Joint Laver Diamonds and Grounded Forcing Axioms

In chapter 1 a notion of independence for diamonds and Laver diamonds is investigated. A sequence of Laver diamonds for κ is joint if for any sequence of targets there is a single elementary embedding j with critical point κ such that each Laver diamond guesses its respective target via j. In the case of measurable cardinals (with similar results holding for (partially) supercompact cardinals) I show that a single Laver diamond for κ yields a joint sequence of length κ, and I give strict separation results for all larger lengths of joint sequences. Even though the principles get strictly stronger in terms of direct implication, I show that they are all equiconsistent. This is contrasted with the case of θ-strong cardinals where, for certain θ, the existence of even the shortest joint Laver sequences carries nontrivial consistency strength. I also formulate a notion of jointness for ordinary ◊κ-sequences on any regular cardinal κ. The main result concerning these shows that there is no separation according to length and a single ◊κ-sequence yields joint families of all possible lengths. In chapter 2 the notion of a grounded forcing axiom is introduced and explored in the case of Martin\u27s axiom. This grounded Martin\u27s axiom, a weakening of the usual axiom, states that the universe is a ccc forcing extension of some inner model and the restriction of Martin\u27s axiom to the posets coming from that ground model holds. I place the new axiom in the hierarchy of fragments of Martin\u27s axiom and examine its effects on the cardinal characteristics of the continuum. I also show that the grounded version is quite a bit more robust under mild forcing than Martin\u27s axiom itself

Ontology and the foundations of mathematics

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1999.Includes bibliographical references."Ontology and the Foundations of Mathematics" consists of three papers concerned with ontological issues in the foundations of mathematics. Chapter 1, "Numbers and Persons," confronts the problem of the inscrutability of numerical reference and argues that, even if inscrutable, the reference of the numerals, as we ordinarily use them, is determined much more, precisely than up to isomorphism. We argue that the truth conditions of a variety of numerical modal and counterfactual sentences (whose acceptance plays a crucial role in applications) place serious constraints on the sorts of items to which numerals, as we ordinarily use them, can be taken to refer: Numerals cannot be taken to refer to objects that exist contingently such as people, mountains, or rivers, but rather must be taken to refer to objects that exist necessarily such as abstracta. Chapter 2, "Modern Set Theory and Replacement," takes up a challenge to explain the reasons one should accept the axiom of replacement of Zermelo-Fraenkel set theory, when its applications within ordinary mathematics and the rest of science are often described as rare and recondite. We argue that this is not a question one should be interested in; replacement is required to ensure that the element-set relation is well-founded as well as to ensure that the cumulation of sets described by set theory reaches and proceeds beyond the level w of the cumulative hierarchy. A more interesting question is whether we should accept instances of replacement on uncountable sets, for these are indeed rarely used outside higher set theory. We argue that the best case for (uncountable) replacement comes not from direct, intuitive considerations, but from the role replacement plays in the formulation of transfinite recursion and the theory of ordinals, and from the fact that it permits us to express and assert the (first-order) content of the modern cumulative view of the set theoretic universe as arrayed in a cumulative hierarchy of levels. Chapter 3, "A No-Class Theory of Classes," makes use of the apparatus of plural quantification to construe talk of classes as plural talk about sets, and thus provide an interpretation of both one- and two-sorted versions of first-order Morse-Kelley set theory, an impredicative theory of classes. We argue that the plural interpretation of impredicative theories of classes has a number of advantages over more traditional interpretations of the language of classes as involving singular reference to gigantic set-like entities, only too encompassing to be sets, the most important of these being perhaps that it makes the machinery of classes available for the formalization of much recent and very interesting work in set theory without threatening the universality of the theory as the most comprehensive theory of collections, when these are understood as objects.by Gabriel Uzquiano.Ph.D

Contingent valuation of river pollution control and domestic water supply in Kenya

The basic theme of this study is that determination of the economic value of water resources is a necessary condition for rational decision-making and management of these environmental assets, and their associated public goods, in developing countries. The research particularly evaluates the contingent valuation (CV) method as a technique for evaluating increments and decrements in environmental and natural resource service flows, and estimates households' evaluations for improvements in river water quality and connections to piped water supply for domestic uses. The study objectives were to (a) estimate the economic value of piped water supply and improved water quality in the Nzoia River Basin, Kenya, (b) evaluate the feasibility of using the CV technique to value an environmental amenity and its related quasi-public service in rural settings where respondents have limited education and monetary resources, (c) examine the role of temporal dimensions of bid payments (i e, frequency of payments) in contingent values for environmental commodities, (d) empirically investigate embedding effect bias in contingent valuation of improvements in river water quality improvement in a less developed economy, and (e) evaluate the role of water connection charges in households' willingness to hook onto piped water supply in Webuye Division, Kenya. Empirical analysis and estimates of the non-market value which local people assign to water quality in the Nzoia River and a private household water connection is based on a detailed survey of a representative sample of 311 households in Webuye Division of Bungoma District, Kenya. In an on-site survey carried out in May through September 1995, contingent markets were developed for the two goods, (1) improved river water quality, and, (2) provision of a private connection to water supply. The corresponding willingness to pay (WTP) values are explained using Ordinary Least Square regression models. Whatever the good, the WTP is seen to increase with income. However, the effects of other factors are more specific to the contingent good. In order of strength, the other determinants of WTP "quality" are sex, age, household ranking of status of domestic water source, distance from river to household residence, the other factors affecting WTP "connections" are existing source of water supply, household size, ranking of river water quality, and age of household head. On the whole, residents accepted the exercise of contingent valuation and were willing to pay important amounts (Ksh 459 and Ksh 386 on average per household per year, respectively, for goods 1 and 2). Discussion issues include policy significance of the resulting WTPs in terms of the demand for river pollution control and individual household water connections, the effect of the goods upon the CV evaluation process, the "Third World" impacts of frequency of payments in contingent valuation, including perceived-frequency and income-smoothing routes, the embedding effect in WTP values for water pollution abatement in the Nzoia River basin, the importance of pricing influences, specially payment profiles for initial connection charges, on household decisions to connect to piped water systems, and limitations of the study

Virtual Reality: Consciousness Really Explained! (Third Edition)

Employing the ideas of modern mathematics and biology, seen in the context of Ernst Cassirer's "Symbolic Forms, the author presents an entirely new and novel solution to the classical mind-brain problem. This is a "hard" book, I'm sorry, but it is the problem itself, and not me which has made it so. I say that Dennett, and, indeed, the whole of academia is wrong

Performativities, Virtualities, Abstractions, and Cunningham's BIPED

This thesis explores the complex relations between subjective perception and dance movements, mainly exemplified by drawing on two short extracts from Merce Cunningham's choreography BIPED (1999). The central aim of the study is to formulate a performative phenomenological inquiry, which moves beyond an identification of essences, and towards an understanding of the lived experience of a dance performance as being grounded on iterations of the "abstract". The concept of the abstract primarily signifies an alternative mode of understanding Henry Bergson's notion of duration. Considering Gilles Deleuze's reading of Bergson's intuition as a method to divide the experience of a lived present into a temporal difference in kind between the virtual and the actual, this thesis suggests a complementary division of duration into virtual and actual kinds of abstraction. In addition to Bergson's method of intuition, the discussion is phenomenologically rooted in Maurice Merleau-Ponty's concept of the body image and Gaston Bachelards idea of non-causal reverberation. As with the case of intuition, those phenomenological concepts are applied unconventionally. Rather than serving as a pre-objective ontological basis for an analytical and scientific understanding of subjective embodiment, the notion of a reverberating body image is here treated as a form of mimesis, performatively constituted through symbolic and representational practices. Hence, in phenomenological terms, the rationale of the thesis is predominantly sustained by the philosophy of Ernst Cassirer, arguing that reality cannot be approached directly, but only through the concept of the symbol. The viewpoint from where I speak has performative cybernetic characteristics, continuously and dynamically transgressing boundaries and reconstituting itself through iterative and citational practices. Additionally, as I move between the analytical and the intuitive, as well as between the virtual and the actual, the formal structure of the thesis corresponds to a liminal transformation of the speaking subjectivity

Emergent Design

Explorations in Systems Phenomenology in Relation to Ontology, Hermeneutics and the Meta-dialectics of Design SYNOPSIS A Phenomenological Analysis of Emergent Design is performed based on the foundations of General Schemas Theory. The concept of Sign Engineering is explored in terms of Hermeneutics, Dialectics, and Ontology in order to define Emergent Systems and Metasystems Engineering based on the concept of Meta-dialectics. ABSTRACT Phenomenology, Ontology, Hermeneutics, and Dialectics will dominate our inquiry into the nature of the Emergent Design of the System and its inverse dual, the Meta-system. This is an speculative dissertation that attempts to produce a philosophical, mathematical, and theoretical view of the nature of Systems Engineering Design. Emergent System Design, i.e., the design of yet unheard of and/or hitherto non-existent Systems and Metasystems is the focus. This study is a frontal assault on the hard problem of explaining how Engineering produces new things, rather than a repetition or reordering of concepts that already exist. In this work the philosophies of E. Husserl, A. Gurwitsch, M. Heidegger, J. Derrida, G. Deleuze, A. Badiou, G. Hegel, I. Kant and other Continental Philosophers are brought to bear on different aspects of how new technological systems come into existence through the midwifery of Systems Engineering. Sign Engineering is singled out as the most important aspect of Systems Engineering. We will build on the work of Pieter Wisse and extend his theory of Sign Engineering to define Meta-dialectics in the form of Quadralectics and then Pentalectics. Along the way the various ontological levels of Being are explored in conjunction with the discovery that the Quadralectic is related to the possibility of design primarily at the Third Meta-level of Being, called Hyper Being. Design Process is dependent upon the emergent possibilities that appear in Hyper Being. Hyper Being, termed by Heidegger as Being (Being crossed-out) and termed by Derrida as Differance, also appears as the widest space within the Design Field at the third meta-level of Being and therefore provides the most leverage that is needed to produce emergent effects. Hyper Being is where possibilities appear within our worldview. Possibility is necessary for emergent events to occur. Hyper Being possibilities are extended by Wild Being propensities to allow the embodiment of new things. We discuss how this philosophical background relates to meta-methods such as the Gurevich Abstract State Machine and the Wisse Metapattern methods, as well as real-time architectural design methods as described in the Integral Software Engineering Methodology. One aim of this research is to find the foundation for extending the ISEM methodology to become a general purpose Systems Design Methodology. Our purpose is also to bring these philosophical considerations into the practical realm by examining P. Bourdieu’s ideas on the relationship between theoretical and practical reason and M. de Certeau’s ideas on practice. The relationship between design and implementation is seen in terms of the Set/Mass conceptual opposition. General Schemas Theory is used as a way of critiquing the dependence of Set based mathematics as a basis for Design. The dissertation delineates a new foundation for Systems Engineering as Emergent Engineering based on General Schemas Theory, and provides an advanced theory of Design based on the understanding of the meta-levels of Being, particularly focusing upon the relationship between Hyper Being and Wild Being in the context of Pure and Process Being

Fourth NASA Langley Formal Methods Workshop

This publication consists of papers presented at NASA Langley Research Center's fourth workshop on the application of formal methods to the design and verification of life-critical systems. Topic considered include: Proving properties of accident; modeling and validating SAFER in VDM-SL; requirement analysis of real-time control systems using PVS; a tabular language for system design; automated deductive verification of parallel systems. Also included is a fundamental hardware design in PVS

Use of wavelet-packet transforms to develop an engineering model for multifractal characterization of mutation dynamics in pathological and nonpathological gene sequences

This study uses dynamical analysis to examine in a quantitative fashion the information coding mechanism in DNA sequences. This exceeds the simple dichotomy of either modeling the mechanism by comparing DNA sequence walks as Fractal Brownian Motion (fbm) processes. The 2-D mappings of the DNA sequences for this research are from Iterated Function System (IFS) (Also known as the Chaos Game Representation (CGR)) mappings of the DNA sequences. This technique converts a 1-D sequence into a 2-D representation that preserves subsequence structure and provides a visual representation. The second step of this analysis involves the application of Wavelet Packet Transforms, a recently developed technique from the field of signal processing. A multi-fractal model is built by using wavelet transforms to estimate the Hurst exponent, H. The Hurst exponent is a non-parametric measurement of the dynamism of a system. This procedure is used to evaluate gene-coding events in the DNA sequence of cystic fibrosis mutations. The H exponent is calculated for various mutation sites in this gene. The results of this study indicate the presence of anti-persistent, random walks and persistent sub-periods in the sequence. This indicates the hypothesis of a multi-fractal model of DNA information encoding warrants further consideration.;This work examines the model\u27s behavior in both pathological (mutations) and non-pathological (healthy) base pair sequences of the cystic fibrosis gene. These mutations both natural and synthetic were introduced by computer manipulation of the original base pair text files. The results show that disease severity and system information dynamics correlate. These results have implications for genetic engineering as well as in mathematical biology. They suggest that there is scope for more multi-fractal models to be developed

Workshop Notes of the Seventh International Workshop "What can FCA do for Artificial Intelligence?"

International audienceThese are the proceedings of the seventh edition of the FCA4AI workshop (http://www.fca4ai.hse.ru/) co-located with the IJCAI 2019 Conference in Macao (China). Formal Concept Analysis (FCA) is a mathematically well-founded theory aimed at classification and knowledge discovery that can be used for many purposes in Artificial Intelligence (AI). The objective of the FCA4AI workshop is to investigate two main issues: how can FCA supports various AI activities (knowledge discovery, knowledge engineering, machine learning, data mining, information retrieval, recommendation. . . ), and how can FCA be extended in order to help AI researchers to solve new and complex problems in their domain

A thousand TV shows : applying a rhizomatic lens to television genres

One frequent technique for studying television is through genre. However, with the complex television environment of the 21st century, many genre studies do not adequately account for how generic television programs intersect other generic traits. This study probes how genre works within complex television narratives and proposes a new way of thinking about genre. Through Deleuze and Guattari's (1987) theory of the rhizome, I will suggest an interconnected understanding of genre characteristics. The television landscape is a complex, dynamic structure; the assortment of programs and the traits of those programs differ greatly from one moment to the next. Therefore, this study will propose a meta-theory that enables studying this landscape. The theory of the generic rhizome challenges simplistic readings of television texts; opens texts up to endless possible interpretations and insights; and it flattens cultural hierarchies. In two studies, which look at sitcoms and Westerns, I tease out this theory and study television shows in a way that mines, rather than flattens, the complexity of the medium.Includes bibliographical reference