A long-awaited edition of Zermelo’s works Content Type Journal Article Pages 1-4 DOI 10.1007/s11016-011-9548-y Authors José Ferreirós, Instituto de Filosofia, CCHS-CSIC, Albasanz, 26-28, 28037 Madrid, Spain Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. -/- Describing a historically oriented, agent-based philosophy of mathematics, (...) Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. -/- Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science. (shrink)
Liberalism is commonly believed, especially by its exponents, to be opposed to interference by way of enforcing value judgments or concerning itself with the individual's morality. My concern is to show that this is not so and that liberalism is all the better for this. Many elements have contributed to liberal thought as we know it today, the major elements being the liberalism of which Locke is the most celebrated exponent, which is based upon a belief in natural, human rights; (...) the liberalism of which Kant is the best known exponent, which is based on respect for persons as ends in themselves; and the liberalism of Bentham and the Mills, which is based upon utilitarian ethical theories and most especially with concern for pleasure and the reduction of pain. These different elements of liberalism have led to different emphases and different political and social arrangements, but all have involved a concern to safeguard values and to use force to that end. Today they constitute strands of thought which go to make up liberal thought as we now know it, hence it is not simply a historical fact about liberalism, but a fact about its philosophical basis, that liberalism is firmly involved in certain value and moral commitments. In the remainder of this paper I shall seek to bring this out. (shrink)
Review by A. Kanamori, Boston University (author of The Higher Infinite), review in The Bulletin of Symbolic Logic: “Notwithstanding and braving the daunting complexities of this labyrinth, José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in (...) mathematics from the early nineteenth century. Much of history is in the details, and much of good history is in tone, emphasis, and the drawing together of different strands. Without being Whiggish, Ferreirós is never far from major synthetic themes, themes that in the main work toward balance and pull back from excesses of emphasis of some recent histories. The main criticism of the book would have to be on matters of broad interpretation. Yet, Ferreirós brings a considerable mathematical acuity and expertise to his enterprise, and this makes his viewpoints the more compelling.” . (shrink)
Hadith scholars are individuals who play an important role in the spread of the Prophetic traditions. in the midst of his people, as an authoritative source after the Qur'an for the complete Islamic legal construct, which was previously discovered and compiled by the Imam of Hadith in their canonical books, like Imam Muḥammad ibn Ismā’īl al-Bukhārī in “Ṣaḥīḥ al-Bukhārī” and Muslim Imam ibn al-Ḥajjāj al-Naysābūrī in “Muslim Ṣaḥīḥ”, through long tracing from one country to another in order to obtain directly (...) one history from the source. The position of the Hadith scholars in this regard, who are at the spearhead of the spread of the Hadiths after their collection by the Imam of the Hadith, as well as their existence and consistency in guarding the Hadith from various forms of deviation of understanding of the people, become an integral part of an integral circle named Hadith, as a saying of the Prophet, the Rabbis and the Imams. (shrink)
Umerez’s analysis made me aware of the fundamental differences in the culture of physics and molecular biology and the culture of semiotics from which the new field of biosemiotics arose. These cultures also view histories differently. Considering the evolutionary span and the many hierarchical levels of organization that their models must cover, models at different levels will require different observables and different meanings for common words, like symbol, interpretation, and language. These models as well as their histories should be viewed (...) as complementary rather than competitive. The relation of genetic language and human language is the central issue. They are separated by 4 billion years and require entirely different models. Nevertheless, these languages have in common a unique unlimited expressive power that allows open-ended evolution and creative thought. Understanding the nature of this expressive power and how it arises remains a basic unsolved problem of biosemiotics. (shrink)
J. H. Hexter, an American historian of early seventeenth-century history, terms himself whiggish and claims whiggishness is returning after the misguided popularity of Marxism. The distinction "whiggish" is more elusive than his claim suggests, and the accuracy of its application to Hexter's claim is unclear. Three characteristics commonly assigned to whig interpretation by its critics can be seen as reflections of broader, unresolved historical issues. These are: attention to political and constitutional issues; a tendency to refer to the present in (...) interpreting the past; and a belief in inevitability. It is difficult to ascertain whether Hexter's attention to political matters is a result of his view of them as intrinsically important to historical inquiry or as particularly relevant to historical accounts of Stuart England. The charge of presentism cannot confidently be made against him, as he is not guilty of anything as crude as anachronism, and subtle presentism is neither avoidable nor necessarily reprehensible. Inevitabilism is not only difficult to define, it is not displayed by Hexter. If he displays the weaknesses of whiggishness it is only through implication, in the body of ideas underlying his text. (shrink)