view of Hilbert's and Bernays's contributions to the foundational discussion in our century has long been overdue. It is almost scandalous that their carefully worked out notes have not been used yet to understand more accurately the evolution of modern logic in general and of Hilbert's Program in particular. One conclusion will be obvious: the dogmatic formalist Hilbert is a figment of historical (de)construction! Indeed, the study and analysis of these lectures reveal a depth of mathematical-logical achievement and of philosophical reflection that is remarkable. In the course of my presentation many questions are raised and many more can be explored; thus, I hope this paper will stimulate interest for new historical and systematic work.



Romantik ◽  
2013 ◽  
Vol 2 (1) ◽  
pp. 77 ◽  
Author(s):  
Gry Hedin

During the first part of the nineteenth century, geologists developed a history of the earth so different from that accepted in previous centuries that it encouraged a rethinking of the relationship between man and nature. In this article I will argue that painters followed these changes closely and that some of them let the narratives and images of geology inform the way they depicted nature. In arguing my point, I will focus on images and descriptions of the chalk cliffs on the Danish island of Møn by both geologists and painters. I will follow the scientific advances in geology by referring to the texts and images of Søren Abildgaard, Henrich Steffens, Johan Georg Forchhammer, and Christopher Puggaard, and discuss how their changing theories correspond with paintings of the cliffs by four artists: Christopher Wilhelm Eckersberg, Frederik Sødring, Louis Gurlitt, and Peter Christian Skovgaard.



2013 ◽  
Vol 19 ◽  
pp. 51-67
Author(s):  
И.В. Хоменко

This paper traces the development of history of logic in Ukraine in the 19th century and early 20th century. The author particularly discusses and compares the logical concepts of representatives of Kyiv philosophies, who made their contribution to the development of logic as a science and academic discipline. Some of them had sunk into oblivion for a long time and their names are still unknown in the logic community.



Author(s):  
Mustolehudin Mustolehudin ◽  
Agus Iswanto ◽  
Nurlaili Noviani ◽  
Umi Masfiah ◽  
Roch Aris Hidayat ◽  
...  

There weren’t many scholars who studied the history of Indonesian literacy practices, even though the written sources were available abundantly. The existed studies from many scholars less concerned about the relationship between literacy practice and religious proselytizing (da’wa) in Indonesia. Whereas, both of them are closely related in Indonesia literacy practices, especially in Indonesia’s pre-contemporary era. This study aims to emphasize the relation between literacy practices and Islamic da’wa through KH. Ahmad Rifai works. He was a prolific Muslim scholar in the 19th century who wrote many religious books and countered colonialism. This study reviewed Ahmad Rifai books through a new literacy practice perspective. The argument of this study is the literacy practices had a tight relation with Islamic proselytizing in Indonesian history. The literacy practice for da’wa often considers the locality in culture. Therefore, the form of literacy practice that emerges is a form of literacy that considers local languages and writings, which in this case is the Javanese language and the Pegon script. This paper gives a contribution to the discussion between accommodative da’wa and literacy practices.



Classics ◽  
2013 ◽  
Author(s):  
Richard D. McKirahan

The word “Presocratic” was invented in the 19th century ce and does not represent a category recognized in antiquity. The expression “Presocratic philosophy” is misleading: first, because some “Presocratics” were Socrates’ contemporaries, some of them surviving him by decades, and second, because they did not call themselves philosophers and because the fields of inquiry they practiced extend far beyond what we think of as philosophy. Nevertheless, the label “Presocratic” is commonly applied to the intellectual figures of the 6th and 5th centuries bce (and a few that lived into the 4th) who dwelt in the Greek-speaking lands from what is now coastal Turkey to Sicily and who are included in this bibliography. Evidence of the influence of Presocratic thought on other areas of culture than philosophy is found in texts ranging from historical and rhetorical works to tragedy and comedy and beyond, to the Hippocratic medical writings and the Derveni Papyrus. Since no original texts of the Presocratics survive entirely, our knowledge of them is based on quotations (“fragments”) from their works and on reports (“testimonia”) about their views, lives, and writings in other authors whose works have been transmitted. Presocratic philosophy is the earliest phase of Greek philosophy; Plato and Aristotle were strongly influenced by the Presocratics and recognized them as their intellectual predecessors. The subsequent interest in the Presocratics in antiquity and in consequence our knowledge of them is largely due to Aristotle. In more recent times, systematic study of them began in the 19th century. Diels’s Doxographi Graeci (Diels 1879, cited under Source Criticism) for the first time permitted a rational reconstruction of much of the testimonial material, and Die Fragmente der Vorsokratiker (Diels and Kranz 1952, cited under Collections of Source Materials; first published in 1903) provided a collection of fragments and testimonia that brought the study of the Presocratics within the range of students and nonspecialist scholars of philosophy, classics, and the history of science. The study of “Presocratic philosophy” has traditionally extended to more subjects than we commonly consider philosophical. It includes topics not only in method, logic, metaphysics, epistemology, ethics, cognition, cosmology, and “psychology”—here meaning views about the nature of the psuchē (frequently translated “soul”)—but also examines connections with science and mathematics, and a variety of social practices. Recently this tendency has further expanded to include religious and mystical beliefs and practices, while by no means excluding the philosophical and scientific aspects of Presocratic thought, which remain the dominant topics of research.



Author(s):  
Guadalupe García

The Cuban city of San Cristóbal de la Habana has been a nodal point of economic, commercial, political, and cultural exchange since its 1519 founding on Cuba’s northern shore. Residents’ decision to locate the city next to the natural deepwater harbor that became today’s harbor, illustrates the importance of geography, space, and environment in Havana’s early history. Through the distinct environs of Havana, enslaved, free black, Spanish, immigrant, criollo (and later Cuban) residents defined and gave new meaning to a geography marked by the city’s colonial origins. The end of the 19th century and early 20th century marked the end of Spanish colonialism in Cuba (1898) and the beginning of the US occupation of the island (1899–1902). The political transition solidified the importance of Havana as the economic and political center of Cuba. The city became a broker of a new set of cultural, social, and political exchanges as the country’s economic prosperity—the result of an affinity for US and global capitalist markets—also inaugurated a booming and pervasive tourist economy. Western influence and a neocolonial relationship between Cuba and the United States engendered an urban renaissance that emphasized cosmopolitanism and a dynamic, highly mobile urban population. Havana’s built environment oriented residents and visitors alike to its modern architecture, seaside resorts, and dynamic nightlife. The city’s concentration of wealth, however, underscored continued disparities between Cuba’s urban and rural populations as well as within sectors of the urban population. There is a well-developed body of scholarship that addresses the complicated history of the city, especially for the colonial period and the early 20th century. Until recently, there was a scarcity of literature on the city following the revolutionary transition of 1959. This changed, however, with the onset of the 1980s. In 1982 UNESCO declared the colonial core city of Havana a World Heritage Site. Urban renewal and preservation became topics of scholarly discussions around administrative efforts to preserve, restore, and orient the direction of the city. Then, in the early 1990s, urban development in Havana (like all development in Cuba) come to an immediate halt after the dissolution of the USSR ended Soviet subsidies and precipitated one of the worst economic disasters in Cuban history. The country’s political and economic situation and the liberalization of the economy and the growth of tourism brought an ever-increasing interest in the issues and environment of the city, with scholars taking up the now familiar themes of access to the city, political inclusion and exclusion, and urban patrimony in their scholarship. As a field of study the literature on Havana mirrors the frameworks found in the broader field of urban history. The literature breaks down into two distinct subfields; those studies that examine “the history of the city” and those that examine “histories that unfold within cities” (See Brodwyn Fisher’s article Urban History in Oxford Bibliographies). The former has long dominated the literature on Havana, and only recently has new scholarship begun to approach the city as a subject in its own right or from the vantage points of disciplinary perspectives outside of history, architecture, and planning. In this essay I have chosen to introduce readers to the vast literature that centers explicitly on the development of the city, much of which was published in Cuba from the 19th century onward. This literature forms part of a well-known cannon in Cuba (including work in the Spanish-language press produced outside of the island) but might be lesser known to non-specialists. I have also included well-established, as well as recent and emerging, works where Havana assumes a central role in the narrative. I have done this in order to broaden the categorical analysis of what constitutes a history of or about Havana. As with any bibliographic essay, I have excluded much in order to provide an overview of Havana and familiarize readers with scholars who explore thematic interests in questions of race, slavery, or culture through the social fabric of the city. Where appropriate, I have organized the essay according to time period or publication date (in order to give the reader an idea of the scholarship on colonial architecture, for example). Finally, most titles on this list can easily be placed in more than one of the categories listed in the Table of Contents; for the sake of space I have cross-listed only a few of these works, but indicated when readers might find other sections of the essay useful.



ENDOXA ◽  
2017 ◽  
pp. 103
Author(s):  
Kurt Plischke ◽  
Alfons Labisch

Contemporary philosophy of science sets the origins of the predominantattributes of the term “gene” in the year 1900 when Gregor Mendel’s work was rediscovered. Yet it was the speculative biology of the second half of the 19th century that opened up the epistemic sphere for a new conception of heredity: heredity as the transmission of particulate, hereditable material units with a tendency for self-preservation. The then young discipline of biology dissociated its terminology from the preconceptions of natural philosophy. In the early 20th century, the postulated hereditary particles were associated with the chromosome and, at least in the 1940s, with nucleic acid: which was being stable and, at the same time, mutable, as well as capable of self-reproduction, self-selectivity, and memory. DNA epitomizes the perfect biological principle. But the most recent conception of the gene is not free from anthropomorphisms.



Author(s):  
Beloglazov I.A. ◽  
Biryukova N.V. ◽  
Nesterova N.V.

The authors of the work analyzed the sources that characterize the influence of absinthe on human culture. Absinthe, an alcoholic drink containing wormwood (Artemisia absinthium L.), was banned in the early 20th century due to unusual properties attributed to the side effects of drinking this alcohol. This review contains information about the history of the drink. On the one hand, absinthe left its mark in the culture as a “muse” for the creators, remaining forever imprinted in the works of various types of art, on the other hand, it became the main enemy for the most part of society because of the harmful properties that was characterized by researchers of the 19th century.



Transilvania ◽  
2021 ◽  
pp. 61-69
Author(s):  
Cosmin Ciotloș

The present study unfolds on several layers.In the first place, it propounds a history of the relationship between the alcoholic drink that is popularly known as „spritz” and Romanian literature, illustrated with examples from the 19th century and the beginning of the 20th. Secondly, it restores a terminology area, determining the first usage of the word (with all its synonyms) and what prominent or less-known authors have frequently utilized it. Thirdly, it inspects documentation data which thus reinstates two potential forerunners of this interstitial phenomenon: Anton Pann and Daniil Scavinschi. In the fourth place, it exposes a series of thresholds in the evolution of the Romanian mentality, based on the level of tolerance or disapproval that writers have expressed, when confronted with this liquor.



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