In the methodology of scientific research programs (MSRP) there are important features on the problem of prediction, especially regarding novel facts. In his approach, Imre Lakatos proposed three different levels on prediction: aim, process, and assessment. Chapter 5 pays attention to the characterization of prediction in the methodology of research programs. Thus, it takes into account several features: (1) its pragmatic characterization, (2) the logical perspective as a proposition, (3) the epistemological component, (4) its role in the appraisal of research (...) programs, and (5) its place as a value for scientific research. -/- The notion of “novel facts” is highly relevant in his conception, where several aspects are involved: the directions of novel facts, the different kinds of novelty, and the transition from six possible options of “novel facts” to four choices. Thereafter, the prediction of novel facts as the criterion of appraisal is considered. On the one hand, this requires analyzing the theoretical, empirical, and heuristic possibilities of appraisal; and, on the other, whether there is an overemphasis on the role of prediction in methodology of scientific research programs. As a consequence, there is an analysis of Lakatos’ criterion of appraisal in MSRP and economics. (shrink)

It is argued that the philosophical and epistemological beliefs about the nature of mathematics have a significant influence on the way mathematics is taught at school. In this paper, the philosophy of mathematics of the NCTM's Standards is investigated by examining is explicit assumptions regarding the teaching and learning of school mathematics. The main conceptual tool used for this purpose is the model of two dichotomous philosophies of mathematics-absolutist versus- fallibilist and their relation to mathematics pedagogy. The main conclusion is (...) that a fallibilist view of mathematics is assumed in the Standards and that most of its pedagogical assumptions and approaches are based on this philosophy. (shrink)

This paper describes an attempt to develop a program for teaching history and philosophy of mathematics to inservice mathematics teachers. I argue briefly for the view that philosophical positions and epistemological accounts related to mathematics have a significant influence and a powerful impact on the way mathematics is taught. But since philosophy of mathematics without history of mathematics does not exist, both philosophy and history of mathematics are necessary components of programs for the training of preservice as well as inservice (...) mathematics teachers. (shrink)

In his famous paper, An Unsolvable Problem of Elementary Number Theory, Alonzo Church identified the intuitive notion of effective calculability with the mathematically precise notion of recursiveness. This proposal, known as Church's Thesis, has been widely accepted. Only a few papers have been written against it. One of these is László Kalmár's An Argument Against the Plausibility of Church's Thesis from 1959. The aim of this paper is to present Kalmár's argument and to fill in missing details based on his (...) general philosophical thoughts on mathematics. (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)

I discuss the relevance of the current predicament in cosmology to the debate over scientific realism. I argue that the existence of two, empirically successful but ontologically inconsistent cosmological theories presents difficulties for the realist position.

Ethical intuitionists regard moral knowledge as deriving from moral intuition, moral observation, moral emotion and inference. However, moral intuitions, observations and emotions are cultural artefacts which often differ starkly between cultures. Intuitionists attribute uncongenial moral intuitions, observations or emotions to bias or to intellectual or moral failings; but that leads to sectarian ad hominen attacks. Intuitionists try to avoid that by restricting epistemically genuine intuitions, observations or emotions to those which are widely agreed. That does not avoid the problem. It (...) also limits epistemically genuine intuitions, observations or emotions to those with meagre content, and the intuitionists offer no plausible explanation for how inference from such insubstantial propositions can engender substantial moral knowledge. Instead of moral knowledge, intuitionism offers the prospect of mutual name-calling between intellectually stagnant groups. I criticise and reject the principle of phenomenal conservatism, to which intuitionists sometimes appeal. (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...

Despite continued attention, finding adequate criteria for distinguishing “good” from “bad” scholarly journals remains an elusive goal. In this essay, I propose a solution informed by the work of Imre Lakatos and his methodology of scientific research programmes (MSRP). I begin by reviewing several notable attempts at appraising journal quality – focusing primarily on the impact factor and development of journal blacklists and whitelists. In doing so, I note their limitations and link their overarching goals to those found within the (...) philosophy of science. I argue that Lakatos’s MSRP and specifically his classifications of “progressive” and “degenerative” research programmes can be analogized and repurposed for the evaluation of scholarly journals. I argue that this alternative framework resolves some of the limitations discussed above and offers a more considered evaluation of journal quality – one that helps account for the historical evolution of journal-level publication practices and attendant contributions to the growth (or stunting) of scholarly knowledge. By doing so, the seeming problem of journal demarcation is diminished. In the process I utilize two novel tools (the mistake index and scite index) to further illustrate and operationalize aspects of the MSRP. (shrink)

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)

For a long time, philosophers of science have expressed little interest in the so-called demarcation project that occupied the pioneers of their field, and most now concur that terms like “pseudoscience” cannot be defined in any meaningful way. However, recent years have witnessed a revival of philosophical interest in demarcation. In this paper, I argue that, though the demarcation problem of old leads to a dead-end, the concept of pseudoscience is not going away anytime soon, and deserves a fresh look. (...) My approach proposes to naturalize and down-size the concept, anchoring it in real-life doctrines and fields of inquiry. First, I argue against the definite article “the” in “the demarcation problem”, distinguishing between territorial and normative demarcation, and between different failures and shortcomings in science apart from pseudoscience. Next, I argue that pseudosciences can be fruitfully regarded as simulacra of science, doctrines that are not epistemically warranted but whose proponents try to create the impression that they are. In this element of imitation or mimicry, I argue, lies the clue to their common identity. Despite the huge variety of doctrines and beliefs gathered under the rubric of “pseudoscience”, and the wide range of defects from which they suffer, pseudosciences all engage in similar strategies to create an impression of epistemic warrant. The indirect, symptomatic approach defended here leads to a general characterization of pseudosciences in all domains of inquiry, and to a useful diagnostic tool. (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)

We give an overview of Lakatos’ life, his philosophy of mathematics and science, as well as of this issue. Firstly, we briefly delineate Lakatos’ key contributions to philosophy: his anti-formalist philosophy of mathematics, and his methodology of scientific research programmes in the philosophy of science. Secondly, we outline the themes and structure of the masterclass Lakatos’ Undone Work – The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science, which gave rise to this special issue. Lastly, (...) we provide a summary of the contributions to this issue. (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)

According to conventional wisdom, local gauge symmetry is not a symmetry of nature, but an artifact of how our theories represent nature. But a study of the so-called theta-vacuum appears to refute this view. The ground state of a quantized non-Abelian Yang-Mills gauge theory is characterized by a real-valued, dimensionless parameter theta—a fundamental new constant of nature. The structure of this vacuum state is often said to arise from a degeneracy of the vacuum of the corresponding classical theory, which degeneracy (...) allegedly arises from the fact that “large” (but not “small”) local gauge transformations connect physically distinct states of zero field energy. If that is right, then some local gauge transformations do generate empirical symmetries. In defending conventional wisdom against this challenge I hope to clarify the meaning of empirical symmetry while deepening our understanding of gauge transformations. I distinguish empirical from theoretical symmetries. Using Galileo’s ship and Faraday’s cube as illustrations, I say when an empirical symmetry is implied by a theoretical symmetry. I explain how the theta-vacuum arises, and how “large” gauge transformations differ from “small” ones. I then present two analogies from elementary quantum mechanics. By applying my analysis of the relation between empirical and theoretical symmetries, I show which analogy faithfully portrays the character of the vacuum state of a classical non-Abelian Yang-Mills gauge theory. The upshot is that “large” as well as “small” gauge transformations are purely formal symmetries of non-Abelian Yang-Mills gauge theories, whether classical or quantized. It is still worth distinguishing between these kinds of symmetries. An analysis of gauge within the constrained-Hamiltonian formalism yields the result that “large” gauge transformations should not be classified as gauge transformations; indeed, nor should “global” gauge transformations. In a theory in which boundary conditions are modeled dynamically, “global” gauge transformations may be associated with physical symmetries, corresponding to translations of these extra dynamical variables. Such translations are symmetries if and only if charge is conserved. But it is hard to argue that these symmetries are empirical, and in any case they do not correspond to any constant phase change in a quantum state. (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)