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Prasenā, Prasīnā & Prasannā: The Evidence of the Niśvāsaguhya and the Tantrasadbhāva

100%
Vasudeva S.
Cracow Indological Studies
|
2014
|
vol. 16: Tantric Traditions in Theory and Practice
369-390
EN
The literature of the Śaiva Mantramārga evidences differing strategies of incorporating prasenā divination into its theoretical frameworks. The early Niśvāsaguhya confines prasenās a prognosticatory role in support of a more common method of dream divination used to determine reasons for failed initiation. Questions of intertextuality and doctrinal dependence are raised when the Trika’s Tantrasadbhāva envisages prasenās as fulfilling exactly the same function.
2
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The Computational and Pragmatic Approach to the Dynamics of Science

80%
Marciszewski W.
Filozofia i nauka. Studia filozoficzne i interdyscyplinarne
|
2020
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vol. 8/1
31-67
EN
Sciencemeans here mathematics and those empirical disciplines which avail themselves of mathematical models. The pragmaticapproachis conceived in Karl R. Popper’s The Logic of Scientific Discovery(p.276) sense: a logical appraisal of the success of a theory amounts to the appraisal of its corroboration. This kind of appraisal is exemplified in section 6 by a case study—on how Isaac Newton justified his theory of gravitation. The computationalapproach in problem-solving processes consists in considering them in terms of computability: either as being performed according to a model of computation in a narrower sense, e.g., the Turing machine, or in a wider perspective—of machines associated with a non-mechanical device called “oracle”by Alan Turing (1939). Oracle can be interpreted as computer-theoretic representation of intuitionor invention. Computational approach in an-other sense means considering problem-solving processes in terms of logical gates, supposed to be a physical basis for solving problems with a reasoning.Pragmatic rationalismabout science, seen at the background of classical ration-alism (Descartes, Gottfried Leibniz etc.), claims that any scientific idea, either in empirical theories or in mathematics, should be checked through applications to problem-solving processes. Both the versions claim the existence of abstract objects, available to intellectual intuition. The difference concerns the dynamics of science: (i) the classical rationalism regards science as a stationary system that does not need improvements after having reached an optimal state, while (ii) the pragmatical ver-sion conceives science as evolving dynamically due to fertile interactions between creative intuitions, or inventions, with mechanical procedures.The dynamics of science is featured with various models, like Derek J.de Solla Price’sexponential and Thomas Kuhn’s paradigm model (the most familiar instanc-es). This essay suggests considering Turing’s idea of oracle as a complementary model to explain most adequately, in terms of exceptional inventiveness, the dynam-ics of mathematics and mathematizable empirical sciences.
3
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The Computational and Pragmatic Approach to the Dynamics of Science

80%
Marciszewski W.
Filozofia i Nauka
|
2020
|
vol. 8
4
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Does Science Progress Towards Ever Higher Solvability Through Feedbacks Between Insights and Routines?

71%
Marciszewski W.
Studia Semiotyczne
|
2018
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vol. 32
|
issue 2
153-185
EN
The affirmative answer to the title question is justified in two ways: logical and empirical. (1) The logical justification is due to Gödel’s discovery (1931) that in any axiomatic formalized theory, having at least the expressive power of PA (Peano Arithmetic), at any stage of development there must appear unsolvable problems. However, some of them become solvable in a further development of the theory in question, owing to subsequent investigations. These lead to new concepts, expressed with additional axioms or rules. Owing to the so-amplified axiomatic basis, new routine procedures like algorithms, can be reached. Those, in turn, help to gain new insights which lead to still more powerful axioms, and consequently again to ampler algorithmic resources. Thus scientific progress proceeds to an ever higher scope of solvability. (2) The existence of such feedback cycles – in a formal way rendered with Turing’s systems of logic based on ordinal (1939) – gets empirically supported by the history of mathematics and other exact sciences. An instructive instance of such a process is found in the history of the number zero. Without that insight due to some ancient Hindu mathematicians there could not arise such an axiomatic theory as PA. It defines the algorithms of arithmetical operations, which in turn help intuitions; those, in turn, give rise to algorithmic routines, not available in any of the previous phases of the process in question. While the logical substantiation of the point of this essay is a well-established result of logico-semantic inquiries, its empirical claim, based on historical evidences, remains open for discussion. Hence the author’s intention to address philosophers and historians of science, and to encourage their critical responses.
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