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FRACTALS: CONSTRUCTION OR EMERGENCE? PART II. FRACTALS' EMERGENCE IN QUASI-EMPIRICAL APPROACH (Fraktale: konstrukcja czy emergencja? Cz.II. Emergencja fraktalna w podejsciu quasi-empirycznym)

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Pietrak J., Szydlowski M., Tambor P.

Zagadnienia Naukoznawstwa

2010

vol. 46

issue 2

271-302

The aim of the second part of this philosophical diptych is an attempt at discussing the place of the meta-subject reflection concerning fractal structures in classical issues of the philosophy of mathematics. The authors show that fractal structures lead toward essential broadening of that issues beyond traditional frames of the questions about the nature of mathematical objects (ontology of mathematics) or the status of mathematical knowledge (epistemology of mathematics). Particularly, they are interested in two problems: (1) Does process of generating fractal structures prove that co-called new mathematics has quasi-empirical character and in what meaning of that? and (2) Can the philosophical idea of emergence be applied to characterise the features of that structures?

FRACTALS: CONSTRUCTION OR EMERGENCE? PART I. FRACTAL UNITS OF EMERGENCE IN CLASSICAL CONCEPTUAL SCHEME (Fraktale: konstrukcja czy emergencja? Czesc I. Fraktalne jednostki emergencji w klasycznym schemacie pojeciowym)

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Pietrak J., Szydlowski M., Tambor P.

Zagadnienia Naukoznawstwa

2010

vol. 46

issue 1(183)

43-64

In the research project, which is to be composed of two substantively and logically connected papers, the authors form such a conceptual framework, that enables characteristic of fractal structures from the point of view of philosophical concept of emergence. In the first part, they present main ideas of the philosophy of emergence as well as they attempt at capturing emergent units in the process of fractals' generating. However, they maintain classical understanding of the relation in question. In the second part, due to demonstration of weaknesses of classical accounts as insufficient in specific context of mathematical structures under scrutiny, the authors show that the discourse about emergence in mathematics becomes meaningful and valid trough adaptation of quasi-empiric approach towards some issues in mathematics, approach grounded in philosophy of formal sciences.

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2 Zagadnienia Naukoznawstwa

2 2010

2 Pietrak J.

2 Szydlowski M.

2 Tambor P.

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FRACTALS: CONSTRUCTION OR EMERGENCE? PART II. FRACTALS' EMERGENCE IN QUASI-EMPIRICAL APPROACH (Fraktale: konstrukcja czy emergencja? Cz.II. Emergencja fraktalna w podejsciu quasi-empirycznym)

FRACTALS: CONSTRUCTION OR EMERGENCE? PART I. FRACTAL UNITS OF EMERGENCE IN CLASSICAL CONCEPTUAL SCHEME (Fraktale: konstrukcja czy emergencja? Czesc I. Fraktalne jednostki emergencji w klasycznym schemacie pojeciowym)