How far should our realism extend? For many years philosophers of mathematics and philosophers of ethics have worked independently to address the question of how best to understand the entities apparently referred to by mathematical and ethical talk. But the similarities between their endeavours are not often emphasised. This book provides that emphasis. In particular, it focuses on two types of argumentative strategies that have been deployed in both areas. The first—debunking arguments—aims to put pressure on realism by emphasising the (...) seeming redundancy of mathematical or moral entities when it comes to explaining our judgements. In the moral realm this challenge has been made by Gilbert Harman and Sharon Street; in the mathematical realm it is known as the 'Benacerraf-Field' problem. The second strategy—indispensability arguments—aims to provide support for realism by emphasising the seeming intellectual indispensability of mathematical or moral entities, for example when constructing good explanatory theories. This strategy is associated with Quine and Putnam in mathematics and with Nicholas Sturgeon and David Enoch in ethics. Explanation in Ethics and Mathematics addresses these issues through an explicitly comparative methodology which we call the 'companions in illumination' approach. By considering how argumentative strategies in the philosophy of mathematics might apply to the philosophy of ethics, and vice versa, the papers collected here break new ground in both areas. For good measure, two further companions for illumination are also broached: the philosophy of chance and the philosophy of religion. Collectively, these comparisons light up new questions, arguments, and problems of interest to scholars interested in realism in any area. (shrink)

We examine how degrees of computably enumerable equivalence relations under computable reduction break down into isomorphism classes. Two ceers are isomorphic if there is a computable permutation of ω which reduces one to the other. As a method of focusing on nontrivial differences in isomorphism classes, we give special attention to weakly precomplete ceers. For any degree, we consider the number of isomorphism types contained in the degree and the number of isomorphism types of weakly precomplete ceers contained in the (...) degree. We show that the number of isomorphism types must be 1 or ω, and it is 1 if and only if the ceer is self-full and has no computable classes. On the other hand, we show that the number of isomorphism types of weakly precomplete ceers contained in the degree can be any member of $[0,\omega ]$. In fact, for any $n \in [0,\omega ]$, there is a degree d and weakly precomplete ceers ${E_1}, \ldots,{E_n}$ in d so that any ceer R in d is isomorphic to ${E_i} \oplus D$ for some $i \le n$ and D a ceer with domain either finite or ω comprised of finitely many computable classes. Thus, up to a trivial equivalence, the degree d splits into exactly n classes.We conclude by answering some lingering open questions from the literature: Gao and Gerdes [11] define the collection of essentially FC ceers to be those which are reducible to a ceer all of whose classes are finite. They show that the index set of essentially FC ceers is ${\rm{\Pi }}_3^0$-hard, though the definition is ${\rm{\Sigma }}_4^0$. We close the gap by showing that the index set is ${\rm{\Sigma }}_4^0$-complete. They also use index sets to show that there is a ceer all of whose classes are computable, but which is not essentially FC, and they ask for an explicit construction, which we provide.Andrews and Sorbi [4] examined strong minimal covers of downwards-closed sets of degrees of ceers. We show that if $\left$ is a uniform c.e. sequence of non universal ceers, then $\left\{ {{ \oplus _{i \le j}}{E_i}|j \in \omega } \right\}$ has infinitely many incomparable strong minimal covers, which we use to answer some open questions from [4].Lastly, we show that there exists an infinite antichain of weakly precomplete ceers. (shrink)

Descartes claimed that the Cogito is ‘so firm and sure that all the most extravagant suppositions of the sceptics were incapable of shaking it’. This paper aims to demonstrate that this claim is false by presenting a sceptical scenario for the Cogito. It is argued that the story ‘The Circular Ruins’ by J. L. Borges illustrates that one can doubt one’s own existence and that pace Descartes (and many others) the claim ‘I am, I exist, is necessarily true whenever it (...) is put forward by me or conceived in my mind’ is false. (shrink)

“Crisis” is a key concept in our political lexicon. Since the beginning of the modern age, it has arguably been, as much as anything, the experience of crisis that has calibrated the aims of both politics and political theory. But as central as crisis experiences have been for the shaping of our political imaginary, the concept itself has proven difficult to incorporate into the political theory enterprise. In this article, I argue that we can think politically about crisis by taking (...) up a “pragmatist” perspective that focuses on how we deploy crisis as a conceptual tool for guiding judgments and coordinating actions. I argue that crisis is a fundamentally reflexive concept that bridges our traditional distinctions between objective phenomena and normative experience, and whose very usage implies the active participation of those involved in it. Only by examining these crucial aspects of the crisis concept can we begin to grasp its normative political content, as well as how it may be deployed in the service of political action and social change. (shrink)

According to Alix Cohen, Kant defines emotions as ‘feelings’. Although I find her account of Kantian feelings compelling, I provide three reasons to doubt that it is an account of emotions: (1) it is unclear why Cohen identifies emotions with Kantian feelings; (2) some Kantian feelings are not emotions; (3) some Kantian desires may be emotions. I propose, however, that with some qualifications Cohen’s account may be upheld, provided its extra-textual assumptions about emotions are explicated. Against her claim that Kantian (...) feelings have a derived intentionality, I argue that the text is compatible with their being intrinsically intentional. (shrink)

In the following pages we propose a theory on cognitive systems and the common strategies of perception, which are at the basis of their function. We demonstrate that these strategies are easily seen to be in place in known cognitive systems such as vision and language. Furthermore we show that taking these strategies into consideration implies a new outlook on immune function calling for a new appraisal of the immune system as a cognitive system.

Recent years have witnessed an explosion of debate re what democratic theory has to say about the boundaries of democratic peoples. Yet the debate over the ‘democratic boundary problem’ has been hindered by the way contributors work with different understandings of democracy, of democratic legitimacy and of what it means to participate in a demos. My argument is that these conceptual issues can be clarified if we recognize that the ‘demos’ constitutive of democracy is essentially dual in character: it must (...) be defined from a third-person, observer’s perspective from which it can be represented as a whole entity; but it must also be seen as arising out of an association of numerous and ongoing second-person relationships that participants negotiate among one another. Both perspectives are essential to conceptualizing the demos, but their relation to each other has been obscured by democratic theory’s historical reliance on the imaginary of the sovereign state. Drawing on literature from deliberative democratic theory, this article reconstructs the concept of the demos in a way that better distinguishes the logic of democracy from the logic of the state, allowing us to think more clearly about how demotic boundaries may be subjected to standards of democratic legitimation. (shrink)

We discuss the problem of finding forcing posets which introduce closed unbounded subsets to a given stationary set.

We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematical structure as an abstract object encoding the truths of a mathematical theory. From such foundations, we derive consequences that address the main questions and issues that (...) have arisen. Namely, elements of different structures are different. A structure and its elements ontologically depend on each other. There are no haecceities and each element of a structure must be discernible within the theory. These consequences are not developed piecemeal but rather follow from our definitions of basic structuralist concepts. (shrink)

This essay explores the problem of legitimation crises in deliberative systems. For some time now, theorists of deliberative democracy have started to embrace a “systemic approach.” But if deliberative democracy is to be understood in the context of a system of multiple moving parts, then we must confront the possibility that that system’s dynamics may admit of breakdowns, contradictions, and tendencies toward crisis. Yet such crisis potentials remain largely unexplored in deliberative theory. The present article works toward rectifying this lacuna, (...) using the 2016 Brexit and Trump votes as examples of a particular kind of “legitimation crisis” that results in a sequence of failures in the deliberative system. Drawing on recent work of Rainer Forst, I identify this particular kind of legitimation crisis as a “justification crisis.”. (shrink)

This paper suggests a new approach (with old roots) to the study of the connection between logic and geometry. Traditionally, most logic diagrams associate only vertices of shapes with propositions. The new approach, which can be dubbed ’full logical geometry’, aims to associate every element of a shape (edges, faces, etc.) with a proposition. The roots of this approach can be found in the works of Carroll, Jacoby, and more recently, Dubois and Prade. However, its potential has not been duly (...) appreciated, probably because of the complexity of the diagrams in these works. The following study demonstrates how the Hexagon of Opposition can be represented as a triangle and Classical Logic as a tetrahedron (rather than a rhombic dodecahedron). It then applies the approach to modal logic, extending the tetrahedron for the logic KT into a dipyramid and a cube for KD, and finally an octahedron for K. Some possible directions for further research are also indicated. (shrink)

This article deals with a tripartite structure applied to a Tannaitic source. This structure is designed in the form of a difficulty and a short resolution, bringing one example for each of the three parts of the Tannaitic source. The uniform formative-stylistic phrasing gives the discussion of the Tannaitic source's three parts a tripartite form. The Tannaitic source utilises a chaining of examples from the first to the second part and from the second to the third part.

We address the following questions in this paper: (1) Which set or number existence axioms are needed to prove the theorems of ‘ordinary’ mathematics? (2) How should Frege’s theory of numbers be adapted so that it works in a modal setting, so that the fact that equivalence classes of equinumerous properties vary from world to world won’t give rise to different numbers at different worlds? (3) Can one reconstruct Frege’s theory of numbers in a non-modal setting without mathematical primitives such (...) as “the number of Fs” ( $$\#F$$ ) or mathematical axioms such as Hume’s Principle? Our answer to question (1) is ‘None’. Our answer to question (2) begins by defining ‘x numbers G’ as: x encodes all and only the properties F such that being-actually-F is equinumerous to G with respect to discernible objects. We answer (3) by showing that the mere existence of discernible objects allows one to reconstruct Frege’s derivation of the Dedekind-Peano axioms in a non-modal setting. (shrink)

Commentators provide two different accounts of desires in Kant: “feeling-based” accounts stress their connection with feelings, while “action-based” accounts view them as causes of action. I argue that “feeling-based” accounts blur the feeling-desire distinction, while the “action-based” accounts conflict with Kantian desires that do not cause action. On my alternative, Kantian desires are dispositions to action normally directed at producing future objects, and so they differ from the feelings they are connected to, which refer to the way we are affected (...) by objects. This account preserves the feeling-desire distinction, is compatible with desires that do not cause action, and anticipates holistic theories of desire that combine dispositional, hedonic, and evaluative components. (shrink)

This book offers a unique analysis of the contradictions and pathologies of the modern international order and develops a new cosmopolitan alternative.

As an emancipatory political project, cosmopolitanism always invited skepticism. This paper focuses on the economic-progressivist line of critique of cosmopolitanism, which has gained momentum in recent years. This critique is based on real concerns that the economic left must prioritize and integrate into its thinking; however, it is also fatally flawed. Any progressive project that takes seriously strong democratic self-determination for all peoples needs some version of a commitment to a global order that is democratically politically integrated, and this means (...) stronger forms of supranational political integration, not weaker ones. I argue that the allure of progressive economic statism rests on erroneous assumptions about the character of the Westphalian state system and its relation to the evolution of global capitalism, which give a misleading impression that this system is somehow less friendly than neoliberal globalization to capitalist imperatives for extraction, accumulation, and growth. But there are equally expropriative and violent versions of capitalism that thrive in a closed Westphalian world. With great power rivalry once again emerging as a structuring feature of world order, signs of such versions are already making their appearance today. (shrink)

Combinatorial operations on sets are almost never well defined on Turing degrees, a fact so obvious that counterexamples are worth exhibiting. The case we focus on is the symmetric-difference operator; there are pairs of degrees for which the symmetric-difference operation is well defined. Some examples can be extracted from the literature, e.g. from the existence of nonzero degrees with strong minimal covers. We focus on the case of incomparable r.e. degrees for which the symmetric-difference operation is well defined.

It is known that every non-universal self-full degree in the structure of the degrees of computably enumerable equivalence relations (ceers) under computable reducibility has exactly one strong minimal cover. This leaves little room for embedding wide partial orders as initial segments using self-full degrees. We show that considerably more can be done by staying entirely inside the collection of non-self-full degrees. We show that the poset can be embedded as an initial segment of the degrees of ceers with infinitely many (...) classes. A further refinement of the proof shows that one can also embed the free distributive lattice generated by the lower semilattice as an initial segment of the degrees of ceers with infinitely many classes. (shrink)

The current study aims to examine how the intense emotions experienced by different Israeli groups during the 2006 Second Lebanon War affected their perceptions of risk. Two weeks after the end of the war, a questionnaire was distributed among 205 people. Some were from the north and had been directly affected by the rocket attacks; others were from the center of Israel. The questionnaires, based on Lerner et al., measured emotions and perceived risk. The results show significant differences between those (...) living in the north and those in the center of Israel. As expected, people living in the north reported more emotional difficulties during the war, greater perceived risk, and more pessimism in comparison to the center group. Moreover, the results point to significant differences between Israeli Jews and Israeli Arabs regarding emotions and perceived risk. In addition, the study results show a positive relation between anger and perceived risk. (shrink)

Putting together Kant's theory of emotion is complicated by two facts: (1) Kant has no term which is an obvious equivalent of "emotion" as used in contemporary English; (2) theorists disagree about what emotions are. These obstacles notwithstanding, my dissertation aims to provide the foundation for a reconstruction of Kant's theory of emotion that is both historically accurate and responsive to contemporary philosophical concerns. In contrast to available approaches which rest on contested assumptions about emotions, I start from the generally (...) accepted and reasonable premise that what we call "emotions" refers in Kant to a set of mental states, some of which he associates with the feeling of pleasure and displeasure ("feelings"), others with the faculty of desire ("desires"). I then proceed to examine the nature of these two kinds of mental states and their proper treatment. I argue that Kantian feelings are representations of objects' relation to the subject, that have a felt quality, and dispose their subject to certain behaviors. While feelings can only motivate action by causing desires and have no temporal direction, desires - except for certain wishes - are future-directed, which allows them to motivate actions immediately (but they need not bring action about). Equipped with this account of feelings and desires, I proceed to examine the kind of treatment Kant prescribes for them, and argue that feelings (except affects) should be cultivated, that is, acquired and improved so that they could be used to pursue rational ends, while inclinations, i.e., habitual sensuous desires, should generally be disciplined, that is, constrained by rules. The resultant picture is compelling because it rests on minimal assumptions about emotions and successfully incorporates the phenomenological, evaluative, and dispositional functions traditionally associated with emotions. (shrink)

Lives of the Prophets: The Illustrations to Hafiz-i Abru’s ‘Assembly of Chronicles’. By Mohamad Reza Ghiasian. Studies in Persian Cultural History, vol. 16. Leiden: Brill, 2018. Pp. xv + 343. $159, €132.

This article explores the bases of Kant’s cosmopolitanism in his more systematic writings on freedom, judgment, and community. My argument is that, if we peer beneath his more explicitly normative prescriptions for achieving “perpetual peace,” we find the tools not just of a cosmopolitan vision but what we might call a “cosmopolitical method.” While many assume Kant’s political thought descends directly from his moral philosophy, a look back at relevant passages in the first Critique reveals an alternative reading that points (...) toward his theory of reflective judgment, which combines practical freedom with judgments based on theoretical concepts. Of particular importance is Kant’s conception of community as commercium, through which Kant discerns all matters of right to concern the way free actors are constrained to share the earth in common. These considerations allow for a broader way of thinking about Kantian cosmopolitanism, one that is responsive to the reflective judgment of world citizens as they encounter new challenges. (shrink)

Human subject research involving brain imaging is likely to reveal signifcant incidental fndings of abnormal brain morphology. Because of this fact and because of the fduciary relationship between researcher and subject, board-certi-fed or board-eligible radiologists should review the scans to look for any abnormality, the scans should be conducted in accordance with standard medical practice for reviewing the clinical status of the whole brain, and the informed consent process should disclose the possibility that incidental fndings may be revealed and what (...) consequences will follow. In the event such fndings are revealed, qualifed physicians should explain to the subject the signifcance of the fndings and the alternatives available. (shrink)

We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the structure comprised of the light ceers. We also show the same for the structure of L-degrees in the dark, light, or complete structure. In each case, we show that there is an interpretable copy of (N, +, \times) .

Assuming the existence of a supercompact cardinal and a weakly compact cardinal above it, we provide a generic extension where there are no Aronszajn trees of height ω 2 or ω 3 . On the other hand we show that some large cardinal assumptions are necessary for such a consistency result.

We describe strongly minimal theories Tn with finite languages such that in the chain of countable models of Tn, only the first n models have recursive presentations. Also, we describe a strongly minimal theory with a finite language such that every non-saturated model has a recursive presentation.

Biological phenomena can be investigated at multiple levels, from the molecular to the cellular to the organismic to the ecological. In typical biology instruction, these levels have been segregated. Yet, it is by examining the connections between such levels that many phenomena in biology, and complex systems in general, are best explained. We describe a computation-based approach that enables students to investigate the connections between different biological levels. Using agent-based, embodied modeling tools, students model the microrules underlying a biological phenomenon (...) and observe the resultant aggregate dynamics. We describe 2 cases in which this approach was used. In both cases, students framed hypotheses, constructed multiagent models that incorporate these hypotheses, and tested these by running their models and observing the outcomes. Contrasting these cases against traditionally used, classical equation-based approaches, we argue that the embodied modeling approach connects more directly to students’ experience, enables extended investigations as well as deeper understanding, and enables “advanced” topics to be productively introduced into the high school curriculum. (shrink)

: Most contemporary attempts to draw inspiration from Kant's cosmopolitan project focus exclusively on the prescriptive recommendations he makes in his article, ‘On Perpetual Peace’. In this essay, I argue that there is more to his cosmopolitan point of view than his normative agenda. Kant has a unique and interesting way of problematizing the way individuals and peoples relate to one another on the stage of world history, based on a notion that human beings who share the earth in common (...) ‘originally’ constitute a ‘commercium’ of thoroughgoing interaction. By unpacking this concept of ‘commercium’, we can uncover in Kant a more critical perspective on world history that sets up the cosmopolitan as a specific kind of historical-political challenge. I will show that we can distinguish this level of problematization from the prescriptive level at which Kant formulates his familiar recommendations in ‘Perpetual Peace’. I will further show how his particular way of framing the cosmopolitan problematic can be expanded and expatiated upon to develop a more critical, reflexive, and open-ended conception of cosmopolitan thinking. (shrink)

We present a theoretical model and corresponding research design (Bronfenbrenner & Ceci 1994) that could yield stronger evidence for (or perhaps against) Howe et al.'s conclusions. The model assesses levels of heritability (h²) under different amounts of training and practice, thus providing estimates of the independent contribution of “innate talent” to the quality of development outcomes. The design can also reveal the extent to which this independent contribution varies systematically as a function of other influential factors identified by Howe et (...) al. (shrink)