This essay explores the works of German artist Gustav Metzger as a potential response to Theodor W. Adorno’s dictum “Nach Auschwitz ein Gedicht zu schreiben, ist barbarisch” (“To write poetry after Auschwitz is barbaric”). It argues that culture, as understood in the Adornian sense, is inextricably barbaric as a result of simply being after Auschwitz. Culture must acknowledge the finitude in its own ability to live up to an ethical demand in response to justice, whose arrival is infinitely deferred. (...) In spite of this, culture, and art in particular, must not refrain from the very act of writing. Metzger’s works are discussed as aesthetic responses to the “new categorical imperative” of Adorno, who addresses art’s failure in light of Auschwitz by pointing to aporias that constitute the inescapable condition of “barbarism.” This essay suggests that Metzger’s aesthetic articulations are nonbarbaric ruptures, in that they challenge our living on irresponsibly within the condition of barbarism via a constant confrontation with complicity. (shrink)

What is the relationship between knowledge and ethics? Does what we know and the reason that secures knowledge determine ethical responsibility, or might ethical responsibility itself awaken and animate the enterprise of knowing? The dissertation affirms the priority of ethics by juxtaposing two accounts of the relationship between truth and goodness. It critiques Hegel's systematic conception of absolute knowing by showing that this knowing elides the anarchical ethical demand arising from the other person. Hegel's dialectic reconciles the problem of the (...) relation with the other by transposing it to the plane of cognition where it becomes spirit's self-knowing. However, Emmanuel Levinas's phenomenological reduction of the structures of knowing exposes an ethical level of experience that both inspires and interrupts this adventure of knowing. ;After the introduction of this problematic, Chapter 1 examines the challenge that Levinas poses to Hegel, discovering in experience and subjectivity a ground where real dialogue can take place. Chapter 2 traces the reconception of subjectivity by which Hegel brings all exteriority within the experience of self-consciousness and compares this with Levinas's notion of "lived experience." In Chapter 3, I show how Levinas's account of sensibility and enjoyment resists incorporation into Hegel's notion of self-consciousness. Chapter 4 examines the encounter with the other person and explicates why Hegel's and Levinas's accounts cannot be reconciled or made to complement one another, for the non-allergic responsibility incurred in the face to face relation is inassimilable to the antagonism of the same and the other experienced as self-consciousness. Then, in Chapter 5, I trace Hegel's pursuit of a more authentic recognition of otherness through the development of the concept of spirit, paying special attention to the role of language. The ultimate accomplishment of spiritual recognition in Hegel's account is again challenged by Levinas's notion of responsibility, which signifies as an ethical "saying" apart from the "said." Finally, I contest the absoluteness of knowing without denying the dialectic that animates it by suggesting that philosophy can be maintained as a human enterprise, a pursuit of knowing that is ever subject to and interrupted by the face of the other. (shrink)

In Religion of Existence, Noreen Khawaja suggests that Kierkegaard is an “ascetic” thinker. By this, she means that he regards religious striving as (1) requiring ceaseless renewal and (2) being an end in itself rather than a means to some further end. In this paper, I raise challenges to both parts of Khawaja’s proposal. I argue that the first part stands in tension with Kierkegaard’s assertion that his infinitely demanding account of religious existence is meant merely as a (...) “corrective.” The second part, I maintain, does not fit well with his claim that our eternal salvation is at stake in religious striving. (shrink)

“Why did God create the World?” is one of the traditional questions of theology. In the twentieth century this question was rephrased in a secularized manner as “Why is there something rather than nothing?” While creation - at least in its traditional, temporal, sense - has little place in Spinoza’s system, a variant of the same questions puts Spinoza’s system under significant pressure. According to Spinoza, God, or the substance, has infinitely many modes. This infinity of modes follow from (...) the essence of God. If we ask: “Why must God have modes?,” we seem to be trapped in a real catch. On the one hand, Spinoza’s commitment to thoroughgoing rationalism demands that there must be a reason for the existence of the radical plurality of modes. On the other hand, the asymmetric dependence of modes on the substance seems to imply that the substance does not need the modes, and that it can exist without the modes. But if the substance does not need the modes, then why are there modes at all? Furthermore, Spinoza cannot explain the existence of modes as an arbitrary act of grace on God’s side since Spinoza’s God does not act arbitrarily. Surprisingly, this problem has hardly been addressed in the existing literature on Spinoza’s metaphysics, and it is my primary aim here to draw attention to this problem. In the first part of the paper I will present and explain the problem of justifying the existence of infinite plurality modes in Spinoza’s system. In the second part of the paper I consider the radical solution to the problem according to which modes do not really exist, and show that this solution must be rejected upon consideration. In the third and final part of the paper I will suggest my own solution according to which the essence of God is active and it is this feature of God’s essence which requires the flow of modes from God’s essence. I also suggest that Spinoza considered radical infinity and radical unity to be roughly the same, and that the absolute infinity of what follow from God’s essence is grounded in the absolute infinity of God’s essence itself. (shrink)

The paper deals with the paradox that rationality demands rational substantiation which can’t be given in principle. Thus it is argued that only intuition can prevail against skepticism and subjectivism. But intuition is "transcendent" to rationality and therefore its acceptance as the substantiation of rationality implies existence of transcendental reality. In itself it has infinite regress qua infinite reiteration of reality levels without any qualitative ontological alteration, therefore only infinite transcendence is able to ground a finite immanence.

The aim of this paper is to clarify Spinoza’s views on some of the most fundamental issues of his metaphysics: the nature of God’s attributes, the nature of existence and eternity, and the relation between essence and existence in God. While there is an extensive literature on each of these topics, it seems that the following question was hardly raised so far: What is, for Spinoza, the relation between God’s existence and the divine attributes? Given Spinoza’s claims that there are (...) intimate connections between God’s essence and his existence – “God’s essence and his existence are one and the same”(E1p20) – and between God’s essence and the attributes – “By attribute I understand what the intellect perceives of substance, as constituting its essence” (E1d4), we would naturally expect that by transitivity, there is a significant relation between God’s existence and the attributes. Yet, as far as I know, there is little, if any, attempt in the existing literature to explicate such a relation, and it is one of my aims of this study to both raise the question and answer it. Eventually, I will argue that for Spinoza God is nothing but existence, and that the divine attributes are just fundamental kinds of existence, or, what is the same, as I will later argue, the intellect’s most fundamental and adequate conceptions of existence. In the first part of the paper I provide some background for Spinoza’s brief discussion in the TTP of God’s name and essence by studying the claims of Maimonides in the Guide of the Perplexed that God’s true essence is necessary existence, and that this essence is denoted by the ineffable Hebrew name of God, the Tetragrammaton (YHVH). In the second part of the paper I point out similar claims Spinoza presents in the TTP, and show how they respond to and echo Maimonides’ discussion in the Guide. In the third part, I examine Spinoza’s apparently conflicting claims in the Ethics about the relationship between God’s essence and existence. In some places Spinoza claims that God’s essence and existence are strictly identical (E1p10: “God’s essence his existence are one and the same”), but in other passages he makes the apparently much more modest claim that God’s essence involves existence (E1d1, E1p7d and E1p11d), which may lead one to believe that there is more to God’s essence than mere existence. I show that Spinoza’s understanding of the relation denoted by the Latin ‘involvit’ is consistent with the strict identification of essence and existence in God, and that Spinoza identifies God’s essence with self-necessitated existence, or eternity. Indeed, Spinoza’s understanding of eternity [aeternitas] as self-necessitated existence (E1d8) is one of the very few Spinozistic concepts that has no trace in Descartes. In this part I will also solve the long-standing problem of the sense in which the infinite modes can be called ‘eternal.’ In the fourth part I turn to the relation between the divine attributes and God’s existence and argue that, for Spinoza, the attributes are self-sufficient and adequate conceptions of existence. Finally, I will attempt to explain what brought Spinoza to deify existence. -/- Part I: “In that Day shall God be One, and his Name One”- Maimonides on God’s Name and Essence. -/- 1.1 Before we delve into the texts, let me suggest a few distinctions between various views on the issue of the relation between essence and existence in God. The view I suspect both Maimonides and Spinoza subscribe to can be termed the divine essence-existence Identity Thesis. -/- Identity Thesis (IT): God’s essence is existence and nothing but existence. We should distinguish the Identity Thesis from the much more common view according to which God’s essence contains existence, or (which I take to be roughly the same) that existence is one of the properties or perfections which constitute God’s essence. The latter view allows for the possibility (though it does not demand) that there is more to God’s essence than bare existence (e.g., God’s essence may include omniscience, omnipotence, etc.). I will term this view the divine essence-existence Containment Thesis. (shrink)

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, (...) and they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

A theory of truth is usually demanded to be consistent, but -consistency is less frequently requested. Recently, Yatabe has argued in favour of -inconsistent first-order theories of truth, minimising their odd consequences. In view of this fact, in this paper, we present five arguments against -inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known -inconsistent theories of truth: the classical theory of symmetric truth FS and the non-classical theory of naïve truth (...) based on ᴌukasiewicz infinitely valued logic: PAᴌT. (shrink)

Linnebo in 2018 argues that abstract objects like numbers are “thin” because they are only required to be referents of singular terms in abstraction principles, such as Hume's principle. As the specification of existence claims made by analytic truths (the abstraction principles), their existence does not make any substantial demands of the world; however, as Linnebo notes, there is a potential counter-argument concerning infinite regress against introducing objects this way. Against this, he argues that vicious regress is avoided in the (...) account of arithmetic based on Hume's principle because we are specifying numbers in terms of the concept of equinumerosity, or its ordinal equivalent. But far from being only a matter for philosophy, this implies a distinct empirical prediction: in cognitive development, the principle of equinumerosity is primary to number concepts. However, by analysing and expanding on the bootstrapping theory of Carey in 2009, I argue in this paper that there are good reasons to think that the development could be the other way around: possessing numerosity concepts may precede grasping the principle of equinumerosity. I propose that this analysis of early numerical cognition can also help us understand what numbers as thin objects are like, moving away from Platonist interpretations. (shrink)

Many have claimed that legitimate constitutional democracy is either conceptually or practically impossible, given infinite regress paradoxes deriving from the requirement of simultaneously democratic and constitutional origins for legitimate government. This paper first critically investigates prominent conceptual and practical bootstrapping objections advanced by Barnett and Michelman. It then argues that the real conceptual root of such bootstrapping objections is not any specific substantive account of legitimacy makers, such as consent or democratic endorsement, but a particular conception of the logic of (...) normative standards—the determinate threshold conception—that the critic attributes to the putatively undermined account of legitimacy. The paper further claims that when we abandon threshold conceptions of the logic of legitimacy in favor of regulative-ideal conceptions, then the objections, from bootstrapping paradoxes to the very idea of constitutional democracy, disappear. It concludes with considerations in favor of adopting a more demanding conception of the regulative ideal of constitutional democracy, advanced by Habermas, focusing on potentials for developmental learning. (shrink)

"This book explores the relationship between performance and activism in Chile as a form of political expression and citizen participation during the period 2010-2020. Since the student mobilizations of 2006, the social movements that have taken place in Chile are characterized, in many cases, by the appropriation of public space and the political use of the body. This became particularly evident during the social outbreak of October 2019. The social upheaval was accompanied by a cultural explosion, where the arts in (...) all their dimensions played a crucial role as new strategies of collective action. The research proposes two hypotheses about this cultural revolution. Firstly, that this explosion of artistic activism had been fermenting for at least a decade (2010-2020) within the social movements, using performance and art as expressions of collective action. These artistic drivers, catalysts of this cultural revolution, have been mobilized around three fundamental axes of social demands: human rights, education, and feminism. The second hypothesis is that artistic activism in Chile between 2010-2020 emerged to exercise citizenship and strengthen the diversity of cultural identities. Chilean artistic activism today, unlike other historical moments, is a direct expression of citizen participation. It is no longer just artists who contribute to social and protest movements with their work: now, it is the citizens who use artistic expression as a practice of political participation. From an intersectional and feminist perspective, this book is an invitation to study and reflect on the aesthetic and political dimension of performance and its potential to establish justice and symbolic reparation when the State is absent. Furthermore, it incentivises a conversation about the ritual, pedagogical, and visionary dimension of art and its infinite possibilities of expressive and discursive resources. Performance art reimagines possible futures embodying the political demand, always loaded with memory, reclaiming the public space. Performance as the 'art of action' conquers the realm of non-formal education, permeating public space and shaping a Pedagogy of memory and hope." -/- . (shrink)

This text tries to give some initial scopes for a constructivist approach to political philosophy and social organization based on the fact of friendship; particularly in the greeting taken as an event of friendship. The mere greeting, the most basic approach to empathy, would be the happening of a world, of a whole world characterized by its demand to be, to be realized and preserved. This requirement would come from an unfathomable archaic background, which would be accessible in the idea (...) of ​​the number of friends. It is an aporia that shows both the open, but not infinite, character of a reference group based on the tenderness of something common. (shrink)

There is a close systematic relationship between panentheism, as a metaphysical theory about the relation between God and the world, and transhumanism, the ethical demand to use the means of the applied sciences to enhance both human nature and the environment. This relationship between panentheism and transhumanism provides a ‘cosmic’ solution to the problem of evil: on panentheistic premises, the history of the world is the one infinite life of God, and we are part of the one infinite divine being. (...) We ourselves are therefore responsible for the future development of the life of the divine being. We should therefore use the means provided by the natural sciences to develop the history of the world in such a way that the existence of evil shall be overcome and shall no longer be part of the divine being in whom we move and live and have our being. The metaphysics of panentheism leads to the ethics of transhumanism. (shrink)

This paper attempts to argue that a radically different notion of freedoms and rights that originates from the other, that is founded on the infinite responsibility for the other, and that demands an encounter with the other as pure alterity, could be a plausible starting point towards the conception and possible realization of a Levinasian society of neighbors. First, an explication is made on why a radical change in the area of freedoms and rights could be the starting point towards (...) a social, political, and moral philosophical framework based on the radical philosophy of Levinas as elaborated in his Otherwise than Being or Beyond Essence. Then, a discussion on conventional conceptions of freedoms and rights, particularly those based on liberalism, libertarianism, and utilitarianism, is presented as groundwork for a comparative analysis between these conventional conceptions and a radical notion that would be entailed by a conception of a Levinasian society of neighbors. Lastly, an attempt is made to characterize a radically different conception of freedoms and rights based on the philosophy of Levinas and to argue how it could be the starting point towards the conception and possible realization of a Levinasian society of neighbors. (shrink)

Lady Gaga’s celebrity DNA revolves around the notion of monstrosity, an extensively researched concept in postmodern cultural studies. The analysis that is offered in this paper is largely informed by Deleuze and Guattari’s notion of monstrosity, as well as by their approach to the study of sign-systems that was deployed in A Thousand Plateaus. By drawing on biographical and archival visual data, with a focus on the relatively underexplored live show, an elucidation is afforded of what is really monstrous about (...) Lady Gaga. The main argument put forward is that monstrosity as sign seeks to appropriate the horizon of unlimited semiosis as radical alterity and openness to signifying possibilities. In this context it is held that Gaga effectively delimits her unique semioscape; however, any claims to monstrosity are undercut by the inherent limits of a representationalist approach in sufficiently engulfing this concept. Gaga is monstrous for her community insofar as she demands of her fans to project their semiosic horizon onto her as a simulacrum of infinite semiosis. However, this simulacrum may only be evinced in a feigned manner as a (dis)simulacrum. The analysis of imagery from seminal live shows during 2011–2012 shows that Gaga’s presumed monstrosity is more akin to hyperdifferentiation as simultaneous employment of heterogeneous and potentially dissonant inter pares cultural representations. The article concludes with a problematisation of audience effects in the light of Gaga’s adoption of a schematic and post-representationalist strategy in the event of her strategy’s emulation by competitive artists. (shrink)

In this paper, building on recent and longstanding work (Warren 2001, Friedman 2013, Glezer 2018), I investigate how the account of the essences or natures of material substances in the Metaphysical Foundations is related to Kant’s demand for the completeness of the system of nature. We must ascribe causal powers to material substances for the properties of those substances to be observable and knowable. But defining those causal powers requires admitting laws of nature, taken as axioms or principles of natural (...) science, which govern anything that can be constructed mathematically or “given as an object of experience” (MAN, 4:474–75). Presenting a complete system of nature requires adumbrating the properties of material substances that can be objects of experience. But it is not possible to show how those properties are involved in explanations of the phenomena without involving the laws that govern interactions between material substances. For Kant, or so I will argue, it is not possible to account for the natures of things, or for the features of laws of nature, independently of each other. The paper will substantiate the Finitist Account (FA) of Kant on laws. The Finitist Account has it that modal judgments about the possible proofs that can be made, or interactions that can be explained, are (1) based on concrete intuitive reasoning and motivated by the desire to avoid appeal to the actual infinite, (2) grounded in finite decision procedures, which are (3) based on reliable systems of axioms or rules of inference. (shrink)

The book aims to examine how a Trinitarian Theism can be formulated through the elaboration of a Relational Ontology and a Trinitarian Metaphysics, in the context of a hyperphatic epistemology. This metaphysics has been proposed by some supporters of the so-called Open Theism as a solution to the numerous dilemmas of Classical Theism. The hypothesis they support is that the Trinitarian nature of God, reflected in a world of multiplicity, relationality, substance and relations, demands that we think of God as (...) dynamic, internally multiple and relational. However, if the expression «God is love» – understood as the formula of the Trinity – is the key to a new theism, it leaves a problem open: how can it be translated philosophically? The research develops on two different levels: first, it assesses whether the expression should be translated into the Trinitarian paradigm, and the aporias it generates; secondly, it tries to assess whether this paradigm (eminently relational) has a correspondence in ontology: is there a satisfactory Relational Metaphysics already available? The suspicion is that such Trinitarian-Relational Ontology, invoked by many as a solution to the incongruities of classical theism, has yet to be formulated in a satisfactorily manner, despite the existence of various attempts to formulate Relational Ontologies. In order to provide an evaluation of all these attempts and to outline some possible new perspectives, the thesis consists of five chapters. It is the aim of the present dissertation to evaluate such attempts, and to outline some possible new solutions. In the chapters some points have been established: 1. there must be at least one irreducible real relation (non-reductionist realism); 2. the relation must be equally fundamental to the substance: this means that it is both external and internal; 3. this relation must be able to account for contingent causality; 4. holism is a plausible position; 5. the Trinity is a good theistic model of the divine, apophatic but rational. The last chapter then returns to ontological questions: several Relational Ontologies are examined – including ontic structural realism and process (or eventist) ontology – together with their applications in philosophy of religion (e.g.: the Relational God, Process Trinitarianism, the Entangled God). This assessment shows how all these ontologies postulate real transcendental relations (subsistent relations), inside the substances or inside the powers, inside the tropes or the structures, describing them as monads or processes (or actual occasions). These relations are the same we need to describe the Trinity. Therefore, they are either possible for both domains – ontology and theology – or they are both impossible. It has been opted for the second conclusion. But they are both impossible and inevitable: the fundamental entities of the world and their interactions (causation) must be described as real transcendental relations because each ontology transforms entities or relations into real transcendental relationships at some point. Thus, neither relationalism nor substantialism are convincing: from the fall of these two dogmas (or, rather, from the fall of their naive interpretations) we can realise that the fundamental reality is something that lies between processism (relationalism) and substantialism. It is impossible to completely substitute the notion of substance with the notion of event, process, structure or relation, both in speaking of God and in speaking about the entities of fundamental ontology. Neither monism nor pluralism can be affirmed in their pure forms. The hypothesis proposed, then, is that the notion of gunk-junk is the only one that can translate the relationality hitherto sought in an ontological model. The central part of the chapter describes the merits and defects of an eventist-infinitive ontology (EIO) based on the concept of gunk, and its potentiality to generate new theistic accounts. Through the notion of infinityings it seems to be possible to find some solutions for the questions left open by the causal relation, and therefore to defend at least the existence of one relation (external and internal). Each fundamental entity is described, in this ontology, through four transcendentals: ‘entity’, ‘relation’, ‘unity’ and ‘multiplicity’. The co-primarity between substance and relations (borrowed from the notion of relatio subsistens) differentiates EIO from the process philosophies precisely because it does not pretend to eliminate the substantial principle, or the category of substance, but wants to think of it with the transcendental of relationality. Of course, EIO poses a challenge to the role, the method and the explicative capacity of metaphysics, because what we can state of the fundamental reality is antinomic. EIO tries to assume the antinomy as a result, to make it the basis of a kind of apophatic ontology. If our best ontology is gunky, then it is possible to confirm what has been said in chap. 4: the ‘how’ of individual substances is unknown to us at least as much as the ‘how’ of God. Even in the world we have the mystery of a distinction that is not division. However, the convergence of these antinomies can find an ultimate explanation in a theistic metaphysics (EIM): God creates inside of Himself and his Trinitarian substance is “contracted” into the worldly entities. They are made contingent and ontologically different by this self-limitation, but it is still the infinity of God that makes space in Himself for something new, even though He is totally present in every entity. It is not absurd to think that the substances of the world keep track of the divine nature, even in His “contraction”. Among the characteristics of the divine nature that each created entity maintains we have the subsistent relationality, the pericoretic indwelling (the infinite gunk-junk), the fact of being always one-and-many. If EIO and EIM are accepted as a good compromise between relationalism and substantialism, even in their apophaticity, then, on this basis, a Trinitarian Philosophy is possible. The picture of reality that emerges represents the world as multiple, substantial, contingent and intrinsically relational, forcing us to postulate the transcendental of relationality and multiplicity. Such transcendental leads us to think of the world and God (and their relations) in a Trinitarian way – With the necessary acknowledgement that this is a reasonable but apophatic discourse. (shrink)

Introduction & Objectives: Norwich’s Entropy Theory of Perception (1975 [1] -present) stands alone. It explains many firing-rate behaviors and psychophysical laws from bare theory. To do so, it demands a unique sort of interaction between receptor and brain, one that Norwich never substantiated. Can it now be confirmed, given the accumulation of empirical sensory neuroscience? Background: Norwich conjoined sensation and a mathematical model of communication, Shannon’s Information Theory, as follows: “In the entropic view of sensation, magnitude of sensation is regarded (...) as a measure of the entropy or uncertainty of the stimulus signal” [2]. “To be uncertain about the outcome of an event, one must first be aware of a set of alternative outcomes” [3]. “The entropy-establishing process begins with the generation of a [internal] sensory signal by the stimulus generator. This is followed by receipt of the [external] stimulus by the sensory receptor, transmission of action potentials by the sensory neurons, and finally recapture of the [response to the internal] signal by the generator” [4]. The latter “recapture” differentiates external from internal stimuli. The hypothetical “stimulus generators” are internal emitters, that generate photons in vision, audible sounds in audition (to Norwich, the spontaneous otoacoustic emissions [SOAEs]), “temperatures in excess of local skin temperature” in skin temperature sensation [4], etc. Method (1): Several decades of empirical sensory physiology literature was scrutinized for internal “stimulus generators”. Results (1): Spontaneous photopigment isomerization (“dark light”) does not involve visible light. SOAEs are electromechanical basilar-membrane artefacts that rarely produce audible tones. The skin’s temperature sensors do not raise skin temperature, etc. Method (2): The putative action of the brain-and-sensory-receptor loop was carefully reexamined. Results (2): The sensory receptor allegedly “perceives”, experiences “awareness”, possesses “memory”, and has a “mind”. But those traits describe the whole human. The receptor, thus anthropomorphized, must therefore contain its own perceptual loop, containing a receptor, containing a perceptual loop, etc. Summary & Conclusions: The Entropy Theory demands sensory awareness of alternatives, through an imagined brain-and-sensory-receptor loop containing internal “stimulus generators”. But (1) no internal “stimulus generators” seem to exist and (2) the loop would be the outermost of an infinite nesting of identical loops. (shrink)

We’ll approach the notion of object in Wittgenstein’s Tractatus LogicoPhilosophicus (1921), initially from the so-called “substance argument”. The discourse about necessary conditions for the propositional sense cannot be treated in terms of truth or falsity in the Tractatus without resulting in a infinite regress. Such a situation is avoided by postulating a substance made up of simple objects, thus ensuring the assumed total determination of sense. Passages from the Notebooks (1914-1916) suggest that the idea of simples is given in the (...) ideia of logical analysis and is reached without the necessity of examples for objects. Another early Wittgenstein’s remarks provide examples for objects based on itens of phenomenical nature, such as a point in the visual field. An important analogy for the phenomenical approach for the object, which is found in the aphorisms 2.013-2.0131 of Tractatus, presents a problem for the absolute simplicity. This problem concerns the notion of form, a concept that attributes an ontological dependence to the object given by its essencial capacity of occurrence in atomic facts. The form of the objects results from an appropriation of the Context Principle used by Frege in his Grundlagen der Arithmetik (1884) and differs from the notions of pictorial form and logical form. The dependence assigned to the object through its form contradicts the independent subsistence established by its simplicity. The Tractarian object results from necessary demands for determination of propositional sense, reached by means of an clarificatory analysis which prioritizes the transformative and regressive modes of analysis. Simplicity and Context Principle are, under this perspective, rules of a syntax for a logical or significative use of language, which are reflected in the Tractarian ontology through the ideia that the logico-philosophical investigation of language reveals essencial aspects of the intimate structure of the world. (shrink)

Supererogatory acts are those that lie “beyond the call of duty.” There are two standard ways to define this idea more precisely. Although the definitions are often seen as equivalent, I argue that they can diverge when options are infinite, or when there are cycles of better options; moreover, each definition is acceptable in only one case. I consider two ways out of this dilemma.

People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable (...) Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

Consider an infinite series whose items are each explained by their immediate successor. Does such an infinite explanation explain the whole series or does it leave something to be explained? Hume arguably claimed that it does fully explain the whole series. Leibniz, however, designed a very telling objection against this claim, an objection involving an infinite series of book copies. In this paper, I argue that the Humean claim can, in certain cases, be saved from the Leibnizian “infinite book copies” (...) objection, and that this provides an interesting way to defuse some cosmological arguments for the existence of God and to give a non-theistic but complete explanation of the Universe. In the course of my argumentation, I also show that circular explanations can be “self-explanatory” as well: explaining two items by each other can explain the couple of items tout court. (shrink)

For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (...) (proposed separately by Arntzenius, Bostrom, and Meacham), which is to compare the prospects for value at each individual location, and to then represent and compare lotteries by their expected values at each of those locations. But, as I show here, this approach violates several key principles of decision theory and generates some implausible verdicts. I propose an alternative—one which delivers plausible rankings of lotteries, which is implied by a plausible collection of axioms, and which can be applied alongside almost any ranking of infinite worlds. (shrink)

In formal ontology, infinite regresses are generally considered a bad sign. One debate where such regresses come into play is the debate about fundamentality. Arguments in favour of some type of fundamentalism are many, but they generally share the idea that infinite chains of ontological dependence must be ruled out. Some motivations for this view are assessed in this article, with the conclusion that such infinite chains may not always be vicious. Indeed, there may even be room for a type (...) of fundamentalism combined with infinite descent as long as this descent is “boring,” that is, the same structure repeats ad infinitum. A start is made in the article towards a systematic account of this type of infinite descent. The philosophical prospects and scientific tenability of the account are briefly evaluated using an example from physics. (shrink)

This paper uses a schema for infinite regress arguments to provide a solution to the problem of the infinite regress of justification. The solution turns on the falsity of two claims: that a belief is justified only if some belief is a reason for it, and that the reason relation is transitive.

A common argument for atheism runs as follows: God would not create a world worse than other worlds he could have created instead. However, if God exists, he could have created a better world than this one. Therefore, God does not exist. In this paper I challenge the second premise of this argument. I argue that if God exists, our world will continue without end, with God continuing to create value-bearers, and sustaining and perfecting the value-bearers he has already created. (...) Given this, if God exists, our world—considered on the whole—is infinitely valuable. I further contend that this theistic picture makes our world's value unsurpassable. In support of this contention, I consider proposals for how infinitely valuable worlds might be improved upon, focusing on two main ways—adding value-bearers and increasing the value in present value-bearers. I argue that neither of these can improve our world. Depending on how each method is understood, either it would not improve our world, or our world is unsurpassable with respect to it. I conclude by considering the implications of my argument for the problem of evil more generally conceived. (shrink)

We can have credences in an infinite number of propositions—that is, our opinion set can be infinite. Accuracy-first epistemologists have devoted themselves to evaluating credal states with the help of the concept of ‘accuracy’. Unfortunately, under several innocuous assumptions, infinite opinion sets yield several undesirable results, some of which are even fatal, to accuracy-first epistemology. Moreover, accuracy-first epistemologists cannot circumvent these difficulties in any standard way. In this regard, we will suggest a non-standard approach, called a relativistic approach, to accuracy-first (...) epistemology and show that such an approach can successfully circumvent undesirable results while having some advantages over the standard approach. (shrink)

This book examines the philosophy of the nineteenth-century Indian mystic Sri Ramakrishna and brings him into dialogue with Western philosophers of religion, primarily in the recent analytic tradition. Sri Ramakrishna’s expansive conception of God as the impersonal-personal Infinite Reality, Maharaj argues, opens up an entirely new paradigm for addressing central topics in the philosophy of religion, including divine infinitude, religious diversity, the nature and epistemology of mystical experience, and the problem of evil.

Suppose we wish to decide which of a pair of actions has better consequences in a case in which both actions result in infinite utility. Peter Vallentyne and others have proposed that one action has better consequences than a second if there is a time after which the cumulative utility of the first action always outstrips the cumulative utility of the second. I argue against this principle, in particular I show how cases may arise in which up to any point (...) of time action a1 produces more utility than action a2, yet for each individual involved a2 produces more utility. (shrink)

It is possible that the world contains infinitely many agents that have positive and negative levels of well-being. Theories have been developed to ethically rank such worlds based on the well-being levels of the agents in those worlds or other qualitative properties of the worlds in question, such as the distribution of agents across spacetime. In this thesis I argue that such ethical rankings ought to be consistent with the Pareto principle, which says that if two worlds contain the (...) same agents and some agents are better off in the first world than they are in the second and no agents are worse off than they are in the second, then the first world is better than the second. I show that if we accept four axioms – the Pareto principle, transitivity, an axiom stating that populations of worlds can be permuted, and the claim that if the ‘at least as good as’ relation holds between two worlds then it holds between qualitative duplicates of this world pair – then we must conclude that there is ubiquitous incomparability between infinite worlds. I show that this is true even if the populations of infinite worlds are disjoint or overlapping, and that we cannot use any qualitative properties of world pairs to rank these worlds. Finally, I argue that this incomparability result generates puzzles for both consequentialist and non-consequentialist theories of objective and subjective permissibility. (shrink)

This paper discusses an infinite regress that looms behind a certain kind of historical explanation. The movement of one barbarian group is often explained by the movement of others, but those movements in turn call for an explanation. While their explanation can again be the movement of yet another group of barbarians, if this sort of explanation does not stop somewhere we are left with an infinite regress of barbarians. While that regress would be vicious, it cannot be accommodated by (...) several general views about what viciousness in infinite regresses amounts to. This example is additional evidence that we should prefer a pluralist approach to infinite regresses. (shrink)

This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

Drawing upon the practice of caregiving and the insights of feminist care ethics, I offer a phenomenology of caregiving through the work of Eva Feder Kittay and Emmanuel Lévinas. I argue that caregiving is a material dialectic of embodied response involving moments of leveling, attention, and interruption. In this light, the Levinasian opposition between responding to another's singularity and leveling it via parity-based principles is belied in the experience of care. Contra much of response ethics’ and care ethics’ respective literatures, (...) this dialectic suggests that they are complementary in ways that productively illuminate themes of each. I conclude by suggesting that when response and care ethics are thought together through the experience of caregiving, such labors produce finite responsibility with infinite hope. (shrink)

Some environmental ethicists and economists argue that attributing infinite value to the environment is a good way to represent an absolute obligation to protect it. Others argue against modelling the value of the environment in this way: the assignment of infinite value leads to immense technical and philosophical difficulties that undermine the environmentalist project. First, there is a problem of discrimination: saving a large region of habitat is better than saving a small region; yet if both outcomes have infinite value, (...) then decision theory prescribes indifference. Second, there is a problem of swamping probabilities: an act with a small but positive probability of saving an endangered species appears to be on par with an act that has a high probability of achieving this outcome, since both have infinite expected value. Our paper shows that a relative concept of infinite value can be meaningfully defined, and provides a good model for securing the priority of the natural environment while avoiding the failures noted by sceptics about infinite value. Our claim is not that the relative infinity utility model gets every detail correct, but rather that it provides a rigorous philosophical framework for thinking about decisions affecting the environment. (shrink)

Once one accepts that certain things metaphysically depend upon, or are metaphysically explained by, other things, it is natural to begin to wonder whether these chains of dependence or explanation must come to an end. This essay surveys the work that has been done on this issue—the issue of grounding and infinite descent. I frame the discussion around two questions: (1) What is infinite descent of ground? and (2) Is infinite descent of ground possible? In addressing the second question, I (...) will consider a number of arguments that have been made for and against the possibility of infinite descent of ground. When relevant, I connect the discussion to two important views about the way reality can be structured by grounding: metaphysical foundationalism and metaphysical infinitism. (shrink)

The idea that demands are a key constituent of any analysis of the negative reactive attitudes is rarely challenged, enjoying a freedom from scrutiny uncommon in philosophy. In this paper I press on this orthodox view, arguing that there are broadly speaking, three ways in which the term ‘demand’ is used in discussions of the negative reactive attitudes and that each is problematic.

This article offers a reconstruction of an argument against infinite regress formulated by Aristotle in Posterior Analytics I 22. I argue against the traditional interpretation of the chapter, according to which singular terms and summa genera, in virtue of having restrict logical roles, provide limits for predicative chains, preventing them from proceeding ad infinitum. As I intend to show, this traditional reading is at odds with some important aspects of Aristotle’s theory of demonstration. More importantly, it fails to explain how (...) his proof is connected to a defence of the existence of ultimate explanations, a connection that must be the case if I 19-22 is advancing a foundationalist way-out to a sceptical challenge raised in I 3. (shrink)

My two principal aims in this essay are interconnected. One aim is to provide a new interpretation of the ‘infinite modes’ in Spinoza’s Ethics. I argue that for Spinoza, God, conceived as the one infinite and eternal substance, is not to be understood as causing two kinds of modes, some infinite and eternal and the rest finite and non-eternal. That there cannot be such a bifurcation of divine effects is what I take the ‘infinite mode’ propositions, E1p21–23, to establish; E1p21–23 (...) show that each and every one of the immanent effects of an infinite and eternal God is an infinite and eternal mode. The other aim is to show that these propositions can be understood as part of an extended critical response to Descartes’s infamous doctrine that God creates eternal truths and true and immutable natures. If we have the correct (Spinozan) conceptions of what God is and how God works, we see that an eternal and infinite God can only be understood to cause ‘eternal truths,’ and that these eternal truths are infinite and eternal modes of God. (shrink)

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch a decomposition result (...) involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels’ question, “Can biology lead to new theorems?”. (shrink)

Draft for presentation at the 14th International Kant-Congress, September 2024. -/- Abstract: Kant claims we intuit infinite space. There’s a problem: Kant thinks full awareness of infinite space requires synthesis—the act of putting representations together and comprehending them as one. But our ability to synthesize is finite. Tobias Rosefeldt has argued in a recent paper that Kant’s notion of decomposing synthesis offers a solution. This talk criticizes Rosefeldt’s approach. First, Rosefeldt is committed to nonconceptual yet determinate awareness of (potentially) infinite (...) space, but I argue that such awareness is (1) prima facie implausible, as well as contravened by textual evidence from Kant’s (2a) definitions of ‘infinity’ and (2b) account of geometrical construction. Second, scrutiny of how Kant thinks awareness of potential infinity is afforded by geometrical construction (e.g., extending a line segment ad indefinitum) indicates no essential role for decomposing synthesis. Familiar synthesis from parts to wholes is sufficient. (shrink)

This paper aims to show that a proper understanding of what Leibniz meant by “hypercategorematic infinite” sheds light on some fundamental aspects of his conceptions of God and of the relationship between God and created simple substances or monads. After revisiting Leibniz’s distinction between (i) syncategorematic infinite, (ii) categorematic infinite, and (iii) actual infinite, I examine his claim that the hypercategorematic infinite is “God himself” in conjunction with other key statements about God. I then discuss the issue of whether the (...) hypercategorematic infinite is a “whole”, comparing the four kinds of infinite outlined by Leibniz in 1706 with the three degrees of infinity outlined in 1676. In the last section, I discuss the relationship between the hypercategorematic infinite and created simple substances. I conclude that, for Leibniz, only a being beyond all determinations but eminently embracing all determinations can enjoy the pure positivity of what is truly infinite while constituting the ontological grounding of all things. (shrink)

In this chapter I explain Spinoza's concept of "infinite modes". After some brief background on Spinoza's thoughts on infinity, I provide reasons to think that Immediate Infinite Modes are identical to the attributes, and that Mediate Infinite Modes are merely totalities of finite modes. I conclude with some considerations against the alternative view that infinite modes are laws of nature.

The Special Composition Question may be formulated as follows: for any xs whatsoever, what are the metaphysically necessary and jointly sufficient conditions in virtue of which there is a y such that those xs compose y? But what is the scope of the sought after explanation? Should an answer merely explain compositional facts, or should it explain certain ontological facts as well? On one natural reading, the question seeks an explanation of both the compositional facts and the ontological; the question (...) seeks to explain how composite objects exist; how there is a y such that the xs compose y. But it turns out that some answers to the Special Composition Question presuppose those ontological facts rather than explain those ontological facts. In this paper, I will indicate what I take to be the different explanatory demands met by the representative answers. I will argue that the wide scope explanatory demands can’t be satisfied. I will also show that this result has bearing on the current debate about composition. (shrink)

In this paper, I suggest that infinite numbers are large finite numbers, and that infinite numbers, properly understood, are 1) of the structure omega + (omega* + omega)Ө + omega*, and 2) the part is smaller than the whole. I present an explanation of these claims in terms of epistemic limitations. I then consider the importance, part of which is demonstrating the contradiction that lies at the heart of Cantorian set theory: the natural numbers are too large to be counted (...) by any finite number, but too small to be counted by any infinite number – there is no number of natural numbers. (shrink)

Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...) naïf, il semblerait que la première soit pure et la seconde impure. Des objections à cette vue naïve sont ici considérées et réfutées. Concernant la preuve euclidienne, la question relève de la logique, notamment de la définissabilité arithmétique de l’addition en termes de successeur et de divisibilité telle que démontrée par Julia Robinson, tandis qu’en ce qui concerne la preuve topologique, la question relève de la sémantique, notamment pour tout ce qui touche au problème de savoir ce qui est « inclus » dans le contenu d’énoncés particuliers.A proof is pure, roughly, if it draws only on what is « close » or « intrinsic » to the statement being proved. The infinitude of prime numbers, a classical theorem of arithmetic, is a rich case study for philosophical investigation of purity. Two different proofs of this result are considered, namely the classical Euclidean proof and a more recent « topological » proof by Furstenberg. Naively the former would seem to be pure and the latter to be impure. Objections to these naive views are considered and met. In the case of the former the issue rests on logical matters, specifically the arithmetic definability of addition in terms of successor and divisibility shown by Julia Robinson, while in the case of the latter the issue rests on semantic matters, specifically with respect to what is « contained » in the content of particular statements. (shrink)

I argue that moral philosophers have either misunderstood the problem of moral demandingness or at least failed to recognize important dimensions of the problem that undermine many standard assumptions. It has been assumed that utilitarianism concretely directs us to maximize welfare within a generation by transferring resources to people currently living in extreme poverty. In fact, utilitarianism seems to imply that any obligation to help people who are currently badly off is trumped by obligations to undertake actions targeted at improving (...) the value of the long-term future. Reflecting on the demands of beneficence in respect of the value of the far future forces us to view key aspects of the problem of moral demandingness in a very different light. GPI Working Paper No. 1-2020. (shrink)

Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano’s mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano’s infinite sums can be equipped (...) with the rich and original structure of a non-commutative ordered ring, and that Bolzano’s views on the mathematical infinite are, after all, consistent. (shrink)

This paper responds to commentaries by Kaiserman and Magidor, and Hawthorne. The case of the infinite clowns can teach us several things.

The infinite judgement has long been forgotten and yet, as I am about to demonstrate, it may be urgent to revive it for its critical and productive potential. An infinite judgement is neither analytic nor synthetic; it does not produce logical truths, nor true representations, but it establishes the genetic conditions of real objects and the concepts appropriate to them. It is through infinite judgements that we reach the principle of transcendental logic, in the depths of which all reality can (...) emerge in its material and sensible singularity, making possible all generalization and formal abstraction. (shrink)

According to one of Leibniz's theories of contingency a proposition is contingent if and only if it cannot be proved in a finite number of steps. It has been argued that this faces the Problem of Lucky Proof , namely that we could begin by analysing the concept ‘Peter’ by saying that ‘Peter is a denier of Christ and …’, thereby having proved the proposition ‘Peter denies Christ’ in a finite number of steps. It also faces a more general but (...) related problem that we dub the Problem of Guaranteed Proof . We argue that Leibniz has an answer to these problems since for him one has not proved that ‘Peter denies Christ’ unless one has also proved that ‘Peter’ is a consistent concept, an impossible task since it requires the full decomposition of the infinite concept ‘Peter’. We defend this view from objections found in the literature and maintain that for Leibniz all truths about created individual beings are contingent. (shrink)