The Hungarian émigré Imre Lakatos earned a worldwide reputation through the influential philosophy of science debates involving Thomas Kuhn, Paul Feyerabend, and Sir Karl Popper. In _Imre Lakatos and the Guises of Reason_ John Kadvany shows that embedded in Lakatos’s English-language work is a remarkable historical philosophy rooted in his Hungarian past. Below the surface of his life as an Anglo-American philosopher of science and mathematics, Lakatos covertly introduced novel transformations of Hegelian and Marxist ideas about historiography, skepticism, criticism, and (...) rationality. Lakatos escaped Hungary following the failed 1956 Revolution. Before then, he had been an influential Communist intellectual and was imprisoned for years by the Stalinist regime. He also wrote a lost doctoral thesis in the philosophy of science and participated in what was criminal behavior in all but a legal sense. Kadvany argues that this intellectual and political past animates Lakatos’s English-language philosophy, and that, whether intended or not, Lakatos integrated a penetrating vision of Hegelian ideas with rigorous analysis of mathematical proofs and controversial histories of science. Including new applications of Lakatos’s ideas to the histories of mathematical logic and economics and providing lucid exegesis of many of Hegel’s basic ideas, _Imre Lakatos and the Guises of Reason_ is an exciting reconstruction of ideas and episodes from the history of philosophy, science, mathematics, and modern political history. (shrink)

In his philosophical history of nineteenth-century mathematics, Proofs and Persuasions: The Logic of Mathematical Discovery, Imre Lakatos asserts that mathematical criticism was the driving force in the growth of mathematical knowledge during the nineteenth century, and provided the impetus for some of the deepest conceptual reformulations of the century. The philosophy of mathematics represented by Proofs and Refutations also presents a rich analysis of how mathematics can be thought of as an essentially historical discipline. Despite protestations by Lakatos that he (...) completely discarded Hegel when he discovered the work of Karl Popper, his philosophy of error closely resembles Hegel's in the Phenomenology of Spirit. According to Lakatos, the impact of proofs and refutations on naive concepts is to erase them completely and replace them by proof-generated concepts. His historical point about proofs and refutations is that this pattern in the growth of mathematical knowledge is a relatively recent innovation. Hegel's and Lakatos' shared vision of theoretical knowledge is that rather than being the inspired work of timeless, totally subjective, intellectual intuition , it is, more often than not, mediated by a lengthy history of speculation and failure. (shrink)

This essay is about mathematics as a written or literate language. Through historical and anthropological observations drawn from the history of Greek mathematics and the oral tradition preceding the rise of literacy in Greece, as well as considerations on the nature of alphabetic writing, it is argued that three essential linguistic features of mathematical discourse are jointly possible only through written, alphabetic language. The essay concludes with a discussion of how both alphabetic principles and issues related to literacy faced by (...) the Greeks in the axiomatization of geometry play a central role in some specific metamathematical theories. Drawing extensively on the work of ArpSd Szatx5, Eric Havelock, and Albert Lord, the implications developed between Szab6's history of Greek mathematics and Havelock and Lord's theories of writing and oral traditions (Homer's in particular) are the author's own, as are the applications to modern logic. (shrink)

This review was prompted by the publication of Paul Feyerabend's autobiography Killing Time, just following his sudden death in 1994.

An approach to describing risk analysis, risk perception and risk interpretation under a single umbrella starting with a general definition of risk as "adverse consequences under uncertainty." The idea of risk representation is introduced as an omnibus term for many different ways of conceptualizing risk and deploying risk messages in science, government or society.

A brief correction to a review of my book Imre Lakatos and the Guises of Reason published in Philosophia Mathematica, regarding the role of George Polya's notion of heuristic in Lakatos' Proofs and Refutations.

Pāṇini's fourth century BC Sanskrit grammar uses rewrite rules utilizing an explicit formal language defined through a semi-formal metalanguage. The grammar is generative, meaning that it is capable of expressing a potential infinity of well-formed Sanskrit sentences starting from a finite symbolic inventory. The grammar's operational rules involve extensive use of auxiliary markers, in the form of Sanskrit phonemes, to control grammatical derivations. Pāṇini's rules often utilize a generic context-sensitive format to identify terms used in replacement, modification or deletion operations. (...) The context-sensitive rule format is itself defined using Pāṇini's more general method of auxiliary markers, the latter used to define many dozens of linguistic categories and rules controlling derivations of Sanskrit sentences through the manipulation of ‘non-terminal’ and ‘terminal’ symbols. This technique for controlling formal derivations was rediscovered by Emil Post in the 1920s and later shown by him to be ca... (shrink)

Chocolate and Chess (Unlocking Lakatos) tells the fascinating story of Imre Lakatos’ life in Hungary before his flight to England following the failed 1956 Hungarian Revolution. The book focuses on Lakatos’ role as a political functionary under Hungarian Stalinism, and compiles what is known of Lakatos’ role in the induced suicide of a young woman, Éva Iszák, at the end of World War II. This historical and biographical study provides essential background for appreciating Lakatos’ cross-cultural role as a philosopher in (...) England and Hungary, through the Anglo-American philosophy and the Hegelian-Marxist traditions in which he was trained and did not leave behind. (shrink)

Chocolate and Chess tells the fascinating story of Imre Lakatos’ life in Hungary before his flight to England following the failed 1956 Hungarian Revolution. The book focuses on Lakatos’ role as a political functionary under Hungarian Stalinism, and compiles what is known of Lakatos’ role in the induced suicide of a young woman, Éva Iszák, at the end of World War II. This historical and biographical study provides essential background for appreciating Lakatos’ cross-cultural role as a philosopher in England and (...) Hungary, through the Anglo-American philosophy and the Hegelian-Marxist traditions in which he was trained and did not leave behind. (shrink)

This paper explains how mathematical computation can be constructed from weaker recursive patterns typical of natural languages. A thought experiment is used to describe the formalization of computational rules, or arithmetical axioms, using only orally-based natural language capabilities, and motivated by two accomplishments of ancient Indian mathematics and linguistics. One accomplishment is the expression of positional value using versified Sanskrit number words in addition to orthodox inscribed numerals. The second is Pāṇini’s invention, around the fifth century BCE, of a formal (...) grammar for spoken Sanskrit, expressed in oral verse extending ordinary Sanskrit, and using recursive methods rediscovered in the twentieth century. The Sanskrit positional number compounds and Pāṇini’s formal system are construed as linguistic grammaticalizations relying on tacit cognitive models of symbolic form. The thought experiment shows that universal computation can be constructed from natural language structure and skills, and shows why intentional capabilities needed for language use play a role in computation across all media. The evolution of writing and positional number systems in Mesopotamia is used to transfer the thought experiment of “oral arithmetic” to inscribed computation. The thought experiment and historical evidence combine to show how and why mathematical computation is a cognitive technology extending generic symbolic skills associated with language structure, usage, and change. (shrink)

This review takes seriously Badiou's use of set theory and mathematics, explaining the book's subtle technical content while maintaining a critical distance on Badiou's interpretative views.