Spinoza’s bold claim that there exists only a single infinite substance entails that finite things pose a deep challenge: How can Spinoza account for their finitude and their plurality? Taking finite bodies as a test case for finite modes in general I articulate the necessary conditions for the existence of finite things. The key to my argument is the recognition that Spinoza’s account of finite bodies reflects both Cartesian and Hobbesian influences. This recognition leads to the surprising realization there must (...) be more to finite bodies than their finitude, a claim that goes well beyond the basic substance-monism claim, namely, that anything that is, is in God. This leads to the conclusion, which may seem paradoxical, that finite bodies have both an infinite as well as a finite aspect to them. Finite bodies, I argue, both actively partially determine all the other finite bodies, thereby partially causing their existence insofar as they are finite, as well as are determined by the totality of other bodies. I articulate precisely what this infinite aspect is and how it is distinct from the general substance-monism dictum. (shrink)

Science is continually faced with describing that which is beyond. This book, through contributions from nine prominent scholars, tackles that challenge.

The dialogue Bruno of 1802 is arguably the natural starting point for any investigation on the concepts of finitude, evil and human freedom in Schelling’s middle metaphysics. In this dialogue the author elaborates for the first time in his system a concept of freedom and independence of the finite, which extends via his reformulation in Philosophy and Religion of 1804 to the Freedom Essay of 1809 and beyond to the works of 1810 and 1811 – Stuttgart Private Lectures and The (...) Ages of the World. The central ontological problem of the dialogue relates to the possibility of a separation between the absolute and the world as space of finite beings, which, according to the system of identity first presented in 1801, cannot exist as such. The question we will then address concerns the status of the finite as such and how would it be possible to admit both its existence for consciousness and the positing of an absolute and infinite principle of philosophy. We will show how Schelling’s interest shifts, almost unintentionally, from the infinite principle to the finite as such, as a principle of freedom and self-initiation independent of the real. (shrink)

For a cardinal, we write for the cardinality of the set of permutations with finitely many non‐fixed points of a set which is of cardinality. We investigate the relationships between and for an arbitrary infinite cardinal in (without the axiom of choice). It is proved in that for all infinite cardinals, and we show that this is the best possible result.

There are many aspects of the Ethics that seem to suggest, or perhaps even require the possibility of deducing finite modes from the infinite substance. Nonetheless, as many have noted even during Spinoza’s own time, it is far from clear that such a deduction can be successfully performed. In this chapter I argue that the expectation of a top-down deduction is unwarranted, and that interestingly enough, it is not only unwarranted with regard to Spinoza but with regard to Descartes as (...) well. I show this by pointing to the crucial role confusion plays for both, noting that our epistemic journey to clear and distinct or adequate knowledge begins with confusion, and that this trajectory is one of emending initially confused ideas. This shows that epistemically a bottom-up trajectory necessarily precedes a top-down one. My claim, however, goes beyond this point regarding the order of discovery. I argue that the state of confusion presupposes a plurality of finite modes, in Spinoza’s case, and substances and modes in Descartes’s. Confusion, I claim, amounts to an inadequate perception of an amalgam of ideas of a real plurality of things. Recognizing the metaphysical ground of confusion along with its central epistemic role brings to light the artificiality, and indeed ultimately the impossibility of a top-down deduction which is divorced from a preceding bottom-up analysis. (shrink)

Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice.

This article compares two dominating conceptual frameworks of the current global environmental crisis, the Anthropocene and climate change, with respect to how they can be deployed to think about the dynamics of political action. Whereas the Anthropocene has attracted the attention of audiences beyond specialists and has radically expanded the temporal horizon for politics, its temporal characteristics risk rendering it unhelpful for thinking critically about how the current environmental crisis can be addressed. Most importantly, by establishing a reference point in (...) a distant future from which the present is evaluated, the Anthropocene framework gives the impression that the future is already determined and that the course of future environmental degradation is set. The Anthropocene thus fails to specify what is at stake for politics in the current crisis. As a contrast, the climate-change framework is structured as a range of scenarios. It establishes a temporal structure that opens the present to different potential futures and manifests the fact that the level of emissions in the coming decades is decisive for future climate change but not yet determined. Further, the presence of tipping points in the climate system can be understood in temporal terms as a risk in some scenarios of falling into a temporality of unfolding, a mode in which game-changing events that lead to even more emissions proceed beyond human influence. The risk of entering such a temporality that closes down the possibility to meaningfully deliberate on fundamental aspects of the future increases with the rate of emissions. The climate-change framework in this way helps us understand the environmental crisis in a new way, namely by conceptualizing the open future as a finite resource that has to be distributed globally and across generations. In sum, as a framework for engaging with environmental derangement, the climate-change framework offers a more specific and politically useful temporality than the Anthropocene. (shrink)

This essay argues that Spinoza believed that each finite mode is absolutely necessitated by God's nature and is causally necessitated by the laws of nature in conjunction with other finite modes. A geometrical analogy from Part 2 of the Ethics is employed in order to give a more suggestive account of the ways in which all things are necessary, according to Spinoza.

This essay articulates a double helix at work in Badiou’s thought on politics as a condition of philosophy and philosophy as such by focusing on what Badiou calls “the Idea of communism” and we will call “the communism of the Idea.” The former refers to communism as an Idea par excellence, while the latter concerns the Idea as a philosophical communism. The first section of the essay unpacks the Idea of communism as a composite interaction of politics, history, and subjectivity (...) insofar as each of these elements cannot be taken in themselves. Contrary to post-ideology, Badiou condemns the claim that we should live without an ideological framework insofar as this asks us to live without an Idea. The second section will focus on the communism of the Idea as the result of Badiou’s broader philosophical project and its major Platonic gestures. Badiou’s broader concerns pertain to the commitment to live with an Idea as finite, infinite, and transfinite to the endpoint that philosophy itself is characterized to be destined for communism. The crux that anyone can become a serious philosopher if, to paraphrase Diotima in Plato’s Symposium, they gracefully lend themselves to the process of truths as their fundamental commitment. (shrink)

Hilary Putnam has argued that computational functionalism cannot serve as a foundation for the study of the mind, as every ordinary open physical system implements every finite-state automaton. I argue that Putnam's argument fails, but that it points out the need for a better understanding of the bridge between the theory of computation and the theory of physical systems: the relation of implementation. It also raises questions about the class of automata that can serve as a basis for understanding the (...) mind. I develop an account of implementation, linked to an appropriate class of automata, such that the requirement that a system implement a given automaton places a very strong constraint on the system. This clears the way for computation to play a central role in the analysis of mind. (shrink)

Adjusting for covariates is a well-established method to estimate the total causal effect of an exposure variable on an outcome of interest. Depending on the causal structure of the mechanism under study, there may be different adjustment sets, equally valid from a theoretical perspective, leading to identical causal effects. However, in practice, with finite data, estimators built on different sets may display different precisions. To investigate the extent of this variability, we consider the simplest non-trivial non-linear model of a v-structure (...) on three nodes for binary data. We explicitly compute and compare the variance of the two possible different causal estimators. Further, by going beyond leading-order asymptotics, we show that there are parameter regimes where the set with the asymptotically optimal variance does depend on the edge coefficients, a result that is not captured by the recent leading-order developments for general causal models. As a practical consequence, the adjustment set selection needs to account for the relative magnitude of the relationships between variables with respect to the sample size and cannot rely on purely graphical criteria. (shrink)

Some passages throughout Spinoza’s body of works suggest that an attribute in its absolute nature provides a sufficient condition for all of its modes, including the finite ones. Other passages suggest that an attribute in its absolute nature fails to provide a sufficient condition for its finite modes. My aim is to dispel this apparent tension. I argue that all finite modes are ultimately entailed by the absolute nature of their attribute. Furthermore, I explain how the Spinozistic positions that appear (...) incompatible with this view are in fact compatible. As I see it, we should read those passages where Spinoza says that no finite mode ultimately follows from the absolute nature of its attribute as saying merely that no finite mode ultimately follows in one-by-one fashion, independent of an infinite series of other modes, from the absolute nature of its attribute. (shrink)

On the rise over the past 20 years has been ‘moderate supernaturalism’, the view that while a meaningful life is possible in a world without God or a soul, a much greater meaning would be possible only in a world with them. William Lane Craig can be read as providing an important argument for a version of this view, according to which only with God and a soul could our lives have an eternal, as opposed to temporally limited, significance, by (...) virtue of our moral choices then making an ultimate difference. I present two major objections to this position. On the one hand, I contend that if God existed and we had souls that lived forever, then, in fact, all our lives would turn out the same. On the other hand, I maintain that, if this objection is wrong, so that our moral choices would indeed make an ultimate difference and thereby confer an eternal significance on our lives (only) in a supernatural realm, then Craig could not capture the view, aptly held by moderate supernaturalists, that a meaningful life is possible in a purely natural world. An eternal significance would be ‘too big’, reducing any meaning possible during an earthly life to nothing by comparison. I conclude that moderate supernaturalists would be wise to avoid appealing to eternal (or infinite) meaning when spelling out the way God and a soul could alone impart a great meaning to our lives; some other notion of greatness should be considered, perhaps one involving a temporary afterlife. (shrink)

This book intends to show that radical naturalism, nominalism and strict finitism account for the applications of classical mathematics in current scientific theories. The applied mathematical theories developed in the book include the basics of calculus, metric space theory, complex analysis, Lebesgue integration, Hilbert spaces, and semi-Riemann geometry. The fact that so much applied mathematics can be developed within such a weak, strictly finitistic system, is surprising in itself. It also shows that the applications of those classical theories to the (...) finite physical world can be translated into the applications of strict finitism, which demonstrates the applicability of those classical theories without assuming the literal truth of those theories or the reality of infinity. Both professional researchers and students of philosophy of mathematics will benefit greatly from reading this book. (shrink)

This volume offer a manifold approach to a less evident and until now much neglected undercurrent in the work of Hannah Arendt., namely her ambiguous relation to the Judeo-Christian relligious heritage. Arendt's dissertation was dedicated to the concept of love in the works of Augustine, where she set her tone and developmed her frame for approaching theological matters. Her understanding of secularity might provide a model for the reconciliation of secularization and the persistence of religious belief in the contemporary world. (...) Thought Hannah Arendt wad certainly and outspokenly a secular thinker, her work also harbors ways of understanding secularization as the possibility of a new, maybe even messianic, attitude towards finite life and earthly reality. She famously depicts this attitude as "faith in and hope for the world". --Book cover. (shrink)

Analytic theologians have proposed numerous “solutions” to the Logical Problem of the Trinity (LPT), mostly versions of Social Trinitarianism (ST) and Relative Identity Trinitarianism (RI). Both types of solution are controversial, but many hold out hope that further “Trinitarian theorizing” may yield some as yet unimagined, and somehow importantly different, solution to the LPT. I first give a precise definition of the LPT and of what would count as a solution to it. I then show how, though there are infinitely (...) many possible solutions, all solutions can be grouped together into a finite, exhaustive taxonomy, based precisely on those features which make them either controversial, heretical, or inconsistent. The taxonomy reveals why ST and RI have been the major proposed solutions, and also proves that there can be no importantly different, new solutions to the LPT. (shrink)

Natural sciences are credited with being the chief force in the process of rendering relative many elements of our world view. To make acceptable the relative character of the order of two poles for the public, however, is the task of (idealist) philosophy. I reduce the division of objective/subjective to sensible duality. To explain the belief in sensible duality, I use unusual means: personifying the sensible content. It is the distinction between present (as extension) and absolute present (as the absence (...) of extension), which I call the trademark of idealist philosophy. This distinction is based on the striking assertion that though finite time can be divided infinitely, but at the same time, this division is not permitted to be performed, protecting the conceptual substance. The noninfinite division of finite time results in the definition: present = an extension-atom. This short extension is an important component of the notion “original environment”. The message “total nonuniversality” does not exist without that “place”. (shrink)

We introduce the $\Sigma _1$ -definable universal finite sequence and prove that it exhibits the universal extension property amongst the countable models of set theory under end-extension. That is, the sequence is $\Sigma _1$ -definable and provably finite; the sequence is empty in transitive models; and if M is a countable model of set theory in which the sequence is s and t is any finite extension of s in this model, then there is an end-extension of M to a (...) model in which the sequence is t. Our proof method grows out of a new infinitary-logic-free proof of the Barwise extension theorem, by which any countable model of set theory is end-extended to a model of $V=L$ or indeed any theory true in a suitable submodel of the original model. The main theorem settles the modal logic of end-extensional potentialism, showing that the potentialist validities of the models of set theory under end-extensions are exactly the assertions of S4. Finally, we introduce the end-extensional maximality principle, which asserts that every possibly necessary sentence is already true, and show that every countable model extends to a model satisfying it. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Little Way:Ferdinand Ulrich on AccidentsRachel M. ColemanWe live in a material reality. Obviously it is not the case that we live in a merely material reality, but it is worth remembering that we are corporeal substances given to be in a corporeal reality. Our materiality informs every aspect of our being, everything about us—including how we come to know.The German philosopher Ferdinand Ulrich never forgets this about the (...) human being or the reality in which the human is given to be—indeed, Ulrich, like his intellectual mentor and constant dialogue partner Thomas Aquinas, is a realist. That is to say that, like Thomas, Ulrich is always thinking about the world as it is given to man to inhabit and understand. This then includes thinking about matter, which, because of its status as lowest rung on the ladder of creation, is often overlooked in our thinking. Our materiality, with all of its implications for man, the world, and the task of man that is philosophy—that is, thinking and knowing being itself—is a touchstone for Ulrich's metaphysics and indeed all of his work.1Ulrich's dense and textured metaphysics can be approached in many ways, but perhaps none is so crucial as his attention to the small and seemingly insignificant, which is why he gives so much time and attention to matter throughout his corpus—for what could be more insignificant than that which does not exist in itself? Ulrich's attention to matter, however, is not simply in the speculative mode, wondering about the nature of potentia pura (though this is also included), but rather this kind of speculation leads [End Page 377] Ulrich to thinking through the implications of materiality for man's being and knowing. One of these is what Ulrich refers to repeatedly throughout Homo Abyssus, his great work of metaphysics and meta-anthropology, as "the little way." In the first chapter of that book, Ulrich writes:The light of being, since it doesn't cling to itself or allow reason to come to an end "next to" God, is therefore precisely what compels speculative reason to transcend beings into the absolute ground. This act of transcendence enraptures reason, which has been illuminated by being, elevating reason into the light of absolute truth, while reason precisely thereby enters onto the "little way" in the multiplicity of finite being.2According to Ulrich, in order to know and understand being itself, or "absolute truth," as quoted just above, human reason must enter onto this "little way," which can be reached only "in the multiplicity of finite being."The materiality of the world and the multiplicity of finite being therein have everything to do with each other, and Ulrich claims that, in order to know and understand absolute truth or being itself, precisely this multiplicity must be our starting point. Already then, at the beginning of Homo Abyssus, Ulrich draws our attention to the significance of matter.Ulrich receives this phrase, "the little way," from none other than St. Thérèse of Lisieux, who, in accepting her littleness, so to speak, not as a burden but as a gift, was given to work great acts.3 We have a clue already, [End Page 378] then, for beginning to understand how Ulrich conceives of matter and multiplicity: as that which, though nothing in itself, allows us to know the greatest truths—indeed, the "absolute truth." [End Page 379]Here we cannot explore every aspect of what Ulrich means when he uses the phrase "the little way," nor can we outline the entirety of how Ulrich's thinking about matter and materiality informs his metaphysics.4 We can, however, approach this topic in Ulrich's thinking through one particular implication of material being: accidents, or accidental being. Accidents do not subsist in themselves, but rather only in another—that is, substance—and as such, according to Ulrich, often get passed over in our thinking in favor of what we think of as more important subjects. And yet, in a certain sense, accidents are all we ever encounter in the world: while the tree could theoretically be any color at all, it... (shrink)

Leibniz conceives of God as a “most perfect being.” That means a being whose essence is the conjunction of all perfections, where a perfection is a simple quality and a positive quality – so purely positive that it involves no limitation at all. He also holds that the attributes of all finite substances are derived by limitation from God's perfections. Among the issues examined here about these views is the relation between Leibniz's and Spinoza's conceptions of the relation between God (...) and finite things. The chapter concludes that the mature Leibniz has a solid conceptual basis for distinguishing his pluralism about substances from Spinoza's monism. (shrink)

ABSTRACT This essay explores the possibility for a phenomenology of Christian vocational calling through conversation with Jean-Paul Sartre’s existential-ontology. By demonstrating how Sartre’s account of nothingness comports with a Rahnerian understanding of God as absolute mystery and how Sartre’s account of bad faith further opens up an understanding of ontological self-identity as a turn away from God, we can establish a phenomenology of Christian vocation as one’s owning each finite situation in terms of its divinely available possibilities rather than simply (...) its given conditions. Divine call thus occurs where one’s possibilities for boundless becoming are freely recognized in any situation and are further apprehended in light of the character of God to become the possibilities for the freedom and calling of others. (shrink)

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative Hasse–Schmidt derivations [13] and about Galois actions [14]. As an application of our methods, we obtain a new model complete theory of actions of a finite group on fields of finite imperfection degree.

Arrhenius’s impossibility theorems purport to demonstrate that no population axiology can satisfy each of a small number of intuitively compelling adequacy conditions. However, it has recently been pointed out that each theorem depends on a dubious assumption: Finite Fine-Grainedness. This assumption states that there exists a finite sequence of slight welfare differences between any two welfare levels. Denying Finite Fine-Grainedness makes room for a lexical population axiology which satisfies all of the compelling adequacy conditions in each theorem. Therefore, Arrhenius’s theorems (...) fail to prove that there is no satisfactory population axiology. In this paper, I argue that Arrhenius’s theorems can be repurposed. Since all of our population-affecting actions have a non-zero probability of bringing about more than one distinct population, it is population prospect axiologies that are of practical relevance, and amended versions of Arrhenius’s theorems demonstrate that there is no satisfactory population prospect axiology. These impossibility theorems do not depend on Finite Fine-Grainedness, so lexical views do not escape them. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:176 BOOK REVIEWS tianity came into being. To take one example: God's involvement with and reaction to genuine novelties introduced into the world as a result of the initiatives of human freedom, rightly renders suspect the conception of God as immutable. But what immutability really claimed was not anything like inertia or unconcern, but only that God was not mutable in any of the ways characteristic of finite realities (...) striving to transcend their limitations. Immutability was predicated as a property of deity whose essence was Pure Actuality-the consummation of all mutation. What this meant to preclude from God was only change that amounted to some sort of further perfecting of his intrinsic being-leaving the way clear for the possibility at least of relational change vis-a-vis a world of creatures. There is no reason why contemporary experiences of God's saving activity in Christ must be articulated only in the conceptual and linguistic categories of the past. But seemingly there ought to be some means of showing that such newer articulations do not repudiate truths achieved in the past and handed on in authentic living tradition. The Catholic University of America Washington, D.C. WILLIAM J. HILL, 0.P. The Church: Communion, Sacrament, Communication. By ROBERT KRESS. New York: Paulist Press, 1985. Pp. iv + 217. $9.95. One of the results of the recent synod is certain to be more attention to deepening our understanding of the church as communion. Robert Kress's fine volume cannot help but be a useful contribution to that discussion. As he succinctly states, "the Church is the communion of believers who exist as the sacrament of Christ, who is the sacrament of God, who is the communion of Father, Son, and Holy Spirit" (p. 59). For Kress any ecclesiology that does not root the church in the triune, perichoretic (a favored word) life of God is a radically truncated one. As a theandric (another favored word) reality, the Church must mirror its ground or source. If that ground is a dynamic, joyous unity-in-diversity, this should be reflected in the life and structures of the ecclesial community. Such is the context in which the author reflects on a variety of themes that are reflective of the post-Vatican II agenda: the relationship among local, regional, and universal churches; the understanding of the church as sacrament; the tension between holiness and office; the meaning of leadership in a community best understood as a perichoretic communion of gifted members. To each of these topics Kress brings a grasp of the BOOK REVIEWS 177 tradition, a wide acquaintance with the relevant theological literature, and a willingness to make provocative judgments ("yes" to the ordination of women; " no " to the new egalitarianism-a church conceived without administrative, pastoral authority.) Kress particularly cherishes the church as "the memory and tradition of Christ." His commitment to this tradition has both rooted him and freed him. He draws knowledgeably on Aquinas and Augustine, Rahner and Heidegger, von Balthasar and the Shepherd of Hermas. Lawrence Cunningham is correct: this book is radically conservative. There is one area where I felt that there was a certain lack. Kress's treatment of the church as sacrament and of the seven sacraments contained much that was valuable: his stress on the sacramentality of ecclesial life as such, his historical analysis of "sacrament", his phenomenolog·y of the nature of Christian worship. Yet all of this seemed strangely abstracted from the liturgical praxis of the Christian community. This lack is especially visible in his admittedly tentative salvation-historical correlation of the sacraments with our sharing in the religious experience of Jesus (pp. 147-148). To make that correlation, especially in the case of Baptism, Confirmation, and Eucharist, without an exp1icit reference to the initiatory, communal dimension of these sacraments is certainly problematic. I would like to make a final comment, not on the substance of the book, but on its editing and proofing. There are a number of errors, the most obvious of which is the elimination of the umlaut from Heribert Miihlen's name. (There is a curious inconsistency, too, in the use of the umlaut. It is used in... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:522 BOOK REVIEWS The Reason of Following: Christology and the Ecstatic I. By ROBERT P. ScHARLEMANN. Chicago: University of Chicago Press, 1992. Pp. 214. $32.50 (cloth). Robert P. Scharlemann is Commonwealth Professor of Religious Studies at the University of Virginia. Writing in the tradition of Bultmann 's observation that speaking of God requires speaking of oneself, he conceives of christology as a distinctive form of reason, a philosophical /theological (...) anthropology in which the logic of discipleship occupies a prominent place. Accordingly, The Reason of Following is a sustained pursuit of " an articulated understanding of the nature and constitution of human being" (p. 1), a theme which Scharlemann sees as a component of christology which has wrongly been eclipsed by other dimensions in more traditional presentations. The goal of Scharlemann's work is to bring into view " the nature of the relation that is implied when it is reported, for example, that Jesus said' Follow me! ' and there were those who 'immediately' followed.... What is the nature of the ' following ' on the part of those who will ' immediately ' follow the summons of one whose name is ' I am '? And who is the ' I ' of the ' I am ' in the person who makes the summons? " (p. 88). Each of the four themes sounded in this cita· tion-the call to discipleship, the immediacy of following, the identification of Jesus as ' I am,' and the designation of the specifics of the disciples' relationship to Jesus as an example, but no more than an ex· ample, of a broader possibility of human existence-is a fundamental element in Scharlemann's conception of christology. Operating on the principle that the traditional definition of a human being as a rational animal can be replaced by the existential definition " ' I ' am here " (cf. p. ix), Scharlemann devotes two lengthy introductory chapters to explicating the significance of this shift from " what " a human being is to " where " and " when " it is. Dr.awing especially on Descartes, Luther, Kierkegaard, Heidegger, and Fichte, his studies of the subjectivity and being of the self accent the import· ance of the I as subject and explore the differences between the I of pure actuality shown in the method of doubt, the I of pure possibility shown in the anticipation of death, and the I of pure freedom shown in the evocation of trust. Against this background, reflections on the na· ture of following envisage an additional possible I, one summoned by the call to be wholly in the world, in finite freedom. Before investigating the christological relation as " a rational form of its own" (p. viii), Scharlemann offers a preliminary analysis of modes of thinking. Distinguishing between thinking ("the openness BOOK REVIEWS 523 of the self to what is other than thinking" [p. 62]) and reason ("the configuration of this openness" [p. 62], i.e., "a definite way in which the self is related to its other through an activity " [p. 103] ), he argues that thinking always appears in one of two basic modes: understanding of being, or faith in God. These two modes-not to he confused with forms of reason-cover the entire field of thinking: " When we trust anyone at all, we are trusting God, just as, when we understand anything at all, we understand being" {p. 76). While aware that his implied definition of faith differs from those of the Christian theological tradition and is not serviceable for purposes of historical theology, Scharlemann opts nonetheless for a terminology which draws " as clearly as possible the parallel between faith and understanding as two modes of thinking whose own object is as such beyond the understanding of being and the faith in God " (p. 77). Turning to the specific form of reason which is the hook's chief concern, Scharlemann devotes a central chapter to " The Exstantial I in Christological Reason." After a critique of traditional christologies, he adumbrates a christology which seeks to depict the self of discipleship as one in which " the other to which the self relates itself is the inwardness of the self without being a projection from that inwardness " (p. 96). Appealing to the principle that the notion of the self as related to... (shrink)

"In this newest installment in Chicagos series of Jacques Derridas seminars, the renowned philosopher attempts one of his most ambitious goals: the first truly philosophical argument against the death penalty. While much has been written against the death penalty, Derrida contends that Western philosophy is massively, if not always overtly, complicit with a logic in which a sovereign state has the right to take a life. Haunted by this notion, he turns to the key places where such logic has been (...) established - and to the place it has been most effectively challenged: literature. With his signature genius and patient yet dazzling readings of an impressive breadth of texts, Derrida examines everything from the Bible to Plato to Camus to Jean Genet, with special attention to Kant and postWorld War II juridical texts, to draw the landscape of death penalty discourses. Keeping clearly in view the death rows and execution chambers of the United States, he shows how arguments surrounding cruel and unusual punishment depend on what he calls an 'anesthesial logic, ' which has also driven the development of death penalty technology from the French guillotine to lethal injection. Confronting a demand for philosophical rigor, he pursues provocative analyses of the shortcomings of abolitionist discourse. Above all, he argues that the death penalty and its attendant technologies are products of a desire to put an end to one of the most fundamental qualities of our finite existence: the radical uncertainty of when we will die. Arriving at a critical juncture in history - especially in the United States, one of the last Christian-inspired democracies to resist abolition - The Death Penalty is both a timely response to an important ethical debate and a timeless addition to Derridas esteemed body of work"--Unedited summary from book jacket. (shrink)

In the paper it will be shown that Reichenbach’s Weak Common Cause Principle is not valid in algebraic quantum field theory with locally finite degrees of freedom in general. Namely, for any pair of projections A, B supported in spacelike separated double cones ${\mathcal{O}}_{a}$ and ${\mathcal{O}}_{b}$ , respectively, a correlating state can be given for which there is no nontrivial common cause (system) located in the union of the backward light cones of ${\mathcal{O}}_{a}$ and ${\mathcal{O}}_{b}$ and commuting with the both (...) A and B. Since noncommuting common cause solutions are presented in these states the abandonment of commutativity can modulate this result: noncommutative Common Cause Principles might survive in these models. (shrink)

When attempting to generalize recursion theory to admissible ordinals, it may seem as if all classical priority constructions can be lifted to any admissible ordinal satisfying a sufficiently strong fragment of the replacement scheme. We show, however, that this is not always the case. In fact, there are some constructions which make an essential use of the notion of finiteness which cannot be replaced by the generalized notion of $\alpha$-finiteness. As examples we discuss bothcodings of models of arithmetic into the (...) recursively enumerable degrees, and non-distributive lattice embeddings into these degrees. We show that if an admissible ordinal $\alpha$ is effectively close to $\omega$ (where this closeness can be measured by size or by cofinality) then such constructions maybe performed in the $\alpha$-r.e. degrees, but otherwise they fail. The results of these constructions can be expressed in the first-order language of partially ordered sets, and so these results also show that there are natu. (shrink)

The prospects and limitations of defining truth in a finite model in the same language whose truth one is considering are thoroughly examined. It is shown that in contradistinction to Tarski's undefinability theorem for arithmetic, it is in a definite sense possible in this case to define truth in the very language whose truth is in question.

Written by a highly respected scholar of Thomas Aquinas's writings, this volume offers a comprehensive presentation of Aquinas's metaphysical thought. It is based on a thorough examination of his texts organized according to the philosophical order as he himself describes it rather than according to the theological order. -/- In the introduction and opening chapter, John F. Wippel examines Aquinas's view on the nature of metaphysics as a philosophical science and the relationship of its subject to divine being. Part One (...) is devoted to his metaphysical analysis of finite being. It considers his views on the problem of the One and the Many in the order of being, and includes his debt to Parmenides in formulating this problem and his application of analogy to finite being. Subsequent chapters are devoted to participation in being, the composition of essence and esse in finite beings, and his appeal to a kind of relative nonbeing in resolving the problem of the One and the Many. Part Two concentrates on Aquinas's views on the essential structure of finite being, and treats substance-accident composition and related issues, including, among others, the relationship between the soul and its powers and unicity of substantial form. It then considers his understanding of matter-form composition of corporeal beings and their individuation. Part Three explores Aquinas's philosophical discussion of divine being, his denial that God's existence is self-evident, and his presentation of arguments for the existence of God, first in earlier writings and then in the "Five Ways" of his Summa theologiae. A separate chapter is devoted to his views on quidditative and analogical knowledge of God. The concluding chapter revisits certain issues concerning finite being under the assumption that God's existence has now been established. -/- John F. Wippel, professor of philosophy at The Catholic University of America, was recently awarded the prestigious Aquinas Medal by the American Catholic Philosophical Association. In addition to numerous articles and papers, Wippel has coauthored or edited several other works, including Metaphysical Themes in Thomas Aquinas and The Metaphysical Thought of Godfrey of Fontaines, both published by CUA Press. (shrink)

According to finite frequentism, the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. I present fifteen arguments against this position.

We present numerous natural algebraic examples without the so-called Canonical Base Property (CBP). We prove that every commutative unitary ring of finite Morley rank without finite-index proper ideals satisfies the CBP if and only if it is a field, a ring of positive characteristic or a finite direct product of these. In addition, we construct a CM-trivial commutative local ring with a finite residue field without the CBP. Furthermore, we also show that finite-dimensional non-associative algebras over an algebraically closed field (...) of characteristic [Formula: see text] give rise to triangular rings without the CBP. This also applies to Baudisch’s [Formula: see text]-step nilpotent Lie algebras, which yields the existence of a [Formula: see text]-step nilpotent group of finite Morley rank whose theory, in the pure language of groups, is CM-trivial and does not satisfy the CBP. (shrink)

In this paper a model for barrecursion is presented. It has as a novelty that it contains discontinuous functionals. The model is based on a concept called strong majorizability. This concept is a modification of Howard's majorizability notion; see [T, p. 456].

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous attempts (...) all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

European Journal of Philosophy, EarlyView.

In the topological semantics for modal logic, S4 is well known to be complete for the rational line and for the real line: these are special cases of S4’s completeness for any dense-in-itself metric space. The construction used to prove completeness can be slightly amended to show that S4 is not only complete but strongly complete, for the rational line. But no similarly easy amendment is available for the real line. In an earlier paper, we proved a general theorem: S4 (...) is strongly complete for any dense-in-itself metric space. Strong completeness for the real line is a special case. In the current paper, we give a proof of strong completeness tailored to the special case of the real line: the current proof is simpler and more accessible than the proof of the more general result and involves slightly different techniques. We proceed in two steps: first, we show that S4 is strongly complete for the space of finite and infinite binary sequences, equipped with a natural topology; and then we show that there is an interior map from the real line onto this space. (shrink)

A logic in a finite language is said to be finitely presentable if it is axiomatized by finitely many finite rules. It is proved that binary non-indexed products of logics that are both finitely presentable and finitely equivalential are essentially finitely presentable. This result does not extend to binary non-indexed products of arbitrary finitely presentable logics, as shown by a counterexample. Finitely presentable logics are then exploited to introduce finitely presentable Leibniz classes, and to draw a parallel between the Leibniz (...) and the Maltsev hierarchies. (shrink)

We provide a finite basis for the class of Borel functions that are not in the first Baire class, as well as the class of Borel functions that are not $\sigma $ -continuous with closed witnesses.

It is standard to think that in Spinoza’s system, all things are necessary and in no sense contingent. However, in his classic book, Spinoza’s Metaphysics, published in 1969, Edwin Curley argues based on the proposition 28 of the first part of the Ethics that Spinoza endorses necessitarianism of only a modest kind, according to which when it comes to finite modes, there is a sense in which they are contingent. In this paper, I revisit Curley’s argument. Commentators have responded to (...) Curley’s argument, showing that Spinoza’s remarks on infinite modes entail that finite modes can in no sense be contingent. But this alone falls short of dispelling Curley’s misgivings about the standard interpretation, for it remains unexplained why Curley is wrong in thinking that the proposition 28 supports his moderate necessitarian interpretation. In defense of the standard interpretation, I bolster the usual response to Curley in greater detail than has been done in the literature and explain why, pace Curley, the proposition 28 plays no evidential role in support of Curley’s interpretation. (shrink)

The neutrosophic automorphisms of a neutrosophic groups G (I) , denoted by Aut(G (I)) is a neu-trosophic group under the usual mapping composition. It is a permutation of G (I) which is also a neutrosophic homomorphism. Moreover, suppose that X1 = X(G (I)) is the neutrosophic group of inner neutrosophic auto-morphisms of a neutrosophic group G (I) and Xn the neutrosophic group of inner neutrosophic automorphisms of Xn-1. In this paper, we show that if any neutrosophic group of the sequence (...) G (I), X1, X2, … is the identity, then G (I) is nilpotent. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous attempts (...) all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

Schutz’s references to literature and arts in his theoretical works are manifold. But literature and theory are both a certain kind of a finite province of meaning, that means they are not easily accessible from the paramount reality of everyday life. Now there is another kind of referring to literature: metaphorizing it. Using it, as may be said with Lakoff and Johnson, to understand and to experience one kind of thing in terms of another. Literally metapherein means “to carry over”. (...) Metaphorizing in this view is then a specific kind of border-crossing between different provinces of meaning. That poses two questions: 1. What means finiteness of those provinces of meaning, what kind of border crossings are possible? What is the ground for metaphorizing meaning? 2. Could this concept used for founding a theory of the constitution of the societal and of society, that overcomes the dichotomy of structure/agency? These questions will be answered with one example in view: Schutz’ report to Kaufmann of his first visit of Husserl describing his experience as feeling like Wilhelm Meister at the Society of the Tower. In a first step this metaphor is presented together with some crumbs of metaphor theory. In a second step these crumbs will be connected to Husserl’s concept of experience. After developing a short overview over Schutz’ “finite provinces of meaning,” the relation of experience, metaphors to the intersubjectivity of these provinces in their dependence from writing and printing is discussed. (shrink)

The logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule: γ, xn → y / γ, xm → y. It is proved that the class of algebraic models for such a logic has the finite embeddability property, meaning that every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. It follows that each such logic has the finite model property (...) with respect to its algebraic semantics and hence that the logic is decidable. (shrink)