A simple interpretation of quantity calculus is given. Quantities are described as two-place functions from objects, states or processes (or some combination of them) into numbers that satisfy the mutual measurability property. Quantity calculus is based on a notational simplification of the concept of quantity. A key element of the simplification is that we consider units to be intentionally unspecified numbers that are measures of exactly specified objects, states or processes. This interpretation of quantity calculus combines all the advantages of (...) calculating with numerical values (since the values of quantities are numbers, we can do with them everything we do with numbers) and all the advantages of calculating with standardly conceived quantities (calculus is invariant to the choice of units and has built-in dimensional analysis). This also shows that the standard metaphysics and mathematics of quantities and their magnitudes is not needed for quantity calculus. At the end of the article, arguments are given that the concept of quantity as defined here is a pivotal concept in understanding the quantitative approach to nature. As an application of this interpretation of quantity calculus, an easy proof of dimensional homogeneity of physical laws is given. (shrink)

The paper aims to establish if Grassmann’s notion of an extensive form involved an epistemological change in the understanding of geometry and of mathematical knowledge. Firstly, it will examine if an ontological shift in geometry is determined by the vectorial representation of extended magnitudes. Giving up homogeneity, and considering geometry as an application of extension theory, Grassmann developed a different notion of a geometrical object, based on abstract constraints concerning the construction of forms rather than on the homogeneity (...) conditions required by the modern version of the theory of proportions. Secondly, Grassmann’s conception of mathematical knowledge will be investigated. Parting from the traditional definition of mathematics as a science of magnitudes, Grassmann considered mathematical forms as particulars rather than universals: the classification of the branches of mathematics was thus based on different operational rules, rather than on empirical criteria of abstraction or on the distinction of different species belonging to a common genus. It will be argued that a different notion of generalization is thus involved, and that the knowledge of mathematical forms relies on the understanding of the rules of generation of the forms themselves. Finally, the paper will analyse if Grassmann’s approach in the first edition of the Ausdehnungslehre should be explained in terms of the notion of purity of method, and if it clashes with Grassmann’s later conventionalism. Although in the second edition the features of the operations are chosen by convention, as it is the case for the anti-commutative property of the multiplication, the choice is oriented by our understanding of the resulting forms: a simplification in the algebraic calculus need not correspond to a simplification in the ‘dimensional’ interpretation of the result of the multiplicative operation. (shrink)

Although Peirce frequently insisted that continuity was a core component of his philosophical thought, his conception of it evolved considerably during his lifetime, culminating in a theory grounded primarily in topical geometry. Two manuscripts, one of which has never before been published, reveal that his formulation of this approach was both earlier and more thorough than most scholars seem to have realized. Combining these and other relevant texts with the better-known passages highlights a key ontological distinction: a collection is bottom-up, (...) such that the parts are real and the whole is an ens rationis, while a continuum is top-down, such that the whole is real and the parts are entia rationis. Accordingly, five properties are jointly necessary and sufficient for Peirce’s topical continuum: rationality, divisibility, homogeneity, contiguity, and inexhaustibility. (shrink)

An ideal constructor produces geometry from scratch, modelled through the bottom-up assembly of a graph-like lattice within a space that is defined, bootstrap-wise, by that lattice. Construction becomes the problem of assembling a homogeneous lattice in three-dimensional space; that becomes the problem of resolving geometrical frustration in quasicrystalline structure; achieved by reconceiving the lattice as a dynamical system. The resulting construction is presented as the introductory model sufficient to motivate the formal argument that it is a fundamental structure; based (...) on which, it is proposed that where mathematics’ numbers conventionally correspond to dimensionless points on the stateless number line, numbers more fundamentally correspond to an ordering of discrete objects constructed within the stateful number lattice. A second observation is that this fundamental lattice structure is helically configured with fractal character, which, as it relates to the geometry underlying spacetime, has relevance to questions in physics, particularly those involving wave-particle duality. (shrink)

Four simple postulates are presented, from which we derive a (3+1)‑dimensional structure, interpreted as ordinary space and time. We then derive further properties of space: isotropy and homogeneity; a rapid expansion within the first instant of time (i.e. inflation); and a continual and uniform expansionary pressure, due to a continual influx of (non-zero-point) energy that is uniformly distributed (i.e. dark energy). In addition, the time dimension is shown to have an "arrow". These results suggest that the four postulates (...) may be fundamental to the construction of the physical universe. (shrink)

In the introduction I argue that the basic element (or primitive) for constructing the physical universe is "displacement from a prior level", and the basic structure is "a sequence of such displacements" (summarized as postulates 1 and 2). The displacements are then defined as one-dimensional objects with a direction (postulate 3). The relations between these displacements are stated in postulate 4. In section 2 we discuss basic consequences of the postulates, and in section 3 we use the postulates to (...) derive a (3+1)-dimensional structure, interpreted as ordinary space and time. We then derive further properties of space --- isotropy, homogeneity, and a rapid early expansion (i.e. inflation). Time, comporting with experience, is shown to be a one-dimensional stream --- with a direction. In section 4 we associate energy with the displacements, and find that the same factors that construct ordinary space (and make it isotropic and homogeneous) also smear the locations of entities/particles across that space --- thereby providing a mechanism/explanation for that iconic and enigmatic aspect of quantum mechanics. We also determine that there must be a continual, uniformly-distributed stream of (non-zero-point) energy coming into the system that constructs new space (i.e. dark energy). The streaming natures of both time and dark energy are shown to have the same basic cause: the processes that input dark energy into the system, and that construct time, are themselves independent of time --- and so they are continual processes. Further consequences follow from the model, including an explanation for why the presence of energy affects space and time, and why quantum vacuum energy is an exception to this rule (i.e. does not gravitate) --- thereby eliminating the cosmological constant problem. A key benefit of the model is that it liberates us from always having to think about the construction of the universe in terms of spatio-temporal relations and evolution (e.g. the big bang model), which is problematic because presumably (and as we will indeed see) space and time are products of the fundamental construction process, not things that govern it. (shrink)

The accelerated development of science and technology, along with the economical growth of countries and the rise of the phenomenon of globalization have had consequences in different aspects of human life. Social injustice, inequality, violence, fighting within and between countries, along with ecological misfortunes calls out for an ethical system that regulates and brings new light to human behaviour in this globalized world. The globalization dynamic of the techno-scientific, world market economic culture suggests the need of an urgent formation of (...) conscience of a global ethics. Having in mind this world panorama, in this process of ethical development we must analyze how bioethics can respond to the great challenge that this globalization plants. We propose that the key to the answer lies within the proposal developed by the personalistic current, which looks to solve real moral problems of concrete human persons, without leaving out anyone and looking to respond to all the dimentions of the human person. -/- El acelerado desarrollo de la ciencia y la tecnología, junto con el crecimiento económico de los países y la consolidación del fenómeno de la globalización ha tenido consecuencias en los diferentes ámbitos de la vida del ser humano. La injusticia social, la desigualdad, la violencia, las luchas dentro de los países y entre los países, así como el descalabro ecológico reclaman un sistema ético que regule y dé nuevas luces al comportamiento humano en este mundo globalizado. La dinámica de globalización de la cultura tecnocientífica y económica de mercado mundial, sugiere la necesidad de una urgente toma de conciencia de una ética global. Teniendo en cuenta este panorama mundial, en este trabajo analizamos cómo la bioética puede responder a este gran desafío que plantea la globalización. Proponemos que la clave fundamental de la respuesta está en la propuesta que ha sido desarrollada por la corriente personalista, la cual plantea y da solución a los problemas morales reales de rostros humanos concretos, sin dejar fuera a nadie y sin dejar fuera ninguna de las dimensiones del hombre. (shrink)

One determining characteristic of contemporary sociopolitical systems is their power over increasingly large and diverse populations. This raises questions about power relations between heterogeneous individuals and increasingly dominant and homogenizing system objectives. This article crosses epistemic boundaries by integrating computer engineering and a historicalphilosophical approach making the general organization of individuals within large-scale systems and corresponding individual homogenization intelligible. From a versatile archeological-genealogical perspective, an analysis of computer and social architectures is conducted that reinterprets Foucault’s disciplines and political anatomy to (...) establish the notion of politics for a purely technical system. This permits an understanding of system organization as modern technology with application to technical and social systems alike. Connecting to Heidegger’s notions of the enframing (Gestell) and a more primal truth (anfänglicheren Wahrheit), the recognition of politics in differently developing systems then challenges the immutability of contemporary organization. Following this critique of modernity and within the conceptualization of system organization, Derrida’s democracy to come (à venir) is then reformulated more abstractly as organizations to come. Through the integration of the discussed concepts, the framework of Large-Scale Systems Composed of Homogeneous Individuals (LSSCHI) is proposed, problematizing the relationships between individuals, structure, activity, and power within large-scale systems. The LSSCHI framework highlights the conflict of homogenizing system-level objectives and individual heterogeneity, and outlines power relations and mechanisms of control shared across different social and technical systems. (shrink)

Principles of chance deference face two kinds of problems. In the first place, they face difficulties with a priori knowable contingencies. In the second place, they face difficulties in cases where you've lost track of the time. I provide a principle of chance deference which handles these problem cases. This principle has a surprising consequence for Adam Elga's Sleeping Beauty Puzzle.

The thesis I should like to advance in this essay is that Plato cannot and, in fact, does not adhere consistently to the doctrine that to know the good is to do the good. First, in order to display the paradoxes in the Platonic ethical system, I shall discuss the concept of the homogeneity of the good which Plato explicitly endorses. Second, by referring to Plato's practice, I shall endeavor to demonstrate that he treats the good as heterogeneous although (...) this treatment is inconsistent with his equation of knowledge with virtue. I shall use the descriptive phrase 'homogeneity of the good' to stand for that conception of the good which identifies the good exclusively with the moral good. I shall use the descriptive phrase 'heterogeneity of the good' to stand for that conception of the good which includes in the definition of good mixed pleasures or the natural good. Our understanding of the good as heterogeneous allows us to clarify many of the paradoxes present in Platonic ethics and affords us a deeper understanding of Plato. (shrink)

Resumen: En el presente artículo me propongo elucidar el significado del concepto “pathos de la distancia” y sus implicaciones ético-políticas, destacando, además, su sentido y coherencia con el conjunto del pensamiento nietzscheano. La tesis fundamental es que el pathosde la distancia, como característica básica del ideal noble, muestra cómo el concepto de preeminencia política en Nietzsche se diluye siempre en un concepto de preeminencia anímica. La reflexión se enmarca dentro de la crítica nietzscheana de la cultura, la política y la (...) educación, y su propuesta de reforma de los valores dominantes de la sociedad, entre ellos, los que configuran la subjetividad y la individualidad. Se estudian las diversas dimensiones del pathos de la distancia: como articulación jerárquica, como principio de individuación, como parte la Gran Política y como elemento del pensamiento de la cría. Palabras clave: Pathos de la distancia, Valor, Moral, Gran Política, Cría. (shrink)

This paper develops a semantic solution to the puzzle of Free Choice permission. The paper begins with a battery of impossibility results showing that Free Choice is in tension with a variety of classical principles, including Disjunction Introduction and the Law of Excluded Middle. Most interestingly, Free Choice appears incompatible with a principle concerning the behavior of Free Choice under negation, Double Prohibition, which says that Mary can’t have soup or salad implies Mary can’t have soup and Mary can’t have (...) salad. Alonso-Ovalle 2006 and others have appealed to Double Prohibition to motivate pragmatic accounts of Free Choice. Aher 2012, Aloni 2018, and others have developed semantic accounts of Free Choice that also explain Double Prohibition. -/- This paper offers a new semantic analysis of Free Choice designed to handle the full range of impossibility results involved in Free Choice. The paper develops the hypothesis that Free Choice is a homogeneity effect. The claim possibly A or B is defined only when A and B are homogenous with respect to their modal status, either both possible or both impossible. Paired with a notion of entailment that is sensitive to definedness conditions, this theory validates Free Choice while retaining a wide variety of classical principles except for the transitivity of entailment. The homogeneity hypothesis is implemented in two different ways, homogeneous alternative semantics and homogeneous dynamic semantics, with interestingly different consequences. (shrink)

This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. Second, the paper establishes complete (...) sequent calculi for S*fde, dS*fde, crossS*fde. Among the other accomplishments of the paper, we generalize the semantics from Bochvar, Hallden, Deutsch and Daniels, we provide a general recipe to define containment logics, we explore the single-premise/single-conclusion fragment of S*fde, dS*fde, crossS*fdeand the connections between crossS*fde and the logic Eq of equality by Epstein. Also, we present S*fde as a relevant logic of meaninglessness that follows the main philosophical tenets of Goddard and Routley, and we briefly examine three further systems that are closely related to our main logics. Finally, we discuss Routley's criticism to containment logic in light of our results, and overview some open issues. (shrink)

The aim of this paper is to show that Priest's modal Meinongianism might benefit from joining forces with two-dimensionalism. For this purpose, I propose a two-dimensional solution to a problem for modal Meinongianism that is posed by Beall, Sauchelli, and Milne, and show that, by taking recourse to two-dimensionalism, divergent intuitions about the question of whether fictional characters might exist can be reconciled. Moreover, two-dimensionalism helps to rebut Kroon's argument to the conclusion that modal Meinongianism cannot rule out the (...) odd claim that some non-existent objects have existence-entailing properties at the actual world. (shrink)

In his recent book, The Dimensions of Consequentialism, Martin Peterson puts forward a new version of consequentialism that he dubs ‘multidimensional consequentialism’. The defining thesis of the new theory is that there are irreducible moral aspects that jointly determine the deontic status of an act. In defending his particular version of multidimensional consequentialism, Peterson advocates the thesis—he calls it DEGREE—that if two or more moral aspects clash, the act under consideration is right to some non-extreme degree. This goes against the (...) orthodoxy according to which—Peterson calls this RESOLUTION—each act is always either entirely right or entirely wrong. The argument against RESOLUTION appeals to the existence of so-called deontic leaps: the idea is that endorsing RESOLUTION would not give each relevant moral aspect its due in the final analysis. Our paper argues that, contrary to Peterson, all moral aspects remain visible in what can properly be called the final analysis of a moral theory that involves RESOLUTION, moral aspects do not have to remain visible in judgements of all-things-considered rightness or wrongness, respectively, introduction of what Peterson calls verdictive reasons does not change the overall picture in favour of DEGREE. We conclude that multi-dimensional consequentialists should accept RESOLUTION rather than DEGREE. (shrink)

This dissertation draws upon historical studies of scientific practice and contemporary issues in the metaphysics and epistemology of science to account for the nature of physical quantities. My dissertation applies this integrated HPS approach to dimensional analysis—a logic for quantitative physical equations which respects the distinct dimensions of quantities (e.g. mass, length, charge). Dimensional analysis and its historical development serve both as subjects of study and as a sources for solutions to contemporary problems. The dissertation consists primarily of (...) three related papers on: (1) the methodological and metaphysical foundations of dimensional analysis, (2) the use of dimensional analysis in determining physical symmetries, (3) the use of dimensional analysis in securing metrological extension. (shrink)

As timely renovation of artificial ideology about authenticity of nature in proportion to contemporaneous historical background of remarkable highlight of microcosmic configuration of matter, “Homogenous Cosmos Originated from Unique Genesis” is innovative cosmos redefinition and thoroughly coherent PNT dynamics about universal existence & motion as spontaneous occurrence in the nature of essence of matter in a class by itself, which is radically extended from newly highlighted factuality that “discretionary particles in cosmos are mutually convertible” as lineal logic system based on (...) unique assumable precondition of Homogenous cosmos originated from unique genesis postulate. (shrink)

In modern, culturally-heterogeneous societies, inefficiency of communication of important moral concepts is often evidenced by asymmetrical moral judgements and hypocritical behaviour, especially in our increasingly compartmentalised social landscapes [Rozuel 2011]. This raises the question of how to present target audiences with some (perhaps novel) moral concept, like an ethical dimension of one’s ecological attitude, in a way which would resonate with them, and be conducive to a coherent moral stance, decreasing action-observer biases. We analyse this problem by introducing a formal (...) moral inconsistency framework. We consider the ways in which the aforementioned problem might be tackled in existing cognitive science of morality (CSM) nativist frameworks, and, secondly, we investigate it from the perspective of moral learning, finally proposing the notion of moral dimensionality of a representation in the context of model-based reinforcement learning, as a useful conceptual tool for studying the problem. (shrink)

I want to differentiate between two very different ways of organizing pictorial elements at a very abstract level: -/- (2D) two-dimensionally: pictorial elements are organized and grouped according to their outline shape on the picture surface and (3D) three-dimensionally: pictorial elements are organized and grouped according to their position in the depicted space. -/- Suppose you need to depict seven identical spheres. On the most general level, there are two ways of doing this: you can arrange the seven spheres in (...) space and then choose a vantage point in this space from which you want to depict them. Or you can arrange seven circles (the outline shapes of the seven spheres) on the two-dimensional surface of the picture. The former method is an instance of three-dimensional pictorial organization, whereas the latter one is an instance of two-dimensional pictorial organization. (shrink)

Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural network structure, implementation attributes, and learning performance. In this work, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the original loss space. We show that saddle points in the (...) original space are rarely correctly identified as such in expected lower-dimensional representations if random projections are used. The principal curvature in the expected lower-dimensional representation is proportional to the mean curvature in the original loss space. Hence, the mean curvature in the original loss space determines if saddle points appear, on average, as either minima, maxima, or almost flat regions. We use the connection between expected curvature in random projections and mean curvature in the original space (i.e., the normalized Hessian trace) to compute Hutchinson-type trace estimates without calculating Hessian-vector products as in the original Hutchinson method. Because random projections are not suitable to correctly identify saddle information, we propose to study projections along dominant Hessian directions that are associated with the largest and smallest principal curvatures. We connect our findings to the ongoing debate on loss landscape flatness and generalizability. Finally, for different common image classifiers and a function approximator, we show and compare random and Hessian projections of loss landscapes with up to about 7×10^6 parameters. (shrink)

This paper endeavors to establish foundations for the interaction between hyperintensional semantics and two-dimensional indexing. I examine the significance of the semantics, by developing three, novel interpretations of the framework. The first interpretation provides a characterization of the distinction between fundamental and derivative truths. The second interpretation demonstrates how the elements of decision theory are definable within the semantics, and provides a novel account of the interaction between probability measures and hyperintensional grounds. The third interpretation concerns the contents of (...) the types of intentional action, and the semantics is shown to resolve a puzzle concerning the role of intention in action. Topic-sensitive two-dimensional truthmaker semantics can be interpreted epistemically and metasemantically. (shrink)

Philosophical views about the logical structure of time are typically divided between proponents of A and B theories, based on McTaggart's A and B series. Drawing on Paul Ricoeur's hermeneutic phenomenology, I develop and defend McTaggart's thesis that the C series and the A series working together give a consistent description of temporal experience, provided that the two series are treated as distinct dimensions internal to time. In the proposed two-dimensional model, the C series expresses a nesting order of (...) the constitutive states of a world, whereas ontological continuity and change are properties of the A series. This, I argue, allows for limited backward causation. (shrink)

Why are cities looking more and more alike? Why do hipster coffee shops and clothing boutiques all share that same vibe? One answer is that gentrification represents an invasive force that forcibly re-models cities, from the top-down, to meet the monotone eye of the gentrifier. Gentrification brings in external developers and designers, who create new businesses which all meet that one monotonous aesthetic mold. But I suggest, using work from Quill Kukla and Jane Jacobs, that this top-down model of gentrification (...) is incomplete. Gentrification also incentivizes local residents to remake their own businesses and properties to meet that monotone eye. Gentrification is a pressure which pushes cities to meet a universalized and therefore homogenized taste, rather than letting diverse tastes flourish. (This piece originally published as part of a symposium on Quill Kukla's City Living.). (shrink)

En la cúspide del conocimiento humano halla su sede la sabiduría. Un saber que se alcanza en la simplicidad más alta del ser humano, allí donde confluyen todas sus potencias y facultades, no solamente la inteligencia, sino también la voluntad y los afectos. Cualquier clase de conocimiento aséptico respecto de cualquier influencia afectiva o volitiva lleva a una reducción que de manera propia puede llamarse “intelectualismo”. El concepto de razón “pura” es un reduccionismo que conduce a una grave disgregación en (...) la criatura racional, y a la enajenación de su mismo ser. El que no conoce amando y no ama conociendo, ni conoce verdaderamente, ni verdaderamente ama. El conocimiento que compendia estas características antropológicas se denomina “conocimiento afectivo”. En este trabajo se hace una exploración sobre el alcance de este tipo peculiar de conocimiento siguiendo los principios de Aristóteles y Tomás de Aquino. (shrink)

What determines whether an object is an artwork? In this paper I consider what I will call ‘social’ theories of art, according to which the arthood of objects depends in some way on the art-related social practices that we have. Though such a dependence claim is plausible in principle, social theories of art tend to unpack the determining link between artworks and social practices in terms of intentional relations between the objects in question and the people involved in the relevant (...) practices. This intentionalism has unappealing upshots. Drawing on two-dimensional approaches in social ontology, I show how social theories of art can be done differently, improving their prospects. (shrink)

La investigación reciente en psicología cognitiva sobre la memoria emocional ha estudiado las distintas formas en que las emociones afectan a la memoria, sin profundizar no obstante en la comprensión de la manera en que los aspectos emocionales, afectivos y mnemónicos se encuentran estrechamente entrelazados en el contenido mismo de un acto de reminiscencia. En este artículo propongo un marco conceptual de análisis que nos permite entender los recuerdos personales como recuerdos esencialmente afectivos, y que se articula en torno a (...) dos variables continuas e independientes: por un lado, la intencionalidad del recuerdo, es decir, el objeto hacia el cual el recuerdo está dirigido, que puede ser descriptiva o evaluativa; por el otro, la perspectiva afectiva del recuerdo, que puede fluctuar desde la perspectiva de primera persona hasta la perspectiva de tercera persona. Las dos dimensiones son analizadas en profundidad y las limitaciones de este marco y las futuras líneas de investigación son igualmente presentadas. (shrink)

Relativity theory is often said to support something called ‘the four-dimensional view of reality’. But there are at least three different views that sometimes go by this name. One is ‘spacetime unitism’, according to which there is a spacetime manifold, and if there are such things as points of space or instants of time, these are just spacetime regions of different sorts: thus space and time are not separate manifolds. A second is the B-theory of time, according to which (...) the past, present, and future are all equally real and there is nothing metaphysically special about the present. A third is perdurantism, according to which persisting material objects are made up of different temporal parts located at different times. We sketch routes from relativity to unitism and to the B-theory. We then discuss some routes to perdurantism, via the B-theory and via unitism. (shrink)

Conscious experience is the direct observation of conscious events. Human conscious experience is four-dimensional. Conscious events are linked (associated) by spacetime intervals to produce a coherent conscious experience. This explains why conscious experience appears to us the way it does. Conscious experience is an orientation in space and time, an understanding of the position of the observer in space and time. Causality, past-future relations, learning, memory, cognitive processing, and goal-directed actions all evolve from four-dimensional conscious experience. A neural (...) correlate for four-dimensional conscious experience can be found in the human brain and is modelled by Einstein's special theory of relativity. The relativistic concept of spacetime interval is central for understanding conscious experience and cognition. (shrink)

A three dimensional hypercube representing all of the 4,096 dyadic computations in a standard bivalent system has been created. It has been constructed from the 16 functions arrayed in a table of functional completeness that can compute a dyadic relationship. Each component of the dyad is an operator as well as a function, such as “implication” being a result, as well as an operation. Every function in the hypercube has been color keyed to enhance the display of emerging patterns. (...) At the minimum, the hypercube is a “multiplication table” of dyadic computations and produces values in a way that shortens the time to do operations that normally would take longer using conventional truth table methods. It also can serve as a theorem prover and creator. With the hypercube comes a deductive system without the need for axioms. The main significance of the 3-D hypercube at this point is that it is the most fundamental way of displaying all dyadic computations in binary space, thus serving as a way of normalizing the rendition of uninterpreted, or raw, binary space. The hypercube is a dimensionless entity, a standard by which in binary spaces can be measured and classified, analogous to a meter stick. (shrink)

A general sketch on how the problem of space dimensionality depends on anthropic arguments is presented. Several examples of how life has been used to constraint space dimensionality (and vice-versa) are reviewed. In particular, the influences of three-dimensionality in the solar system stability and the origin of life on Earth are discussed. New constraints on space dimensionality and on its invariance in very large spatial and temporal scales are also stressed.

This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal …) and properly biological (heart beating, respiration, metabolic …). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocks, which are based on frequencies along the usual (...) (possibly thermodynamical, thus oriented) time. We then suggest a functional representation of biological time by a 2-dimensional manifold as a mathematical frame for accommodating autonomous biological rhythms. The “visual” representation of rhythms so obtained, in particular heart beatings, will provide, by a few examples, hints towards possible applications of our approach to the understanding of interspecific differences or intraspecific pathologies. The 3- dimensional embedding space, needed for purely mathematical reasons, allows to introduce a suitable extra-dimension for “representation time”, with a cognitive significance. (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)

At this point in time the two-dimensional (2D) argument against physicalism is well known (Chalmers 2009; 2010), as are the many responses to it. However there has been a recent development that has yet to be widely discussed. Some philosophers have argued that we have equally compelling reasons to think that dualism is false based on the conceivability of mere physical duplicates which enjoy conscious experience in just the way we do (Martin 1998; Sturgeon 2000; Piccinini 2006; Frankish 2007; (...) Brown 2010; Balog MS). This argument has not yet been properly understood and in this paper I aim to correct the most common misunderstandings. (shrink)

In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help (...) make explicit the restrictions Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to ‘lift’ a Kripke frame for a one- dimensional modal logic into two dimensions. (shrink)

I argue that space has three dimensions, and quantum mechanics does not show otherwise. Specifically, I argue that the mathematical wave function of quantum mechanics corresponds to a property that an N-particle system has in three-dimensional space.

It has generally been assumed that rapid visual search is based on simple features and that spatial relations between features are irrelevant for this task. Seven experiments involving search for line drawings contradict this assumption; a major determinant of search is the presence of line junctions. Arrow- and Y-junctions were detected rapidly in isolation and when they were embedded in drawings of rectangular polyhedra. Search for T-junctions was considerably slower. Drawings containing T-junctions often gave rise to very slow search even (...) when distinguishing arrow- or Y-junctions were present. This sensitivity to line relations suggests that preattentive processes can extract 3-dimensional orientation from line drawings. A computational model is outlined for how this may be accomplished in early human vision. (shrink)

Previous theories of early vision have assumed that visual search is based on simple two-dimensional aspects of an image, such as the orientation of edges and lines. It is shown here that search can also be based on three-dimensional orientation of objects in the corresponding scene, provided that these objects are simple convex blocks. Direct comparison shows that image-based and scene-based orientation are similar in their ability to facilitate search. These findings support the hypothesis that scene-based properties are (...) represented at preattentive levels in early vision. (shrink)

This paper is a study about the social dimension of the philosophical education according to Aristotle. Aristotle is not a individualistic thinker but he understands the philosophical activity in the social context of the friendship.

This paper is divided into three sections. In the first section I briefly outline the background of the problem, i.e. Kripke’s modal argument (Kripke 1980). In the second section I present Chalmers’ account of two- dimensional semantics and two-dimensional argument against physicalism. In the third section I criticize Chalmers’ approach based on two crucial points, one is about necessity of identities and the other is about microphysi- cal descriptions and a priori derivation.

This paper examines connections between concepts of space and extension on the one hand and immaterial spirits on the other, specifically the immanentist concept of spirits as present in rerum natura. Those holding an immanentist concept, such as Thomas Aquinas, typically understood spirits non-dimensionally as present by essence and power; and that concept was historically linked to holenmerism, the doctrine that the spirit is whole in every part. Yet as Aristotelian ideas about extension were challenged and an actual, infinite, (...) class='Hi'>dimensional space readmitted, a dimensionalist concept of spirit became possible—that asserted by the mature Henry More, as he repudiated holenmerism. Despite More’s intentions, his dimensionalist concept opens the door to materialism, for supposing that spirits have parts outside parts implies that those parts could in principle be mapped onto the parts of divisible bodies. The specter of materialism broadens our interest in More’s unconventional ideas, for the question of whether other early modern thinkers, including Isaac Newton, followed More becomes a question of whether they too unwittingly helped usher in materialism. This paper shows that More’s attack upon holenmerism fails. He illegitimately injects his dimensionalist concept of spirit into the doctrine, failing to recognize it as a consequence of the non-dimensionalist concept of spirit, which in itself secures indivisibility. The interpretive consequence for Newton is that there is no prima facie reason to suppose that the charitable interpretation takes him to deny holenmerism. (shrink)

Recent trends in psychiatry involve a transition from categorical to dimensional frameworks, in which the boundary between health and pathology is understood as a difference in degree rather than as a difference in kind. A major tenet of dimensional approaches is that no qualitative distinction can be made between health and pathology. As a consequence, these approaches tend to characterize such a threshold as pragmatic or conventional in nature. However, dimensional approaches to psychopathology raise several epistemological and (...) ontological issues. First, we review major sources of evidence usually recruited in support of the dimensional trend (focusing on clinical observation and biological data), and we show that these are connected to different conceptualizations of how dimensional traits extend across health and pathology. Second, we criticize two unquestioned assumptions that stand at the core of the dimensional trend: a) that there is continuity from health to pathology at the symptomatic level; b) that such continuity reflects an underlying continuity in the genetic liability for pathological conditions. Third, we argue against the idea of a conventional threshold by showing that such a view implies a linear relationship between the genotype and the phenotype. Fourth, drawing on epigenetics and developmental biology, we offer a characterization of mental disorders as stable and dynamic constellations of multi-level variables that differ qualitatively from ‘healthy states’. We conclude by showing that our account has several theoretical advantages over both categorical and dimensional approaches. Notably, it provides crucial insights into psychological development over time and individual differences, with major implications in terms of intervention and clinical decision-making. (shrink)

In this paper I put forward a representationalist theory of conscious experience based on Robert Stalnaker's version of two-dimensional modal semantics. According to this theory the phenomenal character of an experience correlates with a content equivalent to what Stalnaker calls the diagonal proposition. I show that the theory is closely related both to functionalist theories of consciousness and to higher-order representational theories. It is also more compatible with an anti-Cartesian view of the mind than standard representationalist theories.

The topic of this Handbook entry is the relationship between similarity and dimensional analysis, and some of the philosophical issues involved in understanding and making use of that relationship. Discusses basics of the relationship between units, dimensions, and quantities. It explains the significance of dimensionless parameters, and explains that similarity of a physical systems is established by showing equality of a certain set of dimensionless parameters that characterizes the system behavior. Similarity is always relative -- to some system behavior. (...) Other topics discussed: generalization of the notion of similarity, the difference between relative similarity and partial similarity; how the notion of similarity in science differs from similarity as it has been discussed in recent philosophy. Philosophers' views discussed: R. Giere, N. Goodman, P. Bridgman, and B. Ellis. (shrink)

As timely renovation of artificial ideology about authenticity of nature in proportion to contemporaneous historical background of remarkable highlight of microcosmic configuration of matter, “Homogenous Cosmos Originated from Unique Genesis” is innovative cosmos redefinition and thoroughly coherent PNT dynamics about universal existence & motion as spontaneous occurrence in the nature of essence of matter in a class by itself, which is radically extended from newly highlighted factuality that “discretionary particles in cosmos are mutually convertible” as lineal logic system based on (...) unique assumable precondition of Homogenous cosmos originated from unique genesis postulate. (shrink)

I argue that a two-dimensional model of social objects is uniquely positioned to deliver explanations for some of the puzzling metaphysical features of words. I consider how a type-token model offers explanations for the metaphysical features of words, but I give reasons to find the model wanting. In its place, I employ an alternative model from social ontology to explain the puzzling data and questions that are generated from the metaphysical features of words. In the end I chart a (...) new path that foregrounds the agent-dependence and social conditions for word kinds. (shrink)

The aim of this paper is to reconstruct a modal version of the ontological argument (MOA) in a two dimensionally extended way. This modification of MOA, I argue, might respond to Tooley’s (1981) and Findlay’s (1948) prominent objections against the argument. The MOA has two distinct key premises that are criticized by Tooley and Findley. According to Tooley, the structure of the argument allows to define further properties that exclude the existence of God-like beings. Findlay, however, argues against the proof (...) in a Kantian way by claiming that the very property of necessary existence is contradictory, therefore no being can possess it. In this paper, I am going to show how Tooley and Findlay’s critique re-frame the original ontological argument debate. I will provide a comprehensive map over all possible ways of refuting the MOA. Finally, I argue that, once we apply a two dimensional framework, we are in a position to refute Findlay’s criticism. (shrink)

Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I (...) also describe some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem. (shrink)

Detailing the connection between the various functions of Buddhist karma theory and rebecoming is a profoundly difficult aspect of Buddhist philosophy. While there is no definitive answer to these questions, suggestions can be found in early Buddhism that may help to reconcile the early Buddhist interpretations of karma with other philosophical and scientific theories.A great difficulty in analysing the functional aspects of Buddhist karma theory is the conflation of karma as causality with karma as ethics to create a strongly deterministic (...) ethical theory of karmic retribution which de-emphasises notions of free will and personal responsibility that are fundamental to Buddhist practice. This research is intended as a new model to evaluate karma in light of early Buddhist karma theory. Following this model may allow karma theorists to shed our accumulated assumptions from the Abhidharma and western philosophy that bring substance metaphysics into the analysis of Buddhist karma doctrine. This essentialism is an unnecessary obstacle to understanding. When karma as causality is located within early Buddhist process metaphysics it can easily be analysed in a practical fashion and is found to accord with contemporary thought. Karma as ethics is more properly analysed as a satisfactory, but underdeveloped ethical theory. Only with these conceptions in place can the connection between karma and rebecoming can be detailed. (shrink)

Pablo Gilabert and Holly Lawford-Smith have, both in collaboration and individually, provided a compelling account of feasibility, which states that feasibility is both ‘binary’ and ‘scalar’, and both ‘synchronic’ and ‘diachronic’. This two-dimensional analysis, however, has been the subject of four major criticisms: it has been argued that it rests upon a false distinction between ‘hard’ and ‘soft’ constraints, that it ignores the importance of intentional action, and that diachronic feasibility is incoherent and insensitive to the existence of epistemic (...) limitations. In this paper, I will argue that such objections do not undermine the persuasiveness of Gilabert and Lawford-Smith’s analysis. Nevertheless, I will contend that the latter is susceptible to two other challenges. First, it mistakenly appeals to morality, and, second, it lacks an analysis of ability. I will maintain, however, that such criticisms can be addressed and that a revised version of the account should be adopted. (shrink)

Contemporary psychiatry finds itself in the midst of a crisis of classification. The developments begun in the 1980s—with the third edition of the Diagnostic and Statistical Manual of Mental Disorders —successfully increased inter-rater reliability. However, these developments have done little to increase the predictive validity of our categories of disorder. A diagnosis based on DSM categories and criteria often fails to accurately anticipate course of illness or treatment response. In addition, there is little evidence that the DSM categories link up (...) with genetic findings, and even less evidence that they... (shrink)