This paper presents a calculus for mereotopological reasoning in which two-dimensional spatial regions are treated as primitive entities. A first order predicate language ℒ with a distinguished unary predicate c(x), function-symbols +, · and - and constants 0 and 1 is defined. An interpretation ℜ for ℒ is provided in which polygonal open subsets of the real plane serve as elements of the domain. Under this interpretation the predicate c(x) is read as 'region x is connected' and the (...) function-symbols and constants are given their meaning in terms of a Boolean algebra of polygons. We give an alternative interpretation ������ base on the real closed plane which turns out to be isomorphic to ℜ. A set of axioms and a rule of inference are introduced. We prove the soundness and completeness of the calculus with respect to the given interpretation. (shrink)

This paper concerns modal logics appearing from the temporal ordering of domains in two-dimensional Minkowski spacetime. As R. Goldblatt has proved recently, the logic of the whole plane isS4.2. We consider closed or open convex polygons and closed or open domains bounded by simple differentiable curves; this leads to the logics:S4,S4.1,S4.2 orS4.1.2.

We investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.

We investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.

Let J be any proper ideal of subsets of the real line R which contains all finite subsets of R. We define an ideal J * ∣B as follows: X ∈ J * ∣B if there exists a Borel set $B \subset R \times R$ such that $X \subset B$ and for any x ∈ R we have $\{y \in R: \langle x,y\rangle \in B\} \in \mathscr{J}$ . We show that there exists a family $\mathscr{A} \subset \mathscr{J}^\ast\mid\mathscr{B}$ of power (...) ω 1 such that $\bigcup\mathscr{A} \not\in \mathscr{J}^\ast\mid\mathscr{B}$ . In the last section we investigate properties of ideals of Lebesgue measure zero sets and meager sets in Cohen extensions of models of set theory. (shrink)

We introduce a suitable notion of eight-shaped curve in the product S × ℝ of a Suslin line S for the real line ℝ, and we prove that if S is dense in itself, then every collection of pairwise disjoint eight-shaped curves in S × ℝ is countable. This parallels a folklore result which holds for the real plane.

ABSTRACTThe article explores the connection between James's “radical empiricism” and Deleuze's “transcendental empiricism” with a particular focus on the concept of “pure experience.” It argues for the substantial nature of this connection in terms of both philosophical motivations and formal innovations. Both thinkers are motivated to construct “better” empiricisms that do not complacently accept conventional conceptual representations as exhaustive of the real. Moreover, radical empiricism develops a latent critique of representational models of consciousness that is accomplished through a turn (...) to events or processes as ontologically primary. These innovations are further developed by Deleuze in his treatment of the problem of individuation. Taken together, they help to specify the metaphysical reasons for the experimental pluralism that both James and Deleuze affirm, showing how these reasons are inextricable from the radical empiricist impulse to be maximally inclusive of modalities of real experience, including the felt, the vague, and the affective. Emphasizing the metaphysical dimensions of these alternative empiricisms brings into clearer focus the stakes of philosophical thought as part of the open-ended and ongoing relational processes by which the universe continues to unfold. (shrink)

The article explores the connection between James's " radical empiricism " and Deleuze's " transcendental empiricism " with a particular focus on the concept of " pure experience. " It argues for the substantial nature of this connection in terms of both philosophical motivations and formal innovations. Both thinkers are motivated to construct " better " empiricisms that do not complacently accept conventional conceptual representations as exhaustive of the real. Moreover, radical empiricism develops a latent critique of representational models (...) of consciousness that is accomplished through a turn to events or processes as ontologically primary. These innovations are further developed by Deleuze in his treatment of the problem of individuation. Taken together, they help to specify the metaphysical reasons for the experimental pluralism that both James and Deleuze affirm, showing how these reasons are inextricable from the radical empiricist impulse to be maximally inclusive of modalities of real experience, including the felt, the vague, and the affective. Emphasizing the metaphysical dimensions of these alternative empiricisms brings into clearer focus the stakes of philosophical thought as part of the open-ended and ongoing relational processes by which the universe continues to unfold. (shrink)

In this paper we study modal logics of closed domains on the real plane ordered by the chronological future relation. For the modal logic determined by an arbitrary closed convex domain with a smooth bound, we present a finite axiom system and prove the finite modal property.

We investigate the Ramsey theory of continuous graph-structures on complete, separable metric spaces and apply the results to the problem of covering a plane by functions. Let the homogeneity number[Formula: see text] of a pair-coloring c:[X]2→2 be the number of c-homogeneous subsets of X needed to cover X. We isolate two continuous pair-colorings on the Cantor space 2ω, c min and c max, which satisfy [Formula: see text] and prove: Theorem. For every Polish space X and every continuous pair-coloringc:[X]2→2with[Formula: (...) see text], [Formula: see text] There is a model of set theory in which[Formula: see text]and[Formula: see text]. The consistency of [Formula: see text] and of [Formula: see text] follows from [20]. We prove that [Formula: see text] is equal to the covering number of 2 by graphs of Lipschitz functions and their reflections on the diagonal. An iteration of an optimal forcing notion associated to c min gives: Theorem. There is a model of set theory in which ℝ2 is coverable byℵ1graphs and reflections of graphs of continuous real functions; ℝ2 is not coverable byℵ1graphs and reflections of graphs of Lipschitz real functions. Figure 1.1 in the introduction summarizes the ZFC results in Part I of the paper. The independence results in Part II show that any two rows in Fig. 1.1 can be separated if one excludes [Formula: see text] from row. (shrink)

We prove an exponential lower bound on the length of cutting plane proofs. The proof uses an extension of a lower bound for monotone circuits to circuits which compute with real numbers and use nondecreasing functions as gates. The latter result is of independent interest, since, in particular, it implies an exponential lower bound for some arithmetic circuits.

The paper investigates Maurice Merleau-Ponty’s discussion of body and space and Gilles Deleuze’s reading of Francis Bacon’s work, in order to derive a renegotiated interrelation between habitual body, phenomenal space, preferential plane and constructive line. The resulting system is ap- plied as a filter to understand the sartorial fashion of Rei Kawakubo and Hussein Chalayan and their potential as a spatial prosthesis: the operative third skin. If the evolutionary nature of culture demands a constant change, how does the surface (...) of a third skin, which embodies the generative of stable/ unstable, respond to changes of context? The fleeting, shifting conditions of contemporary culture/ lifestyle rely upon, result in, and reflect one constant, change: change of working conditions, family structures, modes of inhabitation, relation networks, of userprofile and identity, of social and territorial boundaries. We occupy the shift- ing spatial parameters of a transitional supermodern environment. Culture, as enacted or embodied through each of these fields, is regulated by a number of abstract and factual variables that interplay constantly: time, space, movement, surface, individual, and data. Elizabeth Grosz argues that culture is an evolutionary effect: it regenerates itself in order to ensure the survival of the species. Each “prosthetic” expression of culture – language, fashion, architecture, etc. – changes repeatedly. Here change is not an end in itself, but a means. And the most successful prosthesis may not be the one that is able to answer the largest number of challenges, but one which itself undergoes a process of learning, self-modification, and differentiation – in short, a process of evolution. Any prosthesis is by nature an extension of the body. In the case of architecture and fashion the prosthesis addressing change is most often external to the body – a “cultural fur” or a surface phenomenon, that is, a highly profiled supplementary skin. As with all prostheses, their respective life-span depends on their ability to reflect a change in context and value systems. They are adapted or updated, if not, they vanish. Any situation of change is processed as a differentiation between the actual and the virtual of a given context. Grosz identifies distinctions between the actual and virtual, the real and the possible: the possible is a preformed real that has not yet received its final materiality, and thus delineates a range of options of becoming. The real is the blueprint of the possible, negotiated by factual limitations, and it is conjoint with the actual through a process of differentiation and divergence. The virtual comprises alternate variations of the actual, it defines a realm of deviation from the blueprint. In order to be responsive to change, the balance between the actual and virtual thus must be rendered unstable: “The virtual requires the actual to diverge, to differentiate itself, to proceed by way of division and disruption, forging modes of actualisation that will transform this virtual into others unforeseen or uncontained within it.” 4 The integration of the virtual allows a re-ordering of the blueprint, a return to the crossroad of possibilities, unlimiting and processing an alternative real, and establishing a state of continual change. A repeated change – not as a choice between a number of options but as a gradual process – marks the moment of evolution, and requires a dynamic system. Such a dynamic can be rendered as an adaptable, flexible, modular, mobile, or morphing system of change. The key lies with the fluency and ability of adaptation for the proposed differentiation between actual and virtual – thus it is an elastic change that is required. The nature of this elasticity is encoded in a repeated repositioning of the variables: a constant fine-tuning of a maximum number of parameters that engineer, alter and define the blueprint. When looking for a dynamic system that incorporates a transformation of skin or space, we are in search of dynamics through an operative surface, controlled by means of the constructive line. Both operative surface and constructive line are generative methods for the formation and form finding of the second and third skin of sartorial fashion and architecture respectively, as they both produce inhabitable or wearable envelopes with a specific responsiveness. Both professions share communication, coding and signage, form information programs, pattern charts, volume outlines, texture fields, surface operations, and implement electronic or digital extensions. In both, the constructive line shapes the surface twice: before production and in operation. The surface demarcates space, spatial envelope, enclosing garment, field of action. In which way can an operative system of the surface with stable/ unstable conditioning generate a phenomenological or evolutionary change in the reconstruction of body and context? How do time, space, movement, surface, individual and data interact in this framework? What is the impact of surface strategies and constructive line on that system? (shrink)

Let ξ ≥ 1 be a countable ordinal. We study the Borel subsets of the plane that can be made [Formula: see text] by refining the Polish topology on the real line. These sets are called potentially [Formula: see text]. We give a Hurewicz-like test to recognize potentially [Formula: see text] sets.

We study the cardinal invariants of measure and category after adding one random real. In particular, we show that the number of measure zero subsets of the plane which are necessary to cover graphs of all continuous functions may be large while the covering for measure is small.

v. 1. Propedêutica filosófia. v. 2. Ontognoseologia juridica.

A presente obra trata, de forma inigualável, das preliminares ao estudo da teoria tridimensional do direito, examinando a Filosofia e a Ciência do Direito, as dimensões da experiência jurídica, a posição do tridimensionalismo jurídico concreto, a dialética de complementaridade, o personalismo e o historicismo axiológico, as estruturas e os modelos do Direito no processo cultural e a visão integral do mundo jurídico.

Em linguagem didática e exposição sistemática, esta obra examina a relação existente entre o Direito e a História, permitindo a compreensão de diversos institutos jurídicos. O leitor poderá apreciar temas fundamentais da História do homem, como o Direito na cultura helênica, o Direito romano, o contratualismo e o Direito no Brasil, contando com citações de Rui Barbosa e Silvio Romero. Constitui leitura obrigatória aos cultores das ciências sociais e jurídicas que buscam uma visão aprofundada dos fundamentos do Direito.

Aristoteles (384-322 a.C.), es uno de los pensadores mas influyentes de la historia de la humanidad. Filosofo y cientifico, su obra incorpora una gran variedad de conocimientos que, a traves de la pedagogia directa, transmitio a sus alumnos. Metafisica es una obra magna del pensamiento occidental, compuesta de catorce libros -de los que presentamos una seleccion- representa un compendio de todo el saber aristotelico en el campo de la filosofia y, tambien, un elemento basico de la misma como ciencia del (...) saber y del conocimiento. Todos los problemas que ha debatido la metafisica hasta hoy tienen su origen en las ideas que Aristoteles plantea y desarrolla en este libro de libros. (shrink)

Notas à margem de um estudo de Clovis Bevilaqua; separata da Revista de Faculdade de Direito de São Paulo, ano 1947, pgs. 51 a 96.--A doutrina de Kant nos primórdios de nossa emancipação cultural. O padre Feijó.