Es wird die Frage untersucht, ob die Annahme der Existenz von universellen Normen für die Annäherung der Wissenschaft an die Wahrheit nicht in praxi lediglich Gegenwartszentrismus und Ethnozentrismus heißt. Die griechisch-römische Zivilisation förderte die Wissenschaft durch ihre Demokratie, aber andere Zivilisationen haben sehr wertvolle Datensammlungen geliefert. Die Universalität der Wissenschaft impliziert u. a. daß, wo verschiedene Zivilisationen mit ihren Wissenschaften einander begegnen, sie von einander lernen können.

In this paper I investigate two notions of concepts that have played a dominant role in 20th century philosophy of mathematics. According to the first, concepts are definite and fixed; in contrast, according to the second notion concepts are open and subject to modifications. The motivations behind these two incompatible notions and how they can be used to account for conceptual change are presented and discussed. On the basis of historical developments in mathematics I argue that both notions of concepts (...) capture important aspects of mathematical and scientific reasoning, and, consequently, that a pluralistic approach that allows for representing both of these aspects is most useful for an adequate account of investigative practices. (shrink)

On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. The distinctions introduced aim at (...) clarifying discussions in philosophy of mathematics and contributing towards a more refined view of mathematical practice. (shrink)

Deviant forms of human thought may provide insight into epistemic standards, such as rationality. A comparative analysis of paranoia and reinforced dogmatism suggests that reinforced dogmatism, such as pseudo-science a-la-Popper, demonstrates a primary epistemic lack of critical rationality, that is, of testability, whereas paranoia demonstrates a lack of range of alternative statements leading secondarily to a lack of testability. This reflects the importance to both epistemology and psychiatry of epistemic standards in addition to testability, such as relevance to problems, and (...) emphasizes the distinction of the context of introduction from the contexts of discovery and of justification. Key Words: context of introduction • paranoia • reinforced dogmatism • relevance • testability. (shrink)

n ‘Modern Moral Philosophy’ Anscombe argues that the moral ‘ought’ should be abandoned as the senseless survivor from a defunct conceptual scheme. I argue 1) That even if the moral ‘ought’ derives its meaning from a Divine Law conception of ethics it does not follow that it cannot sensibly survive the Death of God. 2) That anyway Anscombe is mistaken since ancestors of the emphatic moral ‘ought’ predate the system of Christian Divine Law from which the moral ‘ought’ supposedly derives (...) its meaning (Cicero in particular subscribed to something like the modern conception of a duty which seems to be a generalization of the duties attendant on particular roles). 3) That if the moral ‘ought’ derived its meaning from embodying Gods’ commands then the two should have been equated in the minds of true believers. This was not the case. 4) That Anscombe is absurdly wrong in supposing that Protestant moralists had abandoned a Divine Law conception of ethics. 5) That the virtue-based ought-free Aristotelian alternative suggested by Anscombe is unworkable since the basic idea is that it pays in terms of human flourishing to be good (which means inter alia being just). Since it is pretty obvious that there are plenty of good people who don’t flourish and flourishing people who are not good, the neo-Aristotelian program has gradually undergone a degenerating problem-shift: either the pay-off is deferred to the hereafter or being good is incorporated into the pay-off. 6) That there is a certain amount of sophistry in selling the neo-Aristotelian virtues. Since the unjust person is simply somebody who is NOT systematically just, you cannot prove that it pays to be just by arguing that it is a mistake to be systematically UNjust. So too for many of the other virtues. (shrink)

Abstract This paper explores the role of symbolic languages within and between positivist disciplines. Symbolic languages, of which mathematics is the most important example, consist of tautologically true statements, such as 2 + 2 = 4. These must be operationalized before being useful for positivist research agendas (i.e. two apples and two oranges make four fruit). Disciplines may borrow either the symbolic languages of another discipline or the symbolic language and the accompanying operationalizations. The choice has important theoretical effects, and (...) affects the kind of interdisciplinary community created. The game theory community is an example of a community based on the interdisciplinary exchange of symbolic language only, while the ? political economy? community exchanges both symbolic languages and operationalizations. (shrink)

This paper considers the role of mathematics in the process of acquiring new knowledge in physics and astronomy. The defining of the notions of continuum and discreteness in mathematics and the natural sciences is examined. The basic forms of representing the heuristic function of mathematics at theoretical and empirical levels of knowledge are studied: deducing consequences from the axiomatic system of theory, the method of generating mathematical hypotheses, “pure” proofs for the existence of objects and processes, mathematical modelling, the formation (...) of mathematics on the basis of internal mathematical principles and the mathematical theory of experiment. (shrink)

This paper shows how late 1960’s student protests influenced the thought of Imre Lakatos and Paul Feyerabend. I argue that student movements shaped their work from this period, specifically Lakatos’s “Falsification and the Methodology of Scientific Research Programmes” and Feyerabend’s Against Method. Archival evidence shows that their political environments at London and Berkeley inflected their writing on scientific method, entrenching Lakatos’s search for a rationalist account of scientific development, and encouraging Feyerabend’s ‘anarchistic’ theory of knowledge. I document this influence and (...) draw two broader lessons: one lesson about the role of biography in philosophy and the other about the historiography of student protests. (shrink)

I argue in this article that an aspect of Imre Lakatos’s philosophy has been largely ignored in previous literature. The key feature of Lakatos’s philosophy of the historiography of science is its non-representationalism, which enables comparisons of alternative ‘historiographic research programmes’ without implying that the interpretations of history re-present or mirror the past. I discuss some problems of this interpretation and show specifically that Lakatos’s philosophy does not distort the history of science despite its normative ambitions. The last section is (...) devoted to updating Lakatos’s programme to answer the needs of contemporary history and philosophy of science. The standard of rationality used in comparative assessments should be understood as a tool for measuring the coherence of an account of history with regard to the ‘actual history’. This standard takes two forms: framework-dependent and framework-independent rationality. The latter is decisive in comparative assessments. (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)

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)

Lakatos's Proofs and Refutations is usually understood as an attempt to apply Popper's methodology of science to mathematics. This view has been challenged because despite appearances the methodology expounded in it deviates considerably from what would have been a straightforward application of Popperian maxims. I take a closer look at the Popperian roots of Lakatos's philosophy of mathematics, considered not as an application but as an extension of Popper's critical programme, and focus especially on the core ideas of this programme (...) as they appeared where Popper specifically addressed philosophical problems concerning mathematics. (shrink)

Interest in the demarcation problem is undergoing a boom after being shelved and even given up for dead. Nevertheless, despite current philosophical discussions, there are no substantial advances i...

Peter Anstey has suggested that in our analyses of early modern natural philosophy we should abandon a frequently used distinction: that between rationalism and empiricism. He argues that we should replace it with another distinction, that between experimental and speculative natural philosophy. The second distinction, he argues, was not only widely used at the time, but has a greater explanatory range. It follows, he suggests, that it is a better way of “carving up” the writings of that period.It is clear (...) that a distinction between experimental and speculative natural philosophy did become common in the late seventeenth-century. But I am less convinced that it is a useful one. This.. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

The concept of Mathematical Proof has been controversial for the past few decades. Different philosophers have offered different theories about the nature of Mathematical Proof, among which theories presented by Lakatos and Hersh have had significant similarities and differences with each other. It seems that a comparison and critical review of these two theories will lead to a better understanding of the concept of mathematical proof and will be a big step towards solving many related problems. Lakatos and Hersh argue (...) that, firstly, “mathematical proof” has two different meanings, formal and informal; and, secondly, informal proofs are affected by human factors, such as individual decisions and collective agreements. I call these two thesis, respectively, “proof dualism” and “humanism”. But on the other hand, their theories have significant dissimilarities and are by no means equivalent. Lakatos is committed to linear proof dualism and methodological humanism, while Hersh’s theory involves some sort of parallel proof dualism and sociological humanism. According to linear proof dualism, the two main types of proofs are provided in order to achieve a common goal: incarnation of mathematical concepts and methods and truth. However, according to the parallel proof dualism, two main types of proofs are provided in order to achieve two different types of purposes: production of a valid sequence of signs (the goal of the formal proof) and persuasion of the audience (the goal of the informal proof). Hersh’s humanism is informative and indicates pluralism; whereas, Lakatos’ version of humanism is normative and monistic. (shrink)

Karl R. Popper is “the outstanding philosopher of the twentieth century” (Bryan Magee), even “the greatest thinker of the [twentieth] century” (Gellner). He felt affinity with thinkers of the Age of Reason and developed a new version of rationalism: critical rationalism. As a champion of science and of democracy he was the most influential philosopher of the post-WWII era. He was a close follower of Bertrand Russell and of Albert Einstein in that all three advocated problem-oriented fallibilism (during the peak (...) of the influence of Ludwig Wittgenstein who did not), valued commonsense, taking its theories to be approximations to the scientific truths of the day, and considered scientific truths as series of approximations to the absolute truth [Agassi, 1981, 112-16]. In particular, all three viewed science as the bold flight of the imagination checked and tempered by experience [Russell, 1931, 102]; [Einstein, 1949, 680]. Insofar as Russell adumbrated Popper’s philosophy, it may be fair to consider the latter a streamlined version of the former (the way both Berkeley and Hume deemed their philosophies streamlined versions of Locke’s [Hattiangadi, 1985]; [Wettersten, l985]. Russell raised the level of rational discourse in philosophy while remaining within the empiricist tradition; Popper continued and consolidated Russell’s achievements, adding a broad modification of the rationalist tradition [Popper, 1945, Ch. 24], thus forging new ways of philosophizing [Lakatos, 1978, 10]. Many sought a via media between rationalism and irrationalism, between individualism and collectivism, as well as between radicalism and traditionalism. Many sought a via media between empiricism and intellectualism. Popper’s philosophy is the only viable comprehensive rationalist suggestion in these directions (although it is open to modifications, of course), being thoroughly fallibilist and reformist, thus achieving a new and intensified commonsense philosophy, the only one that is integrated.. (shrink)

Scientists and philosophers routinely talk about phenomena, and the ways in which they relate to explanation, theory and practice in science. However, there are very few definitions of the term, which is often used synonymously with "data'', "model'' and in older literature, "hypothesis''. In this paper I will attempt to clarify how phenomena are recognized, categorized and the role they play in scientific epistemology. I conclude that phenomena are not necessarily theory-based commitments, but that they are what explanations are called (...) to account for, which are not presently explained. (shrink)

In this comprehensive work on theories of rationality, Leslie Allan builds on the seminal insights of Imre Lakatos. Allan begins by critically reviewing Lakatos' theory of rationality (MSRP) and his meta-theory of rationality (MHRP) and suggesting improvements to his scheme. Allan's main task is developing a theory of rationality that avoids Lakatos' Achilles' heel; the presupposition that science is a rational enterprise. To achieve this, he attempts to draw out from the general demands of an objectivist epistemology the various criteria (...) of dependence and independence applying to evidence-statements. He concludes by considering two serious objections to his framework. (shrink)

open journal of Philosophical Investigations (PI) is an international journal dedicated to the latest advancements in philosophy. The goal of this journal is to provide a platform for academicians all over the world to promote, share, and discuss various new issues and developments in different areas of philosophy. -/- All manuscripts to be prepared in English or Persian and are subject to a rigorous and fair peer-review process. Generally, accepted papers will appear online. The journal publishes papers including the following (...) fields: -/- · Analytic Philosophy · Ancient Greek and Roman Philosophy · Art Aesthetics · Comparative Philosophy West and Chinese · Eastern Philosophy . Islamic philosophy · Epistemology · Ethics · Hermeneutics · History of Religious Thought · History of Western Philosophy · Language Logic . (shrink)

The general theme of this article is the actual practice of how definitions are justified and formulated in mathematics. The theoretical insights of this article are based on a case study of topological definitions of chaos. After introducing this case study, I identify the three kinds of justification which are important for topological definitions of chaos: natural-world-justification, condition-justification and redundancy-justification. To my knowledge, the latter two have not been identified before. I argue that these three kinds of justification are widespread (...) in mathematics. After that, I first discuss the state of the art in the literature about the justification of definitions in the light of actual mathematical practice. I then go on to criticize Lakatos’s account of proof-generated definitions—the main account in the literature on this issue—as being limited and also misguided: as for topological definitions of chaos, in nearly all mathematical fields various kinds of justification are found and are also reasonable. (shrink)

Imre Lakatos holds a well-deserved primary place in current philosophy of science. In this essay, Leslie Allan critically examines Lakatos' theory of knowledge in two key areas. The first area of consideration is Lakatos' notion that knowledge is gained through a process of competition between rival scientific research programmes. Allan identifies and discusses four problems with Lakatos' characterization of a research programme. Next, Allan considers Lakatos' proposed test of adequacy for theories of rationality using his methodology of historiographical research programmes. (...) Allan discovers tensions within Lakatos' criteria and suggests ways of strengthening his test. (shrink)

The author challenges both the eliminative idealist's contention that physical objects do not exist and the phenomenalist idealist's view that statements about physical objects are translatable into statements about private mental experiences. Firstly, he details how phenomenalist translations are parasitic on the realist assumption that physical objects exist independently of experience. Secondly, the author confronts eliminative idealism head on by exposing its heuristic sterility in contrast with realism's predictive success.

Drawing on insights from Imre Lakatos' seminal work on theories of rationality, Leslie Allan develops seven criteria for rational theory choice that avoid presuming the rationality of the scientific enterprise. He shows how his axioms of rationality follow from the general demands of an objectivist epistemology. Allan concludes by considering two weighty objections to his framework.

The materialist version of the mind/brain identity theory has met with considerable challenges from philosophers of mind. The author first dispenses with a popular objection to the theory based on the law of indiscernibility of identicals. By means of discussing the vexatious problem of phenomenal qualities, he explores how the debate may be advanced by seeing each dualist and monist ontology through the lens of an evolutionary epistemology. The author suggests that by regarding each ontology as the core of a (...) scientific research programme, each of these logically irrefutable hypotheses can be tested rationally. (shrink)