In this paper, we present and defend an analysis of harm that we call the Negative Influence on Well-Being Account (NIWA). We argue that NIWA has a number of significant advantages compared to its two main rivals, the Counterfactual Comparative Account (CCA) and the Causal Account (CA), and that it also helps explain why those views go wrong. In addition, we defend NIWA against a class of likely objections, and consider its implications for several questions about harm and its role (...) in normative theorizing. (shrink)

In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous logic diagrams. To this end, we first examine the problem of uncertainty or over-specification in syllogistic that became obvious in Euler diagrams. In the 19th century, numerous logicians tried to solve this problem. The most famous was the attempt to introduce dashed circles into Euler diagrams. The solution that John Venn developed for this problem, however, came (...) from a completely different area of logic: instead of orienting to syllogistic like Euler diagrams, Venn applied Boolean algebra to improve visual reasoning. Venn’s contribution to solving the problem of elimination also played an important role. The result of this development is still known today as the ‘Venn Diagram’. (shrink)

According to the standard version of the counterfactual comparative account of harm, an event is overall harmful for an individual if and only if she would have been on balance better off if it had not occurred. This view faces the “preemption problem.” In the recent literature, there are various ingenious attempts to deal with this problem, some of which involve slight additions to, or modifications of, the counterfactual comparative account. We argue, however, that none of these attempts work, and (...) that the preemption problem continues to haunt the counterfactual comparative account. (shrink)

Logic diagrams have seen a resurgence in their application in a range of fields, including logic, biology, media science, computer science and philosophy. Consequently, understanding the history and philosophy of these diagrams has become crucial. As many current diagrammatic systems in logic are based on ideas that originated in the 18th and 19th centuries, it is important to consider what motivated the use of logic diagrams in the past and whether these reasons are still valid today. This paper proposes that (...) transcendental philosophy was a key inspiration for the development of logic diagrams and that such diagrams can be employed in transcendental arguments, even after the linguistic turn. (shrink)

The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. (...) -/- Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. -/- Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study. (shrink)

IntroductionIf we were to identify the beginning of the study of visual argumentation, we would have to choose 1996 as the starting point. This was the year that Leo Groarke published “Logic, art and argument” in Informal logic, and it was the year that he and David Birdsell co-edited a special double issue of Argumentation and Advocacy on visual argumentation . Among other papers, the issue included Anthony Blair’s “The possibility and actuality of visual arguments”. It was also the year (...) that Gail J. Chryslee, Sonja K. Foss and Arthur L. Ranney published their short text on “The construction of claims in visual argumentation” , stating that even though theorists may know a great deal about the process of argumentation, “virtually none of this knowledge is applicable to visual argumentation […] because of the properties that distinguish visual imagery from discursive symbols” .Texts on visual rhetoric have been written as far back as the early 1980s, .. (shrink)

Ein Beispiel für die Rezeption und Fortführung der schopenhauerschen Logik findet man in den Mathematiklehrbüchern Friedrich Adolph Wilhelm Diesterwegs (1790–1866), In diesem Aufsatz werden die historische und systematische Dimension dieser Anwendung von Logikdiagramme auf die Mathematik skizziert. In Kapitel 2 wird zunächst die frühe Rezeption der schopenhauerschen Logik und Philosophie der Mathematik vorgestellt. Dabei werden einige oftmals tradierte Vorurteile, die das Werk Schopenhauers betreffen, in Frage gestellt oder sogar ausgeräumt. In Kapitel 3 wird dann die Philosophie der Mathematik und der (...) Logik Schopenhauers vorgestellt. Es wird gezeigt, dass Schopenhauers Logikdiagramme auf Ideen der Mathematiker Leonhard Euler (1707–1783), Bernhard Friedrich Thibaut (1775–1832) und Franz Ferdinand Schweins (1780–1856) zurückgehen und dass Schopenhauer diese Logikdiagramme auch bereits zur Analyse mathematischer Begriffe verwendet. Kapitel 4 beschäftigt sich mit der Schopenhauer-Rezeption Diesterwegs. Es wird die Frage behandelt, inwieweit Diesterweg in der Mathematik von Schopenhauer beeinflusst war und welche Rolle dieser Einfluss auf sein Verständnis von Logik und Mathematik hatte. In Kapitel 5 wird schließlich gezeigt, dass Diesterweg die schopenhauersche Begriffsanalyse der Mathematik mit Hilfe von Logikdiagrammen aufgreift und weiterführt. Da Diesterweg einer der einflussreichsten Pädagogen und Mathematikdidaktiker des 20. Jahrhunderts war, ist anzunehmen, dass sich Spuren dieser Methode noch heute finden lassen. Inwiefern dies wahrscheinlich ist, wird in der Zusammenfassung (Kapitel 6) thematisiert. (shrink)

Reism or concretism are the labels for a position in ontology and semantics that is represented by various philosophers. As Kazimierz Ajdukiewicz and Jan Woleński have shown, there are two dimensions with which the abstract expression of reism can be made concrete: The ontological dimension of reism says that only things exist; the semantic dimension of reism says that all concepts must be reduced to concrete terms in order to be meaningful. In this paper we argue for the following two (...) theses: (1) Arthur Schopenhauer has advocated a reistic philosophy of language which says that all concepts must ultimately be based on concrete intuition in order to be meaningful. (2) In his semantics, Schopenhauer developed a theory of logic diagrams that can be interpreted by modern means in order to concretize the abstract position of reism. Thus we are not only enhancing Jan Woleński’s list of well-known reists, but we are also adding a diagrammatic dimension to concretism, represented by Schopenhauer. (shrink)

The paper examines Schopenhauer’s complex diagrams from the Berlin Lectures of the 1820 s, which show certain partitions of classes. Drawing upon ideas and techniques from logical geometry, we show that Schopenhauer’s partition diagrams systematically give rise to a special type of Aristotelian diagrams, viz. (strong) α -structures.

Logicians commonly speak in a relatively undifferentiated way about pre-euler diagrams. The thesis of this paper, however, is that there were three periods in the early modern era in which euler-type diagrams (line diagrams as well as circle diagrams) were expansively used. Expansive periods are characterized by continuity, and regressive periods by discontinuity: While on the one hand an ongoing awareness of the use of euler-type diagrams occurred within an expansive period, after a subsequent phase of regression the entire knowledge (...) about the systematic application and the history of euler-type diagrams was lost. I will argue that the first expansive period lasted from Vives (1531) to Alsted (1614). The second period began around 1660 with Weigel and ended in 1712 with lange. The third period of expansion started around 1760 with the works of Ploucquet, euler and lambert. Finally, it is shown that euler-type diagrams became popular in the debate about intuition which took place in the 1790s between leibnizians and Kantians. The article is thus limited to the historical periodization between 1530 and 1800. (shrink)

A prominent objection to the counterfactual comparative account of harm is that it classifies as harmful some events that are, intuitively, mere failures to benefit. In an attempt to solve this problem, Duncan Purves has recently proposed a novel version of the counterfactual comparative account, which relies on a distinction between making upshots happen and allowing upshots to happen. In this response, we argue that Purves’s account is unsuccessful. It fails in cases where an action makes the subject occupy a (...) high well-being level though one of the available alternatives would have made it even higher. In fact, it fails even in some cases where each of the available alternatives to the action that was actually performed would have made the subject’s well-being level lower. (shrink)

In recent years CL diagrams inspired by Lange’s Cubus Logicus have been used in various contexts of diagrammatic reasoning. However, whether CL diagrams can also be used as a formal system seemed questionable. We present a CL diagram as a formal system, which is a fragment of propositional logic. Syntax and semantics are presented separately and a variant of bitstring semantics is applied to prove soundness and completeness of the system.

I raise two objections against Christian List and Peter Menzies' influential account of high-level causation. Improving upon some of Stephen Yablo's earlier work, I develop an alternative theory which evades both objections. The discussion calls into question List and Menzies' main contention, namely, that the exclusion principle, applied to difference-making, is false.

In a recent article, I criticized Anthony L. Brueckner and John Martin Fischer’s influential argument—appealing to the rationality of our asymmetric attitudes towards past and future pleasures—against the Lucretian claim that death and prenatal non-existence are relevantly similar. Brueckner and Fischer have replied, however, that my critique involves an unjustified shift in temporal perspectives. In this paper, I respond to this charge and also argue that even if it were correct, it would fail to defend Brueckner and Fischer’s proposal against (...) my critique. (shrink)

It is little known that Schopenhauer (1788–1860) made thorough use of Euler diagrams in his works. One specific diagram depicts a high number of concepts in relation to Good and Evil. It is, hence, uncharacteristic as logicians of that time seldom used diagrams for more than three terms (the number demanded by syllogisms). The objective of this paper is to make sense of this diagram by explaining its function and inquiring whether it could be viewed as an early serious attempt (...) to construct complex diagrams. (shrink)

The counterfactual comparative account of harm faces problems in cases that involve overdetermination and preemption. An influential strategy for dealing with these problems, drawing on a suggestion made by Derek Parfit, is to appeal to _plural harm_—several events _together_ harming someone. We argue that the most well-known version of this strategy, due to Neil Feit, as well as Magnus Jedenheim Edling’s more recent version, is fatally flawed. We also present some general reasons for doubting that the overdetermination and preemption problems (...) for the counterfactual comparative account can be satisfactorily solved by appealing to plural harm. (shrink)

Some forms of argumentation are best performed through words. However, there are also some forms of argumentation that may be best presented visually. Thus, this paper examines the virtues of visual argumentation. What makes visual argumentation distinct from verbal argumentation? What aspects of visual argumentation may be considered especially beneficial?

Extensions of traditional syllogistics have been increasingly researched in philosophy, linguistics, and areas such as artificial intelligence and computer science in recent decades. This is mainly due to the fact that syllogistics is seen as a logic that comes very close to natural language abilities. Various forms of extended syllogistics have become established. This paper deals with the question to what extent a syllogistic representation in CL diagrams can be seen as a form of extended syllogistics. It will be shown (...) that the ontology of CL enables numerically exact assertions and inferences. (shrink)

This paper presents an analysis of Seneca's 58th letter to Lucilius and Porphyry's Isagoge, which were the origin of the tree diagrams that became popular in philosophy and logic from the early Middle Ages onwards. These diagrams visualise the extent to which a concept can be understood as a category, genus, species or individual and what the method of dihairesis (division) means. The paper explores the dissimilarities between Seneca's and Porphyry's tree structures, scrutinising them through the perspective of modern graph (...) theory. Although traditional trees can be interpreted in a modern way, their terms and definitions defy modern standardisation. These distinctions are not only useful for differentiating between Seneca's and Porphyry's trees, but also for comprehending the evolution of this philosophical tradition. Thus the paper highlights the continued significance of these tree diagrams in analysing concepts and categories in philosophy and structuring objects and information in modern fields such as artificial intelligence, computer science, bioinformatics, graph theory, and many more. (shrink)

Many have argued that there is something that is a priori about all necessary truths, including a posteriori necessities. According to a particularly popular claim of this kind, one can know a priori whether a sentence is G-necessary, i.e. whether it is either necessarily true or necessarily false. In this paper, I identify the most plausible version of this claim and I argue that it fails. My discussion also reveals, and depends upon, an important feature of putative natural kind terms (...) that has been widely overlooked. I conclude by outlining a proposal of what is really a priori about necessities. (shrink)

Published in 1785, Immanuel Kant's Groundwork of the Metaphysics of Morals ranks alongside Plato's Republic and Aristotle's Nicomachean Ethics as one of the most profound and influential works in moral philosophy ever written. In Kant's own words, its aim is to identify and corroborate the supreme principle of morality, the categorical imperative. He argues that human beings are ends in themselves, never to be used by anyone merely as a means, and that universal and unconditional obligations must be understood as (...) an expression of the human capacity for autonomy and self-governance. As such, they are laws of freedom. This volume contains Mary Gregor's acclaimed translation of the text into English, revised by Jens Timmermann, and an accessible, updated introduction by Christine Korsgaard. (shrink)

While in the beginning of the environmental debate, conflicts over environmental and technological issues had primarily been understood in terms of ‘‘risk’’, over the past two decades the relevance of ignorance, or nonknowledge, was emphasized. Referring to this shift of attention to nonknowledge the article presents two main findings: first, that in debates on what is not known and how to appraise it different and partly conflicting epistemic cultures of nonknowledge can be discerned and, second, that drawing attention to nonknowledge (...) in technology conflicts results in significant institutional effects and new constellations of actors in public debates. To illustrate and substantiate this political dynamics of nonknowledge we draw upon examples from the areas of agri-biotechnology and mobile phoning. In a first step, we develop in greater detail the concept of scientific cultures of nonknowledge and identify three such cultures involved in the social conflicts within the two areas. Subsequently, we analyze the specific dynamics of the politicisation of nonknowledge looking at the variety of actors involved and the pluralisation of perceptions and evaluations of what is not known. Then, we point out some of the institutional reactions to the political and cultural dynamics of scientific nonknowledge. We argue that the equal recognition of the diverse cultures of nonknowledge is a key prerequisite for socially legitimate and ‘‘robust’’ decision-making under conditions of politicised scientific nonknowledge. (shrink)

The question of naturalness in logic is widely discussed in today’s research literature. On the one hand, naturalness in the systems of natural deduction is intensively discussed on the basis of Aristotelian syllogistics. On the other hand, research on “natural logic” is concerned with the implicitly existing logical laws of natural language, and is therefore also interested in the naturalness of syllogistics. In both research areas, the question arises what naturalness exactly means, in logic as well as in language. We (...) show, however, that this question is not entirely new: In his Berlin Lectures of the 1820s, Arthur Schopenhauer already discussed in depths what is natural and unnatural in logic. In particular, he anticipates two criteria for the naturalness of deduction that meet current trends in research: (1) Naturalness is what corresponds to the actual practice of argumentation in everyday language or scientific proof; (2) Naturalness of deduction is particularly evident in the form of Euler-type diagrams. (shrink)

The paper examines Schopenhauer's logic lectures and the eristic dialectics of the manuscript remains in particular. The content of the logic lectures is briefly presented, then the characteristics are highlighted and finally Schopenhauer’s Euler diagrams are examined. The section on eristic dialectics summarizes the history of the text and its origin and reflects the content and order of the document.

In this paper, we critically examine Molly Gardner’s favored solution to what she calls “the problem of justified harm.” We argue that Gardner’s view is false and that her arguments in support of it are unconvincing. Finally, we briefly suggest an alternative solution to the problem which avoids the difficulties that beset Gardner’s proposal.

The paper presents the diagrammatic calculus CL, which combines features of tree, Euler-type, Venn-type diagrams and squares of opposition. In its basic form, `CL' (= Cubus Logicus) organizes terms in the form of a square or cube. By applying the arrows of the square of opposition to CL, judgments and inferences can be displayed. Thus CL offers on the one hand an intuitive method to display ontologies and on the other hand a diagrammatic tool to check inferences. The paper focuses (...) mainly on the adaptation of the square of opposition in CL and offers an algebraic notation, which corresponds to the diagrammatic representation. (shrink)

In this paper, we interpret a 19th century diagram, which is meant to visualise G.W.F. Hegel’s entire method of the `Science of Logic' on the basis of bitwise operations. For the interpretation of the diagram we use a binary numeral system, and discuss whether the anti-Hegelian argument associated with it is valid or not. The reinterpretation is intended to make more precise rules of construction, a stricter binary code and a review of strengths and weaknesses of the critique.

In previous research, Schopenhauer is regarded as a consistent representative of a classical picture theory of language. The paper shows, however, that Schopenhauer does not only present a use theory of meaning in his lectures on logic, but also justifies it with the help of the context principle. Furthermore, it is discussed to what extent Schopenhauer's use theory of meaning is similar to the semantic theory of Ludwig Wittgenstein and his successors.

Japanese translation of ""Schopenhauers Gebrauchstheorie der Bedeutung und das Kontextprinzip. Eine Parallele zu Wittgensteins Philosophischen Untersuchungen". In: 97. Schopenhauer-Jahrbuch (2016), S. 29–51" by Tadahiro Oota (太田 匡洋 [訳]).

In the year 1714, Johann Christian Lange published a baroque textbook about a logic machine, supposed to simulate human cognitive abilities such as perception, judgement, and reasoning. From today’s perspective, it can be argued that this blueprint is based on an inference engine applied to a strict ontology which serves as a knowledge base. In this paper, I will first introduce Lange’s approach in the period of baroque logic and then present a diagrammatic modernization of Lange’s principles, entitled Calculus CL. (...) Finally, I would like to discuss the possibilities of how to apply CL to modern cases of concern by using an example from epidemiology. (shrink)

John Martin Fischer and Anthony L. Brueckner have argued that a person’s death is, in many cases, bad for him, whereas a person’s prenatal non-existence is not bad for him. Their suggestion relies on the idea that death deprives the person of pleasant experiences that it is rational for him to care about, whereas prenatal non-existence only deprives him of pleasant experiences that it is not rational for him to care about. In two recent articles in The Journal of Ethics, (...) I have objected that it is irrelevant what it is in fact rational for the person to care about. Fischer and Brueckner have replied to my critique. In this paper I respond to their latest pair of replies. (shrink)

A particularly promising trail on the search for forgotten logic diagrams leads to Upper Lusatia in the 17th century, more precisely to Christian Weise and his students. Samuel Grosser, who later became rector in Görlitz, and Johann Christian Lange, who later became professor of logic at the University of Gießen, are the most prominent to have published remarkable logic diagrams. Even more remarkable, however, is the fact that Lange's interest in these diagrams ultimately gave rise to the idea of building (...) a logic machine. (shrink)

Several attractive principles about prudential concern and moral responsibility seem to speak against animalism. I criticize some animalist responses to this kind of problem, and suggest another answer, which has similarites with the most important argument in favor of animalism: the “thinking animal” argument.

A pure time preference is a preference for something to occur at one point in time rather than another, merely because of when it occurs in time. Such preferences are widely regarded as paradigm examples of irrational preferences. However, Rosemary Lowry and Martin Peterson have recently argued that, for instance, a pure time preference to go to the opera tonight rather than next month may be rationally permissible, even if the amounts of intrinsic value realized in both cases are identical. (...) In this reply, we argue that Lowry and Peterson's argument is unsuccessful. (shrink)

The paper gives an overview of Arthur Schopenhauer's theory of rationality. For Schopenhauer, rationality is a human faculty based on language, which, in addition to language, is primarily concerned with knowledge or philosophy of science and practical action. For Schopenhauer, language is the umbrella term under which he subsumes logic and eristics. This paper will first introduce Schopenhauer's logic and clarify its connection to the philosophy of language. This is followed by eristic dialectics, which reflects on how one can protect (...) oneself from people who argue irrationally in a goal-oriented way. Schopenhauer's philosophy of mathematics belongs to the field of philosophy of science. Unlike many other authors of his time, Schopenhauer does not advocate a rationalist but a representationalist approach, which, however, includes a theory of rationality. Therefore, Schopenhauer's representationalist approach will finally be discussed, emphasizing its relationship to his theory of rationality. (shrink)

In this paper, I examine how nudges affect the autonomy and freedom of those nudged. I consider two arguments put forth by Thaler and Sunstein for the claim that these effects can only be minor. According to the first of these arguments, nudges cannot significantly restrict a person’s autonomy or freedom since they are easy to resist. According to the second argument, the existence of nudges is inevitable, and thus, pursuing libertarian paternalism by nudging people doesn’t make a relevant difference (...) to people’s autonomy and freedom. After arguing that both of these arguments fail, I elucidate the general conditions in which, and the degrees to which, a person’s autonomy and freedom are affected by nudges. One focus of this discussion concerns how people’s autonomy and freedom are affected if—for example, due to progress in information technology—nudges become more effective, more individualized and more common, and affect more people. (shrink)

In this paper, I identify and discuss the following feature of our judgments about hypothetical scenarios concerning the identity of persons: with respect to the vast majority of scenarios, both members of a pair of logically complementary propositions about personal identity are conceivable. I consider a number of explanations of this feature that draw on the metaphysics and the epistemology of personal identity, none of which prove to be satisfactory. I then argue that in order to give an adequate explanation, (...) one needs to recognize an important characteristic of our concept of personal identity: it is such that if there are mental substances (or the like), they constitute personal identity. At the same time, there can still be persons if there are no such substances. Since this finding casts doubts on the way that thought experiments about personal identity are usually set up, I end by outlining its potential consequences for the debate over the identity of persons. (shrink)

In a recent Utilitas article, Neil Feit argues that every person occupies a well-being level of zero at all times and possible worlds at which she fails to exist. Views like his face the problem of the subject': how can someone have a well-being level in a scenario where she lacks intrinsic properties? Feit argues that this problem can be solved by noting, among other things, that a proposition about a person can be true at a possible world in which (...) neither she nor the proposition exists. In this response, we argue that Feit has not solved the problem of the subject, and also raise various related problems for his approach. (shrink)

The 2022 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel was awarded to Ben Bernanke, Douglas Diamond, and Philip Dybvig “for research on banks and financial crises”. Jens van 't Klooster reflects on Bernanke, Diamond, and Dybvig's work.

For Arthur Schopenhauer (1788-1860), logic as a discipline belongs to the human faculty of reason, more precisely to the faculty of language. This discipline of logic breaks down into two areas. Logic or analytics is one side of the coin; dialectic or the art of persuasion is the other. The former investigates rule-oriented and monological language. The latter investigates result-oriented language and persuasive language...

In this paper we present an overview of the current interpretations of the first volume of Arthur Schopenhauer’s main work The World as Will and Representation (W I) and discuss their problems. We discuss four issues, which in our opinion must clarify a current interpretation implicitly or explicitly, if it claims to be an interpretation of the whole book: (1) What does Schopenhauer mean by the fact that his work shares only one (single) thought? (2) How are the individual books (...) of W I related? (3) Do we have to read Schopenhauer’s W I as a normative guide to the denial of will-to-live or as a neutral description of the world? (4) Do the often discussed contradictions and aporias within the book follow a plan or are they errors of thought? (shrink)

In this paper, I argue that, contrary to Robert Stalnaker’s highly influential account of linguistic communication, successful communication does not depend on a common ground between speaker and hearer. The problem for Stalnaker’s account manifests itself in communicative situations that represent both Lingens cases, i.e., cases involving egocentric beliefs, and Frege cases, i.e., cases involving identity confusions. I describe two hypothetical cases that involve successful communication, but in which no common ground of the kind required by Stalnaker’s account is available. (...) I therefore propose an alternative account of communication that is based on epistemic two-dimensionalism. This account maintains that communication requires the transfer of a thought content from speaker to hearer. By holding that this shared content often constitutes common ground, it preserves much of the appeal of Stalnaker’s account. However, my account allows for cases in which the shared thought content does not figure in common ground. (shrink)

The stakes associated with an algorithmic decision are often said to play a role in determining whether the decision engenders a right to an explanation. More specifically, “high stakes” decisions are often said to engender such a right to explanation whereas “low stakes” or “non-high” stakes decisions do not. While the overall gist of these ideas is clear enough, the details are lacking. In this paper, we aim to provide these details through a detailed investigation of what we will call (...) the “Simple Stakes Thesis”. The Simple Stakes Thesis, as it will turn out, is too simple. For even if the stakes associated with a specific one-off decision are low—and hence does not engender a right to an explanation—such decisions may nevertheless form part of a high stakes pattern or aggregate of decisions. In such cases, we argue, even a low stakes decision may engender a right to explanation. Not only does this show that the right to explanation is more demanding than so far recognized. It also shows that the stakes thesis is significantly harder to apply in practice. (shrink)