Quantum Mechanics Versus a Method of Relativized Conceptualization

Mugur-Schächter, Mioara

doi:10.1007/0-306-48144-8_7

Cited by 1 publication

(8 citation statements)

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“…The current author has for many years held that this interpretation is both deep and important (Mugur Schächter 1992c;Mugur Schächter 2002b;Mugur Schächter 2006). However, it does not provide any pragmatic guidance for the effective construction of the factual probability law asserted to apply to the experimental situation.…”

Section: Karl Popper's Propensity Interpretation Of Probabilitiesmentioning

confidence: 92%

“…As a result, this cognitive situation and its consequences have never been characterised explicitly, thoroughly and globally. † For details, see Mugur Schächter (1984;1991;1992b;1992c;1993;1995;1997a;2002a;2002b;2002c;2006; 2011) ‡ Our use of the word 'signify' here and elsewhere in the current paper is similar to its use in semiotics where a signifier (a syntactic element) is used to signify (refer to and communicate) the signified (some concept). § We make a clear distinction here between fundamental quantum mechanics, where no models are explicitly formed, or even permitted in principle, and any preceding or subsequent theories of microscopic physical entities (such as atomic and nuclear physics and elementary particle theories), which quite explicitly introduce models.…”

Section: The Framework For Treating Kolmogorov's Aporiamentioning

confidence: 97%

“…In this way, the concept of a pre-probability tree of the pair (G, V M ) requires an extended and deeper concept of 'probability' unified with a corresponding logic of all the events involved. This programme was partially achieved in the papers Mugur Schächter (1992a;2002a;2002b;2006) in terms that are generalised to any relative description † . 3.3.5.…”

Section: Cn) P(g C)]mentioning

confidence: 99%

“…We believe that the descriptional form D/G, ms G , V M / (with its inherent relativities, its development dominated by methodological decisions, and its epistemological consequences (Mugur Schächter 2002a;2002b;2006;2011;2013)) constitutes a crucial insight into the way humans generate knowledge.…”

Section: Universality and Perception Of The Possibility Of A General mentioning

confidence: 99%

“…Furthermore, the semantic content will be dispersed through the presentation, which hides the flow of its growth during the construction. For a fuller appreciation of how MRC has been developed into a coherent and rigorous whole combining factual content and rationality, see Mugur Schächter (2006) -this is the most accomplished version to date, but, at the moment, only available in French -but also Mugur Schächter (2002b), and perhaps even Mugur Schächter (2002a) -the treatment in these references is more primitive, but they are both available in English.…”

Section: Universality and Perception Of The Possibility Of A General mentioning

confidence: 99%

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On the concept of probability

Mugur-Schächter¹

2014

Math. Struct. Comp. Sci.

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In this paper, we discuss the crucial but little-known fact that, as Kolmogorov himself claimed, the mathematical theory of probabilities cannot be applied to factual probabilistic situations. This is because it is nowhere specified how, for any given particular random phenomenon, we should construct, effectively and without circularity, the specific and stable distribution law that gives the individual numerical probabilities for the set of possible outcomes. Furthermore, we do not even know what significance we should attach to the simple assertion that such a distribution law “exists”. We call this problem Kolmogorov's aporia†.We provide a solution to this aporia in this paper. To do this, we first propose a general interpretation of the concept of probability on the basis of an example, and then develop it into a non-circular and effective general algorithm of semantic integration for the factual probability law involved in a specific factual probabilistic situation. The development of the algorithm starts from the fact that the concept of probability, unlike a statistic, does not apply to naturally pre-existing situations but is a conceptual artefact that ensures, locally in space and time, a predictability that is more stable and definite than that permitted by primary statistical data.The algorithm, which is constructed within a method of relativised conceptualisation, leads to a probability distribution expressed in rational numbers and involving a sort of quantification of the factual concept of probability. Furthermore, it also provides a definite meaning to the simple assertion that a factual probability law exists. We also show that the semantic integration algorithm is compatible with the weak law of large numbers.The results we give provide a complete solution to Kolmogorov's aporia. They also define a concept of probability that is explicitly organised into a semantic, epistemological and syntactic whole. In a broader context, our results can be regarded as a strong, pragmatic and operational specification of Karl Popper's propensity interpretation of probabilities.

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Section: Karl Popper's Propensity Interpretation Of Probabilitiesmentioning

confidence: 92%