Ontologies: On the Concepts of: Possibility, Possible, 'Acaso', Aleatorial and Chaos

Maria Odete Madeira

Massacritica, Lda.

Carlos Pedro Dos Santos Gonçalves

UNIDE - ISCTE Business School - Lisbon University Institute

September 7, 2009

Abstract:
In addressing the interdisciplinary field that is growing at the intersection between chaos theory and risk science it becomes necessary to reconsider the notion of chaos in its linkages with the notions of possible, possibility, “acaso” and aleatorial.

Aiming at such an interdisciplinary effectiveness, the present article addresses the notions of possible, possibility, “acaso”, aleatorial and chaos in terms of their respective constituent and constitutive systemic topoi, from the formative ontological systemic dynamics, structurally dependent upon the initial conditions of the respective systems and cognitively computed/processed by these same systems, from the perception and recognition of themselves, as individuated resonating rotative positions, in the inter-systemic web of survival.

The (inter)systemic risk is, then, addressed in connection with the chaos in the deterministic systems. An example of Malcolm effects and synchronized risk being researched upon for a two-dimensional nonlinear map that produces multifractal chaos. This allows for the signaling of conceptual linkages that occur at the intersection of chaos theory and risk science, between homeostatic mechanisms, synchronization and chaos.

Keywords: Possibility, possible, “acaso”, aleatorial, stochastic, clinamen, chaos, Malcolm effect, multifractal chaos, synchronization, risk, risk science, multifractal self-organized criticality

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1469613

Can an amoeba be a genius?

By Maria Odete Madeira

What does the notion of genius synthesize? What values? What cultural, social and, above all, political values, are involved here?

Any organism is dispositionally gifted to perform tasks that concern its survival, some organisms exhibit greater ease in the performance of some tasks while others exhibit greater ease in the performance of other tasks. Genius is just a name for those that can maximize these abilities in order to transcend patterns considered normal, but this depends on training, willpower, and also of available means. All of us can be geniuses in different ways. For instance, a "simple" domestic worker, especially gifted to that kind of work, can be a genius, even if society would not classify such a worker as a genius, because it is a type of work without sufficiently relevant social value (no Nobel prize for domestic workers).

In certain societies the genius would be the one who found good solutions to the community's problems, and, not necessarily, for instance, the individual capable of feats of abstract reasoning but otherwise socially awkward and capable of having contra-adaptive responses when put before basic survival problems. Thus, for instance, the pattern of genius, in the first case, might depend upon an ability for common sense thinking and/or for finding good responses to adaptive problems. In such a sense, even an amoeba or any organism that reveals robust adaptive effectiveness can be considered a genius.

All the neurobiological cognitive work is supported by an image space and a dispositional space, supported, in turn, by distinct neural bases activated in the limbic cortices and in subcortical nuclei, whose work depends upon and is inseparable of an integrated organismic work, in permanent interface with the environment. And when we speak of organism we speak of bones, flesh, blood, homeostatic mechanisms, emotions, feelings, etc…

Anaximander - "apeiron"

By: Maria Odete Madeira

Maybe the most important notion of Anaximander' s thinking is the notion of apeiron. The apeiron was described and interpreted by the community of the Greek thinkers, and among them Aristotle (Metaph), as a kind of undifferentiated mixture, without defined limits and rigorously uncharacterizable.

But, in the physical system of Anaximander, every process is conceived as a motion of separation. The apeiron corresponds to an initial chaos, which birthed a vortex that initiated a separation process. In the apeiron exists a principle of latent separation.

The mixture must be interpreted as a state of mutual neutralization of potentially separable opposites, a latent state of indifference.

What is a thing?

By: Maria Odete Madeira

What is a thing (Medieval Latin causa)? What do we think, or can think about, when we state and refer ourselves to the word thing? An event is a thing? A feeling is a thing? A thought is a thing? A process is a thing? A system is a thing? Plans, strategies and convictions are things? The beautiful, the good, the bad and the ugly are things? We, the humans, are things? Is God a thing?What makes a thing a thing?

The Latin word causa also means res. From res formed the terms reality and realism. In general terms, the notion of causa applies to all reality and means everything that exists, or can exist.

In scholastic philosophy, res was an attribute of the being, in Thomas Aquinas it was a synonym of quiddity. In modern and contemporaneous philosophy the being of a thing is being an existent, any existent, that, as such, can be thought on and known.

Afairesis, Abstractio or Abstraction

By: Maria Odete Madeira

Abstractio was the term chosen by Boetius for the translation of the Greek term afairesis. Abstractio signalizes a systemic operative cognitive dynamics through which a part, a characteristic or an element of an integrated systemic whole is separated from that same whole upon which it constitutively depends, as concrete existent, particular and contingent, to be constituted (that part) as an object of thought, conceptually existent and available to be approached and cognitively synthesized with a generalizable objective value.

The Problem of Time in Quantum Cosmology and Non-Chronometric Temporality

Carlos Pedro dos Santos Gonçalves

UNIDE - ISCTE Business School - Lisbon University Institute

Maria Odete Madeira

Massacritica, Lda.July 23, 2009

Abstract:

We review two lines of argument regarding the problem of time in quantum cosmology and in quantum gravity, one that invokes the path integral formalism for quantum gravity to state the absence of time between two three-geometries, and another that defends the absence of time, as a fundamental notion in physics, in terms of: (a) the configuration space argument, put forward by Barbour, Smolin and Kauffman, and (b) the Wheeler-DeWitt equation. We argue that although being correct with respect to a space-time dependent physical chronometrizable clock-time frame, both of these lines of argument fail with respect to a general sense of temporality, expressed in terms of the more elementary notions of a before and an after of a quantum computation. With respect to the first line of argument, it is shown that the early works on the subject address two kinds of temporalities, one that is the space-time geometric dependent temporality, which coincides with the usual definition of a space-time dependent physical chronometrizable clock-time frame, the other is a temporality associated to the notions of input and output of a general quantum gravity computation, that is expressed, in the theoretical discourse of quantum gravity, through the usage of the concepts of: (1) propagation of a wave functional in superspace, as addressed by Wheeler; (2) transition amplitudes of three-geometries and (3) the pathintegral formalism, used to calculate such amplitudes, as addressed by Hartle and Hawking. While the first temporality (space-time dependent temporality) disappears from the theory, the second plays a fundamental role, not only in the several aspects of the theory’s construction, but in the clock-time independence as well, as Wheeler showed. Given this notion of time, different from a chronometrizable, space-time geometry internal notion, we search for a general mathematical and logical structure that is capable of addressing it from a formal point of view. This is done through a family of mathematical structures that is more general than the mathematical category. These structures not only will allow us to address the nature of the temporality present in the transition amplitudes between two three-geometries, but they will also allow us to refute the configuration space argument and to show how a static clock-time-independent quantum state, can be put into a non-clock-time processual expression in terms of fine-grained computational histories, obtained from the relations between different observable’s bases.

Keywords: quantum cosmology, time, relational structures, relational nexus

Working Paper Series

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1438013

http://www.scribd.com/doc/14810246/Time-in-Quantum-Cosmology

A Systems Theoretical Formal Logic for Category Theory

by

Carlos Pedro Gonçalves

Mathematics researcher at UNIDE-ISCTE

cpdsg.research@gmail.com (primary); cpdsg@iscte.pt

Maria Odete Madeira

Interdisciplinary researcher in philosophy of science and systems science

mosmg.research@gmail.com (primary), mariaodete.sm@gmail.com

Abstract

A systems theoretical thinking on the categorial object and morphism is developed, leading to areflection on the philosophical and mathematical foundations of category theory, which allowsfor the introduction of a formal language for category theory and of a categorial calculus as amorphic web-based logical calculus. A formal system, built from such calculus, is proposed and the logical semantics is addressed. Both syntax and semantics are independent from set theory.

Keywords: System, object, morphism, morphic web, individuation, entity, identity, categories,n-categories

1. Introduction

"In the present work, we propose a systems theoretical approach to category theory, introducing a formal language (LCat) and a formal system (FCat′ ), that incorporate the main system theoretic foundations of the categorial object and morphism. The formal system is based upon a morphic web calculus that we call categorial calculus. Both the logical syntax and semantics of such calculus are addressed and shown to be independent from set theory, which makes the theory itself independent from set theory.

In section 2., we address the categorial object as a system, providing for the philosophical ground of the main work. In section 3., we introduce the formal language LCat and a formal system FCat1−6 that is able to address the simpler structures of category theory.

In section 4., we address the morphic wholes as systems, through the so-called border marker. This leads to a development of the identity laws into a more ontologically and systemically complete logic, that addresses both systemic individuation and identity. The formal system, developed in section 4., is called FCat′ and it is capable of dealing with category theory, n-category theory and a different class of structures that cross systemic levels, which are more complex hierarchical structures than the ones worked upon in n-category theory.

In section 5., we address the logical semantics. In section 6. we conclude with a few final remarks.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1396841