Hilbert's Programs: 1917–1922

1999 ◽  
Vol 5 (1) ◽  
pp. 1-44 ◽  
Author(s):  
Wilfried Sieg
Keyword(s):  
Mathematical Logic ◽  
19Th Century ◽  
Proof Theory ◽  
Foundations Of Mathematics ◽  
Radical Constructivism ◽  
Standard View ◽  
Modern Logic ◽  
Philosophical Reflection ◽  
Lecture Courses ◽  
The 19Th Century

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.

19th Century Logic Between Philosophy and Mathematics

1999 ◽  
Vol 5 (4) ◽  
pp. 433-450 ◽  
Author(s):  
Volker Peckhaus
Keyword(s):  
Mathematical Logic ◽  
19Th Century ◽  
Early 20Th Century ◽  
Symbolic Logic ◽  
Modern Logic ◽  
History Of ◽  
And Mathematics ◽  
Correct Reasoning ◽  
The 19Th Century ◽  
The Relationship

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?

Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory Probability Theory.

1994 ◽  
Vol 101 (4) ◽  
pp. 369
Author(s):  
Karen Hunger Parshall ◽  
A. N. Kolmogorov ◽  
A. P. Yushkevich
Keyword(s):  
Probability Theory ◽  
Mathematical Logic ◽  
Number Theory ◽  
19Th Century ◽  
The 19Th Century

scholarly journals Pierre Leroux et la religion de l’humanité : une conception post-séculière au XIXe siècle ?

2019 ◽  
Vol 66 ◽  
pp. 25-41
Author(s):  
Tomasz Szymański
Keyword(s):  
19Th Century ◽  
Civil Religion ◽  
Eternal Life ◽  
Philosophical Reflection ◽  
Religion Of Humanity ◽  
Xixe Siecle ◽  
The 19Th Century ◽  
Xixe Siècle

PIERRE LEROUX AND THE RELIGION OF HUMANITY: A POST-SECULAR CONCEPT IN THE 19th CENTURY?The aim of the article is to show, using the example of Pierre Leroux, that the extension of the post-secular perspective to Romanticism is not only possible, but even desirable. Leroux’s work contains in this context two fundamental aspects: first, a philosophical reflection on humanity, its true tradition and eternal life; secondly, a socio-political reflection on the necessity of establishing a civil religion. Some threads that are present in Leroux’s thought, referring to Joachimism, seem to make him closer to the views of contemporary post-secular and post-modern authors.

scholarly journals “A Thing of Dreams and Desires, a Siren, a Whisper, and a Seduction”: Mermaids and the seashore in H. G. Wells’s The Sea Lady: A Tissue of Moonshine

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Emily Alder
Keyword(s):  
19Th Century ◽  
Gender Politics ◽  
Social Practices ◽  
The Novel ◽  
Philosophical Reflection ◽  
The Real ◽  
Social Conventions ◽  
Everyday World ◽  
Ways Of Thinking ◽  
The 19Th Century

The Sea Lady (1901) is one of the more neglected early novels of H. G. Wells, particularly compared to his more famous scientific romances. Both a social satire and a mediation on the limits of human imagination, Wells’s only mermaid story has drawn surprisingly little attention as a mermaid story. The novel is highly intertextual with legends, written tales, and artwork about mermaids in the 19th Century, which, I argue, Wells deploys in pursuit of the narrative’s interests in gender politics, the critique of social conventions, and philosophical reflection on the possibility of reaching for greater knowledge. Traditional associations of mermaid figures with sexual and ontological transgression and with liminal zones of the sea and the seashore are used to invite reflection on late Victorian social practices around sea-bathing and clothing, as the mythological mermaid’s incursion into the real everyday world exposes its profound vulnerability to radical alternative ways of thinking and being.

MATHEMATICAL PRACTICE AND MATHEMATICAL LOGIC: TO THE HISTORY OF RELATIONSHIP

2021 ◽  
pp. 93-99
Author(s):  
Aleksandr Khlebalin
Keyword(s):  
Mathematical Logic ◽  
19Th Century ◽  
Mathematical Practice ◽  
Standards Of Proof ◽  
History Of ◽  
Epistemological Analysis ◽  
The 19Th Century

The article annuls the role of practice in the development of mathematics in the 19th century in the formation of mathematical logic. It is shown that the revolutionary transformations of mathematics of the 19th century, which led to an increase in the abstractness of mathematical theories and concepts, was accompanied by an increase in uncertainty regarding the standards of proof, which led to the universal spread of anxiety (J. Gray) as an element of mathematical practice. It is argued that this element of practice was one of the sources of the emergence of mathematical logic, which claims to give rigor and accuracy to mathematics. The article argues that the socio- epistemological analysis of the practice of mathematics and the formation of mathematical logic will clarify the specifics of the development of relations between mathematics and mathematical logic.

Grammatical Descriptions in Manchu Grammar Books from the Qing Dynasty

2019 ◽  
Vol 41 (1) ◽  
pp. 39-55
Author(s):  
Takashi Takekoshi
Keyword(s):  
19Th Century ◽  
Qing Dynasty ◽  
The Qing Dynasty ◽  
Chinese Scholars ◽  
High Degree ◽  
The 19Th Century

In this paper, we analyse features of the grammatical descriptions in Manchu grammar books from the Qing Dynasty. Manchu grammar books exemplify how Chinese scholars gave Chinese names to grammatical concepts in Manchu such as case, conjugation, and derivation which exist in agglutinating languages but not in isolating languages. A thorough examination reveals that Chinese scholarly understanding of Manchu grammar at the time had attained a high degree of sophistication. We conclude that the reason they did not apply modern grammatical concepts until the end of the 19th century was not a lack of ability but because the object of their grammatical descriptions was Chinese, a typical isolating language.

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