Bayesian and Information Geometry in signal processing

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Bayesian and Information Geometry in signal processing


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        <identifier identifierType="DOI">10.23723/9603/11315</identifier><creators><creator><creatorName>Ali Mohammad-Djafari</creatorName></creator></creators><titles>
            <title>Bayesian and Information Geometry in signal processing</title></titles>
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	    <date dateType="Created">Sat 30 Aug 2014</date>
	    <date dateType="Updated">Mon 2 Oct 2017</date>
            <date dateType="Submitted">Tue 16 Jan 2018</date>
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            <description descriptionType="Abstract"></description>

Cognitive-Constructivism, Quine, Dogmas of Empiricism, and Münchhausen’s Trilemma Julio Michael Stern∗ ∗ Institute of Mathematics and Statistics - University of São Paulo For the last 17 years, the Bayesian research group of IME-USP, at the Uni- versity of São Paulo, has been exploring Cog-Con - a specific version of Cognitive Constructivism that has among its most salient features a distinctive “objective” character and the support of specially designed tools of Bayesian Statistics. In previous presentations about the Cog-Con epistemological framework, we were asked several questions concerning possible parallels or contrasts with Quine’s epistemological framework. This article begins to explore this topic. Section 2 gives a succinct overview of Cog-Con - the Cognitive Construc- tivist epistemological framework used in this article, including Heinz von Foer- ster metaphor of Objects as tokens for eigen-solutions. The following sections explore similarities and differences between Quine’s and Cog-Con epistemologi- cal frameworks. Section 3 analyses the Two Dogmas of Empiricism denounced by Quine, as well as the Third Dogma proposed by Davidson, making some parallels between Quine’s and Cog-Con epistemological frameworks. Section 4 contrasts the two frameworks on their respective strategies to anchor a scientific theory to reality. Section 5 uses the Münchhausen Trilemma to continue the compara- tive analysis of the two frameworks, while Section 6 compares them on the role played by Ontology and Metaphysics. Section 7 brings our final remarks, con- cerning: Self-Identities at Neurath’s Ship, the Handling of Sticky Things, and the Handling of Circular Uncertainties. References - P. Aczel (1988). Non-Well-Founded Sets. CSLI, Stanford University. - V.Akman, M.Pakkan (1996). Nonstandard Set Theories and Information Management. Journal of Intelligent Information Systems. 6, 1, 5-31. - H.Albert (1985). Treatise on Critical Reason. Princeton University Press. - W.Borges, J.M.Stern (2007). The Rules of Logic Composition for the Bayesian Epis- temic e-Values. Logic Journal of the IGPL, 15, 5-6, 401-420. doi:10.1093/jigpal/jzm032 - C.A.B. Pereira, S. Wechsler, J.M. Stern (2008). Can a Significance Test be Genuinely Bayesian? Bayesian Analysis, 3, 1, 79-100. - W.O. Quine (1953). From a Logical Point of View. Harvard University Press. - W.O. Quine (1981a). Theories and Things. Harvard University Press. - W.O. Quine (1981b). Reply to Stroud. Midwest Studies In Philosophy, 6, 1, 473-476. - L.Segal (2001). The Dream of Reality. Heintz von Foerster’s Constructivism. Springer. - J.M.Stern (2011a). Constructive Verification, Empirical Induction, and Falibilist De- duction: A Threefold Contrast. Information, 2, 635-650 - J.M.Stern (2011b). Symmetry, Invariance and Ontology in Physics and Statistics. Symmetry, 3, 3, 611-635. - J.M.Stern, C.A.B.Pereira (2014). Bayesian Epistemic Values: Focus on Surprise, Mea- sure Probability! Logic Journal of the IGPL, 22, 2, 236-254. - J.M.Stern (2014). Jacob’s Ladder and Scientific Ontologies. Accepted for publication, Cybernetics & Human Knowing. 1