In lieu of an abstract, here is a brief excerpt of the content:The Trinity by Thomas Joseph White, O.P.:A Model of Living ThomismSerge-Thomas Bonino O.P."The human being naturally seeks wisdom." From the very first line of the magisterial work we are dealing with, Fr. Thomas Joseph White's 2022 The Trinity: On the Nature and Mystery of the One God, it is all about wisdom. Wisdom was already at the heart of a previous work by Fr. White devoted to the natural (...) theology of St. Thomas, his 2009 Wisdom in the Face of Modernity. Wisdom is more than the accumulation of information or the juxtaposition of knowledge. It is an eminent form of knowledge that, on the one hand, involves the person of the thinker in all its dimensions, intellectual, emotional, existential, and on the other, seeks to understand its object in the light of the most fundamental causes, which are simultaneously the most enlightening and explanatory principles because they are the most universal. The Trinity: On the Nature and Mystery of the One God is undoubtedly a work of wisdom. Fr. White grasps the entire Christian mystery from its Trinitarian source, since, as we shall see, the entire Mystery (in the Pauline sense of the economy of salvation in Jesus Christ as the fulfillment of the Father's benevolent purpose) is at the same time rooted in the eternal mystery of the triune God and makes it known to us as it unfolds its truth and saving power in time.But the sapiential nature of the object studied has some effect on the form of the work itself. Indeed, if Fr. White were not Rector Magnificent of the Angelicum, he would be a magnificent architect, because he possesses a sense of order to the highest degree and knows how to introduce unity in diversity. The presentation of The Trinity is perfectly structured, and therefore very [End Page 461] clear and didactic. Among many other factors that create its unity, I was especially interested in the highlighting of what the philosopher André de Muralt calls "structures of thought": similarities of proportionality between the ways in which authors from even very different theological epochs have treated a problem.1 I am thinking for instance of how Fr. White shows the strong structural similarities between contemporary Trinitarian theologies and the three types of medieval Trinitarian theology (the Franciscan, the Thomist, and the Nominalist). "My claim here is that the modern Trinitarian tradition tends to reproduce various elements of the medieval traditions, … albeit in creative and unexpected ways" (399). So it is a conceptually well-unified work, and where there is unity, there is being, goodness and beauty.The introduction, as I said, is placed under the sign of wisdom. Fr. White takes up there the neo-Scholastic theme of the "three wisdoms": philosophical wisdom, theological wisdom, and mystical wisdom.2 The book's perspective is explicitly that of theological wisdom, as a scientific form of the intelligence of faith, but (we shall return to this point in connection with the place given to philosophy) it puts into practice in an exemplary manner the collaboration, without confusion or separation, between the three wisdoms.3My purpose, of course, is not, nor can it be, to "summarize" the contents of a book of more than seven hundred pages, which manages to be both a comprehensive handbook for higher theological education and a true personal theological essay. I will therefore limit myself to highlighting three partial but significant aspects.(1) The first is the explicit and overt Thomistic character of the book (see 6–7). The Trinity is in fact a vibrant plea in favor of the relevance of the theology of St. Thomas, as indicated by the very last sentence:The Church today can and should still have recourse to the theology of Thomas Aquinas, and to the living Thomistic tradition, as a privileged means of interpreting and advancing her own understanding of the mystery of God.(690) [End Page 462]The Trinity is the demonstration in actu exercito of the truth of this concluding statement. I therefore propose to reflect, in the first part of my paper, on the nature of Fr. White's Thomism, which depends, as we... (shrink)

We answer a question of Blass, Di Nasso, and Forti [2, 7] by proving, assuming Continuum Hypothesis or Martin’s Axiom, that there exists a P-point which is not interval-to-one and there exists an interval-to-one P-point which is neither quasi-selective nor weakly Ramsey.

This article proposes a geostatistical solution for area-to-point spatial prediction (downscaling) taking into account boundary effects. Such effects are often poorly considered in downscaling, even though they often have significant impact on the results. The geostatistical approach proposed in this article considers two types of boundary conditions (BC), that is, a Dirichlet-type condition and a Neumann-type condition, while satisfying several critical issues in downscaling: the coherence of predictions, the explicit consideration of support differences, and the assessment of uncertainty regarding (...) the point predictions. An updating algorithm is used to reduce the computational cost of area-to-point prediction under a given BC. In a case study, area-to-point prediction under a Dirichlet-type BC and a Neumann-type BC is illustrated using simulated data, and the resulting predictions and error variances are compared with those obtained without considering such conditions. (shrink)

We show how to get canonical models from in which the nonstationary ideal on ω1 is ω1 dense and there is no P-point.

We show how to get canonical models from in which the nonstationary ideal on ω1 is ω1 dense and there is no P-point.

The main topics of this thesis are cardinal invariants, P -points and MAD families. Cardinal invariants of the continuum are cardinal numbers that are bigger than $\aleph _{0}$ and smaller or equal than $\mathfrak {c}.$ Of course, they are only interesting when they have some combinatorial or topological definition. An almost disjoint family is a family of infinite subsets of $\omega $ such that the intersection of any two of its elements is finite. A MAD family is a maximal almost (...) disjoint family. An ultrafilter $\mathcal {U}$ on $\omega $ is called a P-point if every countable $\mathcal {B\subseteq U}$ there is $X\in $ $\mathcal {U}$ such that $X\setminus B$ is finite for every $B\in \mathcal {B}.$ This kind of ultrafilters has been extensively studied, however there is still a large number of open questions about them.In the preliminaries we recall the principal properties of filters, ultrafilters, ideals, MAD families and cardinal invariants of the continuum. We present the construction of Shelah, Mildenberger, Raghavan, and Steprāns of a completely separable MAD family under $\mathfrak {s\leq a}.$ None of the results in this chapter are due to the author.The second chapter is dedicated to a principle of Sierpiński. The principle $\left $ of Sierpiński is the following statement: There is a family of functions $\left \{ \varphi _{n}:\omega _{1}\longrightarrow \omega _{1}\mid n\in \omega \right \} $ such that for every $I\in \left [ \omega _{1}\right ] ^{\omega _{1}}$ there is $n\in \omega $ for which $\varphi _{n}\left [ I\right ] =\omega _{1}.$ This principle was recently studied by Arnie Miller. He showed that this principle is equivalent to the following statement: There is a set $X=\left \{ f_{\alpha }\mid \alpha \alpha $ then $f_{\beta }\cap g$ is infinite. Miller showed that the principle of Sierpiński implies that non $\left =\omega _{1}.$ He asked if the converse was true, i.e., does non $\left =\omega _{1}$ imply the principle $\left $ of Sierpiński? We answer his question affirmatively. In other words, we show that non $\left =\omega _{1}$ is enough to construct an $\mathcal {IE}$ -Luzin set. It is not hard to see that the $\mathcal {IE}$ -Luzin set we constructed is meager. This is no coincidence, because with the aid of an inaccessible cardinal, we construct a model where non $\left =\omega _{1}$ and every $\mathcal {IE}$ -Luzin set is meager.The third chapter is dedicated to a conjecture of Hrušák. Michael Hrušák conjectured the following: Every Borel cardinal invariant is either at most non $\left $ or at least cov $\left $. Although the veracity of this conjecture is still an open problem, we were able to obtain some partial results: The conjecture is false for “Borel invariants of $\omega _{1}^{\omega }$ ” nevertheless, it is true for a large class of definable invariants. This is part of a joint work with Michael Hrušák and Jindřich Zapletal.In the fourth chapter we present a survey on destructibility of ideals and MAD families. We prove several classic theorems, but we also prove some new results. For example, we show that every almost disjoint family of size less than $\mathfrak {c}$ can be extended to a Cohen indestructible MAD family is equivalent to $\mathfrak {b=c}$. A MAD family $\mathcal {A}$ is Shelah–Steprāns if for every $X\subseteq \left [ \omega \right ] ^{<\omega }\setminus \left \{ \emptyset \right \} $ either there is $A\in \mathcal {I}\left $ such that $s\cap A\neq \emptyset $ for every $s\in X$ or there is $B\in \mathcal {I}\left $ that contains infinitely many elements of X $ denotes the ideal generated by $\mathcal {A}$ ). This concept was introduced by Raghavan which is connected to the notion of “strongly separable” introduced by Shelah and Steprāns. We prove that Shelah–Steprāns MAD families have very strong indestructibility properties: Shelah–Steprāns MAD families are indestructible for “many” definable forcings that does not add dominating reals. According to the author’s best knowledge, this is the strongest notion that has been considered in the literature so far. In spite of their strong indestructibility, Shelah–Steprāns MAD families can be destroyed by a ccc forcing that does not add unsplit or dominating reals. We also consider some strong combinatorial properties of MAD families and show the relationships between them.The fifth chapter is one of the most important chapters in the thesis. A MAD family $\mathcal {A}$ is called $+$ -Ramsey if every tree that branches into $\mathcal {I}\left $ -positive sets has an $\mathcal {I}\left $ -positive branch. Michael Hrušák’s first published question is the following: Is there a $+$ -Ramsey MAD family? It was previously known that such families can consistently exist. However, there was no construction of such families using only the axioms of ZFC. We solve this problem by constructing such a family without any extra assumptions.In the fourth and fifth chapters, we introduce several notions of MAD families, in the sixth chapter we prove several implications and non implications between them. We construct several MAD families with different properties.In the seventh chapter we build models without P -points. We show that there are no P -points after adding Silver reals either iteratively or by the side by side product. These results have some important consequences: The first one is that is its possible to get rid of P -points using only definable forcings. This answers a question of Michael Hrušák. We can also use our results to build models with no P -points and with arbitrarily large continuum, which was also an open question. These results were obtained with David Chodounský.prepared by Osvaldo Guzmán GonzálezE-mail : [email protected] : https://arxiv.org/abs/1810.09680. (shrink)

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

A P-point ultrafilter over \(\omega \) is called an interval P-point if for every function from \(\omega \) to \(\omega \) there exists a set _A_ in this ultrafilter such that the restriction of the function to _A_ is either a constant function or an interval-to-one function. In this paper we prove the following results. (1) Interval P-points are not isomorphism invariant under \(\textsf{CH}\) or \(\textsf{MA}\). (2) We identify a cardinal invariant \(\textbf{non}^{**}({\mathcal {I}}_{\tiny {\hbox {int}}})\) such that every (...) filter base of size less than continuum can be extended to an interval P-point if and only if \(\textbf{non}^{**}({\mathcal {I}}_{\tiny {\hbox {int}}})={\mathfrak {c}}\). (3) We prove the generic existence of slow/rapid non-interval P-points and slow/rapid interval P-points which are neither quasi-selective nor weakly Ramsey under the assumption \({\mathfrak {d}}={\mathfrak {c}}\) or \(\textbf{cov}({\mathcal {B}})={\mathfrak {c}}\). (shrink)

The notion of a [Formula: see text]-generic sequence of P-points is introduced in this paper. It is proved assuming the Continuum Hypothesis that for each [Formula: see text], any [Formula: see text]-generic sequence of P-points can be extended to an [Formula: see text]-generic sequence. This shows that the CH implies that there is a chain of P-points of length [Formula: see text] with respect to both Rudin–Keisler and Tukey reducibility. These results answer an old question of Andreas Blass.

In lieu of an abstract, here is a brief excerpt of the content:Mercy in Aquinas: Help from the Commentatorial TraditionRomanus Cessario O.P. and Cajetan Cuddy O.P.Omnes semitae Domini misericordia et veritas(Psalm 24:10)IN QUESTION 21, article 3 of the first part of the Summa theologiae, St. Thomas Aquinas outlines the dynamics of mercy:A person is said to be merciful [misericors], as being, so to speak, miserable at heart [miserum cor]; being affected with sorrow [tristitia] at the misery of another as though (...) it were his own. Hence it follows that he endeavors to dispel the misery of this other, as if it were his; and this is the effect of mercy.1However, when explaining the mercy of God, Aquinas carefully distinguishes the effective and the affective within mercy: “Mercy is especially to be attributed to God, as seen in its effect, but not as an affection of passion.”2 “It does most properly belong to Him to dispel that misery,” but “to sorrow, therefore, over the misery of others belongs not to God.” How then can one claim that God is merciful? Aquinas locates the formal nature of God’s mercy within his power to relieve the misery of the miserable: “in so far as perfections given to things by God expel defects, it [i.e., the communication of perfection] belongs [End Page 329] to mercy.”3 Aquinas, therefore, situates the divine mercy within the divine perfection—a perfection powerful enough to remove all defects.Contemporary theologians may find this account of the divine mercy somewhat unsatisfying. In our conception, a sharing in the misery of another stands as an essential element of authentic mercy. Hence, our untutored experience may incline us to press Aquinas and to ask, Why, exactly, does sorrow over the misery of others not belong to God? If one seeks clarification regarding this point within the abovementioned passage, one does not find it. Aquinas does not here expound at any length upon the reasons why God does not share the misery of the miserable.Thankfully we are not the first students of theology to approach the writings of Aquinas. Nor are we the first to observe the prima facie oddness of a seemingly impassive God within Aquinas’s consideration of mercy. Throughout history, theologians of profound elegance and insight have sought wisdom from the Angelic Doctor. Some have even devoted their academic lives to the task of studying, expounding, and “commenting” upon the Thomistic text. In this essay, we intend to rely upon—and thereby highlight—a few of the valuable insights into divine mercy these Thomist commentators offer within their commentaries. Because the Thomist commentatorial tradition includes far too many figures to summarize in a few pages, we have decided to draw from only a small handful of the major Thomist commentators within a limited period of theological history, roughly from the sixteenth through the eighteenth centuries.4 Moreover, while the Thomist commentators exhibit a wide range of uniqueness and nuance amongst themselves, we might observe in our analysis a fundamental first principle uniting these major figures: the real distinction between act and potency (as well as between form and matter). [End Page 330] While philosophical in nature, this key Thomistic principle serves as the hermeneutical key for understanding what drew the commentators to Aquinas and the essential unity of their theological project.I. Infinitely Powerful MercyWhy does God’s mercy lack any misery? The sixteenth-century Thomist commentator Thomas de Vio Cardinal Cajetan (1469–1534) explains that “misery” implies some defect in the commiserating subject.5 God is actus purus. His being admits to no potentiality and no passivity within himself. The seventeenth-century Carmelite commentators, the Salmanticenses, note the relevance of the act-potency distinction for understanding the divine mercy: “In God, mercy is not given through the mode of a potency, but through the mode of the highest actuality... which extends to the relieving of all misery.”6 The defect of misery requires some degree of potentiality and passivity within its subject. Therefore, God can experience no misery—or even co-misery.7The seventeenth-century French Dominican Jean-Baptiste Gonet (1616–81) quotes with approval Cardinal Cajetan’s commentary on question... (shrink)

We define a family of non‐principal ultrafilters on which are, in a sense, very far from P‐points. We prove the existence of such ultrafilters under reasonable conditions. In subsequent articles, we intend to prove that such ultrafilters may exist while no P‐point exists. Though our primary motivations came from forcing and independence results, the family of ultrafilters introduced here should be interesting from combinatorial point of view too.

In lieu of an abstract, here is a brief excerpt of the content:Locating Heaven:Modern Science and the Place of Christ's Glorified BodyThomas Davenport O.P.It seems only fitting to respond to mysteries of faith with awe and astonishment, but there is something dangerous about being embarrassed by them. Unfortunately, when it comes to the mystery of the Ascension, Christians sometimes cannot help but gravitate toward the latter response. There are those nagging "why" questions, as we wonder if things would not have (...) been better off if Christ had stayed on earth. On top of that, there are the dumbfounded "where" questions by which we wonder where Christ went when he left the Apostles' sight and where he actually is right now, if anywhere. These are not new questions, of course, and the tradition of the Church offers a great deal of reflection to guide us, reflection which seems quite apt at answering the "why" questions, but which can appear inadequate to answer the "where" question.1Every Sunday, Catholics profess: "He ascended into heaven and is seated at the right hand of the Father." The Church has always been clear that the "right hand of the Father" should not be understood physically, for the [End Page 93] Father has no body, no physical hands; but does that mean we should understand everything about the Ascension in some non-physical sense, too?2 If Christ is "in heaven" only in a sort of spiritual sense, not a physical one, is he somehow non-physical too? If so, is he still human? If not, where is this body of his? It is hard—arguably impossible—to conceive of any physical body that is not in some place, let alone a living human body that is not in a place. What would it mean for a body to exist completely disconnected from any relation to other physical things? These would seem to be pressing questions for the mystery of the Ascension, but they are questions that, like the Ascension itself, are little talked about by theologians. A recent scholar has summed it up curtly by saying of the Ascension: "Once it was seen as the climax of the mystery of Christ.... Today it is something of an embarrassment."3Doubt and embarrassment about where Christ's glorified human body is breeds doubt and embarrassment about the present existence of Christ's human body, and there are a whole host of theological problems which arise if we deny the present existence of that body. In this paper I will first look at the theological importance of Christ's glorified body, from Scripture, the theological tradition, and particularly from the mystery of the Eucharist. Then, I will consider where ancient and medieval theologians thought Christ's glorified body was and point out the contemporary difficulties of their positions. Finally, I will argue that contemporary physics presents new avenues for a reasonable imagining of where the glorified body of Christ could be.The Importance of the Glorified BodyThe Scriptures make it quite clear: even though there was something new about Christ's body after the resurrection, it really was a human body, and specifically the same human body he had before his death, identifiable most [End Page 94] especially by the very wounds of his crucifixion.4 "While the senses could be fooled in the resurrection appearances, the sense of touch in particular was used to confirm both the reality of his body and its identity, most memorably when he told Thomas to probe his wounds.5 Aquinas argues in the Summa theologiae [ST] that, for a "true resurrection of Christ, it was necessary for the same body of Christ to once more be united to the same soul."6 If these resurrection appearances are not a manifestation of the continuity between the body that was crucified and the one in this new glorified state, then they seem to be mere parlor tricks used to assuage the disciple's fears or, worse, mislead them.While Christ took pains to manifest that he had the same human body, it clearly operated under different rules from the corruptible physical world we are so familiar with, disappearing from sight, entering locked rooms, even ascending into the... (shrink)

We construct a model in which the splitting number is large and every ultrafilter has a small subset with no pseudo-intersection.

We study the degree of (weak) Q-pointness, and that of (weak) P-pointness, of ideals on a regular infinite cardinal.

In lieu of an abstract, here is a brief excerpt of the content:318 BOOK REVIEWS ture. But when it comes to love, " we should measure the love of different persons according to the different kinds of union." Thomas underscores what Outka calls the " inclusive " conception of universal love. God is to be loved as the supreme good, as the source of all happiness; the neighbor is loved as sharing in the happiness we receive from God. Charity eviscerates (...) neither our natural inclination for happiness nor our natural associations with others. Rather, it " commands each act of other sorts of friendship " in relation to our friendship with God. Charity is inherently prudential and thus an account of " special relations,'' which Werpehowski and others address, is incorporated into the discussion of charity. Of course one might make the same objection against Thomas's appropriation of Aristotle that I have leveled against the appropriation of modern notions. But Aristotle is not so much a secular rival of Christianity as he is a philosopher of human nature. A return to Christian Aristotelianism is suggested by Kierkegaard's dictum that we have forgotten what it means to be Christian because we have forgotten what it means to be human. THOMAS s. HIBBS Boston College Chestnut Hill, MA The Trinity: An Analysis of St. Thomas Aquinas' Expositio of the "De Trinitate" of Boethius. By DOUGLAS C. HALL. Studien und Texte zur Geistesgeschichte des Mittelalters 33. Leiden/New York: Brill, 1992. Pp. vi + 131. $40 (cloth). Aquinas's expositio of the De Trinitate of Boethius is an admirable paradigm of profound analysis and interpretive genius. Adhering closely to a literal reading of the short sexpartite Boethian tractate, but breaking off his analysis (for reasons unknown) just before the end of section two where Boethius begins his ex professo treatment of the Trinity, Aquinas ends up mainly plumbing the depth of Boethius's prefatory remarks about the epistemological status of theology, and thus in six questions (comprising 24 articles) constructs the most extensive treatment in all his works of the nature and method of theology. Little wonder, then, that Leo Elders titles his introduction to the expositio of Aquinas Faith and Science (Rome, 1974) or that Armand Maurer names his two volume translation of it Faith, Reason and Theology and The Division and Methods of the Sciences (Toronto, 198687 ). In Thomas's commentary, only the fourth article of question three treats the doctrine of the Trinity directly, though the four articles of BOOK REVIEWS 319 question four also discuss the cause of plurality, a crucial topic for trinitarian theology. I was mildly surprised, then, that Douglas Hall gives the title The Trinity to what professes to offer a " careful textual analysis and criticism " (112) of the methods and contents of Aquinas's commentary. In this slender book of four chapters, Hall inserts, between a short introduction and a conclusion, a second chapter on all five of Boethius's tractates and a third on Aquinas's commentary on the De Trinitate. He has some interesting things to say about the dating and contents of the Boethian works, and also makes some good points about Thomas's commentary, especially as regards questions five and six. But the title is a misnomer, for Hall skips over lightly the five articles mentioned above where Aquinas treats trinitarian issues, devoting only three pages to them. Hall's main concern, like Aquinas's, is theological methodology and epistemology. Hall attempts a rather Hegelian, dialectical appraisal of Aquinaswhich stresses Aquinas's reconstruction of Boethius by highlighting their common methodological theme of agnosia-and links it with an integrative approach which grounds itself in " a transcendental reading of Aquinas, while retaining themes from participationist and analogical literature" (112). The first chapter discusses the participationist, analogical, and transcendental strains of contemporary Thomism, and evinces a certain predilection for Rahner (his influence is also evident on pages 50, 58, 92-95). In sum, Hall combines a Rahnerian and dialectical reading of Aquinas. Due to his presupposition, however, he frequently does not engage Aquinas on his own grounds but burdens him with false problems and dubious theses as he seeks to sort out Aquinas's " dialectical tensions." Often the result is a rather gratuitous reading encumbered with unsubstantiated non sequiturs that... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:542 BOOK REVIEWS sires. Rather, the Subjects need to want to do those things that bring about the Bosses' satisfaction. And this raises the question of the control of the imagination. explores the subtle power relations between controllers and the controlled, to the end of exploring ways that imagination offers control over power relationships. Yet Rorty ends with a bleak vision: we are a basically conservative species, whose capacities (...) for imagining new forms of power relationships tend to be dominated by the archetypes gleaned from our collective and individual experience, often reflecting malign structures. Even benign experiences, Rorty argues, tend to reinforce our inclination to seek refuge in submission to authority. What are we to make of this collection which stretches from philosophy of mind through Freudian analyses to a chastened Hobbesian vision of our social and moral order? There is much here to interest philosophers of mind and those who are concerned with the frontier between that field and empirical psychology. While she does not supply a theory of mind, Rorty shows clearly how much heterogeneous material such a theory must encompass. JOHN CHURCHILL Hendrix College Conway, Arkansas Faith and Reason From Plato to Plantinga: An Introduction to Reformed Epistemology. DEWEY J. HOITENGA, JR. S.U.N.Y. Press, 1991. Pp. 263. $18.95. This is an excellent and important book. Most of those who have written about the ' Reformed ' epistemology of religious belief have done so with either polemical or systematic interests in mind. That is not inappropriate, since the interests of those who have propounded Reformed epistemology have also been mainly polemical and systematic. Though here and there they have pointed to historical antecedents, they have not traced those antecedents in any detail. Hoitenga's contribution is to do exactly that. For the most part, his understanding of Reformed epistemology is accurate. He himself crisply summarizes his understanding in these words: "Its central claim is the immediacy of our knowledge of God. We do not, in the first instance, know God by inference or testimony but by direct acquaintance with him. A closely related claim fa that we cannot easily remain indifferent to the God whom we know by such direct acquaintance. Thus our knowledge of God is like our knowl- BOOK REVIEWS 543 edge of every other fundamental kind of reality-physical objects, their properties and relationships, others persons, right and wrong, good and evil, and the elementary objects of logic and mathematics. Furthermore, the claim is that everyone knows God in this way, not just the Christian believer. If someone does not believe in God, that is, does not trust in God as Christians do, this is not because one does not know God. All human beings by nature have what Calvin calls an awareness of divinity.... Although the fall has clouded over this natural awareness of God and led to the loss of faith in him, it has not eradicated this awareness. Christian faith does not alter this direct awareness of God but rather presupposes it, rejuvenates it, and enlarges it " {235). Hoitenga discusses in detail three precursors of this view: Plato, Augustine, and Calvin, thus showing that the contemporary Reformed epistemology of religious belief stands in a long intellectual tradition. Though shortly I will offer a few critical comments about his interpretations, his discussion of the three thinkers is, in each case, extremely helpful. The full view of each of these thinkers, on the matters under consideration, must be constructed from passages scattered around in a large number of different texts. Hoitenga conducts this recovery of the relevant sources and the construction of his interpretation with wide knowledge of the primary texts, with apt use of the secondary literature, and with the judiciousness and balance which such interpretation requires. Though I shall now make critical comments on three points, I view these criticisms as entirely compatible with my judgment that Hoitenga has made a very important contribution with this historical introduction to Reformed epistemology. I begin with one point in his exposition of contemporary Reformed epistemology. Plantinga observes that there are perhaps some cases in which, though a person has a prima facie right to believe some theistic proposition immediately, that right is... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kenneth Burke on Dialectical-Rhetorical TranscendenceJames P. ZappenKenneth Burke's concept of rhetoric is complex and elusive, increasingly so as it becomes intertwined and infused with dialectic in the long third part of A Rhetoric of Motives and in some essays published shortly thereafter (1951; 1955; 1969b [1950], 183–333).1 The connection between Burke's rhetoric and dialectic is well established (Brummett 1995; Crusius 1986; 1999, 120–21; Wess 1996, 136–216; Wolin 2001, 143–204), (...) and his concept of rhetoric as identification is widely recognized for its broadening of the traditional view of rhetoric as persuasion to include identification as a means of inducing cooperation and building communities (Crusius 1999, 120–21; Hauser 1986, 120–37; Henderson 1988, 33–34). Timothy W. Crusius establishes the fundamental relationship between A Grammar of Motives and A Rhetoric of Motives as dialectical and rhetorical counterparts and explains both the strengths and the limitations of identification as a means of inducing cooperation (1986). According to Crusius, dialectic explores the substance of a person or thing—all that "supports or 'substands'" it—from multiple and shifting perspectives, viewing human action dramatistically as act, scene, agent, agency, and purpose (24–28). Rhetoric complements dialectic and its multiple dramatistic perspectives by promoting "identification" and "cooperation," building "a community, a sense of oneness amid diversity of conflicting interests and values" (28–30). As Crusius and others observe, [End Page 279] however, identification as a means of inducing cooperation is inherently limited since any identification necessarily also entails a division: "Every 'us' requires a 'them'" (29; Biesecker 1997, 47–49; Wolin 2001, 177–78). Thus, for example, while Christianity provides a powerful instance of identification, it also provides an equally powerful illustration of its division from other peoples—"Satan and his counter-kingdom," "the Turk infidel," and "the pagan hordes of Asia" (28–29). For Burke, these divisions were largely political (George and Selzer 2007, 16–57, 110–32; Lentricchia 1983, 21–38). For us, they are differences of gender, culture, and economic and social class (Condit 1992), compounded by political, economic, and religious differences on a global scale. By this account, the first two parts of the Rhetoric offer at best a partial solution to the problem. The third part challenges and mystifies and in itself seems to offer little more than a utopian vision without purpose or outcome (Crusius 1999, 120–21; Wess 1996, 211–16; Wolin 2001, 201–3).2 Situated within the broader context of Burke's work, however, the third part seems rather to offer a bold and creative solution to the problem by merging dialectic and rhetoric with dialogue and poetic myth in a dialectical-rhetorical transcendence—a concept that merits a place alongside identification as a major contribution to rhetorical theory (1969b, 197–208, 221–33).3Burke's concept of dialectical-rhetorical transcendence developed over the course of more than twenty years, from the mid 1930s to the mid 1950s and beyond. Its sources are partly Hegelian and Marxist but increasingly Platonic,4 as Burke comes to perceive the Hegelian and Marxist concepts of history as part of the problem of competing ideologies and his version of Platonic transcendence as the solution—a solution that leads, on the one hand, toward "pure persuasion" and "ultimate identification" and, on the other, toward the pragmatics of a new rhetoric and a revolutionary program of lifelong education (1951; 1955; 1969b, 267–94, 328–33; Biesecker 1997, 43–47; Lee 2004; Wess 1996, 203–5, 211–16; Wolin 2001, 201–3). In the midst of the political divisiveness of the 1930s, Burke glimpsed in Hegel and even Marx the possibility of bridging conflicting ideologies via transcendence, but he turned to Plato in the Grammar and again in the Rhetoric to explain the processes by which opposing ideas and ideologies might merge in transcendent visions or myths that encompass what he perceived to be partial and partisan points of view. In the Grammar, his solution is dialectical—a merger of opposing ideas at higher levels of generalization through a process of linguistic abstraction and transformation that respects a diversity of individual interests, even as it seeks to transcend them in larger [End... (shrink)

In his paper ‘Has the Ontological Argument Been Refuted?’, 97–110) William F. Vallicella argues that my attempt to show that the Ontological Argument begs the question is unsuccessful. 1 I believe he is wrong about this, but before endeavouring to vindicate my position I must first make clear what precisely is the point at issue between us. The Ontological Argument is not a single argument, but a family of arguments. Newly devised formulations of the argument are frequently put forward (...) by philosophers in an effort to avoid difficulties that have been pointed out in previous versions. As a consequence there is no possibility of a conclusive proof that every form of the argument embodies the same fallacy. Nevertheless, one can, I believe, prove that all the standard versions of the argument embody a certain fallacy and that, given the nature of the argument, it is therefore unlikely that the argument can be formulated in such a way as to avoid this difficulty. What I tried to show in my paper is that the six best-known versions of the argument all beg the question and that they do so at the same point in the argument, namely when it is asserted that it is possible that an absolutely perfect being exists. It is difficult to see how an ontological argument could be formulated without including this claim as one of its premises, since the distinguishing badge of the argument is the inference from the possibility of an absolutely perfect being to its actuality. It must be unlikely then, if my criticism of these six versions is correct, that there is any way of formulating the argument that avoids this fallacy. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The De Auxiliis Controversy, Molinism, and Physical Premotion:The Christological Implications*Pachomius Walker O.P.From 1582 until 1607, the de Auxiliis controversy consumed much of the attention of Dominicans, Jesuits, and the Papacy.1 The controversy began in 1582 at Salamanca when a Scholastic debate entertained the question of [End Page 607] how Christ's sacrifice was both free and meritorious.2 The Jesuit, Prudencio de Montemayor, claimed that if Christ had been commanded to (...) lay down his life and be crucified, then his action was not free and, therefore, not meritorious.3 The Dominicans, on the other hand, resolved the question of Christ's merit and freedom using what would later come to be known as physical premotion.4 In a word, the de Auxiliis controversy has Christological roots. Even though the controversy quickly engaged other, related questions, a successful adjudication of these conflicting positions must have reference to the Christological truths implicated in the controversy.5 [End Page 608] The goal of this present study, therefore, is to exposit the Christological implications of the de Auxiliis controversy in an effort to reexamine the conflicting proposals about grace.Historically, in order to resolve the confusion about the God-man, the partisans of the debate needed to clarify their differing principles regarding God and man generally. As was soon apparent, however, the parties of the debate had contradictory understandings of basic philosophical principles.6 The participants in the controversy engaged other topics such as man's freedom, God's foreknowledge of future contingents, and predestination.7 It is understandable, therefore, that when Domingo Báñez († 1604), one of Montemayor's principal interlocutors, submitted his list of theses that summarized Montemayor's position, many of them dealt with questions other than those of Christ's merit.8Eventually, the controversy centered upon Luis de Molina's Concordia after its publication in 1588.9 The Concordia became the focus and [End Page 609] touch-point for the debate, since various parties aligned themselves based on their support for or condemnation of the work. The papal Congregation de Auxiliis (1594–1607), initially convoked by Pope Clement VIII, analyzed Molina's work and the positions contained therein. This, again, helped specify the debate. To keep the relevant parties focused and to make clear the lineaments of the controversy, it was helpful to have a standard text to which all parties had reference. Questions about God's grace and man's freedom were concretized through specific questions about Molina's approach to grace, God's knowledge, and predestination and whether his positions agreed with Thomas, Augustine, the Fathers of the Church, and Church councils. Hence, the Controversy de Auxiliis, which began by dealing with questions of Christology, resulted in a debate about the Molinist position as described in the Concordia.The subsequent years of the controversy have retained much of the same breadth: grace, freedom, God's foreknowledge, and predestination.10 The original impetus for the debate—Christology—can many times be overlooked or seen as a historical curiosity11 On one level, passing over the [End Page 610] Christological issues is reasonable: Molina's Concordia was first published after the lines of the debate had already been formed, and thus it is not a work of Christology. In fact, it was only in response to certain objections from Francisco Zumel that Molina included a more explicit treatment of Christ in his second edition.12 While those involved in the debate understood the details of Christ's merit to be a related and important issue, Molina's theological position was no longer seen primarily in terms of Christology.13 Even so, since the action of God in the human soul is nowhere clearer and nowhere more powerful than in the soul of Christ, any attempt to resolve these questions must take the original arena of Christology into account.14 [End Page 611]What follows is an attempt to reexamine the two proposals on grace—that of Molina and that of the Thomists on physical premotion—in Christological terms.15 The main Christological tenets at play are: (1) the fact that the hypostatic union is not of persons, but in the person; (2) that Christ... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Toward an East–West Ultramontane Polyphony:On Dogma, Ecclesial Unity, and the FilioqueThomas Joseph White O.P.The book that the contributors to this symposium have commented upon with graciousness and remarkable intellectual acuity is a work consisting of four parts. There are four main claims to the book associated with these four parts, each of which is divided into sub-themes. Thus, one can denote a number of inevitably controversial ideas advanced by (...) the book. In clarifying the nature of these claims, I can initially respond to some of the main points advanced by various of the helpful review essays in this symposium.Framing the Argument of the BookThe first part of the work posits that there is a fundamental developmental continuity between Old and New Testament revelation, wherein God is revealed first to Israel as the one Creator, and subsequently in Jesus Christ as three distinct persons, the eternal Father, Son, and Holy Spirit.1 This revelation is in turn received in the pre-Nicene era of the early Church, principally under a twofold conceptual format, according firstly to a model of God as a single transcendent subject of wisdom who sends his Word into the world in human nature, and inspires the prophets by his Spirit (the apologists' monotheistic model, exemplified by Justin Martyr) and, secondly, to [End Page 569] a model of economic Trinitarian activity, of the Father, Son and Spirit, who are each divine and one in being, active in sacred history (Irenaeus).2 Nicene Trinitarian authors sought in various ways to find a deeper concordance of the two approaches, one of which emphasized more the immanent unity of God (potentially tending toward a danger of Sabellianism) and the other of which emphasized real distinction of persons active in the economy (potentially tending toward the danger of subordinationism).3 Pro-Nicene figures like Athanasius, Gregory of Nazianzus, and Augustine, among others, paved the way for a mature doctrine of immanent Trinitarian life, in which God was understood to be characterized, mysteriously, by eternal processions of the Word and the Spirit who originate from the Father, and receive from him the plenitude of their deity or divine nature, and thus are equally and identically the one God.4 God is mysteriously three persons who are truly one both in essence and being.The second part of the book is concerned with the theological exploration of what it means to speak of God as one, and of the divine nature of God. This determination of Christian theological wisdom stems from a threefold exigency: first, to uncover the inner unity of revelation itself, as indeed the Israelite revelation of the divine unity and the oneness of God the transcendent Creator is thematic to both Testaments;5 second, to consider the preconditions of Nicene orthodoxy, as indeed the claim that the three persons in God are one in essence or nature presupposes that there is a nature of God that is one common to the three persons;6 third, to consider what must be said about the inner life of God as truth and love, as a precondition for thinking about the processional life of the Word and Spirit, who are immanent distinct persons in God who receive and possess this fullness of life but who do not divide this one eternal life in God or cause it to evolve due to their relational proceeding.7I argue that a consideration of God's nature as simple, perfect, good, eternal, immutable, and so forth is essential to any theology that takes the biblical revelation of the unity and transcendence of God seriously, and therefore confesses the revelation of the Trinity integrally.8 Furthermore, regarding [End Page 570] the apophatic contours of this form of reflection, I hold that it is precisely in order to guarantee the kind of circumspect avoidance of "non-biblical speculation" about positive knowledge of God outside of Christ that it is necessary to qualify rightly how God is not identifiable with creation and thus remains unknown in his inner divine nature and eternal life apart from and outside of his divine self-disclosure in the revelation of the Old and New Testaments. Philosophical... (shrink)

Between 1787, and the end of his life in 1832, Bentham turned his attention to the development and application of economic ideas and principles within the general structure of his legislative project. For seventeen years this interest was manifested through a number of books and pamphlets, most of which remained in manuscript form, that develop a distinctive approach to economic questions. Although Bentham was influenced by Adam Smith's An Inquiry into the Nature and Causes of the Wealth of Nations, he (...) neither adopted a Smithian vocabulary for addressing questions of economic principle and policy, nor did he accept many of the distinctive features of Smith's economic theory. One consequence of this was that Bentham played almost no part in the development of the emerging science of political economy in the early nineteenth century. The standard histories of economics all emphasize how little he contributed to the mainstream of late eighteenth and early nineteenth-century debate by concentrating attention on his utilitarianism and the psychology of hedonism on which it is premised. Others have argued that the calculating nature of his theory of practical reason reduced the whole legislative project to a crude attempt to apply economics to all aspects of social and political life. Put at its simplest this argument amounts to the erroneous claim that Bentham's science of legislation is reducible to the science of political economy. A different but equally dangerous error would be to argue that because Bentham's conception of the science of legislation comprehends all the basic forms of social relationships, there can be no science of political economy as there is no autonomous sphere of activity governed by the principles of economics. This approach is no doubt attractive from an historical point of view given that the major premise of this argument is true, and that many of Bentham's ‘economic’ arguments are couched in terms of his theory of legislation. Yet it fails to account for the undoubted importance of political economy within Bentham's writings, not just on finance, economic policy, colonies and preventive police, but also in other aspects of his utilitarian public policy such as prison reform, pauper management, and even constitutional reform. All of these works reflect a conception of political economy in its broadest terms. However, this conception of political economy differs in many respects from that of Bentham's contemporaries, and for this reason Bentham's distinctive approach to problems of economics and political economy has largely been misunderstood. (shrink)

Signed languages display a variety of pointing signs that serve the functions of deictic and anaphoric pronouns, possessive and reflexive pronouns, demonstratives, locatives, determiners, body part labels, and verb agreement. We consider criteria for determining the linguistic status of pointing signs. Among those criteria are conventionality, indexicality, phonological compositionality, being subject to grammatical constraints, and marking the kinds of grammatical distinctions expected of pronouns. We conclude that first-person points meet all these proposed criteria, but that nonfirst person points are in (...) part gestural. Lastly, we review evidence for the grammaticization over time of systems of pointing signs within signed languages. (shrink)

The no-miracles argument and the pessimistic induction are arguably the main considerations for and against scientific realism. Recently these arguments have been accused of embodying a familiar, seductive fallacy. In each case, we are tricked by a base rate fallacy, one much-discussed in the psychological literature. In this paper we consider this accusation and use it as an explanation for why the two most prominent `wholesale' arguments in the literature seem irresolvable. Framed probabilistically, we can see very clearly why realists (...) and anti-realists have been talking past one another. We then formulate a dilemma for advocates of either argument, answer potential objections to our criticism, discuss what remains (if anything) of these two major arguments, and then speculate about a future philosophy of science freed from these two arguments. In so doing, we connect the point about base rates to the wholesale/retail distinction; we believe it hints at an answer of how to distinguish profitable from unprofitable realism debates. In short, we offer a probabilistic analysis of the feeling of ennui afflicting contemporary philosophy of science. (shrink)

We study ultrafilters onω2produced by forcing with the quotient of${\cal P}$(ω2) by the Fubini square of the Fréchet filter onω. We show that such an ultrafilter is a weak P-point but not a P-point and that the only nonprincipal ultrafilters strictly below it in the Rudin–Keisler order are a single isomorphism class of selective ultrafilters. We further show that it enjoys the strongest square-bracket partition relations that are possible for a non-P-point. We show that it is not (...) basically generated but that it shares with basically generated ultrafilters the property of not being at the top of the Tukey ordering. In fact, it is not Tukey-above [ω1]<ω, and it has only continuum many ultrafilters Tukey-below it. A tool in our proofs is the analysis of similar (but not the same) properties for ultrafilters obtained as the sum, over a selective ultrafilter, of nonisomorphic selective ultrafilters. (shrink)

Let P be any one of the following combinatorial properties: weak P-pointness, weak (semi-) Q-pointness, weak (semi-)selectivity, ω-closedness. We deal with the following two questions: (1) What is the least cardinal κ such that there exists an ideal with κ many generators that does not have the property P? (2) Can one extend every ideal with the property P to a prime ideal with the property P?

... 243-) INTRODUCTION §§243- constitute the eighth 'chapter' of the book. Its point of departure is a natural query with respect to the conclusion of the ...

I've previously suggested that the historical evidence used to challenge scientific realism should lead us to embrace what I call Uniformitarianism, but many recently influential forms of scientific realism seem happy to share this commitment. I trace a number of further points of common ground that collectively constitute an appealing Middle Path between classical forms of realism and instrumentalism, and I suggest that many contemporary realists and instrumentalists have already become fellow travelers on this Middle Path without recognizing how far (...) they have thereby diverged from those who share their labels and slogans. I conclude by describing their central remaining disagreement and the sorts of evidence needed to resolve it. (shrink)

We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta’s theory of truth over arithmetic using \emph{fully varied revision} sequences yields a complete \Pi13 set of integers; (iii) the set of \emph{stably categorical} sentences using their revision operator ψ is similarly \Pi13 and which (...) is complete in Gödel’s universe of constructible sets L; (iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points. (shrink)

There are complex unresolved ethical, legal and social issues related to the use of human tissues obtained in the course of research or diagnostic procedures and retained for further use in research. The question of intellectual property rights over commercially viable products or procedures that are derived from these samples and the suitability or otherwise of participants relinquishing their rights to the samples needs urgent attention. The complexity of these matters lies in the fact that the relationship between intellectual property (...) rights and ownership or rights pertaining to the samples on which the intellectual property right is based may either be overlooked or taken for granted. What equally makes the matter complex is that samples may be obtained from participants in developing countries and exported to developed countries for analysis and research. It is important for research ethics committees to tread carefully when reviewing research protocols that raise such issues for purposes of ensuring that appropriate benefit sharing agreements, particularly with developing countries, are in place.This paper attempts to analyse the key questions related to ownership and intellectual property rights in commercially viable products derived from human tissue samples. Patent law is used as a point of reference as opposed to other forms of intellectual property rights such as industrial designs because it is the right that most inventors apply for in respect of human tissue-related inventions. The key questions are formulated following a systematic analysis of peer reviewed journal articles that have reported original investigations into relevant issues in this field. Most of the cases and reported studies that are referred to in this paper do not directly deal with HIV/AIDS research but the underlying principles are helpful in HIV/AIDS research as well. Pertinent questions, which members of ethics review committees should focus on in this regard are discussed and suggestions on appropriate approaches to the issues are proposed in the form of specific questions that an ethics review committee should consider. Specific recommendations regarding areas for further research and action are equally proposed. (shrink)

Modernism is both a contested aesthetic category and a powerful political statement. Modernist music was condemned as degenerate by the Nazis and forcibly replaced by socialist realism under the Soviets. Sympathetic philosophers and critics have interpreted it as a vital intellectual defence against totalitarianism, yet some American critics consider it elitist, undemocratic, and even unnatural. Drawing extensively on the philosophy of Heidegger and Badiou, Quilting Points proposes a new dialectical theory of faithful, reactive, and obscure subjective responses to musical modernism, (...) which embraces all the music of Western modernity. (shrink)