The March 2002 symposium Human Dignity and Reproductive Technology brought together philosophers, theologians, scientists, lawyers, and scholars from across the United States. The essays of this book are the contributions of the symposium's participants.

This article discusses Cardinal Newman’s view of education, with special reference to the lecture “Discipline of Mind” in The Idea of a University and also to the essays on the Benedictines collected in Historical Sketches (volume 2).

We extend the core model induction technique to a choiceless context, and we exploit it to show that each one of the following two hypotheses individually implies that , the Axiom of Determinacy, holds in the of a generic extension of : every uncountable cardinal is singular, and every infinite successor cardinal is weakly compact and every uncountable limit cardinal is singular.

Creationism about fictional entities requires a principle connecting what fictions say exist with which fictional entities really exist. The most natural way of spelling out such a principle yields inconsistent verdicts about how many fictional entities are generated by certain inconsistent fictions. Avoiding inconsistency without compromising the attractions of creationism will not be easy.

This article sets out to analyse some of the most basic elements of our number concept - of our awareness of the one and the many in their coherence with multiplicity, succession and equinumerosity. On the basis of the definition given by Cantor and the set theoretical definition of cardinal numbers and ordinal numbers provided by Ebbinghaus, a critical appraisal is given of Frege’s objection that abstraction and noticing (or disregarding) differences between entities do not produce the concept of (...) number. By introducing the notion of subject functions, an account is advanced of the (nominalistic) reason why Frege accepted physical, kinematic and spatial properties (subject functions) of entities, but denied the ontic status of their quantitative properties (their quantitative subject function). With reference to intuitionistic mathematics (Brouwer, Weyl, Troelstra, Kreisel, Van Dalen) the primitive meaning of succession is acknowledged and connected to an analysis of what is entailed in the term ‘Gleichzahligkeit’ (‘equinumerosity’). This expression enables an analysis of the connections between ordinality and cardinality on the one hand and succession and wholeness (totality) on the other. The conceptions of mathematicians such as Frege, Cantor, Dedekind, Zermelo, Brouwer, Skolem, Fraenkel, Von Neumann, Hilbert, Bernays and Weyl, as well as the views of the philosopher Cassirer, are discussed in order to arrive at an assessment of the relation between ordinality and cardinality (also taking into account the relation between logic and arithmetic) - and on the basis of this evaluation, attention is briefly given to the definition of an ordered pair in axiomatic set theory (with reference to the set theory of Zermelo-Fraenkel) and to the defmition of an ordered pair advanced by Wiener and Kuratowski. (shrink)

We prove within K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K}$$\end{document} that the axiom of determinacy is equivalent to the assertion that for each ordinal λ λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa > \lambda}$$\end{document}. Here Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Theta}$$\end{document} is the supremum of the ordinals which are the surjective image of the set of reals R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document}.

We reimplement the creature forcing construction used by Fischer et al. :1045–1103, 2017. https://doi.org/10.1007/S00153-017-0553-8. arXiv:1402.0367 [math.LO]) to separate Cichoń’s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our construction by adding uncountably many additional cardinal characteristics, sometimes referred to as localisation cardinals.

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...) out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. (shrink)

We continue investigating variants of the splitting and reaping numbers introduced in [4]. In particular, answering a question raised there, we prove the consistency of and of. Moreover, we discuss their natural generalisations $\mathfrak {s}_{\rho }$ and $\mathfrak {r}_{\rho }$ for $\rho \in (0,1)$, and show that $\mathfrak {r}_{\rho }$ does not depend on $\rho $.

Motivated by recent results and questions of Raghavan and Shelah, we present ZFC theorems on the bounding and various almost disjointness numbers, as well as on reaping and dominating families on uncountable, regular cardinals. We show that if $\kappa =\lambda ^+$ for some $\lambda \geq \omega $ and $\mathfrak {b}=\kappa ^+$ then $\mathfrak {a}_e=\mathfrak {a}_p=\kappa ^+$. If, additionally, $2^{<\lambda }=\lambda $ then $\mathfrak {a}_g=\kappa ^+$ as well. Furthermore, we prove a variety of new bounds for $\mathfrak {d}$ in terms of (...) $\mathfrak {r}$, including $\mathfrak {d}\leq \mathfrak {r}_\sigma \leq \operatorname {\mathrm {cf}}]^\omega )$, and $\mathfrak {d}\leq \mathfrak {r}$ whenever $\mathfrak {r}<\mathfrak {b}^{+\kappa }$ or $\operatorname {\mathrm {cf}})\leq \kappa $ holds. (shrink)

In _The Priority of Prudence_, Daniel Mark Nelson proposes a reappropriation of a moral perspective that focuses on the cardinal virtues of courage, temperance, justice, and prudence. The study aims to recover and rehabilitate the virtue of prudence as a way of resuming a moral conversation that has been stalemated for too long. Nelson's main source for reviving the virtue of prudence is St. Thomas Aquinas's account of the cardinal virtues in the _Summa Theologica_. A primary problem (...) with using Aquinas as a source for reviving an ethics of virtue centered on prudence is that he is commonly perceived as the most prominent figure in the conflicting natural-law tradition. According to Nelson's reinterpretation, however, Aquinas teaches that moral understanding depends first and foremost on prudence working in accord with other cardinal virtues and that natural law functions to explain moral reasoning rather than to guide it. This study serves to advance the debate about the contemporary relevance of an ethics of virtue by way of its significantly more detailed explication of prudence. Nelson makes important connections between influential reinterpretations of the ethical theory of Aquinas that have been published during the last thirty years and widespread interest in an ethics of virtue that has been expressed by Alasdair Maclntyre, Stanley Hauerwas, William Sullivan, Robert Bellah, and others. _The Priority of Prudence _represents a significant contribution to the scholarly literature both in the study of Aquinas and in the debate on the ethics of virtue. (shrink)

Plato's "laches" is an investigation into the nature of courage with the intention of demonstrating the difficulty of singling out one virtue, namely courage, and defining it separately from the other cardinal virtues such as bravery, wisdom, justice, temperance, and piety. As the dialogue proceeds it becomes evident that socrates not only relates courage with the battlefield, but also with other spheres of life. Of special interest is his reference of being courageous regarding desires and pleasures where an overlap (...) of virtues is anticipated. This extension of the range of manifestations of courage indicates that his conception of courage transcends the traditional one in which he hints at a new sort of unity of courage and temperance, and on the other of courage and justice. One of plato's main aims in writing this dialogue was to mark out the intellectual limits of the two generals' positions, especially that of nicias, whose philosophical position could appear to be deceptively similar to the socratic one which he did not fully understand. (shrink)

In this paper I shall attempt to outline a nominalistic theory of mathematical truth. I call my theory nominalistic because it avoids a real (see [4]) ontological commitment to abstract entities. Traditionally, nominalists have found it difficult to justify any reference to infinite collections in mathematics. Even those who have tried to do so have typically restricted themselves to predicative and, thus, denumerable realms. I Indeed, many have linked impredicative definitions to platonism; nominalists have tended to agree with Weyl that (...) impredicative analysis is "a house built on sand" in a "logician's paradise."2 As a result, they have either worried about how much of mathematics empirical science requires (e.g., [34]) or renounced mathematical truth altogether (e.g., [12], [17]). My theory, in contrast, seeks a nominalistic interpretation of the entire body of classical mathematics. It tries to secure for the nominalist not merely the natural numbers but the reals, the ordinals, and inaccessible cardinals as well. If I am right, then nominalists can declare, with Goodman and Quine, that "any system that countenances abstract entities we deem unsatisfactory as a final philosophy" ([17],105), and, at the same time, with Hilbert, that "no one shall drive us out of the paradise which Cantor has created for us" ([20], 141). I cannot hope to convince you, in this small space, that my goal is fully achievable. Here I shall try to justify a smaller contention: that if we can explain our knowledge of logic (and of language generally), we can also explain our knowledge of mathematics. Given a nominalistic theory of logic, therefore, we can construct a nominalistic theory of mathematical truth. I shall thus argue for an epistemological thesis of logicism: any epistemology that suffices for our knowledge of logic also suffices for mathematics. (shrink)

Popular sovereignty - the doctrine that the public powers of state originate in a concessive grant of power from 'the people' - is perhaps the cardinal doctrine of modern constitutional theory, placing full constitutional authority in the people at large, rather than in the hands of judges, kings, or a political elite. Although its classic formulation is to be found in the major theoretical treatments of the modern state, such as in the treatises of Hobbes, Locke, and Rousseau, this (...) book explores the intellectual origins of this doctrine and investigates its chief source in late medieval and early modern thought. Long regarded the principal source for modern legal reasoning, Roman law had a profound impact on the major architects of popular sovereignty such as François Hotman, Jean Bodin, and Hugo Grotius. Adopting the juridical language of obligations, property, and personality as well as the model of the Roman constitution, these jurists crafted a uniform theory that located the right of sovereignty in the people at large as the legal owners of state authority. In recovering the origins of popular sovereignty, the book demonstrates the importance of the Roman law as a chief source of modern constitutional thought. (shrink)

Despite the importance of Kant's claims about mathematical cognition for his philosophy as a whole and for subsequent philosophy of mathematics, there is still no consensus on his philosophy of arithmetic, and in particular the role he assigns intuition in it. This inquiry sets aside the role of intuition for the nonce to investigate Kant's conception of natural number. Although Kant himself doesn't distinguish between a cardinal and an ordinal conception of number, some of the properties Kant attributes to (...) number can be characterized as cardinal or ordinal. This essay argues that Kant's conception of number includes both cardinal and ordinal elements; it suggests that the cardinal elements provide the basis of a conception of number in general, while the ordinal elements contribute to specifying the exact size of particular collections. In considering these elements, roles for intuition begin to emerge, setting the stage for a reevaluation of the role of intuition in Kant's arithmetic. (shrink)

Ultrafilters play a significant role in model theory to characterize logics having various compactness and interpolation properties. They also provide a general method to construct extensions of first-order logic having these properties. A main result of this paper is that every class $\Omega $ of uniform ultrafilters generates a $\Delta $ -closed logic ${\mathcal {L}}_\Omega $. ${\mathcal {L}}_\Omega $ is $\omega $ -relatively compact iff some $D\in \Omega $ fails to be $\omega _1$ -complete iff ${\mathcal {L}}_\Omega $ does not (...) contain the quantifier “there are uncountably many.” If $\Omega $ is a set, or if it contains a countably incomplete ultrafilter, then ${\mathcal {L}}_\Omega $ is not generated by Mostowski cardinality quantifiers. Assuming $\neg 0^\sharp $ or $\neg L^{\mu }$, if $D\in \Omega $ is a uniform ultrafilter over a regular cardinal $\nu $, then every family $\Psi $ of formulas in ${\mathcal {L}}_\Omega $ with $|\Phi |\leq \nu $ satisfies the compactness theorem. In particular, if $\Omega $ is a proper class of uniform ultrafilters over regular cardinals, ${\mathcal {L}}_\Omega $ is compact. (shrink)

Using a countable support product of creature forcing posets, we show that consistently, for uncountably many different functions the associated Yorioka ideals’ uniformity numbers can be pairwise different. In addition we show that, in the same forcing extension, for two other types of simple cardinal characteristics parametrised by reals, for uncountably many parameters the corresponding cardinals are pairwise different.

We show, using the fine structure of K, that the theory ZF + AD + X R[X K] implies the existence of an inner model of ZF + AD + DC containing a measurable cardinal above its Θ, the supremum of the ordinals which are the surjective image of R. As a corollary, we show that HODK = K for some P K where K is the Dodd-Jensen Core Model relative to P. In conclusion, we show that the theory (...) ZF + AD + ¬DCR implies that R† exists. (shrink)

Working in ZF+AD alone, we prove that every set of ordinals with cardinality at least Θ can be covered by a set of ordinals in HOD of K (ℝ) of the same cardinality, when there is no inner model with an ℝ-complete measurable cardinal. Here ℝ is the set of reals and Θ is the supremum of the ordinals which are the surjective image of ℝ.

After showing that \ refutes \ for all regular cardinals \, we present a diamond-plus principle \ concerning all subsets of \. Using a forcing argument, we prove that \ holds in Steel’s core model \}}\), an inner model in which the axiom of determinacy can hold. The combinatorial principle \ is then extended, in \}}\), to successor cardinals \ and to certain cardinals \ that are not ineffable. Here \ is the supremum of the ordinals that are the surjective (...) image of the set of reals \. (shrink)

Given that \(L(\mathbb {R})\models {\text {ZF}}+ {\text {AD}}+{\text {DC}}\), we present conditions under which one can generically add new elements to \(L(\mathbb {R})\) and obtain a model of \({\text {ZF}}+ {\text {AD}}+{\text {DC}}\). This work is motivated by the desire to identify the smallest cardinal \(\kappa \) in \(L(\mathbb {R})\) for which one can generically add a new subset \(g\subseteq \kappa \) to \(L(\mathbb {R})\) such that \(L(\mathbb {R})(g)\models {\text {ZF}}+ {\text {AD}}+{\text {DC}}\).

This essay deals with two seventeenth-century intellectuals, the Aristotelian philosopher at Padua, Cesare Cremonini, and the Jesuit controversist, Robert Bellarmine. In the years of the cosmological affair of 1616, both defended their cosmological conceptions by relying on the principle of authority. However, they embraced different sources of legitimation in matters of natural philosophy. While the Padua professor stick to (what he considered to be) the letter of Aristotle, basically a secular interpretation of his world conception, Cardinal and Inquisitor Bellarmine (...) understood the cosmos against a theological background. In particular, Bellarmine subordinated natural philosophy to exegesis and the authority of the Scriptures, and this allowed him to depart from Aristotle to some extent (for instance on the fluidity and possibly the corruptibility of the heavens). Yet, the two thinkers also shared the criticism of the major astronomical novelty of their time, namely the planetary system of Copernicus and his followers. But their objections rested on different worldviews and authorities (Aristotle and the Scriptures, respectively). Cremonini also supported a vision of celestial animation which was received with much preoccupation by religious authorities as they feared that his views might revive forms of astral worshipping. This essay discusses the manner in which Cremonini and Bellarmine received geocentrism and cosmology in very different, even opposite, manners, especially concerning the relation between natural philosophy and theology, and the reconcilability of cosmology with the Scriptures. (shrink)

The Dodd–Jensen Covering Lemma states that “if there is no inner model with a measurable cardinal, then for any uncountable set of ordinals X, there is a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Y\in K}$$\end{document} such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq Y}$$\end{document} and |X| = |Y|”. Assuming ZF+AD alone, we establish the following analog: If there is no inner model with an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} (...) \begin{document}$${\mathbb {R}}$$\end{document} –complete measurable cardinal, then the real core model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K(\mathbb {R})}$$\end{document} is a “very good approximation” to the universe of sets V; that is, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K(\mathbb {R})}$$\end{document} and V have exactly the same sets of reals and for any set of ordinals X with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${|{X}|\ge\Theta}$$\end{document}, there is a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Y\in K(\mathbb {R})}$$\end{document} such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq Y}$$\end{document} and |X| = |Y|. Here \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}$$\end{document} is the set of reals and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Theta}$$\end{document} is the supremum of the ordinals which are the surjective image of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}$$\end{document}. (shrink)

This article seeks to reconstruct the phrase τὸν ἄρτον ἡμῶν τὸν ἐπιούσιον in the light of an African predicament with the Ewe-Ghanaian context in focus. The article posits that the various interpretations of the phrase throughout the epochs of Christianity have arisen as a result of the ambiguity associated with ἐπιούσιος and the quest to make the Lord’s Prayer in general relevant to the life situation of the recipient communities. Although the Lord’s Prayer is still regarded as a prayer par (...) excellence in the Ewe-Ghanaian Christian community, its central theme in popular Ewe-Ghanaian spirituality has been demonological instead of eschatological. The demonological interpretation is premised on the primal Ewe belief that successful spiritual warfare against the evil forces believed to be militating against one’s destiny in life can restore one’s fortunes and lead to the blessing of material prosperity. Thus, the phrase τὸν ἄρτον ἡμῶν τὸν ἐπιούσιον in popular Ewe-Ghanaian Christian spirituality is a call on God to ‘grant us the blessing of material prosperity, good health and longevity’. The demonological approach towards material prosperity, however, is discontinuous with the evangelisation approach, which was introduced into Ewe-Ghanaian spirituality through missionary activities in the mid-19th century. The missionaries identified the cardinal Ewe-Ghanaian predicament – poverty of the mind and spirit – and addressed them holistically through the message of the Gospel and the establishment of schools, hospitals, and agriculture to guarantee food security. This holistic approach to alleviating the poverty of the spirit and mind laid the foundation for the socio-economic development of their Ewe-Ghanaian Christian converts and the communities in which they practise their faith.Contribution: This article forms part of the researcher’s contribution to the academic knowledge on the Lord’s Prayer and inspires the use of Mother Tongue Biblical hermeneutics in the development of theological materials for the Ewe-Ghanaian Christian communities in Ghana, Togo, and Benin. (shrink)

In the years after the first circulation of Sidereus Nuncius, Galileo’s Padua anti-Copernican colleague, the staunch Aristotelian philosopher, Cesare Cremonini, published a book on ‘traditional’ cosmology, Disputatio de coelo in tres partes divisa which puzzled the Roman authorities of the Inquisition and the Index much more than any works on celestial novelties and ‘neo-Pythagorean’ astronomy. Cremonini’s disputation on the heavens has the form of an over-intricate comment of Aristotle’s conceptions, in the typi­cally argumentative style of Scholasticism. Nonetheless, it immediately raised (...) the concern of Cardinal Bellarmin, the Pope and other Inquisitors. At a close reading, Cremonini’s interpretation of Aristotle’s cosmos proved radically anti- Christian. It represented a radicalization of Pomponazzian Alexandrism. In fact, Cremonini did not only circulate Aristotelian principles used by Pom­ponazzi to argue for the soul’s mortality. He also wiped away all transcendence from the Aristotelian cosmos. In fact, he marginalized the function of the motive Intelligences by explaining heavenly motions through the action of animal-like inseparable souls although he did not erase nor reduced all Intelligences to only one, in accordance with Alexander. Also, he put at the center of Aristotle’s cosmos the idea of its eternity, a thesis which he explicitly connected with the rejection of the idea of God the Creator. Cremonini assumed that the univer­sal efficiens, that is the efficient cause of all motion and change in the world, is nothing but the first heaven. As a result of this radically naturalist reading of Aristotle, he banned God from the cosmos, reduced Him to the final cause of the world, and deprived Him of any efficiency and will. This essay on less ex­plored sources of Renaissance astronomical debates considers the institutional, cultural and religious setting of Cremonini’s teaching and conceptions. It as­sesses the reasons for his troubles with the religious authorities, and the politi­cal support he was granted by the Serenissima Republic of Venice inspite of the scandalous opinions he circulated as a university professor. My reconstruction of his views is based on the Disputatio de coelo of 1613 and later works, which are directly connected with cosmo-theological polemics with the religious au­thorities: his Apologia dictorum Aristotelis de quinta coeli substantia and the unpublished book De coeli efficientia, two manuscript copies of which are preserved in the libraries of Padua and Venice. (shrink)

The study of complexity and optimization in decision theory involves both partial and complete characterizations of preferences over decision spaces in terms of real-valued monotones. With this motivation, and following the recent introduction of new classes of monotones, like injective monotones or strict monotone multi-utilities, we present the classification of preordered spaces in terms of both the existence and cardinality of real-valued monotones and the cardinality of the quotient space. In particular, we take advantage of a characterization of real-valued monotones (...) in terms of separating families of increasing sets to obtain a more complete classification consisting of classes that are strictly different from each other. As a result, we gain new insight into both complexity and optimization, and clarify their interplay in preordered spaces. (shrink)

Axiom weakening is a technique that allows for a fine-grained repair of inconsistent ontologies. Its main advantage is that it repairs on- tologies by making axioms less restrictive rather than by deleting them, employing the use of refinement operators. In this paper, we build on pre- viously introduced axiom weakening for ALC, and make it much more irresistible by extending its definitions to deal with SROIQ, the expressive and decidable description logic underlying OWL 2 DL. We extend the definitions of (...) refinement operator to deal with SROIQ constructs, in particular with role hierarchies, cardinality constraints and nominals, and illustrate its application. Finally, we discuss the problem of termi- nation of an iterated weakening procedure. (shrink)

The Prussian Protestant Daniel Hermann is an important Neo-Latin poet. He lived from probably 1543 until 1601. Hermann studied at Königsberg, Straßburg, Basel and Wittenberg. Afterwards he served as a secretary at the Imperial Court at Vienna, later as a secretary of the city of Danzig and permanent ambassador of Danzig at the Royal Polish court during the wars against Russia. After the war he married and settled down in Riga and became the secretary of the Polish governor (...) class='Hi'>Cardinal Radziwil and later of the general Georg Fahrensbach. Besides lots of poems on academical, political and private occasions he wrote letters in poetic form as well as theological, philosophical and political poems. This paper provides an overview over Hermann ’s life and his poetry, especially the poems written and published in Riga, and a short summary of the research on this poet. (shrink)

Daniel Russell's Practical Intelligence and the Virtues is principally a defense of the Aristotelian claim that phronesis is part of every unqualified virtue—a defense of what Russell calls "hard virtue theory" and "hard virtue ethics." The main support for this is the further claim that we would be unable to act well reliably, or form our character reliably, without phronesis performing its "twin roles": correctly identifying the mean of each virtue, and integrating the mean of each virtue with those (...) of others so as to enable us to act in an overall virtuous manner. In following Russell's argument for these claims, we find much else of interest, including a persuasive account of right action and a resurrection of the old doctrine of cardinal virtues. Here I seek first to give readers a sense of the range and depth of this important book by summarizing the main lines of its argument. But I also raise some critical points, the most substantive of which concern his treatments of the unity of the virtues and of responsibility for character. (shrink)

In the last homily he gave before becoming Pope Benedict XVI, Cardinal Joseph Ratzinger described modern life as ruled by a “dictatorship of relativism which does not recognize anything as definitive and whose ultimate goal consists solely” of satisfying “the desires of one’s own ego.” An eminent scholar familiar with the centuries-old debates over relativism, Ratzinger chose to oversimplify or even caricature a philosophical approach of great sophistication and antiquity. His homily depicts the relativist as someone blown about “by (...) every wind of doctrine,” whereas the relativist sticks firmly to one argument—that human knowledge is not absolute. Gathering prominent intellectuals from disciplines most relevant to the controversy—ethics, theology, political theory, anthropology, psychology, cultural studies, epistemology, philosophy of science, and classics—this special double issue of _Common Knowledge_ contests Ratzinger’s denunciation of relativism. One essay relates the arguments of Ratzinger to those of two other German scholars—the conservative political theorist Ernst Wolfgang Böckenförde and the liberal philosopher and sociologist Jürgen Habermas—since all three men assume that social order depends on the existence of doctrinal authority. The contributors here argue for an intellectual and social life free of the desire for an “infantilizing” authority. One proposes that the Christian god is a relativist who prefers limitation and ambiguity; another, initially in agreement with Ratzinger about the danger relativism poses to faith and morals, then argues that this danger is what makes relativism valuable. The issue closes with the first English translation of an extract from a book on Catholic-Jewish relations by Cardinal Carlo Maria Martini, one of the Catholic Church’s most progressive figures. _Contributors_. David Bloor, Daniel Boyarin, Mary Baine Campbell, Lorraine Daston, Arnold I. Davidson, John Forrester, Kenneth J. Gergen, Simon Goldhill, Jeffrey F. Hamburger, Julia Kristeva, Carlo Maria Cardinal Martini, Christopher Norris, Joseph Cardinal Ratzinger, Richard Shusterman, Barbara Herrnstein Smith, Jeffrey Stout, Gianni Vattimo. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 351 raise questions for his thesis. Casey seems to want to suggest that our moral responses that do not fit well with the tradition of the virtues are simply the last remnants of a particular religion. But his own men· tion of the Stoics as one important source for the ' Christian ' tradition suggests that the commitments that Casey traces to Christianity-for example, to some version (...) of equality-may be more deeply rooted in the wider Western culture than he allows. And on the other hand, it is not obvious that everything that he associates with ' pagan ' virtues is necessarily incompatible with Christianity; after all, Aquinas, in addition to his extensive appropriation of the framework of the cardinal virtues, also argues that self-love is the first injunction of charity, after love of God (Summa theologiae 11-11, 26, 4). Even so, Casey's work raises important questions for contemporary moral theory. He succeeds in challenging too easy an appropriation of the tradition of the virtues by Christian ethics, and his challenge must he answered by anyone who would attempt to defend a contemporary Christian theory of the virtues. Moreover, by calling attention to the complexity and inner tensions that characterize our moral reflection, Casey reminds us that the category of ' the moral ' is not as straightforward as we sometimes take it to be. His book deserves to be widely read and carefully debated. University of Notre Dame Notre Dame, Indiana JEAN PORTER Nature and Scientific Method. Edited By DANIEL 0. DAHLSTROM. Studies in Philosophy and the History of Philosophy, vol. 22. Washington: Catholic University of America Press, 1991. Pp. 328. $48.95. William A. Wallace is a careful scholar and clear teacher of the history and philosophy of science. This volume is dedicated to him; the sixteen contributors were chosen because they have all been influenced by him, directly or indirectly. A comprehensive chronological list of Father Wallace's works, provided at the end of the book, reveals his two primary interests: contemporary issues in the philosophy of science and studies in the history of science. To reflect this, the first part of this book consists of seven essays on various contemporary issues in the philosophy of science; the second part is nine historical studies. This review will address each part in turn. Part I, "Contemporary Issues," suffers from a notable lack of unity. 352 BOOK REVIEWS Some authors directly and appropriately acknowledge the influence or inspiration of Wallace upon their contributions, the sole factor that might provide cohesion to the book as a whole. Other contributions are surprisingly devoid of any explicit connection to Wallace, save a tangential one. Wallace has provided the scholarly community with consistent and well-grounded work in the philosophy of science from a realist perspective. This realist position is shared by Rom Harre, the author of the opening essay, "Causality and Reality." Harre argues that the classical concept of causality, at least in part, survives as an ineliminable element of contemporary physics. To accomplish this, Harre distin· guishes weak from strong causality, the former as the expression of a causal mechanism, the latter as that connection stimulated by an event. This distinction is central to his Varieties of Realism. Realism is of two kinds: that which can be defined in terms of truth and falsity, and that which he terms " policy realism," which remains open to unlimited revisability of concepts, while preserving ontological categories. Having argued for these distinctions, Harre uses quantum field theory in his pursuit of a post-Humean conception of causality that transcends strict event ontology. Laudable as this pursuit may be, I wonder whether it can be achieved without reference to any conception of nature (s), a concept lamentably absent in Harre's more recent work. The realist theme is admirably pursued in Robert Sokolowski's " Explaining." Sokolowski argues for the irreducibility of names and explanations and their obvious correlates, things and causes. Form is in things; natural kinds exist; "ones" come in a splended variety reflecting the diversity of forms. Such unpopular claims are expertly defended in this essay, one of the best contributions in the book. Sokolowski also paints a fine picture of the mind... (shrink)

: What is at stake in the debate between those, such as Sam Harris and me, who contend that we would lack free will on the supposition that we are causally determined agents, and those that defend the claim that we might then retain free will, such as Daniel Dennett? I agree with Dennett that on the supposition of causal determination there would be robust ways in which we could shape, control, and cause our actions. But I deny that (...) on this supposition we would have the control in action required for us to basically deserve to be blamed, praised, punished or rewarded. In this response, I argue that this is the core issue that divides compatibilists and incompatiblists about free will and causal determination, and that the incompatibilist position is the right one to accept. Keywords: Sam Harris; Daniel Dennett; Free Will Skepticism; Compatibilism; Incompatibilism Risposta a Daniel Dennet sullo scetticismo circa il libero arbitrio Riassunto: Qual è la posta in gioco nel dibattito che vede contrapporsi chi – come Sam Harris e me – sostiene che non avremmo libertà di volere sulla scorta dell’ipotesi per cui siamo agenti causalmente determinati e chi, al contrario – come Daniel Dennett – difende l’idea che possa darsi un libero volere? Concordo con Dennett circa il fatto che, anche nell’ipotesi della determinazione causale, resterebbe lo spazio per sostenere che per vari e importanti aspetti saremmo comunque noi a modellare, controllare e causare le nostre azioni. E tuttavia rifiuto che su questa base avremmo il controllo in azioni richieste per meritare di essere biasimati, lodati, puniti o premiati. A mio avviso questo è l’elemento cardine che divide i compatibilisti dagli incompatibilisti all’interno del dibattito sul libero arbitro e sulla determinazione causale e ritengo che la posizione corretta sia quella incompatibista. Parole chiave: Sam Harris; Daniel Dennett; Scetticismo verso il libero arbitrio; Compatibilismo; Incompatibilismo. (shrink)

Partindo do tratamento da questão sobre a função social do filósofo, constroem-se os aportes teóricos para direcionar alguns apontamentos para uma temática semelhante: a função social do professor de filosofia. Serão propostas quatro funções sociais para o filósofo como aportes para a discussão a respeito do papel social do professor de filosofia. É para chegar a esses aportes que a investigação é dividida em dois momentos. No primeiro a função social do filósofo é discutida com amparo das reflexões de Franklin (...) Leopoldo e Silva. Serão extraídas quatro funções sociais do filósofo. No segundo momento é discutida a relação entre filosofia e educação. As quatro funções sociais do filósofo serão aplicadas no contexto da atividade do professor de filosofia. O artigo se encerra com as Considerações Finais. (shrink)

Kunst schaffen -- Kunst rahmen -- Birgit Spalts reflektierende Urteilskraft -- Kunst einordnen -- Kunst: immanent.

This is a reply by the author to the contributors to a symposium on the book, The Range of Reasons (Oxford University Press, 2021).

We point out some concepts that appear rather frequently in physics discussions, which, despite a seemingly innocent initial appearance, turn out to have important implicit implications that put into question the very assumption of their meaningfulness. The message of this essay is that, in order to avoid the ensuing confusions, their usage should be accompanied with clarifications that make them meaningful, and then to confront the often uncomfortable underlying assumptions required to do so. In particular, we will visit the notions (...) of novel physics occurring at a certain energy scale, or at certain distance from a black hole’s event horizon, and the various meanings of the word “fluctuations”. (shrink)

A psychedelic renaissance is currently taking place in mental healthcare. The number of psychedelic-assisted therapy trials is growing steadily, and some countries already grant psychiatrists special permission to use psychedelics in non-research contexts under certain conditions. These clinical advances must be accompanied by ethical inquiry. One pressing ethical question involves whether patients can even give informed consent to psychedelic-assisted therapy: the treatment’s transformative nature seems to block its assessment, suggesting that patients are unable to understand what undergoing psychedelic-assisted therapy actually (...) means for them and whether it aligns with their values. The present paper argues that patients often have sufficient knowledge to give informed consent because they know that they want to change their negative status quo and that psychedelic-assisted therapy offers an effective way to do so. Accordingly, patients can understand what the transformative nature of psychedelic-assisted therapy means for them and a make a value-aligned choice even if they are unable to anticipate the manifestation of a psychedelic experience. (shrink)

This study takes as its starting point CousinCousin, Victor’s HegelianHegelianism-sounding claim in his 1828 lectures that the history of philosophy is identical to philosophy itself—and it does so in order to interrogate the various resemblances and divergences between CousinCousin, Victor and Hegel when it comes to determining the relationship between philosophy and the history of philosophy. In particular, the study investigates the difference between the “official” position CousinCousin, Victor takes up in 1833 in which spiritualistSpiritualism philosophy grounds eclectic history of (...) philosophy and his earlier more experimental and provisional positions, which map roughly onto Hegel’s own various ways of articulating the philosophy-history of philosophy relationship. (shrink)