Falsification

This paper deals with a relatively recent trend in the history of analytic philosophy, philosophical logic, and theory of science: the philosophical study of the role of inconsistency in empirical science. This paper is divided in three sections that correspond to the three types of inconsistencies identified: (i) factual, occurring between theory and observations, (ii) external, occurring between two mutually contradictory theories, and (iii) internal, characterising theories that entail mutually contradictory statements.

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.

The possibility of testing contradictory statements about the factual world has been suggested but barely discussed in the relevant literature. Here I argue that if we assume that there are contradictory observation sentences, it would be logically impossible to falsify them. Accordingly, the extension of the dialetheist programme into empirical science would be non-advisable, for it would introduce logically unfalsifiable claims.

This paper discusses the logical possibility of testing inconsistent empirical theories. The main challenge for answering this affirmatively is to avoid that the inconsistent consequences of a theory both corroborate it and falsify it. I answer affirmatively by showing that we can define a class of empirical sentences whose truth would force us to abandon such inconsistent theory: the class of its potential rejecters. Despite this, I show that the observational contradictions implied by a theory could only be verified (provided (...) we make some assumptions), but not rejected. From this, it follows that, although inconsistent theories are rejectable, they cannot be rejected qua inconsistent. (shrink)

In this paper, I draw attention to a revolution in the metaphysical commitments of Western astrology. Although I do not wish to promote astrology, I propose a rational route to this revolution. But there is a strong argument, from a Popperian perspective, that my proposal fails to establish rationality. I then consider whether we should say that astrology is either false or unfalsifiable, drawing attention to some surprising findings from schizophrenia research. Also, in a footnote I present “Tompkins’ paradox.”.

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)

Preuves et Réfutations est écrit comme une série de dialogues socratiques entre un groupe d'étudiants discutant de la démonstration des caractéristiques d'Euler définies pour les polyèdres. Le livre explique de nombreuses idées logiques importantes, mettant l'accent sur l'idée d'heuristique positive. Le livre comprend deux annexes. Dans le premier, Lakatos donne des exemples du processus heuristique de la découverte mathématique en particulier et du processus scientifique en général. Deuxièmement, il oppose les approches déductives et heuristiques et propose des analyses heuristiques des (...) concepts « preuves ». DOI: 10.13140/RG.2.2.20798.31042. (shrink)

Karl Popper, ca raționalist critic, a fost un oponent al tuturor formelor de scepticism, convenționalism și relativism în știință. Multe dintre argumentele sale sunt îndreptate împotriva membrilor "Cercului Vienez". Popper este de acord cu aceștia cu privire la aspectele generale ale metodologiei științifice și neîncrederea lor în metodologia filosofică tradițională, dar soluțiile sale au fost semnificativ diferite. A contribuit semnificativ la dezbaterile privind metodologia științifică generală, demarcarea științei de pseudoștiință, natura probabilității și metodologia științelor sociale. DOI: 10.13140/RG.2.2.27356.85127/1 .

One justification for preregistering research hypotheses, methods, and analyses is that it improves the transparent evaluation of the severity of hypothesis tests. In this article, I consider two cases in which preregistration does not improve this evaluation. First, I argue that, although preregistration can facilitate the transparent evaluation of severity in Mayo’s error statistical philosophy of science, it does not facilitate this evaluation in Popper’s theory-centric approach. To illustrate, I show that associated concerns about Type I error rate inflation are (...) only relevant in the error statistical approach and not in a theory-centric approach. Second, I argue that a preregistered test procedure that allows deviations in its implementation does not provide a more transparent evaluation of Mayoian severity than a non-preregistered procedure. In particular, I argue that sample-based validity-enhancing deviations cause an unknown inflation of the test procedure’s Type I (familywise) error rate and, consequently, an unknown reduction in its capability to license inferences severely. I conclude that preregistration does not improve the transparent evaluation of severity in Popper’s philosophy of science or when deviations are allowed. (shrink)

A scientific theory, according to Popper, can be legitimately saved from falsification by introducing an auxiliary hypothesis to generate new, falsifiable predictions. Also, if there are suspicions of bias or error, the researchers might introduce an auxiliary falsifiable hypothesis that would allow testing. But this technique can not solve the problem in general, because any auxiliary hypothesis can be challenged in the same way, ad infinitum. To solve this regression, Popper introduces the idea of ​​a basic statement, an empirical statement (...) that can be used both to determine whether a given theory is falsifiable and, if necessary, to corroborate falsification assumptions. DOI: 10.13140/RG.2.2.22162.09923. (shrink)

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)

Priest's theory of motion is based on Leibniz's Continuity Condition (LCC), which states that any state that exists at each instant in a continuous set of moments also exists at its temporal limit. If we accept the CCL, a free-falling pen would have to be simultaneously in motion and at rest at the instant of change: the critical moment when it hits the ground, thus passing from the state of motion to that of rest. This seems to be a contradictory (...) state of affairs, which is precisely what Priest claims to be the case. In this article, I discuss the logical possibility of empirically testing whether such a contradictory state of affairs occurs. (shrink)

The predictive processing account of action, cognition, and perception is one of the most influential approaches to unifying research in cognitive science. However, its promises of grand unification will remain unfulfilled unless the account becomes theoretically robust. In this paper, we focus on empirical commitments of PP, since they are necessary both for its theoretical status to be established and for explanations of individual phenomena to be falsifiable. First, we argue that PP is a varied research tradition, which may employ (...) various kinds of scientific representations, differing in the scope of empirical commitments they entail. Two major perspectives on PP qua cognitive theory may then be distinguished: generalized vs. hierarchical. The first one fails to provide empirical detail, and the latter constrains possible physical implementations. However, we show that even hierarchical PP is insufficiently restrictive to disallow incorrect models and may be adjusted to explain any neurocognitive phenomenon–including non-existent or impossible ones–through flexible adjustments. This renders PP a universal modeling tool with an unrestricted number of degrees of freedom. Therefore, in contrast with declarations of its proponents, it should not be understood as a unifying theoretical perspective, but as a computational framework, possibly informing further theory development in cognitive science. (shrink)

In this paper I formalise the falsificationist proposal omitting Popper’s requirement of consistency. This omission results in (i) trivial theories being falsifiable in an inappropriate sense of the term, but also in (ii) some inconsistent non-trivial theories being so in an appropriate one. This justifies a slight alteration of the definition of falsifiability that excludes (i) but allows (ii). Instead of requiring that a falsifiable theory be consistent, my proposal only requires that the intersection of its classes of potential corroborators (...) and falsifiers be empty. (shrink)

Introduction: In the past, psychoanalysis was classified as a pseudoscience. Karl Popper was one of those who objected to the idea that psychoanalysis is a science, using falsifiability. However, falsifiability cannot be considered sufficient anymore, since it carries major weaknesses and better alternatives to address the issue are available. Objective: This article intends to evaluate the scientific status of psychoanalysis concerning the demarcation problem. Method: In order to do so, Sven Ove Hansson’s criteria were used. His proposal consists of a (...) set of sufficient and necessary conditions which is complemented by a multicriteria list that helps identifying pseudosciences. It was analyzed how much psychoanalysis fits each of Hansson's seven items, besides proposing the addition of an eighth. Results: The results showed that psychoanalysis was compatible with all eight demarcation of pseudoscience’s items. Conclusion: In the end, the conclusion was that even if falsifiability was to be dismissed, the evidence suggests that there are still enough reasons to affirm that psychoanalysis is a pseudoscience, since it significantly deviates from scientific quality standards. (shrink)

According to Karl Popper, science cannot verify its theories empirically, but it can falsify them, and that suffices to account for scientific progress. For Popper, a law or theory remains a pure conjecture, probability equal to zero, however massively corroborated empirically it may be. But it does just seem to be the case that science does verify empirically laws and theories. We trust our lives to such verifications when we fly in aeroplanes, cross bridges and take modern medicines. We can (...) do some justice to this apparent capacity of science to verify if we make a number of improvements to Popper’s philosophy of science. The key step is to recognize that physics, in accepting unified theories only, thereby makes a big metaphysical assumption about the nature of the universe. The outcome is a conception of scientific method which facilitates the criticism and improvement of metaphysical assumptions of physics. This view provides, not verification, but a perfect simulacrum of verification indistinguishable from the real thing. (shrink)

Bilim ve çarpık bilim arasına sınır çizebilmek için yapılan girişimler farklı teorilerin gelistirilmesini sağlamıştır. Henüz net bir sınır çizilememiştir ve tartışmalar devam etmektedir. İlk olarak doğrulama ve yanlışlama teorileri daha sonraları ise bilim çalışmalarını bir bütün olarak ele alan, araştırma programları olarak gören teoriler sunulmuştur. Bilimsel çalışmaların, yeni sorunlar üretmesi ve eleştirel bakış açısına sahip olması da bilim olanın sınırlarını çizebilmek için ölçütler arasında sayılmıştır. Bu çabalar ile bilim pratiklerinin irdelenmesi zamanla bilim insanına ve bilim kurumlarına yönelmiştir. Bu konunun önemli (...) bir sorunu bilim yolu ile ulaşabileceğimiz doğru bilginin ne olduğu ile neyin bilim olarak ele alınabileceğinin tek bir sorun gibi ele alınmasıdır. Bilimsel doğrunun ne olduğu ile bilimsel bilginin ne olduğu tartışması iç içe yürütülmektedir. Bir diğer sorun ise bilimin sınırlarını belirlerken bilim çalışmaları dışında etik ve sosyal ölçütler aranmasıdır. Bu yaklaşımlar konuyu çözümsüz bir noktaya götürmektedir. Diğer önemli nokta Astroloji örneğinin yanlış bilgilerle ele alınmasıdır. Bu çalışmada tartışmanın bilim pratiklerinde kalması gerektiği savunulmuştur. Çarpık bilimi ayırmak için sık kullanılan Astroloji örneği yeniden ele alınarak yanlış yargılara sebep olan bilgiler düzeltilmeye çalışılmıştır. Ayrıca önermelerin bilimsel doğruyu ayırma konusundaki önemi ve durumu tartışılmış böylece neyin bilim, neyin bilimsel doğru ve neyin bilim dışı olduğu netleştirilmeye çalışılmıştır. (shrink)

This dissertation offers a proof of the logical possibility of testing empirical/factual theories that are inconsistent, but non-trivial. In particular, I discuss whether or not such theories can satisfy Popper's principle of falsifiablility. An inconsistent theory Ƭ closed under a classical consequence relation implies every statement of its language because in classical logic the inconsistency and triviality are coextensive. A theory Ƭ is consistent iff there is not a α such that Ƭ ⊢ α ∧ ¬α, otherwise it is inconsistent. (...) We say, instead, that Ƭ is non-trivial iff there is at least one α such that Ƭ ⊢ α, otherwise we say that it trivial. This happens because classical logic satisfies the principle of explosion, according ex contradictione sequitur quodlibet (from a contradiction anything follows). Under these conditions inconsistent classical theories would be compatible with any well-formed formula, which makes them useless for science. There are, however, so-called paraconsistent logics in which the principle of explosion does not generally hold and in which a theory can be (simply) inconsistent, but also absolutely consistent. It is in this logical framework that we can prove that some inconsistent theories can be falsifiable. (shrink)

Retractions play an important role in research communication by highlighting and explaining how research projects have failed and thereby preventing these mistakes from being repeated. However, the process of retraction and the data it produces is often sparse or incomplete. Drawing on evidence from 2046 retraction records, Quan-Hoang Vuong discusses the emerging trends this data highlights and argues for the need to enforce reporting standards for retractions, as a means of de-stigmatising retraction and rewarding practising integrity in the scholarly record.

Popper restricted his definition of falsifiability to consistent theories through what we may call his requirement of consistency. His main argument was that an inconsistent theory does not distinguish the sentences that corroborate it from those that contradict it, for all sentences follow from it. I propose to replace this requirement by the more basic requirement that the classes of potential corroborators and falsifiers of a theory do not overlap. This results not only in an unrestricted definition of falsifiability but (...) also in some inconsistent theories being falsifiable whenever that inconsistency is not located among its observational statements. Although this assumes a restriction of the principle of explosion or ex contradictione sequitur quodlibet (ECQ), it does not depend on any particular system or approach of paraconsistent logic. Finally, I propose to define the class of potential refuters of a theory, which is obtained by subtracting the class of potential corroborators from the class of potential falsifiers. Given that, by definition, the classes of potential refuters and corroborators of a theory do not overlap, it immediately follows that some observationally inconsistent theories are refutable in this sense. This establishes the bases for a new and more general formal theory of falsifiability of scientific factual/empirical theories. (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)

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)

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)

Peer review is an opportunity to perform an unlawful censorship which ensures that no apostate notion ever get published in mainstream journals. Or such peer review censorship is an opportunity to steal any content and to claim afterward the priority of first publication. And last but not least, the peer review is an academic tool to promote the mainstream pseudoscience.

Chapter 3 surveys objectivity in the natural sciences. Thomas Kuhn problematized the logicist understanding of the objectivity or rationality of scientific change, providing a very different picture than that of the cumulative or step-wise progress of theoretical science. Theories often compete, and when consensus builds around one competitor it may be for a variety of reasons other than just the direct logical implications of experimental successes and failures. Kuhn pitted the study of the actual history of science against what Hans (...) Reichenbach referred to as the “logical substitutes” logicists used to reconstruct the rationality of theory change. Such substitutes were promoted to show that theory confirmation is a purely epistemic affair, where purely epistemic implies purely inferential. But where the positivists saw logical compulsion as the reason for theory change, Kuhn saw psychology in values as relevant to how theories are actually confirmed or accepted by the scientific community. (shrink)

En el presente trabajo expongo la propuesta falsacionista de Karl Popper como resultado de su solución al problema de la inducción. En este sentido, la analizo bajo sus dos aspectos, el lógico y el metodológico. La idea detrás de ello es mostrar, en primer lugar, que su solución lógica al problema de la inducción es totalmente independiente de los criterios metodológicos que propone para la elección entre teorías rivales, y en segundo lugar, que estos últimos constituyen una transgresión a su (...) pretendida exclusión de la inducción en la práctica científica. (shrink)

F.A. Hayek argued that the sciences of complex phenomena, including (perhaps especially) economics, are limited to incomplete “explanations of the principle” and “pattern predictions.” According to Hayek, these disciplines suffer from (what I call) a data problem, i.e., the hopelessness of populating theoretical models with data adequate to full explanations and precise predictions. In Hayek’s terms, explanations in these fields are always a matter of “degree.” However, Hayek’s methodology implies a distinct theory problem: theoretical models of complex phenomena may be (...) underspecified so that, even were all the data available, a full explanation could not be inferred from the model. Where the sciences of complex phenomena are subject to both the data and theory problems, explanations and predictions will be of even lesser “predictive degree.” The paper also considers how to interpret Hayek’s claim that pattern predictions are falsifiable. (shrink)

Imre Lakatos' views on the philosophy of mathematics are important and they have often been underappreciated. The most obvious lacuna in this respect is the lack of detailed discussion and analysis of his 1976a paper and its implications for the methodology of mathematics, particularly its implications with respect to argumentation and the matter of how truths are established in mathematics. The most important themes that run through his work on the philosophy of mathematics and which culminate in the 1976a paper (...) are (1) the (quasi-)empirical character of mathematics and (2) the rejection of axiomatic deductivism as the basis of mathematical knowledge. In this paper Lakatos' later views on the quasi-empirical nature of mathematical theories and methodology are examined and specific attention is paid to what this view implies about the nature of mathematical argumentation and its relation to the empirical sciences. (shrink)

State of the art paper on the problem of induction: how to justify the conclusion that ‘all Fs are Gs’ from the premise that ‘all observed Fs are Gs’. The most prominent theories of contemporary philosophical literature are discussed and analysed, such as: inductivism, reliabilism, perspective of laws of nature, rationalism, falsificationism, the material theory of induction and probabilistic approaches, according to Carnap, Reichenbach and Bayesianism. In the end, we discuss the new problem of induction of Goodman, raised by the (...) grue predicate. (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)

Selectionist evolutionary theory has often been faulted for not making novel predictions that are surprising, risky, and correct. I argue that it in fact exhibits the theoretical virtue of predictive capacity in addition to two other virtues: explanatory unification and model fitting. Two case studies show the predictive capacity of selectionist evolutionary theory: parallel evolutionary change in E. coli, and the origin of eukaryotic cells through endosymbiosis.

The critique of the dogmatism of a-priorism from the Popperians suffered from the fact that Popper, too, was moving towards a certain dogmatic derivation. According to the a-priorists, in wanting to protect himself from any would-be-critics who would argue against the dogmatism of his approach, Popper left his philosophical foundation free to the critics. In fighting against German essentialism, he found himself in a position that necessitated the abandonment of either his presupposed anti-essentialism, or his critique of the positivists. Popper's (...) success stems less from his ability to rally the anti-historicist positivists towards the search for scientific foundations, than the fact that he was one of the greatest, if not the greatest, theoreticians of the scientific method, and critic of ideological simplicity. (shrink)

Abstract One cannot discount experimental errors and turn the attention to the logicomathematical structure of a physical theory without distorting the nature of the scientific method. The occurrence of errors in experiments constitutes an inherent feature of the attempt to test theories in the physical world. This feature deserves proper attention which has been neglected. An attempt is made to address this problem.

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.

I confront Feyerabend's position and critical rationalism in order to have a foundation or starting point for my (historical) investigation. The main difference of his position towards falsificationism is the belief that different theories cannot be discussed rationally. Feyerabend is convinced that Galilei's observations with the telescope in the historical context of the Copernican revolution supports his criticism. In particular, he argues that the Copernican theory was supported by deficient hypotheses, and falsifications were disposed by ad hoc hypotheses and propaganda. (...) Furthermore, he claims that his philosophy of science reconstructs Galilei's defence of the Copernican theory. He introduces a central principle of his position (the principle of tenacity) in order to justify a research strategy of not eliminating falsified theories. He tries to show that the tenacious defence of a theory corresponds to Galilei's defence of the Copernican theory. Remarkably, Feyerabend's approach to explain the development of science earns an important support from his interpretation of Galilei's observations. On this basis I give a falsificationist interpretation of Galilei's observations with the telescope, and oppose this interpretation to Feyerabend's. From a falsificationist perspective, auxiliary hypotheses compete during the Copernican revolution which can (with some effort) be critically discussed. Then I analyse the historical case in order to test Feyerabend's interpretation of the Copernican revolution. Inter alias I investigate thoroughly whether Galilei, as Feyerabend claims, immunised falsifications of the Copernican theory by the introduction of ad hoc hypotheses. The investigation considers Galilei's explanation of Venus' phases, his establishment of the irradiation hypothesis, the explanation of the telescope's functionality, and the role of the reproducibility of the observations with the telescope. Finally I provide a rational reconstruction of Galilei's falsification of the Ptolemaic theory. The formalisation shows that Galilei was not a cautious critical rationalist, but a very confident scientist using the method of falsification. (shrink)