This is Part B of an article that defends non-eliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A motivated an understanding of unlabeled graphs as structures sui generis and developed a corresponding axiomatic theory of unlabeled graphs. Part B turns to the philosophical interpretation and assessment of the theory: it points out how the theory avoids well-known problems concerning identity, objecthood, and reference that have been attributed to non-eliminative structuralism. The part (...) concludes by explaining how the theory relates to set theory, and what remains to be accomplished for non-eliminative structuralists. (shrink)

This is Part A of an article that defends non-eliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A summarizes the general attractions of non-eliminative structuralism. Afterwards, it motivates an understanding of unlabeled graphs as structures sui generis and develops a corresponding axiomatic theory of unlabeled graphs. As the theory demonstrates, graph theory can be developed consistently without eliminating unlabeled graphs in favour of sets; and the usual structuralist criterion of identity can (...) be applied successfully in graph-theoretic proofs. Part B will turn to the philosophical interpretation and assessment of the theory. (shrink)

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles (...) are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. (shrink)

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its prequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism (...) follow from the norm, while the characteristic claim of the Objectivist Bayesian follows from the norm along with an extra assumption. Finally, we consider Richard Jeffrey’s proposed generalization of conditionalization. We show not only that his rule cannot be derived from the norm, unless the requirement of Rigidity is imposed from the start, but further that the norm reveals it to be illegitimate. We end by deriving an alternative updating rule for those cases in which Jeffrey’s is usually supposed to apply. (shrink)

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its sequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In this paper, we make this norm mathematically precise in various ways. We describe three epistemic dilemmas that an agent might face if she attempts (...) to follow Accuracy, and we show that the only inaccuracy measures that do not give rise to such dilemmas are the quadratic inaccuracy measures. In the sequel, we derive the main tenets of Bayesianism from the relevant mathematical versions of Accuracy to which this characterization of the legitimate inaccuracy measures gives rise, but we also show that Jeffrey conditionalization has to be replaced by a different method of update in order for Accuracy to be satisfied. (shrink)

In discussions about whether the Principle of the Identity of Indiscernibles is compatible with structuralist ontologies of mathematics, it is usually assumed that individual objects are subject to criteria of identity which somehow account for the identity of the individuals. Much of this debate concerns structures that admit of non-trivial automorphisms. We consider cases from graph theory that violate even weak formulations of PII. We argue that (i) the identity or difference of places in a structure is not to be (...) accounted for by anything other than the structure itself and that (ii) mathematical practice provides evidence for this view. We want to thank Leon Horsten, Jeff Ketland, Øystein Linnebo, John Mayberry, Richard Pettigrew, and Philip Welch for valuable comments on drafts of this paper. We are especially grateful to Fraser MacBride for correcting our interpretation of two of his papers and for other helpful comments. CiteULike Connotea Del.icio.us What's this? (shrink)

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...) predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE’s logical connectives. Furthermore, HYPE’s first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work. (shrink)

In this article, we examine which challenges aesthetics and ethics puts pedagogy before. We discuss the intersection of Emmanuel Lévinas's notion of ethics and Jacques Rancière's notion of aesthetics in a pedagogical context through the praxis of Expressive Arts. We begin by introducing Lévinas's ethics and its role in his philosophical system, and also, its implications for relation between human beings. Thereafter we introduce Rancière's aesthetics and its potential to evoke ethics by reproaching non-art as art. After these presentations, we (...) introduce the praxis of EXA through four interviews with participants from an EXA-based work that we ourselves are previously familiar with. We analyze this praxis in the light of the above mentioned philosophical notions and conclude with a discussion on the pedagogical implications of this philosophical perspective on the uses of art in education. We mean that EXA is an advantageous praxis for a pedagogy that aims at taking into account the challenges and the complexity of this aesthetic-ethical approach. Our conclusion is that this approach puts all pedagogy that aims at being more than just knowledge mediating before three challenges: it should originate from equality-in-alterity, it should invite to an ethical subject-hood, and it should have tools for both breaking the prevailing discourse and to constantly continue this process, without reaching an end. (shrink)

Is it possible to give an explicit definition of belief in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve a contextual “cautiousness” threshold, there (...) is but one way of determining the extension of the concept of belief that does the job. The qualitative concept of belief is not to be eliminated from scientific or philosophical discourse, rather, by reducing qualitative belief to assignments of resiliently high degrees of belief and a “cautiousness” threshold, qualitative and quantitative belief turn out to be governed by one unified theory that offers the prospects of a huge range of applications. Within that theory, logic and probability theory are not opposed to each other but go hand in hand. (shrink)

This article outlines what a formal theory of truth should be like, at least at first glance. As not all of the stated constraints can be satisfied at the same time, in view of notorious semantic paradoxes such as the Liar paradox, we consider the maximal consistent combinations of these desiderata and compare their relative advantages and disadvantages.

This paper suggests a bridge principle for all-or-nothing belief and degrees of belief to the effect that belief corresponds to stably high degree of belief. Different ways of making this Humean thesis on belief precise are discussed, and one of them is shown to stand out by unifying the others. The resulting version of the thesis proves to be fruitful in entailing the logical closure of belief, the Lockean thesis on belief, and coherence between decision-making based on all-or-nothing beliefs and (...) on degrees of belief. (shrink)

Transfers of critically ill neonates are frequent phenomena. Even though parents’ participation is regarded as crucial in neonatal care, a transfer often means that parents and neonates are separated. A systematic review of the parents’ experiences of neonatal transfer is lacking. This paper describes a meta‐study addressing qualitative research about parents’ experiences of neonatal transfer. Through deconstruction and reflections of theories, methods, and empirical data, the aim was to achieve a deeper understanding of theoretical, empirical, contextual, historical, and methodological issues (...) of qualitative studies concerning parents’ experiences of neonatal transfer over the course of this meta‐study (2000–2017). Meta‐theory and meta‐method analyses showed that caring, transition, and family‐centered care were main theoretical frames applied and that interviewing with a small number of participants was the preferred data collection method. The meta‐data‐analysis showed that transfer was a scary, unfamiliar, and threatening experience for the parents; they were losing familiar context, were separated from their neonate, and could feel their parenthood disrupted. We identified ‘wavering and wandering’ as a metaphoric representation of the parents’ experiences. The findings add knowledge about meta‐study as an approach for comprehensive qualitative research and point at the value of meta‐theory and meta‐method analyses. (shrink)

The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years, such as relevance logics, paraconsistent logics, fuzzy logics and so on. In this note, we investigate some of these paradoxes and classify them, over minimal logic. We provide proofs of equivalence and semantic models separating the paradoxes where appropriate. A number of equivalent groups arise, all of which collapse with unrestricted use of double negation elimination. Interestingly, the principle ex falso quodlibet, and several (...) weaker principles, turn out to be distinguishable, giving perhaps supporting motivation for adopting minimal logic as the ambient logic for reasoning in the possible presence of inconsistency. (shrink)

Humans are one of the most cooperative and altruistic species on the planet. At the same time, humans have a long history of violent and deadly intergroup conflicts, i.e. wars. Recently, contemporary evolutionary theorists have revived Charles Darwin’s idea that human in-group altruism and out-group hostility might have co-evolved. Groups with more cooperatively aggressive men, they suggest, were more likely to prevail in the frequent lethal quarrels of human pre-history, and these men, therefore, more likely to have passed on their (...) genes. After a short introduction to evolutionary perspectives on war heroism, we describe selected characteristics of 988 modern war heroes, the US-American Medal of Honor recipients of WWI, WWII, the Korean and the Vietnam War, and discuss whether an evolutionary perspective can help us understand why these men risked their lives ‘beyond the call of duty’. (shrink)

When do children acquire a propositional attitude folk psychology or theory of mind? The orthodox answer to this central question of developmental ToM research had long been that around age 4 children begin to apply “belief” and other propositional attitude concepts. This orthodoxy has recently come under serious attack, though, from two sides: Scoffers complain that it over-estimates children’s early competence and claim that a proper understanding of propositional attitudes emerges only much later. Boosters criticize the orthodoxy for underestimating early (...) competence and claim that even infants ascribe beliefs. In this paper, the orthodoxy is defended on empirical grounds against these two kinds of attacks. On the basis of new evidence, not only can the two attacks safely be countered, but the orthodox claim can actually be strengthened, corroborated and refined: what emerges around age 4 is an explicit, unified, flexibly conceptual capacity to ascribe propositional attitudes. This unified conceptual capacity contrasts with the less sophisticated, less unified implicit forms of tracking simpler mental states present in ontogeny long before. This refined version of the orthodoxy can thus most plausibly be spelled out in some form of 2-systems-account of theory of mind. (shrink)

In interdisciplinary research scientists have to share and integrate knowledge between people and across disciplinary boundaries. An important issue for philosophy of science is to understand how scientists who work in these kinds of environments exchange knowledge and develop new concepts and theories across diverging fields. There is a substantial literature within social epistemology that discusses the social aspects of scientific knowledge, but so far few attempts have been made to apply these resources to the analysis of interdisciplinary science. Further, (...) much of the existing work either ignores the issue of differences in background knowledge, or it focuses explicitly on conflicting background knowledge. In this paper we provide an analysis of the interplay between epistemic dependence between individual experts with different areas of expertise. We analyze the cooperative activity they engage in when participating in interdisciplinary research in a group, and we compare our findings with those of other studies in interdisciplinary research. (shrink)

This is part A of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘ifAthenB’ to be true even in the presence of relevant ‘Aand notB’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. (...) Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false. (shrink)

Die populäre Vorstellung, exzessiver Drogenkonsum sei in der Weimarer Republik ein gesellschaftlich weit verbreitetes Phänomen gewesen, hält einer empirischen Überprüfung nicht stand. Obwohl Mediziner die Öffentlichkeit und die Politik vor einer „Kokainwelle“ warnten, die die „Volksgesundheit“ bedrohe, existieren keine Belege, die auf eine signifikante Zunahme des Kokainkonsums in den Zwanziger Jahren hindeuten. Die entscheidende Ursache für diese moralische Panik lag vielmehr im Krankheitsbild des Kokainismus begründet. Die Sucht trug das Gepräge einer Infektionskrankheit und sollte den Körper, den Willen und die (...) bürgerliche Existenz der Betroffenen vernichten. Gemäß der medizinischen Lehrmeinung erzeugte chronischer Kokainkonsum die Neigung zu abweichenden Sexualpraktiken und kriminellen Handlungen. Daher wurde der Gebrauch der Substanz vor allem mit ohnehin als deviant markierten sozialen Milieus wie der sogenannten Bohème und Halbwelt verknüpft. Tatsächlich zeigen historische Quellen jedoch, das es sich hierbei primär um ein Problem der medizinischen Berufe handelte. Vor dem Hintergrund der desolaten politischen, sozialen und ökonomischen Lage Deutschlands nach dem Ersten Weltkrieg betrachteten viele Mediziner Suchtkrankheiten wie Kokainismus und Morphinismus als Bedrohung für den erhofften politischen und biologischen Wiederaufstieg der Nation. (shrink)

This is a response to comments on my book "Praktische Intelligenz und die Zweiteilung des Wissens" by Romy Jaster and Martin Weichold.

The limit of language is one of the most pervasive notions found in Wittgenstein's work, both in his early Tractatus Logico-Philosophicus and his later writings. Moreover, the idea of a limit of language is intimately related to important scholarly debates on Wittgenstein's philosophy, such as the debate between the so-called traditional and resolute interpretations, Wittgenstein's stance on transcendental idealism, and the philosophical import of Wittgenstein's latest work On Certainty. This collection includes thirteen original essays that provide a comprehensive overview of (...) the various ways in which Wittgenstein appeals to the limit of language at different stages of his philosophical development. The essays connect the idea of a limit of language to the most important themes discussed by Wittgenstein--his conception of logic and grammar, the method of philosophy, the nature of the subject, and the foundations of knowledge--as well as his views on ethics, aesthetics, and religion. The essays also relate Wittgenstein's thought to his contemporaries, including Carnap, Frege, Heidegger, Levinas, and Moore. (shrink)

Was können Eltern und erwachsene Kinder voneinander erwarten? Und welche Verantwortung sollten sie füreinander übernehmen und warum? Durch einen kulturellen und demographischen Wandel sind unsere Vorstellungen von Familie in Bewegung geraten und müssen neu ausgehandelt werden. Hier setzt Hannes Foth mit ethischen und sozialphilosophischen Überlegungen an. Er legt dar, was Eltern-Kind-Beziehungen im Erwachsenenalter auszeichnet, welche Rolle Verantwortung und Freundschaft dabei spielen und welches Verständnis von Familie zeitgemäß ist - ein Perspektivenwechsel, der nicht nur philosophische, sondern auch interdisziplinäre und alltagstaugliche Anknüpfungspunkte (...) aufweist. (shrink)

The thesis defended in this article is that by uttering or publishing a great many declarative sentences in assertoric mode, one does not actually assert that their conjunction is true – one rather asserts that the vast majority of these sentences are true. Accordingly, the belief that is expressed thereby is the belief that the vast majority of these sentences are true. In the article, we make this proposal precise, we explain the context-dependency of belief that corresponds to it, we (...) point out why our everyday oral practice of single assertions is not affected by it, and we argue that the proposal leads to a way out of the Paradox of the Preface. (shrink)

This monograph provides a new account of justified inference as a cognitive process. In contrast to the prevailing tradition in epistemology, the focus is on low-level inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to describe (...) and analyze such inferences. Part 1 gives a purely system-theoretic explication of belief and inference. Part 2 adds a reliabilist theory of justification for inference, with a qualitative notion of reliability being employed. Part 3 recalls and extends various systems of deductive and nonmonotonic logic and thereby explains the semantics of absolute and high reliability. In Part 4 it is proven that qualitative neural networks are able to draw justified deductive and nonmonotonic inferences on the basis of distributed representations. This is derived from a soundness/completeness theorem with regard to cognitive semantics of nonmonotonic reasoning. The appendix extends the theory both logically and ontologically, and relates it to A. Goldman's reliability account of justified belief. This text will be of interest to epistemologists and logicians, to all computer scientists who work on nonmonotonic reasoning and neural networks, and to cognitive scientists. (shrink)

In everyday life we either express our beliefs in all-or-nothing terms or we resort to numerical probabilities: I believe it's going to rain or my chance of winning is one in a million. The Stability of Belief develops a theory of rational belief that allows us to reason with all-or-nothing belief and numerical belief simultaneously.

Le domaine numérique déploie ce que l’on pourrait appeler une ekphrasis opérationnelle : les textes n’y représentent pas des images, mais les exécutent en les mettant en œuvre de manière informatique. Correspondant à deux approches différentes, l’une connexionniste, l’autre séquentielle, deux types distincts d’ ekphrasis opératives, impliquant deux notions distinctes du langage peuvent être dégagées : l’une mettant l’accent sur une dimension pragmatique, l’autre sur une dimension sémantique.

This is a personal, incomplete, and very informal take on the role of logic in general philosophy of science, which is aimed at a broader audience. We defend and advertise the application of logical methods in philosophy of science, starting with the beginnings in the Vienna Circle and ending with some more recent logical developments.

Pure mathematical truths are commonly thought to be metaphysically necessary. Assuming the truth of pure mathematics as currently pursued, and presupposing that set theory serves as a foundation of pure mathematics, this article aims to provide a metaphysical explanation of why pure mathematics is metaphysically necessary.

It is well known that aggregating the degree-of-belief functions of different subjects by linear pooling or averaging is subject to a commutativity dilemma: other than in trivial cases, conditionalizing the individual degree-of-belief functions on a piece of evidence E followed by linearly aggregating them does not yield the same result as rst aggregating them linearly and then conditionalizing the resulting social degree- of-belief function on E. In the present paper we suggest a novel way out of this dilemma: adapting the (...) method of update or learning such that linear pooling com- mutes with it. As it turns out, the resulting update scheme – imaging on the evidence – is well-known from areas such as the study of conditionals and cau- sal decision theory, and a formal result from which the required commutativity property is derivable was supplied already by Gärdenfors in a different con- text. We end up determining under which conditions imaging would seem to be right method of update, and under which conditions, therefore, group update would not be affected by the commutativity dilemma. (shrink)

The literatures on both authentic leadership and behavioral integrity have argued that leader integrity drives follower performance. Yet, despite overlap in conceptualization and mechanisms, no research has investigated how authentic leadership and behavioral integrity relate to one another in driving follower performance. In this study, we propose and test the notion that authentic leadership behavior is an antecedent to perceptions of leader behavioral integrity, which in turn affects follower affective organizational commitment and follower work role performance. Analysis of a survey (...) of 49 teams in the service industry supports the proposition that authentic leadership is related to follower affective organizational commitment, fully mediated through leader behavioral integrity. Next, we found that authentic leadership and leader behavioral integrity are related to follower work role performance, fully mediated through follower affective organizational commitment. These relationships hold when controlling for ethical organizational culture. (shrink)

Drawing on the results of modem psychology and cognitive science we suggest that the traditional theory of concepts is no longer tenable, and that the alternative account proposed by Kuhn may now be seen to have independent empirical support quite apart from its success as part of an account of scientific change. We suggest that these mechanisms can also be understood as special cases of general cognitive structures revealed by cognitive science. Against this background, incommensurability is not an insurmountable obstacle (...) to accepting Kuhn's position, as many philosophers of science still believe. Rather it becomes a natural consequence of cognitive structures that appear in all human beings. (shrink)

This article suggests that scientific philosophy, especially mathematical philosophy, might be one important way of doing philosophy in the future. Along the way, the article distinguishes between different types of scientific philosophy; it mentions some of the scientific methods that can serve philosophers; it aims to undermine some worries about mathematical philosophy; and it tries to make clear why in certain cases the application of mathematical methods is necessary for philosophical progress.

This article investigates the role of historical references and arguments in the current policy debate on non‐invasive prenatal testing (NIPT) in Germany. It analyses major documents and opinion statements, including the recent parliamentary debate (2019). The implementation of NIPT is accompanied by concerns and strong criticism, particularly in Germany. Many perceive the new test to be a problematic step that facilitates selective practices and is reminiscent of eugenics. Analysis of the German policy discourse shows that ‘eugenics’, and even more strongly, (...) ‘selection’, are pivotal terms for rejecting NIPT and its coverage by public health insurance. They touch on a historical dimension in public deliberation, namely the fundamental distancing from the inhuman practices of the National Socialist period and anything that resembles them. However, using these terms to criticize prenatal genetic testing is controversial, and recent discourse demonstrates their avoidance as well, with many supporters of a limited coverage by public health insurance contrasting their approach with more widespread screening. Here, ‘screening’ has a negative connotation, and functions to demarcate the debate in a way that may reflect distance from certain modes of historical reasoning, but still expresses a special need to reconcile prenatal testing with the principles of dignity, inclusion and diversity. This article aims to elucidate the concerns involved in the national debates on prenatal testing and to increase awareness of the historical dimensions of the language and reasoning with which such methods are negotiated today and in future. (shrink)

On the basis of impossibility results on probability, belief revision, and conditionals, it is argued that conditional beliefs differ from beliefs in conditionals qua mental states. Once this is established, it will be pointed out in what sense conditional beliefs are still conditional, even though they may lack conditional contents, and why it is permissible to still regard them as beliefs, although they are not beliefs in conditionals. Along the way, the main logical, dispositional, representational, and normative properties of conditional (...) beliefs are studied, and it is explained how the failure of not distinguishing conditional beliefs from beliefs in conditionals can lead philosophical and empirical theories astray. (shrink)