Perceptual experiences seem to in some sense have singular contents. For example, a perceptual experience of a dog as fluffy seems to represent some particular dog as being fluffy. There are important phenomenological, intuitive, and semantic considerations for thinking that perceptual experiences represent singular contents, but there are also important phenomenological, epistemic, and metaphysical considerations for thinking that they do not. This paper proposes a two-tier picture of the content of singular perceptual experiences that is based on (...) phenomenal intentionality theories of intentionality combined with self-ascriptivism about derived representation, a combination of views that allows mental states to have two types of contents: phenomenal contents and derived contents. On the proposed picture, singular perceptual experiences represent singular phenomenal contents, which do not involve worldly objects, as well as singular derived contents, which do involve worldly objects. This picture accommodates and reconciles the considerations for and against thinking that perceptual experiences have singular contents. (shrink)

This paper is a new non-descriptivist defense of nonconceptualism based on a new interpretation of Kant’s metaphysics of concepts. We advance the following claim: What distinguishes non-conceptual from conceptual singular representations is the way partial representations of the object’s features are integrated into the whole representation of the object, while at the non-conceptual level, this integration takes the form of images of the object’s features that are stored and projected, at the conceptual level this integration takes the (...) form of the recognition that those features are properties of a same object, what Kant calls “synthetic unity of Aperception”. (shrink)

This essay develops the thesis that Frege’s notion of grasping does not refer to some special psychological relation between a subject and a proposition. Instead, the verb “to grasp” is a contextually defined technical term that, taken by itself, has no meaning. If that is right, then not only Frege’s resentment to the idea of grasping singular propositions is unfounded. The view that intentionality without representations is possible, championed by some advocates of the New Theory of Reference, is (...) groundless as well. (shrink)

This paper is a new non-descriptivist defense of non- conceptualism, based on a new interpretation of Kant’s metaphysics of concepts. We advance the following claim: What distinguishes non-conceptual from conceptual singular representations is the way partial representations of the object’s features are integrated into the whole representation of the object: while at the non-conceptual level this integration takes the form of images of the object’s features that are stored and projected, at the conceptual level this integration takes (...) the form of the recognition that those features are properties of a same object, what Kant calls “synthetic unity of Aperception”. (shrink)

This is a chapter from my introductory book *Perception* covering the representational view of experience. I use the Ramsey-Lewis method to define the theoretical term "experiential representation". I clarify and discuss various questions for representationalists, for instance, "how rich is the content of experience?" and "is the content of visual experience singular or general?" Finally, I address some objections to representationalism - in particular, that it cannot explain perceptual presence (John Campbell), and that it cannot explain the "laws of (...) appearance" (constraints on how things can appear). (shrink)

This paper argues in the first place that nominalists are right in insisting against ontological realists that semantic universality does not require commitment to universal entities. However, Ockham, in his zeal to get rid of Scotus’s universal entities, swept under the carpet the issue of universal representational content of genuinely universal symbols, conflating it with the mere indifference of the information content of non-distinctive singular representations. Buridan did come up with an abstractionist theory of the formation of genuinely (...) universal representational content to solve the resulting issues, however, the paper argues further, his solution is committed to attributing the sort of “aspectuality” to universal absolute concepts that his Ockhamist semantics denies to them. The conclusion of the paper suggests how Aquinas’s “moderate realism” can provide a consistent solution without the ontological extravaganza of ontological realists, without conflating the mere indifference of singular representation with genuine universality, and without having to deny aspectuality to our quidditative universal concepts formed by abstraction. (shrink)

The main goal of this dissertation is to offer both an interpretation to the theory of singular representations as presented by Leibniz in his writings from the 1680’s, as well as a hypothesis of a criticism made by Kant to what we take to be the cornerstones of such a theory. These cornerstones consist in (i) the Principle of Identity of Indiscernibles (ii) the Doctrine of the Complete Notion of the Individual Substance (iii) the Intensional Definitions of the (...) Truth Values. Once the writings in which (ii) and (iii) are presented only began to be published in the XIX century, we argue in favor of the plausibility of such a hypothesis by means of logical arguments, which intend to show that Kant could have deduced (ii) and (iii) from Leibniz’ commitment to (i) as well as to the existence of a parfaite représentation of ordinary objects in the divine understanding, and historical arguments, which intend to show that Kant could have had access to both (ii) and (iii) and even ascribed these to Leibniz by means of Meier’s Auszug aus der Vernunftlehre and Wolff’s Philosophia Rationalis sive Logica. We will add to these, also textual arguments in order to show that there is in Kant’s philosophy not only a critique to (i), but also to (ii) e (iii), as well as an interpretation of what this criticism consists in. (shrink)

One of the most pressing questions concerning singular demonstrative mental contents is what makes their content singular: that is to say, what makes it the case that individual objects are the representata of these mental states. Many philosophers have required sophisticated intellectual capacities for singular content to be possible, such as the possession of an elaborate scheme of space and time. A more recent reaction to this strategy proposes to account for singular content solely on the (...) basis of empirical models of visual processing. We believe both sides make good points, and offer an intermediate way of looking into singular content. Our suggestion is that singular content may be traced to psychological capacities to form flexible, abstract representations in the prefrontal cortex. This allows them to be sustained for increasingly longer periods of time and extrapolated beyond the context of perception, thus going beyond lowlevel sensory representations while also falling short of more sophisticated intellectual abilities. (shrink)

Almost any mainstream reading about the nature of Kant's 'content of cognition' in both non-conceptualist and conceptualist camps agree that 'singular representations' (sensible intuitions) are, at least in some weak sense, objectdependent because they supervene on a manifold of sensations that are given through the disposition of our sensibility and parallel thus the real and physical components of the world (cf. McDowell 1996, Allison 1983, Ginsborg 2008, Allais 2009). The relevant class of sensible intuitions should refer, as they (...) argue, only to empirical and not to pure ones. Kant's transcendental argument creates, however, no implications as to the metaphysics of properties. Neither does he consider the world to be consisted of sensory content simpliciter nor do sensations refer to objects per se. Instead, he provides an all-encompassing pattern for sensible intuitions of any kind through the representation of space as a cognitive map in that an object can be represented if spatial properties are attributed to it. Sensible intuitions of any kind could be referring, that is to say, and can be conceptualized if they are spatial. Consequently and unlike the contemporary philosophy of perception, Kant contrasts sensible intuitions and pure concepts of understanding 'altogether' against one single experience, from which the justification of objects should proceed. In other words, what stands at the core of exposing the content of cognition concerns not the phenomenological status and actuality of sensible intuitions in the sense of 'bits of experiential intake', but the logical structure of possibility of sensible intuitions of any (external or internal) causal background. The aim of this discussion is to clarify that Kant's transcendental idealism mutatis mutandis reviews multiple and diverse kinds of 'data of mind' and cognition in the background, without reducing the content of cognition to metaphysically determined referents as 'matters of fact' and to pure concepts of understanding. Sensible intuitions in the sense of content of cognition vary, most importantly, from unstructured and unjustifiable data of mind including (physical) contents of perception and stuff of mind and also from reflective and intellectual intuitions that are the cognates of the structured complex singular representations. Put it in simple terms, Kant advocates the thesis that 'facts' are objects for concepts if they are already well-founded trough the cognitive map of the representation of space. -/- . (shrink)

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

Fred Dretske?s (1988) account of the causal role of intentional mental states was widely criticized for missing the target: he explained why a type of intentional state causes the type of bodily motion it does rather than some other type, when what we wanted was an account of how the intentional properties of these states play a causal role in each singular causal relation with a token bodily motion. I argue that the non-reductive metaphysics that Dretske defends for his (...) account of behavior can be extended to the case of intentional states, and that this extension provides a way to show how intentional properties can play the causal role that we wanted explained. (shrink)

When fat people are depicted in popular media, we often take their behavior to be representative of all fat people. How one fat person acts becomes representative of a broader pattern of behavior that all fat people are presumed to share, shaping the way we understand fatness. This way of generalizing presents fatness as a singular experience, reducing fat people to a monolithic narrative that often reinforces anti-fat bias. How do we avoid this reduction? How can we responsibly depict (...) fat characters without perpetuating negative stereotypes about real fat people? Using the case of “Fat Thor” from Avengers: Endgame, I propose the beginnings of an account of responsible artistic agency which can be used to improve the ways that marginalized communities are depicted in art, with a particular focus on fat communities. Central to this account are two features: inclusion of and deference to members of the communities depicted from a variety of backgrounds throughout the production process, and mindfulness of the preexisting narrative web built around the communities depicted. I will use this discussion to highlight the need for a drastic shift in how we consider marginalized populations in art—in reimagining both who tells their stories, and what stories are told on their behalf. (shrink)

This paper provides an analysis of Rudolph Otto's understanding of the structures of human consciousness making possible the appropriation of revelation. Already in his dissertation on Luther's understanding of the Holy Spirit, Otto was preoccupied with how the " outer " of revelation could be united to these inner structures. Later, in his groundbreaking Idea of the Holy, Otto would explore the category of the numinous, an element of religious experience tied to the irrational element of the holy. This paper (...) first provides a brief account of Otto's account of the holy, especially its numinous, irrational elements. Second, the paper analyzes Otto's understanding of the structures of consciousness grounding the experience of the numinous and allowing the irrational element to be " schematized " by the rational element. Otto's exposition of these structures is heavily influenced by his reception of Kant's analysis of the two stems of human cognition, namely understanding and sensibility, and their possible relation to a common root, which Otto identified with what the mystics called the ground of the soul. Yet it is in Otto's reception of Kant's Critique of Judgment that all of these ideas find their completion, and it is here where we must look to understand the relation between the religious a priori and Otto's category of the numinous. Kant's aesthetic idea is a singular representation given in intuition; it is infinitely saturated and as such intimates the ideas of God, the soul, and the world as a whole. I show how Otto appropriates Kant's aesthetic idea and its relation to ideas of reason in order to make sense of how an empirically given revelation, for instance, an experience of the numinous, can connect with the inner structures of consciousness and thereby have the singular import that it does. (shrink)

We present a formal mechanical analysis using sweeping net methods to approximate surfacing singularities of saddle maps. By constructing densified sweeping subnets for individual vertices and integrating them, we create a comprehensive approximation of singularities. This approach utilizes geometric concepts, analytical methods, and theorems that demonstrate the robustness and stability of the nets under perturbations. Through detailed proofs and visualizations, we provide a new perspective on singularities and their approximations in analytic geometry.

According to an influential variety of the representational view of perceptual experience—the singular content view—the contents of perceptual experiences include singular propositions partly composed of the particular physical object a given experience is about or of. The singular content view faces well-known difficulties accommodating hallucinations; I maintain that there is also an analogue of Frege's puzzle that poses a significant problem for this view. In fact, I believe that this puzzle presents difficulties for the theory that are (...) unique to perception in that strategies that have been developed to respond to Frege's puzzle in the case of belief cannot be employed successfully in the case of perception. Ultimately, I maintain that this perceptual analogue of Frege's puzzle provides a compelling reason to reject the singular content view of perceptual experience. (shrink)

The article re-visits the different scholarly approaches to Hegel's end-of-art scenario, and then proposes a new reading whereby ending and finitude are presented as essential features of beautiful art. The first and most determinant of art's endings is the death of the Christly art object, not representations of Christ, but the actual death of (the son of) God himself as the last classical artwork. The death of God represents the last word in Greco-Roman art, the accomplishment of the beautiful (...) individuality and its failure to present the Absolute in a singular, naturally infected, lively, human (made) form. The ending of art brings about a new form of the sacred: the representational language of revelatory religion. The ongoing production of modern artistic forms is a feature of actuality ("Wirklichkeit") and as such is condemned to an infinite approximation of what has been. Such actuality nonetheless "ends" in the ironic discourse of contemporary artistic expression, which Hegel qualifies as a "Vereitelung". The final realization of the beautiful art form, as a human-informed singularity embodying absolute content, may well be the Encyclopedia of Philosophical Sciences, whose performative iteration takes place in the form of "worship" practiced in the modern, state university. (shrink)

Engrams—physical memory traces resulting from specific experiences—are the central posits of modern memory science. In this paper, I examine engrams through the lens of the theory of mental files. Integrating evidence from a variety of research programs, I argue that engrams exhibit the core functional properties of mental files. I characterize them as discrete informational structures, formed upon individual experiences of events and causally involved in their subsequent recall. Engrams are plausibly structurally complex in a file-like way, consisting of a (...) stable hippocampal index, which may function as an atomic pointer-like component, and a distributed cortical representation of an event’s properties. As such, they afford transmission of content and referential stability during potential content change. Their deployment is constitutive of the capacity for singular reference in episodically remembering particular previously experienced events. This emerging picture of engrams should engender reasonable optimism about the prospects of causal-representational theories of memory. (shrink)

Book synopsis: New work on a hot topic by an outstanding team of authors At the intersection of several central areas of philosophy It is the linguistic job of singular terms to pick out the objects that we think or talk about. But what about singular terms that seem to fail to designate anything, because the objects they refer to don't exist? We can employ these terms in meaningful thought and talk, which suggests that they are succeeding in (...) fulfilling their representational task. A team of leading experts presents new essays on the much-debated problem of empty reference and thought. In the 1960s and 1970s Keith Donnellan, David Kaplan, Saul Kripke and Hilary Putnam initiated a revolution in the then standard conception of reference—a concept at the core of philosophical inquiry. The repercussions of the revolution, particularly felt in metaphysics and epistemology, were soon refined by other influential writers such as Tyler Burge, Gareth Evans, and John Perry. They argued that some linguistic and mental representations have contents individuated by what they are about—by ordinary referents of expressions such as proper names, indexicals, definite descriptions and common nouns, i.e. by planets, people or natural kinds. The view was at odds with a central philosophical presumption at that time: that cognitive and linguistic access to objective reality is indirect and accidental, mediated by general descriptive characterizations, the only constitutive semantic feature of the expressions; hence its ontological and epistemological repercussions. A turning-point in the debate about how linguistic and mental representation reach external contents concerned the nature of empty mental and linguistic representations, framed by means of the very same expressions crucially invoked in the Donnellan-Kaplan-Kripke-Putnam arguments. The papers in this volume address different aspects of reference and thought about the non-existent. (shrink)

I like the view that the fundamental facts are logically simple, not complex. However, some universal generalizations and negations may appear fundamental, because they cannot be explained by logically simple facts about particulars. I explore a natural reply: those universal generalizations and negations are true because certain logically simple facts—call them —are the fundamental facts. I argue that this solution is only available given some metaphysical frameworks, some conceptions of metaphysical explanation and fundamentality. It requires a ‘fitting’ framework, according to (...) which metaphysical theories explain the aptness of representations in terms of how things are fundamentally. Fitting frameworks conceive of the fundamental facts as those that are metaphysically ‘real’; call them the ‘facts-in-reality’. Moreover, we must take as primary a plural notion of the facts-in-reality, not the singular notion of a fact-in-reality. By contrast, a metaphysics that grounds facts is incompatible with my strategy for keeping the fundamental facts logically simple. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (shrink)

There are passages in Kant’s writings according to which empirical intuitions have to be (a) singular, (b) object-dependent, and (c) immediate. It has also been argued that empirical intuitions (d) are not truth-apt, and (e) need to provide the subject with a proof of the possibility of the cognized object. Having relied on one or another of the a-e constraints, the naïve realist readers of Kant have argued that it is not possible for empirical intuitions to be representations. (...) Instead they have argued for a relationalist reading of empirical intuitions in terms of an acquaintance relation between the subject and the intuited object. -/- For the sake of argument, I will grant the naïve realist reader of Kant that empirical intuitions should satisfy all the a-e constraints. Nevertheless, by incorporating these constraints, one by one, into a representationalist theory of empirical intuitions, I will show that not only doesn’t a naïve realist reading of empirical intuitions follow, but also that the naïve realist has hastily overlooked a range of perfectly representationalist readings of intuitions available to Kant and his representationalist allies. On the positive side, I will argue that there is an extra constraint on intuitions—i.e., that givenness does not require presence to consciousness—that directly goes against any naïve realist account of intuitions. (shrink)

There are many bodies, neurons, interacting in a brain. For bodies and interactions to produce consciousness might depend on specific matter and matter interactions, such as specifically those of the neural grey matter and voltages of the brain, or abstract representations and information patterns, such as just the neural firing patterns or those that can be simulated on GPUs. My flipbook thought experiment, elaborated on later in this work, reduces the latter possibility to absurdity. We're able to feel complex (...) emotional experiences at the same time, and observe many concurrent phenomena, including, for example, the visual image before our eyes. This singular observation might be an illusion, or might be a literal singularization of phenomena into a single observer. My physics explanation for how this singularization might happen, elaborated on later in this work, is evidenced by a measured phenomenon in standard physics. Thus, the best explanation for consciousness remaining will be specific physical matter and modes of interactions (via biological neurons and reactions) and singularization (via my hypothesized physics theory, lacking any other). Then one more point is made about how assuming consciousness as a fundamental property of the universe leads to a new answer to the mystery of cosmogenesis. That answer is specified. Finally, all of this together paints a strongly evidenced theory of consciousness, as well as cosmogenesis, whose alternatives have much less justification. (shrink)

Formal relationism in the philosophy of mind is the thesis that folk psychological states should be individuated, at least partially, in terms of the purely formal inference-licensing relations between underlying mental representations. It's supposed to provide a Russellian alternative to a Fregean theory of propositional attitudes. I argue that there's an inconsistency between the motivation for formal relationism and the use to which it's put in defense of Russellian propositions. Furthermore, I argue that formal relationism is committed to epiphenomenalism (...) about singular mental content. (shrink)

Representationalists hold that perceptual experience is a conscious representational state with content, something which is accurate or inaccurate in certain conditions. The most common version of Representationalism takes perceptual content to be singular in the object-place and otherwise consisting of attribution of properties (Singularism/Attributionism). Schellenberg has recently developed a version on which perceptual content is singular even in the property-place in containing a de re mode of presentation of a property-instance (Particularism). In this paper, I show that Particularism (...) faces a version of the problem of the Unity of Perceptual Content. Namely, its supporters haven’t told us how objects can be bound together with property-instances into a content such that it represents them and has accuracy-conditions. Furthermore, I argue that Particularists face an in-principle obstacle in solving it. In contrast, Attributionists can solve the problem and that establishes their view as the only game in town. (shrink)

It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion of logical (...) extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (shrink)

Donkey sentences have existential and universal readings, but they are not often perceived as ambiguous. We extend the pragmatic theory of nonmaximality in plural definites by Križ (2016) to explain how context disambiguates donkey sentences. We propose that the denotations of such sentences produce truth-value gaps — in certain scenarios the sentences are neither true nor false — and demonstrate that Križ’s pragmatic theory fills these gaps to generate the standard judgments of the literature. Building on Muskens’s (1996) Compositional Discourse (...) Representation Theory and on ideas from supervaluation semantics, the semantic analysis defines a general schema for quantification that delivers the required truth-value gaps. Given the independently motivated pragmatic theory of Križ 2016, we argue that mixed readings of donkey sentences require neither plural information states, contra Brasoveanu 2008, 2010, nor error states, contra Champollion 2016, nor singular donkey pronouns with plural referents, contra Krifka 1996, Yoon 1996. We also show that the pragmatic account improves over alternatives like Kanazawa 1994 that attribute the readings of donkey sentences to the monotonicity properties of the embedding quantifier. (shrink)

In its hegemonic definition, biopolitical governmentality is characterised by a seemingly infinite capacity of expansion, susceptible to colonise the landscape and timescape of the living present in the name of capitalistic productivity. The main trait of biopower is its normative, legal and political plasticity, allowing it to reappropriate critiques and resistances by appealing to bioethical efficacy and biological accuracy. Under these circumstances, how can we invent rebellious forms-of-life and alternative temporalities escaping biopolitical normativity? In this essay, I interrogate the theoretical (...) presuppositions of biopolitical rationality. I provide a deconstruction of the conceptual and temporal structures upholding the notion of biopolitics, in view of laying the ground for new forms of resistance. The articulation between life and power has a long philosophical history, which has been largely ignored by social theorists and political thinkers using biopolitics as an interpretative model. I re-inscribe this model within the tradition of critical materialism, by articulating Foucault’s ‘critical ontology’ to recent philosophical works on biological plasticity (Malabou). In these discourses, the logic of biopower depends on a representation of life – ‘the living’ – as living present. Biopower finds itself anchored in the authority of the present, that is to say, of being-as-presence (ontology); it sustains presentist definitions of life and materiality, be it under the form of a ‘plastic’ ontology. By drawing on Derrida’s notions of ‘spectrality’ and ‘life-death’ and Francesco Vitale’s work on ‘biodeconstruction’, I deconstruct these discourses on life and materiality and attempt to dissociate them from their ontological grounding, in order to suggest new paths of resistance to biopower. In particular, I follow the tracks of “the monster” in the work of Foucault, Derrida and Malabou. Foucault tells us that the monster is a singular figure, parasitic and subversive, beckoning a life beyond life, at once organic and non-organic, located at the limit between the normal and the exceptional, and exceeding the scope of biopolitical normativity in both theoretical and practical terms. It exists at the intersection of what Foucault names “the symbolics of blood” and “the analytics of sex”. As such, it materialises a self-transformative dimension of the living which remains, I argue, inadequate to Malabou’s representation of plasticity. The monstrous is a self-deconstructive motif calling for another biopolitical rationality, before or beyond ontological reductions or reconstructions. (shrink)

Two objections are raised against Oliver and Smiley’s analysis of the collective–distributive opposition in their 2016 book: They take it as a basic premise that the collective reading of ‘baked a cake’ corresponds to a predicate different from its distributive reading, and the same applies to all predicate expressions that admit both a collective and a distributive interpretation. At the same time, however, they argue that inflectional forms of the same lexeme reveal a univocity that should be preserved in a (...) formal representation of English. These two assumptions sit uneasily. In developing their analysis, Oliver and Smiley come to the conclusion that even a singular predication such as ‘Tom baked a cake’ must be regarded as ambiguous between a collective and a distributive reading. This is so artificial that it hardly makes sense, and yet there seems to be no way out of the difficulty unless we are prepared to give up the basic premise just mentioned. (shrink)

Propositionalism is the view that all intentional states are propositional states, which are states with a propositional content, while objectualism is the view that at least some intentional states are objectual states, which are states with objectual contents, such as objects, properties, and kinds. This paper argues that there are two distinct ways of understanding propositionalism and objectualism: (1) as views about the deep nature of the contents of intentional states, and (2) as views about the superficial character of the (...) contents of intentional states. I argue that we should understand the views in the second way. I also argue that the propositionalism debate is fairly independent from debates over the deep nature of intentionality, and that this has implications for arguments for propositionalism and objectualism from claims about the nature of intentional content. I close with a short discussion of how related points apply to the debate over singular content. (shrink)

The purpose of this article is to examine the objective side of subjectivity formation through music. I attempt to show how music is a way to configure subjectivity in its interiority, but in a way that it can be shared between other individual subjectivities. Music has an objective structure, but this structure is the temporal and sonorous interiority of subjectivity. It has as its objective manifestation and consequence the feelings and emotions. These feelings are subjective, and in the level of (...) subjective Geist they are related to intuition. Hegel believes that such intuition cannot be properly communicated, due to its exclusive access to the individual subject himself. Despite that, music is an art, and it takes part in the level of absolute Geist. That means that music is the connection between the objective and subjective sides of Geist, being a product of social relations, including the sharing, experience and recognition of subjective operations by the participants in society as something in common. Art is related to intuition but it is not intuition itself, nor it is reduced to the capacity of intuition. All three capacities of the subjective Geist in the theoretical Geist (namely intuition, representation and thinking) can be part of the relationship between art and the individual perspective.However, the link between art and intuition is an analogy between the subjective Geist and the absolute Geist, considering that art is a level of manifestation of social self-consciousness where the people and the social group have not yet become conscious of its content in its manifestation. The exposition of the ideal content of social relations is manifested through absolute Geist, beginning with its sensible manifestation. After this process, it is signified through a practice related to representation, and finally it is related to a conceptually and linguistically mediated practice, philosophy. These products cannot be a consequence of a mere subjective connections, but must be (as part of absolute Geist) a consequence of the objective relation between individuals in its subjective manifestations. Furthermore, subjective capacities are a condition without which the development of the absolute Geist is not possible. At the same time, it is not possible that subjective Geist’s capacities can be fully realized without social relations. Science is not a product of an individual-solipsistic relationship with the environment, but a product of a social relations, including language, shared experiences and shared ways of comprehension, such as the common way to feel and receive the environment in a subjective level discussed below. I divide this exposition into three parts: (1) music and subjectivity, where I deal with the relation between body vibration, time, sound and the formal interiority of the listener/musical subject, analyzing the form of music in its subjective side (the relation to the listener); (2) music and content, where I examine the content generated by music as being the process of formation itself (i.e. the process of given form to the interiority of subjectivity through sounds becomes its own content, namely, the feelings); and (3) music and words, where I scrutinize the relationship between music and words’ capacities to make reference and to have content, considering the connection between pure music and lyrics, and between music and poetry as singular forms of art. I conclude with the idea that music has a specific role in Hegel’s system, which is to bring to light and develop absolute Geist’s (understood as the objectivation and formation of a social and cultural subjectivity) internal aesthetic form. (shrink)

What is history about? This Element shows that answers centred on the keyword 'past events' are incomplete, even if they are not simply wrong. Interweaving theoretical and historical perspectives, it provides an abstract overview of the thematic plurality that characterizes contemporary academic historiography. The reflection on different sorts of pasts that can be at focus in historical research and writing encompasses events as well as non-events, especially recursive social structures and cultural webs. Some consequences of such plurality for discussions concerning (...) historical methodology, explanation, exemplification, and representation are also outlined. The basic message, reinforced throughout, is that the great relevance of non-event-centred approaches should prompt us to talk more about “histories” in the plural and less about “history” in the singular. (shrink)

Why interdisciplinary research in AI is so important, according to Jurassic Park. -/- “Your scientists were so preoccupied with whether or not they could, they didn’t stop to think if they should.” -/- I think this quote resonates with us now more than ever, especially in the world of technological development. The writers of Jurassic Park were years ahead of their time with this powerful quote. -/- As we build new technology, and we push on to see what can actually (...) be achieved there is an undertone of sales to whatever we build. The end product must be sold somewhere and to someone. This can derail any good intentions, just as building a resort full of dinosaurs was sold as a fun attraction, we see later in the film that it became a resort of terror. -/- In the field of AI we are certainly late to the party with ethics and regulation. Indeed, even existing modelling protocols have been, in many cases, circumvented or potentially ignored. This has led to a widening of the gap in the interdisciplinary field of AI. This is compounded by pop culture representations of AI and the Ethicist’s potential lack of knowledge surrounding technical progression in the field of AI. There are now seemingly two separate branches that ought to be in sync. The first branch is a group of Philosophers led by the Author of Superintelligence, Nick Bostrom, who believe that there is a singularity where AI takes over the world and starts to kill off humans. The second branch is the Technical Cohort who are led by companies such as Google and Deepmind. The remit of these developers is to see what can be developed and produced. Ultimately a separate sales team will determine what products can be sold. -/- We have seen multiple failures of AI due to lack of interdisciplinary discourse. Some cases include misallocated or cut off financial support and healthcare. This indicates the prevalence of issues that can grow and become ever more complex. -/- So, we have to ask ourselves two questions: One, do the Philosophers have a point? Two, does that point refer to humans programming AI in such a way that the destruction of the human race is its optimal aim in order to create a better future world? -/- Is the development of AI that different to an island of genetically engineered Dinosaurs? -/- The only solution, in my view, is interdisciplinary discourse. (shrink)

In Against the Day, Pynchon is obsessed with twoness, double worlds, as well as dual realities, and like Deleuze’s concept of repetition, these duplications and twinships are not merely repetition of the same, rather they allow for creativity, reinvention, and becoming. Pynchon’s duplication of fictional and spectral characters intends to critique the notion of identity as does Deleuzian concept of repetition. Not attached to the representational concept of identity as the recurrence of the same, Pynchon’s duplications decenter the transcendental concept (...) in favor of a perpetual becoming and reproduces difference and singularity. Like Deleuze, Pynchon eschews an identity that is always guaranteed, and shows that the repetition of an object or a subject is not the recurrence of the original self-identical object or person. Moreover, Iceland spar, the mystifying calcite, with its doubling effect provides the reader with a view of a world beyond the ordinary, actual world, which is quite similar to what Pynchon’s novel does per se. (shrink)

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)

The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The invariance to the axiom of (...) choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying their unification. Its deformation is representable correspondingly as gravitation in the deformed pseudo-Riemannian space of general relativity and the entanglement of two or more quantum systems. The standard model studies a single quantum system and thus privileges a single reference frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the standard model. As the standard model refers to a single quantum system, it is necessarily linear and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the initial position of a privileged reference frame as the corresponding breaking of the symmetry. The standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the “Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the “Big Bang” with the observed nonlinearity of the further expansion of the universe described very well by general relativity. Quantum information links the standard model and general relativity in another way by mediation of entanglement. The linearity and absoluteness of the former and the nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same whole divided into parts entangled in general. (shrink)

This paper is a new defense of the view that visual hallucinations lack content. The claim is that visual hallucinations are illusory not because their content is nonveridical, but rather because they seem to represent when they fail to represent anything in the first place. What accounts for the phenomenal character of visual experiences is not the content itself (content-representationalism), but rather the vehicle of content (vehicle-representationalism), that is, not the properties represented by visual experience, but rather the relational properties (...) of experience (or of the brain) of representing singular contents, namely particular instantiations of properties. I argue that the Russellian particular-involving proposition is the only appropriate model for the representational content of visual experience and hence that visual hallucinations are just like failed demonstrations. (shrink)

Three-dimensional material models of molecules were used throughout the 19th century, either functioning as a mere representation or opening new epistemic horizons. In this paper, two case studies are examined: the 1875 models of van ‘t Hoff and the 1890 models of Sachse. What is unique in these two case studies is that both models were not only folded, but were also conceptualized mathematically. When viewed in light of the chemical research of that period not only were both of these (...) aspects, considered in their singularity, exceptional, but also taken together may be thought of as a subversion of the way molecules were chemically investigated in the 19th century. Concentrating on this unique shared characteristic in the models of van ‘t Hoff and the models of Sachse, this paper deals with the shifts and displacements between their operational methods and existence: between their technical and epistemological aspects and the fact that they were folded, which was forgotten or simply ignored in the subsequent development of chemistry. (shrink)

Architecture often relies on mathematical models, if only to anticipate the physical behavior of structures. Accordingly, mathematical modeling serves to find an optimal form given certain constraints, constraints themselves translated into a language which must be homogeneous to that of the model in order for resolution to be possible. Traditional modeling tied to design and architecture thus appears linked to a topdown vision of creation, of the modernist, voluntarist and uniformly normative type, because usually (mono)functionalist. One available instrument of calculation/representation/prescription (...) orders this conception of architecture: indeed the search for an optimal solution through mathematical calculation of a model itself mathematical, thus homogeneous and simple, is only possible when one or two functions or functional constraints are formulated, never more, and this, on a global level, therefore starting from a unique and homogenizing viewpoint. It is essential to grasp that, even applied to material and its properties or towards a particular esthetic or functional dimension, this viewpoint is thus abstractive and generalizing: disregarding singularity of context, insertion and relationship to the environment or local, social behavior. It leaves aside functional specificity and heterogeneousness – re-contextualized each time – of functions that the object or edifice are required to fulfill and optimize under diverse constraints, in their different parts. The computational turning point today’s digital design and computational architecture embody modifies these instrumental, original prescriptions, rendering them more flexible. Perhaps in light of this turnabout we should retrospectively interpret 20th century calls for modernism, functionalism and even biomorphism as being just as many ex post rationalizations in respect to techniques of strongly prescriptive modeling since our only instrument is a monolithic language, and so being, incites a top-down conception, (naturally weakly reactive to contexts), including forms whose overall appearance resembles in fine a living form. In order to liberate oneself from this and despite everything, emerge as its initiators, one has constructed from ideology and philosophy (of object, habitat, the urban) ex post, even while it is the instrument of modeling and conception that largely determines, normalizes and dictates ex ante, the possibilities and limitations of the creation of forms and living experiments4 in a given time. (shrink)

En The Varieties of Reference, Evans sostiene que el contenido perceptual posee una naturaleza no conceptual. Precisamente, los vínculos informacionales entre sujeto y objeto habilitan el pensamiento singular, al permitir la localización del objeto en un entorno egocéntrico. Anclados en algunos casos en estos vínculos, los pensamientos singulares contienen Ideas adecuadas del objeto, dependientes de una determinada clasificación del mismo. Nada en el contenido perceptual equivale a este recorte conceptual del objeto en el pensamiento. Sostendré entonces la necesidad de (...) introducir la idea de una representación no conceptual de cosa que recortaría, de dicho contenido, un punto de anclaje para la representación informacional. In The Varieties of Reference, Evans claims that perceptual content has a non-conceptual nature. Concretely, the informational links between subject and object allow singular thought by permitting the localization of the object in an egocentric space. Anchored in some cases in these links, singular thoughts contain adequate Ideas of the object that depend on a certain classification of it. Nothing in the perceptual content corresponds to this conceptual cut of the object in thought. I will therefore underline the need to introduce the idea of a non-conceptual representation of thing that will cut, in that content, an anchoring point for the informational representation. (shrink)

So-called mass nouns, however precisely they are defined, are in any case a subset of non-count nouns. Count nouns are either singular or plural; to be non-count is hence to be neither singular nor plural. This is not, as such, a metaphysically significant contrast: 'pieces of furniture' is plural whereas 'furniture' itself is non-count. This contrast is simply between 'the many / few' and 'the much / little' - between counting and measuring. However not all non-count nouns are, (...) like 'furniture', semantically atomic - 'wine' and 'water' are not. And here there are serious difficulties in the assignment of a range of values for variables, in a formal representation of quantified sentences involving such non-atomic non-count nouns. (shrink)

This research essay was published in the monograph dedicated to the first major exhibition dedicated to photography and drawings by theAkbar Padamsee in India after his demise early 2022 at the age of 91. “Searching for the present, where?...” is drawn from The Guild and some important private collections. The exhibition is a tribute to Padamsee’s commendable contribution to the Indian art. This is also the first time the photographs and drawings spanning from over a decade are contextualised in an (...) exhibition form. Padamsee’s previous exhibition of photographs at The Guild was in 2006, titled, Akbar Padamsee, Photographs 2004-2006. This exhibition celebrates Padamsee’s cognitive pondering of body as form. Curator Srajana Kaikini delicately brings in art historical and philosophical discourses around human form and representation while delving into varied dimensions of artist’s practice. “These series of drawings and photographs speak about the body as a place of being and becoming. These are figurations, subjects set in motion. In this world view of the self, perhaps social signifiers like clothes, location, context and thinking of the body singularly may be perceived superfluous. Embodiment of the self, here, is presupposed. The interest is, therefore, to look for when and where these embodiments become present to us. While some drawings bring to us glimpses from other selves - lives enmeshed in sanchaari bhaavas (fleeting emotions), the photographic images speak in their own language trying to grow from the moment captured into new kinds of beings, creating their own sthaayi bhaavas (foundational emotions). They are not so much abstract as they are intentional – they need us to speak to them, for them to speak to us.” Excerpt from the Curatorial note by Srajana Kaikini. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

The concept of universal in Aristotle’s philosophy has several aspects. 1) Universal and plurality Aristotle posits universal (καθόλου) versus particular (καθ᾿ ἕκαστον) each covering a range of elements: some elements are universal while others are particulars. Aristotle defines universal as ‘that which by nature is predicated (κατηγορεῖσθαι) of many subjects’ and particular as ‘that which is not’ so. (OI ., I, 7, 17a38-b1) The plurality of possible subjects of universal is what Aristotle insists on. The inclusion of the notion of (...) ‘plurality’ in the definition of universal might make us expect to have ‘singularity’ in the definition of particular. So, when Aristotle says that universal is that which is naturally predicable of many subjects, we expect him to define the particular as ‘that which is predicable of one subject only.’ Nonetheless, Aristotle does not and indeed cannot define it this way. We cannot find a text in which he defines particular as such simply because particulars are not predicable of any subject unless we regard their predication of themselves a predication, which Aristotle does not, at least in a genuine sense. Thus, he defines a particular only negatively. Hence, the capability of predication of a plurality is indeed the capability of predication itself because the particular cannot be predicated of anything. A particular is that which cannot be predicated of anything (or: of anything else, if saying of a thing of itself is to be considered as predication). It is ‘numerically one’ and what of which the universal is predicated (Met., B, 999b34-1000a1). Those that cannot be predicated of anything, or particulars, are of two kinds: primary substances and individual accidents. Besides Categories we can hardly find a text where Aristotle discusses individual accidents maybe because they are of much less importance for him compared with substances. However, substances are what he mentions repeatedly so that we can confine particulars to substances. In fact, it is substance that Aristotle considers so repeatedly as what cannot be predicated. As the main particulars and individuals, substances are posited as the main things that are not universal. The closeness of the two concepts of ‘substance’ and ‘unpredicability’ is to the extent that he ignores individual accidents and makes these concepts equal and as the opposite of universal: ‘what is not predicated of a subject is said a substance (οὐσία λέγετα τὸ μὴ καθ᾿ ὑποκειμένου) but what is always said of some subject is called a universal.’ (Met., Z, 1038b15-16. cf. Met., B, 1003a7-9) Therefore, since particulars cannot be predicated of any subject and, thus, every predication is necessarily a predication of a plurality of subjects, the inclusion of ‘plurality’ in the definition of universal is either i) in the sense of ‘representation’ or it must be regarded as ii) an unnecessary addition mentioned just for clarification or iii) only for avoiding cases where something is predicated of itself. By the first we mean this: though a substance is not said of anything, it represents some one thing and there is some one thing that is that substance. A universal, on the other hand, can represent a plurality of things. There is, however, a third possibility that has no essential difference with the sense of representation. Aristotle might have ‘arbitrary predication’ in mind when he suses ‘plurality’ in the definition of universal: while a particular can be the arbitrary predicate of just one thing, a universal can be predicated, both really and arbitrarily, of many things. Whatever Aristotle’s intention was, what is important for our investigation is this: Aristotle uses the notion of plurality in the definition of universal in spite of the fact that it is not necessary. What this implies is that this notion is so important for Aristotle that albeit every predictability is a predictability of a possible plurality, he adds the notion of plurality. What makes this notion important, I believe, is that he has something like a class in mind when he defines a universal because the notion of plurality is indistinguishable from a class. 2) Universal and whole; particular and part In Aristotle, the concepts of universal and whole are so close: ‘That which is true of a whole class and is said to hold good as a whole (which implies that it is a kind of whole) is true of a whole in the sense that it contains many things by being predicated of each, and that each and all of them, e.g. man, horse, god, are one because all are living things (τὸ μὲν γὰρ καθόλου καὶ τὸ ὃλως λεγόμενον ὡς πολλὰ περιέχον τῷ κατηγορεῖσθαι καθ’ ἑκάστου καὶ ἓν ἃπαντα εἶναι ὡς ἑκαστον, ...). Phil Corkum points to Aristotle’s distinction between quantitative and integral wholes in Met., 5, 26, 1023b26-33 where a quantitative whole is called homoiomerous, as the sum of animal while an integral whole, e.g. a house, is called heteromerous. He links the notion of homoiomerous to the notion of indivisibility of individuals (in 1b6-9 and 3b10-18) and indivisibility of universals. He believes that in PrA., I, 4, 25b32-26a2 it is the transitivity of mereological containment that is discussed. 3) Universal is common between instances Universal is common (κοινόν) between all the plurality of subjects it can be predicated of because what belongs to more than one thing must be common between them. (Met., Z, 1038b10-12) In the Same way, what is common cannot be a particular and, thus, a substance. (Met., Z, 1040b23-24) An individual or substance is a ‘this’ and a ‘this’ cannot be what common indicates simply because it is here in ‘this’ and can be nowhere else while common must be common between several things. In fact, what can be indicated by a common is indeed a ‘such.’ (Met., B, 1003a7-9) 4) Universal is the same in its instances We have a universal i) in all of its instances and ii) in the same way (ταὐτὸ ἐπὶ πὰντων). (Met, Γ, 1005a9-10) While the first point is evident (otherwise how could it be their universal?), the second point might seem not only ambiguous but the cause of many problems. For Aristotle, therefore, a universal must be ‘one’ in number and not many. This numerically one universal is the very universal for all its instances. It is the same universal that is predicated on each of its instances. This sameness is not, however, a mere homonymous sameness or the sameness of a homonymous word. All these three points, namely oneness, sameness and rejection of mere homonymous sameness are asserted in Aristotle’s own words τι ἕν καὶ τὸ αὐτὸ ἐπὶ πλειόνων μη ὁμώνυμον. (PsA., A, 11, 77a8-9) This non-homonymous unity is asserted also in PsA., A, 24, 85b15-16. 5) Universal as predicate Contrary to substance that cannot be a predicate, universal is what cannot be prevented from being in the place of predicate. Therefore, Aristotle distinguishes universal from subject because while the latter must necessarily be capable of being a predicate, though it might take the position of subject as well, the latter does not necessarily have such a capability especially when it is a this because it cannot be a predicate in such a case: ‘For the subject and universal differ in being or not being a ‘this’; like man and body and soul are the subject of accidents while the accident is something like musical or white.’ (Met., Θ, 1049a27-30) This indicates that a universal is basically different from subject and although it can be posited in the place of subject, it is the position of predicate that is its position as a universal. In Metaphysics, Z, 13, Aristotle asserts that ‘no universal can be substance.’ The same is asserted in Met., I, 1053b16-17 cf. 1060b21. As James H. Lesher points out, Aristotle’s position is that ‘nothing predicated universally is a substance.’ 6) Universal in substance In Met., 10388b8-9 Aristotle says that no universal is a substance. While a universal cannot be a substance in the way essence (to ti en einai) is, it is, Aristotle asserts, ‘in’ it (ἐν τούτῳ δὲ ἐνυπάρχειν) (Met., Ζ, 1038b16-18). Aristotle’s examples are: animal in man and horse. A universal is ‘in’ the thing it is its universal. But in what sense a universal can be in a thing? It cannot be in it as ‘in a subject’, which is denied in Categories for secondary substances. If we check the senses of being in, we can find some other senses of ‘being in’ some of which are compatible with this sense of ‘being in.’ Michael J. Loux believes that contrary to his earlier works like Peri Ideaon and Organon in which the immanence of universals signals a reproduction of the platonic two worlds picture, in his later works like Physics and Metaphysics, when Aristotle tells us that universals are in particulars he means that they are ‘components of or ingredients in sensible particulars.’ In Metaphysics (Δ, 1014b3-9) Aristotle compares elements with universals and call them ‘the most universal things because elements are present either in all or in many things. 7) Logos is of universal Not only universals have logos (Met., Z, 1038b18-19) but ‘Every logos and every science is of universals and not of particulars.’ (Met., K, 1059b25-26) The reason is that they are the same: the logos of the unjiversal ‘circle’ is nothing but ‘being circle’ and the logos of the universal ‘soul’ is ‘being soul.’ (Met., Z, 1035b33-1036a2) The same is said about definition. (Met, Z, 1036a27-29) 8) Universal: in the soul Contrasting individuals, universals are in the soul (So., 3, 5, 417b22-23; cf. PsA., B, 19, 100a6-7). Aristotle also says that the form, i.e. the essence, of the artwork is in the soul. (met., Z, 1032a32-b2) Moreover, as Michael J. Loux points out, ‘the Peri Ideon tells us that we need universals to serve as the objects of noetic acts.’ 9) Universal: not beside individual In spite of the fact that demonstration creates the opinion that demonstrating is based on the existence of universals as existing among the existing things, they do not have existence besides individuals (PsA., A, 24, 85a31-35; Met, Λ, 1071a19-23). Aristotle believes that universals of a P-series (B203, 71) are not παρὰ τὰ εἴδη: 999a6ff. Also check De Anima, II, 3, 414b20-25 10) Primary or commensurate universal Aristotle distinguishes ‘πρῶτον καθόλού’ (PsA., B, 17, 99a33-35) literally meaning ‘primary universal’ but mostly, and truly, translated as commensurate universal. While a universal merely ‘μὴ ἀντιςτρέφει,’ a primary universal ‘ᾧ ἓκαςτον μὲν μὴ ἀντιςτρέφει’ (PsA., B, 17, 99a33-35). Aristotle mentions three conditions for a commensurate universal. It is an attribute that i) belongs to every instance of its subject (without exception!!!), and this belonging is ii) essentially and iii) qua that subject itself (ᾗ αύτό). (PsA., A, 4, 73b26-28) However, he insists that the second and the third conditions are indeed the same. (PsA., A, 4, 73b28-30) The first condition he paraphrases as ‘to belong to any random instance of that subject’ and the second and the third as ‘when the subject is the first thing to which it can be shown to belong.’ (PsA., A, 4, 73b32-74a3) Aristotle’s example is ‘the equality of its angles to two right angles’. This attribute is not a commensurate universal of figure due to the first condition: it cannot be demonstrated of any figure. Nonetheless, though it can be demonstrated of every isosceles because every isosceles has angles equal to two right angles, it is not a commensurate universal of isosceles due to the other conditions: it is not predicated of isosceles qua isosceles but qua triangle. These conditions seem to be like regulators: they organize everything to match to the right group. The method of finding commensurate universal is like test and error method based on elimination: you must eliminate each of the higher or lower universals and check if the attribute remains or not. The commensurate universal is that which remains in between eliminated universals. (cf. PsA., A, 5, 74a37-b4) Brad Inwoodpresents an understanding of commensurate universal that is different from what I have understood and, thus, must be checked: ‘These universals are propositions in which, for example, ‘all A are B’ is true and which are still true universal statements if converted: ‘all B are A’ is also true.’ -/- . (shrink)

The Husserlian concept of intersubjectivity has been criticized for the fact that it belongs exclusively to a philosophy of representation and to a solipsistic consciousness. In this conceptual framework, the other (ego) appears to be constituted by a singular ego through the synthesis of the series of its appearances (perceptive or imaginative representations) and by extrapolation (transposition) of its own “sphere of originality”. For this theory of constitution seemed to be essentially related to the concept of objective representation (...) that post-Husserlian phenomenologists have criticized and eventually replaced with another, in which affectivity is supposed to open the way to otherness, as we can see in Heidegger, Levinas, Merleau-Ponty, Michel Henry or Jacques Derrida. Our hypothesis is that the difficulty does not regard the theory of constitution, but the fact that the other and the community that he forms with me and with many others are thought only in terms of representation. Even those who discharged the “abstract” objective representation of Husserl’s function and replaced it with “affectivity” were not finally able to overpass the representational framework, because the other has always been for me (and vice-versa, I have been for him) only a “picture” (no matter whether representative or “affective”), something which simply “stands” before my eyes. But this is certainly a reductive way of understanding the relation between the I and the other. If we focus our attention on the phenomenon of community and not on some interpretations or simplifications of it, we realize that it is not sufficient that objective representation or affectivity or any other faculty constitute or disclose the other for the I (even if that is a necessary starting point). As a multilayered concept, “intersubjectivity”, in Husserl’s sense, is a system of transitions from mere appearance to transcendence, from passivity to activity, from cognitive and affective representation to volition and action. As soon as we see the relation between the I and the other as active, as an influence or intrusion of one consciousness in another, as an intention to “move” the other, to determine him to assume or to begin an action (a real one, effected in real life), the concept of intersubjectivity changes drastically, even though the “representation” of the other before the I and of the I in the eyes of the other remains a necessary interface. Accordingly, constitutive phenomenology has to take into consideration volition, action and communication not simply as extensions of the constitution of the thing. A reform of the theory of constitution, or rather its enlargement, to encompass this new type of “objectivity” (praxis) which would thus offer an adequate conceptual framework is strongly recommended. (shrink)

We argue the thesis that if (1) a physical process is mathematically representable by a Cauchy sequence; and (2) we accept that there can be no infinite processes, i.e., nothing corresponding to infinite sequences, in natural phenomena; then (a) in the absence of an extraneous, evidence-based, proof of `closure' which determines the behaviour of the physical process in the limit as corresponding to a `Cauchy' limit; (b) the physical process must tend to a discontinuity (singularity) which has not been reflected (...) in the Cauchy sequence that seeks to describe the behaviour of the physical process. We support our thesis by mathematical models of the putative behaviours of (i) a virus cluster; (ii) an elastic string; and (iii) a Universe that recycles from Big Bang to Ultimate Implosion, in which parity and local time reversal violation, and the existence of `dark energy' in a multiverse, need not violate Einstein's equations and quantum theory. We suggest that the barriers to modelling such processes in a mathematical language that seeks unambiguous communication are illusory; they merely reflect an attempt to ask of the language chosen for such representation more than it is designed to deliver. (shrink)

According to actualism about possible worlds everything that exists is actual. Possible worlds and individuals are actually existing abstract parts of the actual world. Aristotelian actualism is a view that there are only actual individuals but no possible ones, nor their individual abstract representatives. Because of that, our actualist account of modality should differ depending on whether it concerns actual individuals or possible ones. The main goal of the dissertation is to develop a metaphysical framework for Aristotelian actualism. Chapter 1 (...) explains basic issues associated with the possible world approach to modality. I overview modal realist and actualist views on possible worlds and explain why I support the actualist approach. Subsequently, I introduce a distinction between Platonic and Aristotelian actualism, and discuss some semantic issues associated with actualism as such. In Chapter 2 I argue that Aristotelian actualism, modeled on linguistic ersatzism, is preferable over its Platonic counterpart. Subsequently, I propose a metaphysical framework for Aristotelian ersatzism which is based on a claim that our modal concepts work differently for actual and possible individuals. In order to explain that claim I introduce three specific differences concerning modal features of actual and possible individuals: (a) Representational Difference, according to which actual and possible individuals are represented differently by possible worlds; (b) Metaphysical Difference, according to which actual and possible individuals are represented by possible worlds as having different metaphysical nature; (c) Modal Difference, which says while there are singular and contingent possibilities involving actual individuals, all possibilities about possible individuals are general and necessary. I propose to interpret those differences in terms of the doctrines of haecceitism, antihaecceitism and existentialism. There is however no consensus on how those views should be characterized. Chapters 3, 4, and 5 focus on providing a precise characterization of those doctrines. Chapter 3 focuses on the doctrines of modal haecceitism and antihaecceitism, which I view as opposite accounts of how possible worlds represent possibilities. According to modal haecceitism what possible worlds say about particular individuals does not supervene on what they say qualitatively. Modal antihaecceitism is a denial of such a claim. Chapter 4 concerns metaphysical haecceitism and antihaecceitism, which I take to be alternative accounts of the fundamental structure of reality. For the metaphysical haecceitist reality contains irreducible singular facts, while for the metaphysical antihaecceitist reality is purely qualitative and general. Chapter 5 focuses on an argument between existentialists and antiexistentialists. Existentialists claim that there are contingent singular propositions, while antiexistentialists deny that. I defend existentialism against antiexistentialist counterarguments, as well as criticize some of the antiexistentialist accounts of singular propositions modeled on the notion of individual essence. In Chapter 6, by appealing to the results of investigations conducted in Chapters 3, 4 and 5, I reconsider Representational, Metaphysical and Modal Differences. According to a view that I propose: (a) Representational Difference entails (extreme) modal haecceitism for actual individuals but (extreme) modal antihaecceitism for possible individuals; (b) Metaphysical Difference entails metaphysical haecceitism (individualism) for actual individuals, but metaphysical antihaecceitism (generalism) for possible individuals; finally (c) Modal Difference entails existentialism: while there are singular and contingent possibilities involving actual individuals, all possibilities about possible individuals are general and necessary. In Chapter 6, I also explain the implications of those views for the various issues, including transworld identity, essentialism, or the modal status of modal space. Lastly, Chapter 7 overviews some semantic and metaphysical applications of Aristotelian ersatzism. I explain how it manages to accommodate Kripkean semantics and how it is able to account for the possibilities of indiscernibles, alien individuals and iterated modalities. I also address some possible objections to my proposal, including an issue of implicit representation and the Humphrey objection. (shrink)

This qualitative research aims to explore and unravel the theory of natural law within its Greek context and its influence on political thought, particularly addressing the need to counteract the damages of tyranny and the cyclical succession of regimes, as articulated by Plato. This study reveals that the concept of natural law predates Stoics and it is rooted within the pre-Socratic natural philosophy. The study exposes that Aristotelian ethics and politics are rooted in the concept of natural law, ultimately giving (...) rise to the Aristotelian "mixed form of government" and laying the groundwork for republicanism. In extending this inquiry, I attempt to identify a parallel argument in ancient Iran, investigating the presence of natural law and its impact on the political landscape. The concept of natural law, emphasizing the alignment of social and political affairs with nature's rules, played a significant role in shaping the Indo-Iranian communities. The Sanskrit term rta and its Avestan equivalent, Aša, denote this foundational concept. However, the ascendancy of Zoroastrianism and its new theology led to the consolidation of all Indo-Iranian gods into the singular omnipotent deity, Ahura Mazdā. Ahura Mazdā, along with its prophet Zaraθuštra, possessed the authority to govern both earthly life and the afterlife. The exclusive attributes of Ahu and Ratu empowered God and its messenger to formulate and enact laws ensuring a place in heaven. Consequently, Divine Law and positive law became intricately intertwined within a unified legal framework. This divine law, sanctioned by God and enforced by the King, diverges from the Greek perspective, particularly that of Aristotle, where tyranny is seen as a deviation from the ideal political order. In the Iranian context, tyranny is synonymous with God's representation, sharing the holiness and regal attributes of a King, who, in the Iranian and Avestan sense, enjoys God's blessing as Xvarənah or Faer-e Izadi. The intertwining of law and authority of the King precludes the possibility of an independent legal sovereignty apart from the King’s authority. The monotheistic tenets of Zaraθuštra’s religion, officially established in the 4th century AD as the Religion of the State, solidify this integrated system. Consequently, the coexistence of republicanism or any mixed form of government within Iran becomes unattainable under the influence of this monotheistic doctrine. (shrink)

In Mental Files, Recanati proposes a non-descriptivist approach to reference in terms of mental files, mental representations that play the role of Fregean mode of presentation. Recanati argues that we refer via mental files and that the reference of a file is determined relationally, rather than satisficationally; files are not to be equated to the information they contain, but typed by their function—to store information gained through certain epistemically rewarding relation to objects in the environment. I offer a critical (...) overview of Recanati’s framework and raise two questions about the nature and workings of files. (shrink)

When characterizing the content of a subject’s perceptual experience, does their seeing an object entail that their visual experience represents it as being a certain way? If it does, are they thereby in a position to have perceptually-based thoughts about it? On one hand, representationalists are under pressure to answer these questions in the affirmative. On the other hand, it seems they cannot. This paper presents a puzzle to illustrate this tension within orthodox representationalism. We identify several interesting morals which (...) may be drawn in response, each of which teaches us something interesting and important about perceptual experience and its interface with cognition and related phenomena. (shrink)