Falsification

Philosophical treatments of scientific controversies usually focus on theory, excluding important practice related aspects. However, scientists in conflict often appeal to extra-theoretical and extra-empirical elements. To understand better the role that non-empirical elements play in scientific controversies, we introduce the notion of borrowed epistemic credibility, illustrating our proposal with a recent controversy in a field of evolutionary biology known as phylogeography. Our analysis shows how scientific controversies that spring from disagreements about methodological issues potentially involve deeper debates regarding what constitutes (...) good science, prompting the re-examination of more general issues, such as the nature of inference, rationality, and objectivity. (shrink)

The principle of economy favours the theory which gives the most accurate predictions; of two equally accurate theories, economy favours the one which incorporates least metaphysics. The intention is to show that were metaphysical commitments of theories openly acknowledged and simplicity and other virtues generally accepted as judges in theory choice, the progress rate of science would likely become more optimal.

We information-theoretically reformulate two measures of capacity from statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. We show these capacity measures count the number of hypotheses about a dataset that a learning algorithm falsifies when it finds the classifier in its repertoire minimizing empirical risk. It then follows from that the future performance of predictors on unseen data is controlled in part by how many hypotheses the learner falsifies. As a corollary we show that empirical VC-entropy quantifies the message (...) length of the true hypothesis in the optimal code of a particular probability distribution, the so-called actual repertoire. (shrink)

The paper demonstrates that falsifiability is fundamental to learning. We prove the following theorem for statistical learning and sequential prediction: If a theory is falsifiable then it is learnable -- i.e. admits a strategy that predicts optimally. An analogous result is shown for universal induction.

There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as the length of the shortest program producing it [1]. The second, Shannon information, takes events as belonging to ensembles and quantifies the information resulting from observing the given event in terms of the number of alternate events that have been ruled out [2]. The third, statistical learning (...) theory, has introduced measures of capacity that control (in part) the expected risk of classifiers [3]. These capacities quantify the expectations regarding future data that learning algorithms embed into classifiers. Solomonoff and Hutter have applied algorithmic information to prove remarkable results on universal induction. Shannon information provides the mathematical foundation for communication and coding theory. However, both approaches have shortcomings. Algorithmic information is not computable, severely limiting its practical usefulness. Shannon information refers to ensembles rather than actual events: it makes no sense to compute the Shannon information of a single string – or rather, there are many answers to this question depending on how a related ensemble is constructed. Although there are asymptotic results linking algorithmic and Shannon information, it is unsatisfying that there is such a large gap – a difference in kind – between the two measures. This note describes a new method of quantifying information, effective information, that links algorithmic information to Shannon information, and also links both to capacities arising in statistical learning theory [4, 5]. After introducing the measure, we show that it provides a non-universal analog of Kolmogorov complexity. We then apply it to derive basic capacities in statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. A nice byproduct of our approach is an interpretation of the explanatory power of a learning algorithm in terms of the number of hypotheses it falsifies [6], counted in two different ways for the two capacities. We also discuss how effective information relates to information gain, Shannon and mutual information. (shrink)

The received view of an ad hochypothesis is that it accounts for only the observation(s) it was designed to account for, and so non-ad hocness is generally held to be necessary or important for an introduced hypothesis or modification to a theory. Attempts by Popper and several others to convincingly explicate this view, however, prove to be unsuccessful or of doubtful value, and familiar and firmer criteria for evaluating the hypotheses or modified theories so classified are characteristically available. These points (...) are obscured largely because the received view fails to adequately separate psychology from methodology or to recognise ambiguities in the use of ''ad hoc''. (shrink)

The problem of rational prediction, launched by Wesley Salmon, is without doubt the Achilles heel of the critical method defended by Popper. In this paper, I assess the response given both by Popper and by the popperian Alan Musgrave to this problem. Both responses are inadequate and thus the conclusion of Salmon is reinforced: without appeal to induction, there is no way to make of the practical prediction a rational action. Furthermore, the critical method needs to be vindicated if one (...) pretends that its application be suitable for the preference of hypothesis. I argue that the nature of this vindication is such that it may be applied also to induction. Thus, to be a popperian is a good reason also to be an inductivist. (shrink)

In paragraph 21 of his "Logic of Scientific Discovery", Karl Popper characterizes with the help of two seemingly synonymous definitions the falsifiability of a theory as a logical relation between the theory itself and its basic statements. It is shown that his definitions do not agree with each other, and this result is applied to the problem of the falsifiability of contradictions, to the difference between falsifiable and empirical statements and to the demarcation criterion.

Deterministic Chaos: Some Interesting Points of View from the Philosophy of Science. A comparatively simple example is used to present some of the main features of deterministic chaos. From the point of view of the philosophy of science, three questions are dealt with: if the equations of motion of chaotic systems are falsifiable in a strict sense; whether experiments on chaotic systems are reproducible; to what extent the development of chaotic systems is predictable. It emerges that in these respects chaotic (...) systems, though being deterministic, behave essentially in the same way as stochastic (indeterministic) systems do. (shrink)

A very brief outline of Popper's methodology.

Susan Haack criticises the US courts' use of Karl Popper's epistemology in discriminating acceptable scientific testimony. She claims that acceptable testimony should be reliable and that Popper's epistemology is useless in discriminating reliability. She says that Popper's views have been found acceptable only because they have been misunderstood and she indicates an alternative epistemology which she says can discriminate reliable theories. However, her account of Popper's views is a gross and gratuitous misrepresentation. Her alternative epistemology cannot do what she claims (...) for it. The courts should not be concerned with reliability and, insofar as they use the term 'reliability,' it should be construed in a procedural rather than a substantive sense. Since Popper's epistemology gives something like a characterisation of science at its best, the courts should continue to invoke Popper's theories in their discrimination of acceptable testimony. (shrink)

Prompted by the "Panel Discussion of Grünbaum's Philosophy of Science" (Philosophy of Science 36, December, 1969) and other recent literature, this essay ranges over major issues in the philosophy of space, time and space-time as well as over problems in the logic of ascertaining the falsity of a scientific hypothesis. The author's philosophy of geometry has recently been challenged along three main distinct lines as follows: (i) The Panel article by G. J. Massey calls for a more precise and more (...) coherent account of the Riemannian conception of an intrinsic as opposed to an extrinsic metric, which the author has invoked as his basis for the distinction between non-conventional and convention-laden ascriptions of metrical equality and inequality; (ii) the latter distinction has been claimed to suffer from the liabilities of the so-called "standard conception" of scientific theories [36]; and (iii) pursuant to H. Putnam's "An Examination of Grünbaum's Philosophy of Geometry" [56], J. Earman [16, 17] and R. Swinburne [65] have contended that the difference between intrinsic and extrinsic metrics is scientifically unilluminating, and that the associated distinction between non-conventional and convention-laden metrical comparisons does not have the kind of relevance to extant scientific theories that the author has claimed for it. The essay consists of two installments. The present installment, comprising the Introduction and Part A, is devoted to the clarification, correction and further development of the author's prior writings on the philosophy of geometry. Its main objective is constructive elaboration rather than offering polemics. But rebuttals to Earman, [16, 17], Swinburne [65] and Demopoulos [13] are included, because their inclusion conduced to clarity in giving the new exposition. Part B is to appear in a subsequent issue and will be devoted to replies to critiques contained in the Panel Discussion and in other recent literature. It will range over issues in the philosophy of geometry and in the logic of ascertaining the falsity of a scientific hypothesis. By way of merely elliptical anticipation of much more precise statements given in Part A, section 3(ii), the Introduction dissociates the notion of convention-ladenness developed in Part A from the quite different notion integral to the so-called "standard conception" of scientific theories. Thereby, the Introduction prepares the ground for seeing, as a corollary to Part A, section 3(ii), that the notion advocated in the present essay has nothing to fear from the following fact, noted by C. G. Hempel ([36]; cf. also his 1970 Carus Lectures): "even though a sentence may originally be introduced as true by stipulation, it soon joins the club of all other member-statements of the theory and becomes subject to revision in response to further empirical findings and theoretical developments." Part A, which begins with a fairly detailed table of contents, endeavors to meet the aforementioned three-fold challenge to the author's philosophy of geometry. Massey's call for the provision of clear and detailed characterizations of intrinsic and extrinsic metrics is answered with the invaluable aid rendered personally by Massey himself. These characterizations are shown to permit a precise explication of the portions of Riemann's Inaugural Dissertation relevant to (1) Riemann's brilliant anticipation of Einstein's dynamical conception of physical geometry, and (2) the author's philosophical characterization of the metrics and geometries of space, time, and space-time {section 2(c)}. A byproduct of the analysis is to raise two major philosophical doubts concerning Clifford's sketch of a so-called "space-theory of matter" as elaborated in J. A. Wheeler's relativistic geometrodynamics. That theory's vision of understanding matter as a manifestation of empty curved space is questioned in regard to (1) the existence of an intra-geometrodynamic basis for individuating the metrically homogeneous world points of its space-time manifold {section 1(a)}, and (2) the compatibility of the theory with the Riemannian metrical philosophy apparently espoused by its proponents {section 2(c)(i)}. (shrink)

1. Object of this note . In his lively essay, “Between Analytic and Empirical,” , Mr. J. W. N. Watkins challenges the empiricist identification of synthetic statements with empirical ones by arguing that there exists an important class of statements which are synthetic, i.e. not analytically true or false, and yet not empirical. I find Mr. Watkins's arguments very stimulating, but I do not think they provide a sound basis for his contention. In the present note, I wish to indicate (...) what seem to me the principal flaws in Mr. Watkins's reasoning, and to make some additional comments on the issues raised by his discussion. (shrink)

Summary The article argues thatceteris paribus clauses have to be separated from another type of clauses called closure clauses. The former are associated with laws and theories, the latter with test situations of a particular kind. It is also argued that closure clauses, but notceteris paribus clauses, make Popper's falsifiability principle untenable. In that way, it also resolves the quarrel between Popper and Lakatos aboutceteris paribus clauses and falsifiability by saying that both are partly wrong and partly right.

One of the most focused research programs in the science-religion dialogue that has taken place up to the present is the series of volumes published jointly by the Vatican Observatory and the Center for Theology and the Natural Sciences. Originating with the encouragement of Pope John Paul II, this series has produced seven volumes focusing on how divine action can be understood in light of contemporary science. A retrospective volume published in 2008, Scientific Perspectives on Divine Action: Twenty Years of (...) Challenge and Progress, contains articles reviewing the series as a whole. In this article I analyze the series as a whole as well as some of the pivotal problems discussed throughout the series, such as the zero-sum game, scientific “traction,” falsifiability in theories of divine action, and locating special divine action in the physical world. (shrink)

Analysis of Competing Hypotheses (ACH) promises a relatively objective and tractable methodology for ranking the plausibility of competing hypotheses. Unlike Bayesianism, it is computationally modest. Unlike explanationism, it appeals to minimally subjective judgments about relations between hypotheses and evidence. Yet the canonical procedures for ACH allow a certain kind of instability in applications of the methodology, by virtue of supporting competing rankings despite common evidential bases and diagnosticity assessments. This instability should motivate advocates of ACH to focus their efforts toward (...) creating structured methods for individuating items of evidence. (shrink)

From the time of its birth, Popper’s theory of falsifiability has been fiercely criticized from various viewpoints. In the author’s view, however, those various criticisms all have the same root in their assumption that a falsification must be certain and conclusive. As the theory of falsifiability has never had such an assumption, it is the source of misunderstanding. By discarding it, we can reply to every criticism and thereby clarify the role of falsifiability in our search for better knowledge; that (...) is, it makes our attitude open to a yet unknown world. Key Words: Popper • falsifiability • openness • inconclusive falsification • second Popper legend. (shrink)

In their critique of Klein (2014a), Trafimow and Earp present two theses. First, they argue that, contra Klein, a well-specified theory is not a necessary condition for successful replication. Second, they contend that even when there is a well-specified theory, replication depends more on auxiliary assumptions than on theory proper. I take issue with both claims, arguing that (a) their first thesis confuses a material conditional (what I said) with a modal claim (T&E’s misreading of what I said), and (b) (...) their second thesis has the unfortunate consequence of refuting their first thesis. (shrink)

Popper Proposed the criterion of falsifiability as a solution to the problem of demarcation i.e. of distinguishing science from pseudo-science and not, as many of his contemporaries in the Vienna Circle mistook it to be, a solution to the quite different problem with which they themselves were preoccupied, viz. of providing a criterion of meaning to distinguish the meaningful from the meaningless. While the positivists were concerned to damn metaphysics and exalt science, by identifying the empirically verifiable with the meaningful, (...) Popper was concerned to separate science from scientism, to damn astrology and to extol astronomy. In other words his preoccupation belongs not to the philosophy of language but to the philosophy of science. (shrink)

The sheer multitude of criteria of empirical significance has been taken as evidence that the pre-analytic notion being explicated is too vague to be useful. I show instead that a significant number of these criteria—by Ayer, Popper, Przełęcki, Suppes, and David Lewis, among others—not only form a coherent whole, but also connect directly to the theory of definition, the notion of empirical content as explicated by Ramsey sentences, and the theory of measurement; two criteria by Carnap and Sober are trivial, (...) but can be saved and connected to the other criteria by slight modifications. A corollary is that the ordinary language defense of Lewis, the conceptual arguments by Ayer and Popper, the theoretical considerations by Przełęcki, and the practical considerations by Suppes all apply to the same criterion or closely related criteria. Furthermore, the equivalence of some criteria allows for their individual justifications to be taken cumulatively and, together with the entailment relations between nonequivalent criteria, suggest criteria for general auxiliary assumptions, comparative criteria, and more liberal conceptions of observation. (shrink)

Carnap’s search for a criterion of empirical significance is usually considered a failure. I argue that the results from two out of his three different approaches are at the very least problematic, but that one approach led to success. Carnap’s criterion of translatability into logical syntax is too vague to allow for definite results. His criteria for terms—introducibility by chains of reduction sentences and his criterion from “The Methodological Character of Theoretical Concepts”—are almost trivial and have no clear relation to (...) the empirical significance of sentences. However, his criteria for sentences—translatability, verifiability, falsifiability, confirmability—are usable, and under the assumptions needed for the Carnap sentence approach, verifiability, falsifiability, and translatability become equivalent. As a result of the Carnap sentence approach, metaphysics is rendered analytic. (shrink)

There has been little research into the weak kindsof negating hypotheses. Hypotheses may be unfalsifiable. In this case it is impossible tofind a contradiction in some area of the conceptualsystems in which they are incorporated.Notwithstanding this fact, it is sometimes necessaryto construct ways of rejecting the unfalsifiablehypothesis at hand by resorting to some external forms of negation, external because wewant to avoid any arbitrary and subjectiveelimination, which would be rationally orepistemologically unjustified. I will consider akind of ``weak'''' (unfalsifiable) hypotheses that (...) arehard to negate and the ways for making it easy. Inthese cases the subject can ``rationally'''' decide towithdraw his hypotheses even in contexts where it is``impossible'''' to find ``explicit'''' contradictions: theuse of negation as failure (an interestingtechnique for negating hypotheses and accessing newones suggested by artificial intelligence) isilluminating. I plan to explore whether this kind ofnegation can be employed to model hypothesiswithdrawal in Poincaré''s conventionalism of theprinciples of physics and in Freudian analyticreasoning. (shrink)

Karl Popper rightly contests the possibility of a verification of basic statements. At the same time he strictly believes in the possibility of growth of empirical knowledge. Knowledge growth, however, is only possible if empirical theories can be falsified. This raises the question, how theories can be falsified, if a verification of those statements that falsify theories – i.e. basic statements – is not possible. This problem is often referred to as the “basic problem” or “problem of the empirical basis”. (...) In this paper I show that – from a logical point of view – a falsification of theories is possible without a verification of basic state-ments. Furthermore I show that knowledge growth in the empirical sciences will be possible if two assumptions are valid. These assumptions can neither be proven nor falsified. However, they have to be postulated by everybody in eve-ryday life. (shrink)

The paper aims to expound on the issue of science being different from non science or prescience in the form of the scientific methodology used. Popper’s method of falsifiability ensures the aim of science to be successful. The aim of science which also needs a critical attitude, can enable scientific progress by rejecting inductivism as its scientific methodology. Popper’s view on what the aim of science is and why and how inductivism fails in the case of science, along with examples (...) from history of science besides its impact on philosophical foundations of science, has been stressed in the paper. (shrink)

This paper is a detailed critical study of Adolf Grünbaum's work on the Duhemian thesis. I show that (a) Grünbaum's geometrical counterexample to the (D1) subthesis is unsuccessful, even with minimal claims made for what the counterexample is supposed to show, and (b) the (D2) subthesis is not a reasonable one (and cannot correctly be attributed to Duhem). The paper concludes with an argument about the relation between the Duhemian thesis, concerning component hypotheses of a scientific theory, and the view (...) that it is impossible to falsify entire theories conclusively. (shrink)

On the basis of the Suppes–Sneed structuralview of scientific theories, we take a freshlook at the concept of refutability,which was famously proposed by K.R. Popper in 1934 as a criterion for the demarcation of scientific theories from non-scientific ones, e.g., pseudo-scientificand metaphysical theories. By way of an introduction we argue that a clash between Popper and his critics on whether scientific theories are, in fact, refutablecan be partly explained by the fact Popper and his criticsascribed different meanings to the term (...) theoryThen we narrow our attention to one particular theory,namely quantum mechanics, in order to elucidate general matters discussed. We prove that quantum mechanics is irrefutable in a rather straightforward sense, but argue that it is refutable in a more sophisticated sense, which incorporates someobservations obtained by looking closely at the practiceof physics. We shall locate exactly where non-rigourous elements enter the evaluation of a scientific theory – thismakes us see clearly how fruitful mathematics isfor the philosophy of science. (shrink)

Hempel, Popper, and Kuhn argue that to be scientific is to be testable, to be falsifiable, and most nearly to do normal science, respectively. I argue that to be scientific is largely to be interactive, offering some examples from science to show that the ideas from different fields of science interact with one another. The results of the interactions are that hypotheses become more plausible, new phenomena are explained and predicted, we understand phenomena from a new perspective, and our worldview (...) becomes simpler. I also argue that given that the interactions are impressive features of science, astrology and religion would be regarded as science, provided that there are similar interactions in those enterprises. (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.

From the early-1950s on, F.A. Hayek was concerned with the development of a methodology of sciences that study systems of complex phenomena. Hayek argued that the knowledge that can be acquired about such systems is, in virtue of their complexity (and the comparatively narrow boundaries of human cognitive faculties), relatively limited. The paper aims to elucidate the implications of Hayek’s methodology with respect to the specific dimensions along which the scientist’s knowledge of some complex phenomena may be limited. Hayek’s fallibilism (...) was an essential (if not always explicit) aspect of his arguments against the defenders of both socialism ([1935] 1948, [1940] 1948) and countercyclical monetary policy ([1975] 1978); yet, despite the fact that his conceptions of both complex phenomena and the methodology appropriate to their investigation imply that ignorance might beset the scientist in multiple respects, he never explicated all of these consequences. The specificity of a scientific prediction depends on the extent of the scientist’s knowledge concerning the phenomena under investigation. The paper offers an account of the considerations that determine the extent to which a theory’s implications prohibit the occurrence of particular events in the relevant domain. This theory of “predictive degree” both expresses and – as the phenomena of scientific prediction are themselves complex in Hayek’s sense – exemplifies the intuition that the specificity of a scientific prediction depends on the relevant knowledge available. (shrink)