Nonstandard set theories and information management

Akman, Varol; Pakkan, Müjdat

doi:10.1007/bf00712384

Cited by 5 publications

(4 citation statements)

References 23 publications

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“…Formally, a set of circular (coss-referent and recursive) definitions can be handled rigorously using non-well-founded set theories, see Aczel (1988), Barwise and Etchemendy (1987), and Barwise and Moss (1996). Computationally, circularly defined data sets can be represented, stored and manipulated using appropriate data structures, see Akman and Pakkan (1996), Iordanov (2010), and Pakkan and Akman (1995).…”

Section: Objects Are Tokens For Eigen-solutions: Precision Stabilitymentioning

confidence: 99%

A sharper image: the quest of science and recursive production of objective realities

Stern

2020

Principia

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This article explores the metaphor of Science as provider of sharp images of ourenvironment, using the epistemological framework of Objective Cognitive Constructivism.These sharp images are conveyed by precise scientific hypotheses that, in turn, are encodedby mathematical equations. Furthermore, this article describes how such knowledge is pro-duced by a cyclic and recursive development, perfection and reinforcement process, leadingto the emergence of eigen-solutions characterized by the four essential properties of preci-sion, stability, separability and composability. Finally, this article discusses the role playedby ontology and metaphysics in the scientific production process, and in which sense theresulting knowledge can be considered objective.

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Section: Objects Are Tokens For Eigen-solutions: Precision Stabilitymentioning

confidence: 99%

A sharper image: the quest of science and recursive production of objective realities

Stern

2020

Principia

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“…In fact, every object that can be defined in AFA ends up being isomorphic to an element in the universe of ZFC. The only advantage in this change is that it simplifies the treatment of circularities, in particular those that arise in the use of information and knowledge [Akman- Pakkan 1996]. Using coalgebraic methods-i.e.…”

Section: Existence Of States Of the Worldmentioning

confidence: 99%

“…The entire program of research that Jon Barwise initiated on situation theory and related formalisms, based on his idea that logic is a branch of applied mathematics, is clearly an inspiration for the approach we follow here [Barwise-Etchemendy 1987], [Barwise-Moss 1996], [Barwise-Seligman 1997]. In computer science, the advantages of adopting set theories closer to common sense have been emphasized in [Pakkan-Akman 1994] [Akman- Pakkan 1996]. More recently, Jan Mycielski has presented a universal set theory in which the class of mathematical objects can be given physical interpretations [Mycielski 2006], [Mycielski 2007].…”

Section: Introductionmentioning

confidence: 99%

Economic theory and the Alternative Set Theory AFA-+AD+DC

Tohmé

2009

Logic Journal of IGPL

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Many authors in the discipline as well as outsiders have claimed that the main results from Mathematical Economics are far removed from real world phenomena. A more precise version of this position is that one of the main reasons for this unrealistic stance is the use of the wrong formal tools. So, for example, it has been pointed out that the computability of choice functions as well as the existence of economic equilibria and of states of the world may not be ensured in general if the assumed set theory is ZFC. We will show that there exists a very natural set theory that overcomes some formal limitations of contemporary economic theory. A switch to an alternative set theory helps to obtain in a more natural way results widely accepted by mathematical economists. Moreover, alternative set-theoretical frameworks convey different intuitions about how agents behave when solving problems. We claim that AFA − +AD +DC is the adequate alternative set-theoretical universe for economic theory.

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“…The variation in these predictions can be explained by a combination of the level of imprecision in the theory and by properties of the end-user's experiment. For instance, the latter source of variation is influenced by properties of the equipment, including the precision, accuracy, and resolution of measuring devices [16,17], and also error bounds for fundamental constants and calibration factors [18][19][20][21][22][23][24][25][26]. We propose to choose a pragmatic hypothesis in such a way that the imprecision in the end-user's predictions is mostly due to his experimental conditions and not due to the level of imprecision in the theory that he uses.…”

Section: Introductionmentioning

confidence: 99%

Pragmatic Hypotheses in the Evolution of Science

Esteves

Izbicki

Stern

et al. 2019

Entropy

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This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais.

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Nonstandard set theories and information management

Cited by 5 publications

References 23 publications

A sharper image: the quest of science and recursive production of objective realities

A sharper image: the quest of science and recursive production of objective realities

Economic theory and the Alternative Set Theory AFA-+AD+DC

Pragmatic Hypotheses in the Evolution of Science

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