In Logik der Forschung (1934) and later works, Karl Popper proposed a set of methodological rules for scientists. Among these were requirements that theories should evolve in the direction of increasing content, and that new theories should only be accepted if some of their novel predictions are experimentally confirmed. There are currently two, viable theories of cosmology: the standard cosmological model, and a theory due to Mordehai Milgrom called MOND. Both theories can point to successes and failures, but only MOND (...) has repeatedly made novel predictions that were subsequently found to be correct. Standard-model cosmologists, by contrast, have almost always responded to new observations in a post-hoc manner, adjusting or augmenting their theory as needed to obtain correspondence with the facts. I argue that these methodological differences render a comparison of the two theories in terms of their ‘truthlikeness’ or ‘verisimilitude’ essentially impossible since the two groups of scientists achieve correspondence with the facts in fundamentally different ways, and I suggest that a better guide to the theories’ progress toward the truth might be the methodologies themselves. (shrink)

A methodology of science must satisfy two requirements: (i) It must be ampliative: the theories which it generates must make statements that go far beyond any data or observations that may have motivated those theories in the first place. (ii) It must be epistemically probative: it must somehow provide a warrant for believing that the theories so produced are correct, or at least partially correct, even if they can never be fully confirmed. These two requirements pull in opposite directions, and (...) attempts to specify the “scientific method” often focus on one to the exclusion of the other. On a few points there now exists something approaching a consensus. (i) Scientific hypotheses — including, particularly, statements about unobserved or unobservable entities or mechanisms — remain conjectural, no matter how frequently predictions based on those hypotheses are found to coincide with data. (ii) A good (best?) indicator of a theory’s verisimilitude is its ability to successfully predict phenomena which it was not specifically designed to predict. I discuss these ideas with particular reference to cosmological theories. (shrink)

Predmet istraživanja su izazovi nastavnika u radu sa učenicima iz osetljivih socijalnih grupa, tokom nastave u vanrednim okolnostima, uslovljenim pandemijom koronavirusa. U radu su prikazani rezultati kvalitativnog istraživanja, sprovedenog krajem 2021. godine, u okviru projekta Pravo na obrazovanje u periodu krize izazvane pandemijom virusa COVID-19 u Srbiji. U polustrukturisanim individualnim intervjuima učestvovalo je 50 nastavnika osnovnih, srednjih i škola za obrazovanje učenika sa smetnjama u razvoju i invaliditetom, iz 14 gradova u Srbiji. Tokom obrazovno-vaspitnog procesa sa učenicima iz osetljivih socijalnih (...) grupa, nastavnici su suočeni sa brojnim izazovima: digitalni jaz prvog i drugog nivoa, diskontinuitet u procesu obrazovanja, neodgovarajuća podrška u učenju od strane roditelja, nemotivisanost učenika za učenje, otežana komunikacija, teškoće u praćenju nastave, nemogućnost sprovođenja epidemioloških mera i individualnih tretmana itd. Sudeći na osnovu izazova nastavnika, učenici iz osetljivih grupa više su pogođeni obrazovnom krizom nego njihovi vršnjaci iz privilegovanih grupa. Neophodno je sprovođenje sistemskih mera podrške u cilju obezbeđivanja inkluzivnog pristupa obrazovanju. (shrink)

The books’ goal is to answer the question: Do the weaknesses of value-free economics imply the need for a paradigm shift? The author synthesizes criticisms from different perspectives (descriptive and methodological). Special attention is paid to choices over time, because in this area value-free economics has the most problems. In that context, the enriched concept of multiple self is proposed and investigated. However, it is not enough to present the criticisms towards value-free economics. For scientists, a bad paradigm is better (...) than no paradigm. Therefore, the author considers whether value-based economics with normative approaches such as economics of happiness, capability approach, libertarian paternalism, and the concept of multiple self can be the alternative paradigm for value-free economics. This book is essential reading to everyone interested in the current state of economics as a discipline. (shrink)

Paul Feyerabend argued that theories can be faced with experimental anomalies whose refuting character can only be recognized by developing alternatives to the theory. The alternate theory must explain the experimental results without contrivance and it must also be supported by independent evidence. I show that the situation described by Feyerabend arises again and again in experiments or observations that test the postulates in the standard cosmological model relating to dark matter. The alternate theory is Milgrom’s modified dynamics. I discuss (...) three examples: the failure to detect dark-matter particles in laboratory experiments; the lack of evidence for dark-matter sub-haloes and the dwarf galaxies that are postulated to inhabit them; and the failure to confirm the predicted orbital decay of Milky Way satellite galaxies and other systems due to dynamical friction against the dark matter. In each case, Feyerabend’s criterion directs us to interpret the experimental or observational results as an indirect refutation of the standard cosmological model in favor of Milgrom’s theory. (shrink)

Three competing ‘methods’ have been endorsed for inferring phylogenetic hypotheses: parsimony, likelihood, and Bayesianism. The latter two have been claimed superior because they take into account rates of sequence substitution. Can rates of substitution be justified on its own accord in inferences of explanatory hypotheses? Answering this question requires addressing four issues: (1) the aim of scientific inquiry, (2) the nature of why-questions, (3) explanatory hypotheses as answers to why-questions, and (4) acknowledging that neither parsimony, likelihood, nor Bayesianism are inferential (...) actions leading to explanatory hypotheses. The aim of scientific inquiry is to acquire causal understanding of effects. Observation statements of organismal characters lead to implicit or explicit why-questions. Those questions, conveyed in data matrices, assume the truth of observation statements, which is contrary to subsequently invoking substitution rates within inferences to phylogenetic hypotheses. Inferences of explanatory hypotheses are abductive in form, such that some version of an evolutionary theory(ies) is/are included or implied. If rates of sequence evolution are to be considered, it must be done prior to, rather than within abduction, which requires renaming those putatively-shared nucleotides subject to substitution rates. There are, however, no epistemic grounds for renaming characters to accommodate rates, calling into question the legitimacy of causally accounting for sequence data. (shrink)

I offer an explicit account of the underdetermination thesis as well as of the many challenges it poses to scientific realism; a way to answer to these challenges is explored and outlined, by shifting attention to the content of theories. I argue that, even if we have solid grounds (as I contend we do) to support that some varieties of the underdetermination thesis are true, scientific realism can still offer an adequate picture of the aims and achievements of science.

I explain how Karl Popper resolved the problem of induction but not the pragmatic problem of induction. I show that Popper’s solution to the pragmatic problem of induction is inconsistent with his solution to the problem of induction. I explain how Popper’s falsificationist epistemology can solve the pragmatic problem of induction in the same negative way that it solves the problem of induction.

Malgré les critiques de la théorie de Karl Popper sur la falsifiabilité pour la démarcation entre la science et la non-science, principalement la pseudo-science, ce critère est toujours très utile et parfaitement valide après avoir été perfectionné par Popper et ses disciples. De plus, même dans sa version originale, qualifiée de « dogmatique » par Lakatos, Popper n’a pas affirmé que cette méthode constituait un critère absolu de démarcation : un seul contre-exemple ne suffit pas à falsifier une théorie ; (...) une théorie peut légitimement être sauvée de la falsification en introduisant une hypothèse auxiliaire. Comparé à la théorie des révolutions de Kuhn, de qui lui-même s'est dissocié pour la transformer en une théorie des « micro-révolutions », j'estime que la méthode de démarcation de Popper, ainsi que le développement ultérieur proposé par lui, incluant la corroboration et la vraisemblance, même imparfait, n’est pas seulement valable aujourd’hui, mais c’est la meilleure méthodologie de démarcation. -/- SOMMAIRE: -/- Abstract Introduction 1. Le problème de la démarcation 2. Pseudoscience 3. Falsifiabilité 4 Falsification et réfutation 5 Extension de la falsifiabilité 6. Critiques de la falsifiabilité 7 Support de la falsifiabilité 8 Tendance actuelle Conclusions Bibliographie Notes -/- DOI: 10.13140/RG.2.2.19124.60805 . (shrink)

Kerr coined the term ‘HARKing’ to refer to the practice of ‘hypothesizing after the results are known’. This questionable research practice has received increased attention in recent years because it is thought to have contributed to low replication rates in science. The present article discusses the concept of HARKing from a philosophical standpoint and then undertakes a critical review of Kerr’s twelve potential costs of HARKing. It is argued that these potential costs are either misconceived, misattributed to HARKing, lacking evidence, (...) or that they do not take into account pre- and post-publication peer review and public availability to research materials and data. It is concluded that it is premature to conclude that HARKing has led to low replication rates. (shrink)

scientific progress, natural philosophy of the Late Medieval Period is seen as playing the role of apologetics. For philosophers of science, with their repudiation of metaphysics, the task of providing a rational reconstruction of how scientific progress has occurred is nigh on impossible. Even explanations such as the Popperian and the Kuhnian strain under great difficulty and provide only partly satisfactory results. In his “Logik der Forschung” (1934) Karl Raimund Popper argues that metaphysics plays an accidental part in the emergence (...) of new scientific ideas. Correspondingly, in “Structure of Scientific Revolutions” (1962), by carrying out theoretical interpretations and classification of empirical facts without their metaphysical premises, Thomas Kuhn comes to the conclusion that natural science was formed under the influence of erroneous interpretations of Aristotelian natural philosophy presented by medieval natural philosophers. These are some of the reasons why medievalists are still made to defend late medieval natural philosophy from shallow convictions that at medieval universities nothing of any significance to contemporary science and philosophy took place at all. Seeking to render a fragment of a coherent reconstruction of the development of natural philosophy, I will investigate one idea of late medieval philosophy – the explanation of motion (impetus). The main statement of the paper holds that the ideas of late medieval natural philosophy have a decisive significance for the development of modern natural science instead of accidental or negative one. In the paper, following Aristotelian philosophical approach, premises of Jean Buridan’s theory of impetus will be exposed. Then, debates over the explanation of projectile motion are going to be presented, and finally, the necessary significance of this metaphysical idea on the modifications of natural philosophy is going to be ascertained. (shrink)

Despite the criticism of Karl Popper's falsifiability theory for the demarcation between science and non-science, mainly pseudo-science, this criterion is still very useful, and perfectly valid after it was perfected by Popper and his followers. Moreover, even in his original version, considered by Lakatos as "dogmatic", Popper did not assert that this methodology is an absolute demarcation criterion: a single counter-example is not enough to falsify a theory; a theory can legitimately be saved from falsification by introducing an auxiliary hypothesis. (...) Compared to Kuhn's theory of revolutions, which he himself later dissociated from it transforming it into a theory of "micro-revolutions," I consider that Popper's demarcation methodology, along with the subsequent development proposed by him, including the corroboration and the verisimilitude, though imperfect, is not only valid today, but it is still the best demarcation methodology. For argumentation, I used the main works of Popper dealing with this issue, and his main critics and supporters. After a brief presentation of Karl Popper, and an introduction to the demarcation problem and the falsification methodology, I review the main criticisms and the arguments of his supporters, emphasizing the idea that Popper has never put the sign of equality between falsification and rejection. Finally, I present my own conclusions on this issue. CONTENTS -/- Abstract Introduction 1 The demarcation problem 2 Pseudoscience 3 Falsifiability 4 Falsification and refutation 5 Extension of falsifiability 6 Criticism of falsifiability 7 Support of falsifiability 8 The current trend Conclusions Bibliography Notes -/- DOI: 10.58679/MM99220. (shrink)

În această lucrare argumentez faptul că, în ciuda criticilor teoriei falsificabilității propuse de Karl Popper pentru demarcarea între știință și ne-știință, în principal pseudoștiință, acest criteriu este încă foarte util, și perfect valabil după perfecționarea lui de către Popper și adepții lui. Mai mult, chiar și în versiunea sa inițială, considerată de Lakatos ca ”dogmatică”, Popper nu a afirmat că această metodologie este un criteriu absolut de demarcare: un singur contra-exemplu nu este suficient pentru a falsifica o teorie; mai mult, (...) o teorie poate fi salvată în mod legitim de falsificare prin introducerea unei ipoteze auxiliare. În comparație cu teoria lui Kuhn a revoluțiilor, de care el însuși s-a dezis ulterior transformând-o într-o teorie a ”micro-revoluțiilor”, consider că metodologia de demarcare a lui Popper, împreună cu dezvoltarea ulterioară propusă de acesta, inclusiv coroborarea și verosimilitudinea, deși imperfectă, nu numai că este valabilă și azi, dar este încă cea mai bună metodologie de demarcare. Pentru argumentare, m-am folosit de principalele lucrări ale lui Popper care tratează această problemă, și a principalilor săi critici și susținători. După o scurtă prezentare a lui Karl Popper, și o introducere în problema demarcației și metodologia falsificabilității, trec în revistă principalele critici aduse și argumentele susținătorilor săi, accentuând pe ideea că Popper nu a pus niciodată semnul egalității între falsificare și respingere. În final prezint propriile concluzii în această problemă. -/- DOI: 10.58679/TW55590. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

This paper explores early Australasian philosophy in some detail. Two approaches have dominated Western philosophy in Australia: idealism and materialism. Idealism was prevalent between the 1880s and the 1930s, but dissipated thereafter. Idealism in Australia often reflected Kantian themes, but it also reflected the revival of interest in Hegel through the work of ‘absolute idealists’ such as T. H. Green, F. H. Bradley, and Henry Jones. A number of the early New Zealand philosophers were also educated in the idealist tradition (...) and were influential in their communities, but produced relatively little. In Australia, materialism gained prominence through the work of John Anderson, who arrived in Australia in 1927, and continues to be influential. John Anderson had been a student of Henry Jones, who might therefore be said to have influenced both main strands of Australian philosophical thought. (shrink)

First, I answer the controversial question ’What is scientific realism?’ with extensive reference to the varied accounts of the position in the literature. Second, I provide an overview of the key developments in the debate concerning scientific realism over the past decade. Third, I provide a summary of the other contributions to this special issue.

Bayesian confirmation theory is rife with confirmation measures. Many of them differ from each other in important respects. It turns out, though, that all the standard confirmation measures in the literature run counter to the so-called “Reverse Matthew Effect” (“RME” for short). Suppose, to illustrate, that H1 and H2 are equally successful in predicting E in that p(E | H1)/p(E) = p(E | H2)/p(E) > 1. Suppose, further, that initially H1 is less probable than H2 in that p(H1) < p(H2). (...) Then by RME it follows that the degree to which E confirms H1 is greater than the degree to which it confirms H2. But by all the standard confirmation measures in the literature, in contrast, it follows that the degree to which E confirms H1 is less than or equal to the degree to which it confirms H2. It might seem, then, that RME should be rejected as implausible. Festa (2012), however, argues that there are scientific contexts in which RME holds. If Festa’s argument is sound, it follows that there are scientific contexts in which none of the standard confirmation measures in the literature is adequate. Festa’s argument is thus interesting, important, and deserving of careful examination. I consider five distinct respects in which E can be related to H, use them to construct five distinct ways of understanding confirmation measures, which I call “Increase in Probability”, “Partial Dependence”, “Partial Entailment”, “Partial Discrimination”, and “Popper Corroboration”, and argue that each such way runs counter to RME. The result is that it is not at all clear that there is a place in Bayesian confirmation theory for RME. (shrink)

A success-to-truth inference has always been at the heart of scientific realist positions. But all attempts to articulate the inference have met with very significant challenges. This paper reconstructs the evolution of this inference, and brings together a number of qualifications in an attempt to articulate a contemporary success-to-truth inference which is realistic. I argue that this contemporary version of the inference has a chance, at least, of overcoming the historical challenges which have been proffered to date. However, there is (...) a price to pay: the developments which help the realist answer the historical challenges also serve to increase the number of non-historical challenges. (shrink)

The traditional conception of knowledge is justified, true belief. If one looks at a modern textbook on epistemology, the great bulk of questions with which it deals are to do with personal knowledge, as embodied in beliefs and the proper experiences that someone ought to have had in order to have the right (or justification) to know. I intend to argue that due to the explosive growth of knowledge whose domain is “outside the head”, this conception has outlived its relevance. (...) -/- On the other hand, Karl Popper’s (1934) Falsificationism, with its emphasis on the objective character of knowledge, is not only a sounder, but also a more appropriate theory of knowledge for understanding the nature and growth of civilization. Later, Popper (1945) generalized this approach to obtain critical rationalism, in which all claims to knowledge, whether scientific or otherwise, are understood as objective solutions to objective problems and can be evaluated by other non-observational - types of criticism. I will first argue that Popper’s methodology is quite suited to the view that knowledge is an objective autonomous product and then adduce his theory of world 3, an ontology that neatly wraps up various considerations. World 3 is the domain of abstract products of the human mind that now have a life of their own, outside of human heads: theories, arguments, problems, plans, etc. I then adduce some other arguments for the autonomous quality of knowledge. (shrink)

Natural resources are infinite. This is possible because humans can create theories whose potential goes beyond the limited imaginative capacity of the inventor. For instance, no number of people can work out all the economic potential of quantum theory. Economic Resources are created by an interaction of Karl Popper's Worlds 1, 2 and 3, the worlds of physics, psychology and the abstract products of the human mind, such as scientific theories. Knowledge such as scientific theories has unfathomable information content, is (...) universally applicable, and infinitely copyable. The point can be made with technological knowledge such as that embodied in the wheel. The theory of the wheel has un- bounded potential to be embodied in unforeseeable new technologies, is useful on the Moon as on Earth, and can be infinitely copied. Unlike a piece of land (using fixed factors), such knowledge shows increasing returns. This helps to explain Julian Simon's observation that "natural" resources are now less scarce than they used to be and why an increasing population can increase resources in the long-run. It was Simon's breakthrough to elaborate on the abstract character of "natural" resources. I further explore this abstract character and thereby explain why natural resources are infinitely expandable. Economic growth and the creation of natural resources depends on the rate of invention. F. Machlup's suggestion (Machlup 1962) that the opportunity for new inventions increases geometrically with the number of inventions at hand is acknowledged for its suggestiveness, but criticised for its conservative position. Frank Tipler's fascinating argument for indefinite economic growth (Tipler 1994), is reinforced by my argument by making a distinction between information in the engineer's sense and the infinite potential "information" in our scientific knowledge based on Popper's notion of information content. (shrink)

ArgumentThis paper investigates whether there is a discrepancy between stated and actual aims in biomechanical research, particularly with respect to hypothesis testing. We present an analysis of one hundred papers recently published inThe Journal of Experimental BiologyandJournal of Biomechanics, and examine the prevalence of papers which have hypothesis testing as a stated aim, contain hypothesis testing claims that appear to be purely presentational, and have exploration as a stated aim. We found that whereas no papers had exploration as a stated (...) aim, 58 per cent of papers had hypothesis testing as a stated aim. We had strong suspicions, at the bare minimum, that presentational hypotheses were present in 31 per cent of the papers in this latter group. (shrink)

In his Bayesian Nets and Causality, Jon Williamson presents an ‘Objective Bayesian’ interpretation of probability, which he endeavours to distance from the logical interpretation yet associate with the subjective interpretation. In doing so, he suggests that the logical interpretation suffers from severe epistemological problems that do not affect his alternative. In this paper, I present a challenge to his analysis. First, I closely examine the relationship between the logical and ‘Objective Bayesian’ views, and show how, and why, they are highly (...) similar. Second, I argue that the logical interpretation is not manifestly inferior, at least for the reasons that Williamson offers. I suggest that the key difference between the logical and ‘Objective Bayesian’ views is in the domain of the philosophy of logic; and that the genuine disagreement appears to be over Platonism versus nominalism. (shrink)

Karl Popper (1902-1994) was one of the most influential philosophers of science of the 20th century. He made significant contributions to debates concerning general scientific methodology and theory choice, the demarcation of science from non-science, the nature of probability and quantum mechanics, and the methodology of the social sciences. His work is notable for its wide influence both within the philosophy of science, within science itself, and within a broader social context. Popper’s early work attempts to solve the problem of (...) demarcation and offer a clear criterion that distinguishes scientific theories from metaphysical or mythological claims. Popper’s falsificationist methodology holds that scientific theories are characterized by entailing predictions that future observations might reveal to be false. When theories are falsified by such observations, scientists can respond by revising the theory, or by rejecting the theory in favor of a rival or by maintaining the theory as is and changing an auxiliary hypothesis. In either case, however, this process must aim at the production of new, falsifiable predictions. While Popper recognizes that scientists can and do hold onto theories in the face of failed predictions when there are no predictively superior rivals to turn to. He holds that scientific practice is characterized by its continual effort to test theories against experience and make revisions based on the outcomes of these tests. By contrast, theories that are permanently immunized from falsification by the introduction of untestable ad hoc hypotheses can no longer be classified as scientific. Among other things, Popper argues that his falsificationist proposal allows for a solution of the problem of induction, since inductive reasoning plays no role in his account of theory choice. Along with his general proposals regarding falsification and scientific methodology, Popper is notable for his work on probability and quantum mechanics and on the methodology of the social sciences. Popper defends a propensity theory of probability, according to which probabilities are interpreted as objective, mind-independent properties of experimental setups. Popper then uses this theory to provide a realist interpretation of quantum mechanics, though its applicability goes beyond this specific case. With respect to the social sciences, Popper argued against the historicist attempt to formulate universal laws covering the whole of human history and instead argued in favor of methodological individualism and situational logic. Table of Contents 1. Background 2. Falsification and the Criterion of Demarcation a. Popper on Physics and Psychoanalysis b. Auxiliary and Ad Hoc Hypotheses c. Basic Sentences and the Role of Convention d. Induction, Corroboration, and Verisimilitude 3. Criticisms of Falsificationism 4. Realism, Quantum Mechanics, and Probability 5. Methodology in the Social Sciences 6. Popper’s Legacy 7. References and Further Reading a. Primary Sources b. Secondary Sources -/- . (shrink)

in this paper i assess Pierre Duhem’s criticism of crucial experiments, and argue that we have reasons to vindicate their existence. i then analize the experiments carried out by Fizeau and Foucault in 1850, and criticize Duhem’s interpretation of their results. i contend that the results of crucial experiences can be described in terms that are neutral with respect to the competing theories. For that reason an experimental result is relatively stable and open to different interpretations in the light of (...) new theories. i conclude by distinguishing successful crucial experiments from decisive experiments. The former are meant to provide evidence that confirms one theory and disconfirms its rivals, but not necessarily to provide sufficient reasons for accepting or rejecting one of those theories. (shrink)

Stanford’s argument against scientific realism focuses on theories, just as many earlier arguments from inconceivability have. However, there are possible arguments against scientific realism involving unconceived (or inconceivable) entities of different types: observations, models, predictions, explanations, methods, instruments, experiments, and values. This paper charts such arguments. In combination, they present the strongest challenge yet to scientific realism.

First, I argue that scientific progress is possible in the absence of increasing verisimilitude in science’s theories. Second, I argue that increasing theoretical verisimilitude is not the central, or primary, dimension of scientific progress. Third, I defend my previous argument that unjustified changes in scientific belief may be progressive. Fourth, I illustrate how false beliefs can promote scientific progress in ways that cannot be explicated by appeal to verisimilitude.

Although there are quite a few directions in modern philosophy of mathematics that invoke some essential role for (quasi-)empirical material, this chapter will be devoted exclusively to what may be considered the seminal tradition. This enabled me to present the subject as one coherent whole and to forestall the discussion getting scattered in a diversity of directions without doing justice to any one of them. -/- Quasi-empiricism in this tradition is the view that the logic of mathematical inquiry is based, (...) like the logic of scientific discovery, on the bottom-up retransmission of falsity (by means of counterexamples) rather than the top-down transmission of axiomatic truth. Imre Lakatos, who originally introduced the distinction between Euclidean and quasi-empirical theories, construed mathematics as a quasi-empirical science following in essence Popper’s method of conjectures and refutations. His essay on Proofs and Refutations was an attempt to apply, and thereby to test, Popper’s critical method and fallibilist theory of knowledge in a field – mathematics – to which it had not primarily been intended to apply. While Popper’s proposal stood up gloriously to this test, the new application gave rise also to new insights, in particular the construal of proofs as thought experiments with a role similar to that of testing and corroborating experiments in science. -/- After examination of a number of examples of mathematical thought-experiments from this perspective, the doctrine of the relative autonomy of objective knowledge is focussed upon, a doctrine which is part and parcel of the dialectic of proofs and refutations and hence of the quasi-empiricist programme. -/- Some remarks on the educational implications of quasi-empiricism conclude this chapter. These implications have no direct bearing on the actual practice of teaching mathematics in the classroom, but are mainly, if not exclusively, concerned with the image of mathematics that is conveyed in education. (shrink)

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

Experiments with the simple pendulum are easy, but its motion is nevertheless confounded with simple harmonic motion. However, refined theoretical models of the pendulum can, today, be easily taught using software like CALCODE. Similarly, the cycloidal pendulum is isochronous only in simplified theory. But what are theoretically equal intervals of time? Newton accepted Barrow’s even tenor hypothesis, but conceded that ‘equal motions’ did not exist – the refutability of Newtonian physics is independent of time measurement. However, time measurement was the (...) key difficulty in reconciling Newtonian physics with electrodynamics. On Poincaré’s criterion of convenience, equal intervals of time ought be so defined as to make the enunciation of physics simple. Hence he postulated constancy of the speed of light. (The Michelson–Morley experiment was not critical.) The theory of relativity followed. But does there exist a proper clock? (shrink)

Bayes’ rule shows how one might rationally change one’s beliefs in the light of evidence. It is the foundation of a statistical method called Bayesianism. In health care research, Bayesianism has its advocates but the dominant statistical method is frequentism. There are at least two important philosophical differences between these methods. First, Bayesianism takes a subjectivist view of probability (i.e. that probability scores are statements of subjective belief, not objective fact) whilst frequentism takes an objectivist view. Second, Bayesianism is explicitly (...) inductive (i.e. it shows how we may induce views about the world based on partial data from it) whereas frequentism is at least compatible with non-inductive views of scientific method, particularly the critical realism of Popper. Popper and others detail significant problems with induction. Frequentism’s apparent ability to avoid these, plus its ability to give a seemingly more scientific and objective take on probability, lies behind its philosophical appeal to health care researchers. However, there are also significant problems with frequentism, particularly its inability to assign probability scores to single events. Popper thus proposed an alternative objectivist view of probability, called propensity theory, which he allies to a theory of corroboration; but this too has significant problems, in particular, it may not successfully avoid induction. If this is so then Bayesianism might be philosophically the strongest of the statistical approaches. The article sets out a number of its philosophical and methodological attractions. Finally, it outlines a way in which critical realism and Bayesianism might work together. (shrink)

This paper argues that talk of ‘the aim of science’ should be avoided in the philosophy of science, with special reference to the way that van Fraassen sets up the difference between scientific realism and constructive empiricism. It also argues that talking instead of ‘what counts as success in science as such’ is unsatisfactory. The paper concludes by showing what this talk may be profitably replaced with, namely specific claims concerning science that fall into the following categories: descriptive, evaluative, normative, (...) and definitional. There are two key advantages to this proposal. First, realism and its competitors may be understood to consist of highly nuanced variants. Second, scientific realism and its competitors may be understood as something other than ‘all or nothing’ theses about science. More particularly, one may accept that there are general claims concerning science in some of the identified categories, but deny that there are such claims in the others. (shrink)

The discussion about the Raven Paradox is ever-renewing: after nearly 70 years, many authors propose from time to time new solutions, and many authors state that these solutions are unsatisfactory. It is worthy to be carefully noted that though most arguments in favor or against the paradox are based on the notion of “probability” and on the application of Bayes’ law, not one of them makes use of the Kolmogorov axiomatic theory of probability and on the subsequent notion of “random (...) variable”. This seems to be due to a preference for the purely logical interpretation of the notion of “probability” which makes it possible to assign a probability value to propositions expressing natural (universal) laws. This paper aims at presenting an attempt to contribute a solution to the paradox by the proposal of a different way to express universal natural laws and by the use of a language which does not allow one to apply probability to universal statements. (shrink)

In this paper I argue that aim-oriented empiricism (AOE), a conception of natural science that I have defended at some length elsewhere[1], is a kind of synthesis of the views of Popper, Kuhn and Lakatos, but is also an improvement over the views of all three. Whereas Popper's falsificationism protects metaphysical assumptions implicitly made by science from criticism, AOE exposes all such assumptions to sustained criticism, and furthermore focuses criticism on those assumptions most likely to need revision if science is (...) to make progress. Even though AOE is, in this way, more Popperian than Popper, it is also, in some respects, more like the views of Kuhn and Lakatos than falsificationism is. AOE is able, however, to solve problems which Kuhn's and Lakatos's views cannot solve. [Back to Top]. (shrink)

Karl Popper is famous for having proposed that science advances by a process of conjecture and refutation. He is also famous for defending the open society against what he saw as its arch enemies – Plato and Marx. Popper’s contributions to thought are of profound importance, but they are not the last word on the subject. They need to be improved. My concern in this book is to spell out what is of greatest importance in Popper’s work, what its failings (...) are, how it needs to be improved to overcome these failings, and what implications emerge as a result. The book consists of a collection of essays which dramatically develop Karl Popper’s views about natural and social science, and how we should go about trying to solve social problems. Criticism of Popper’s falsificationist philosophy of natural science leads to a conception of science that I call aim-oriented empiricism. This makes explicit metaphysical theses concerning the comprehensibility and knowability of the universe that are an implicit part of scientific knowledge – implicit in the way science excludes all theories that are not explanatory, even those that are more successful empirically than accepted theories. Aim-oriented empiricism has major implications, not just for the academic discipline of philosophy of science, but for science itself. Popper generalized his philosophy of science of falsificationism to arrive at a new conception of rationality – critical rationalism – the key methodological idea of Popper’s profound critical exploration of political and social issues in his The Open Society and Its Enemies, and The Poverty of Historicism. This path of Popper, from scientific method to rationality and social and political issues is followed here, but the starting point is aim-oriented empiricism rather than falsificationism. Aim-oriented empiricism is generalized to form a conception of rationality I call aim-oriented rationalism. This has far-reaching implications for political and social issues, for the nature of social inquiry and the humanities, and indeed for academic inquiry as a whole. The strategies for tackling social problems that arise from aim-oriented rationalism improve on Popper’s recommended strategies of piecemeal social engineering and critical rationalism, associated with Popper’s conception of the open society. This book thus sets out to develop Popper’s philosophy in new and fruitful directions. The theme of the book, in short, is to discover what can be learned from scientific progress about how to achieve social progress towards a better world. (shrink)

Tarski's manner of defining truth is generally considered highly significant. About why, there is less consensus. I argue first, that in his truth-definitions Tarski was trying to solve a set of philosophical problems; second, that he solved them successfully; third, that all of these that are simply problems about defining truth are as well or better solved by a simpler account of truth. But one of his crucial problems remains: to give an account of validity, one requires an account not (...) just of truth but of truth under varying interpretations. Tarski's account has the merit of generalizing to this, to model theory and to abstract algebra. (shrink)

This paper argues that Duhem’s thesis does not decisively refute a corroboration-based account of scientific methodology (or ‘falsificationism’), but instead that auxiliary hypotheses are themselves subject to measurements of corroboration which can be used to inform practice. It argues that a corroboration-based account is equal to the popular Bayesian alternative, which has received much more recent attention, in this respect.

We examine three critical aspects of Popper’s formulation of the ‘ Logic of Scientific Discovery ’—evidence, content and degree of corroboration—and place these concepts in the context of the Tree of Life (ToL) problem with particular reference to molecular systematics. Content, in the sense discussed by Popper, refers to the breadth and scope of existence that a hypothesis purports to explain. Content, in conjunction with the amount of available and relevant evidence, determines the testability, or potential degree of corroboration, of (...) a statement; content distinguishes scientific hypotheses from metaphysical assertions. Degree of corroboration refers to the relative and tentative confidence assigned to one hypothesis over another, based upon the performance of each under critical tests. Here we suggest that systematists attempt to maximize content and evidence to increase the potential degree of corroboration in all phylogenetic endeavors. Discussion of this “total evidence” approach leads to several interesting conclusions about generating ToL hypotheses. (shrink)

RésuméJe me penche sur un aspect de la philosophie sociale de Popper, à savoir les principes d'évaluation des interprétations historiques. Ma thèse globale est que suivant la perspective poppèrienne, notre choix parmi des interprétations historiques doit user d'au moins deux des critères qu'applique Popper au choix parmi diverses théories scientifiques : une interprétation devrait logiquement se prêter à une réfutation et elle devrait être consistante. Afin de montrer la pertinence et la fécondité de cette approche, je me concentre sur l'interprétation (...) historique des causes de la montée du nazisme que propose Erich Fromm, en particulier dansEscape from Freedom.Je montrerai que l'application de notions psychanalytiques dans le cadre de son interprétation historique a une valeur explicative faible, voire nulle. Son échec à expliquer certaines questions sociales tient à plusieurs raisons. Premièrement, l'auteur ne fournit pas, quoi qu'il en dise, d'explication causale convaincante. Ensuite, les concepts et les multiples hypotheèsesad hocauxquels il a recours tendent è rendre son interprétation irréfutable. Enfin, Fromm s'appuie sur des assomptions théoriques contradictoires. Mon analyse est basée sur la notion fondamentale de Popper voulant que la connaissance scientifique empirique exige au strict minimum une ouverture des interprétations historiques à la critique intersubjective. C'est cette exigence qui permet de les critiquer — c'est-à-dire les accepter, les réfuter et les corriger — sur une base rationnelle. (shrink)

More powerful methods for studying and integrating the historical track record of scientific episodes and scientific judgment, or what Faust and Meehl describe as a program of meta‐science and meta‐scientific studies, can supplement and extend more commonly used case study methods. We describe the basic premises of meta‐science, overview methodological considerations, and provide examples of meta‐scientific studies. Meta‐science can help to clarify or resolve long‐standing questions in the history and philosophy of science and provide practical help to the working scientist.

According to a popular view of scientific methodology, scientific methods are prescriptive rules (methodological rules) which are justified in so far as they realize or promote the aims of science. This paper considers several different interpretations of the phrase aims of science, arguing that none of these interpretations allow aims to provide a satisfactory justification of methodological rules.

Can the axioms of probability theory and the classical patterns of statistical inference ever be falsified by observation? Various possible answers to this question are examined in a set theoretical context and in relation to the findings of microphysics.

Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and long-standing problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test's (pre-data) error probabilities are to be used for (post-data) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities (...) is to ensure that only statistical hypotheses that have passed severe or probative tests are inferred from the data. The severity criterion supplies a meta-statistical principle for evaluating proposed statistical inferences, avoiding classic fallacies from tests that are overly sensitive, as well as those not sensitive enough to particular errors and discrepancies. Introduction and overview 1.1 Behavioristic and inferential rationales for Neyman–Pearson (N–P) tests 1.2 Severity rationale: induction as severe testing 1.3 Severity as a meta-statistical concept: three required restrictions on the N–P paradigm Error statistical tests from the severity perspective 2.1 N–P test T(): type I, II error probabilities and power 2.2 Specifying test T() using p-values Neyman's post-data use of power 3.1 Neyman: does failure to reject H warrant confirming H? Severe testing as a basic concept for an adequate post-data inference 4.1 The severity interpretation of acceptance (SIA) for test T() 4.2 The fallacy of acceptance (i.e., an insignificant difference): Ms Rosy 4.3 Severity and power Fallacy of rejection: statistical vs. substantive significance 5.1 Taking a rejection of H0 as evidence for a substantive claim or theory 5.2 A statistically significant difference from H0 may fail to indicate a substantively important magnitude 5.3 Principle for the severity interpretation of a rejection (SIR) 5.4 Comparing significant results with different sample sizes in T(): large n problem 5.5 General testing rules for T(), using the severe testing concept The severe testing concept and confidence intervals 6.1 Dualities between one and two-sided intervals and tests 6.2 Avoiding shortcomings of confidence intervals Beyond the N–P paradigm: pure significance, and misspecification tests Concluding comments: have we shown severity to be a basic concept in a N–P philosophy of induction? (shrink)