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Stathis Livadas
University of Patras (Alumnus)
  1.  13
    Talking About Models: The Inherent Constraints of Mathematics.Stathis Livadas - 2020 - Axiomathes 30 (1):13-36.
    In this article my primary intention is to engage in a discussion on the inherent constraints of models, taken as models of theories, that reaches beyond the epistemological level. Naturally the paper takes into account the ongoing debate between proponents of the syntactic and the semantic view of theories and that between proponents of the various versions of scientific realism, reaching down to the most fundamental, subjective level of discourse. In this approach, while allowing for a limited discussion of physical (...)
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  2.  55
    What is the Nature of Mathematical–Logical Objects?Stathis Livadas - 2017 - Axiomathes 27 (1):79-112.
    This article deals with a question of a most general, comprehensive and profound content as it is the nature of mathematical–logical objects insofar as these are considered objects of knowledge and more specifically objects of formal mathematical theories. As objects of formal theories they are dealt with in the sense they have acquired primarily from the beginnings of the systematic study of mathematical foundations in connection with logic dating from the works of G. Cantor and G. Frege in the last (...)
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  3.  20
    The Subjective Roots of Forcing Theory and Their Influence in Independence Results.Stathis Livadas - 2015 - Axiomathes 25 (4):433-455.
    This article attempts a subjectively based approach, in fact one phenomenologically motivated, toward some key concepts of forcing theory, primarily the concepts of a generic set and its global properties and the absoluteness of certain fundamental relations in the extension to a forcing model M[G]. By virtue of this motivation and referring both to the original and current formulation of forcing I revisit certain set-theoretical notions serving as underpinnings of the theory and try to establish their deeper subjectively founded content (...)
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  4.  8
    Husserl’s Sachhaltigkeit and the Question of the Essence of Individuals.Stathis Livadas - 2020 - International Philosophical Quarterly 60 (4):449-471.
    Phenomenology can be roughly described as the theory of the pure essences of phenomena. Yet the meaning of essence and of concepts traditionally tied to it are far from settled. This is especially true given the impact modern science has had on established philosophical views and the need for revisiting certain core notions of philosophy. In this paper I intend to review Husserl’s view on thingness-essence and his conception of the essence of individuals, based mainly in his writings from the (...)
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  5.  8
    Abolishing Platonism in Multiverse Theories.Stathis Livadas - 2020 - Axiomathes 32 (2):321-343.
    A debated issue in the mathematical foundations in at least the last two decades is whether one can plausibly argue for the merits of treating undecidable questions of mathematics, e.g., the Continuum Hypothesis, by relying on the existence of a plurality of set-theoretical universes except for a single one, i.e., the well-known set-theoretical universe V associated with the cumulative hierarchy of sets. The multiverse approach has some varying versions of the general concept of multiverse yet my intention is to primarily (...)
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  6.  10
    Why is Cantor’s Absolute Inherently Inaccessible?Stathis Livadas - 2020 - Axiomathes 30 (5):549-576.
    In this article, as implied by the title, I intend to argue for the unattainability of Cantor’s Absolute at least in terms of the proof-theoretical means of set-theory and of the theory of large cardinals. For this reason a significant part of the article is a critical review of the progress of set-theory and of mathematical foundations toward resolving problems which to the one or the other degree are associated with the concept of infinity especially the one beyond that of (...)
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  7.  16
    The Plausible Impact of Phenomenology on Gödel's Thoughts.Stathis Livadas - 2019 - Theoria 85 (2):145-170.
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  8.  4
    THE TRANSCENDENCE OF THE EGO IN CONTINENTAL PHILOSOPHY — CONVERGENCES AND DIVERGENCES.Stathis Livadas - 2019 - HORIZON. Studies in Phenomenology 8 (2):573-601.
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  9. The Expressional Limits of Formal Language in the Notion of Quantum Observation.Stathis Livadas - 2012 - Axiomathes 22 (1):147-169.
    In this article I deal with the notion of observation, from a phenomenologically motivated point of view, and its representation mainly by means of the formal language of quantum mechanics. In doing so, I have taken the notion of observation in two diverse contexts. In one context as a notion related with objects of a logical-mathematical theory taken as registered facts of phenomenological perception ( Wahrnehmung ) inasmuch as this phenomenological idea can also be linked with a process of measurement (...)
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  10. The Relevance of Phenomenological Analysis Within Current Epistemology.Stathis Livadas - 2020 - Phainomenon 30:107-134.
    This article is primarily concerned with the articulation of a defensible position on the relevance of phenomenological analysis with the current epistemological edifice as this latter has evolved since the rupture with the classical scientific paradigm pointing to the Newtonian-Leibnizian tradition which took place around the beginning of 20th century. My approach is generally based on the reduction of the objects-contents of natural sciences, abstracted in the form of ideal objectivities in the corresponding logical-mathematical theories, to the content of meaning-acts (...)
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  11.  59
    Are Mathematical Theories Reducible to Non-Analytic Foundations?Stathis Livadas - 2013 - Axiomathes 23 (1):109-135.
    In this article I intend to show that certain aspects of the axiomatical structure of mathematical theories can be, by a phenomenologically motivated approach, reduced to two distinct types of idealization, the first-level idealization associated with the concrete intuition of the objects of mathematical theories as discrete, finite sign-configurations and the second-level idealization associated with the intuition of infinite mathematical objects as extensions over constituted temporality. This is the main standpoint from which I review Cantor’s conception of infinite cardinalities and (...)
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  12.  10
    The Enigma of ‘Being There’: Choosing Between Ontology and Epistemology.Stathis Livadas - forthcoming - Axiomathes:1-21.
    The aim of this paper is to show, based on Heidegger’s ontology of being and Husserl’s ontological aspects of phenomenology, the ways in which may be highlighted the ontological turned epistemological enigma of the actual presence of being-in-the-world. In such perspective the content of the philosophical term ‘being there’, in the sense of an original presence in the actuality of the world, is the key issue of discussion both in terms of the ontological implication of the accompanying notion of transcendence (...)
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  13.  6
    The Notion of Process in Nonstandard Theory and in Whiteheadian Metaphysics.Stathis Livadas - 2013 - Manuscrito 36 (1):103-137.
    In this article I intend to show that certain aspects of A.N. Whitehead's philosophy of organism and especially his epochal theory of time, as mainly exposed in his well-known work Process and Reality, can serve in clarify the underlying assumptions that shape nonstandard mathematical theories as such and also as metatheories of quantum mechanics. Concerning the latter issue, I point to an already significant research on nonstandard versions of quantum mechanics; two of these approaches are chosen to be critically presented (...)
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  14. Arguing for the “Destruction” of the a Priori. The Prompts From Husserlian Phenomenology.Stathis Livadas - 2022 - HORIZON. Studies in Phenomenology 11 (1):114-140.
    This article argues against the concept of a priori and essence as they have been traditionally thematized in the course of the old metaphysical-idealist tradition. Specifically, I argue against the existence of an ontological a priori, often endowed with metaphysical-platonic connotations, by attempting to “relocate” it in the subjective sphere and thus reduce it to the being and modes of being of a transcendental subjectivity. To do so, I will be appealing to a phenomenological, Husserlian approach, while pointing to a (...)
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  15.  10
    The Relevance of Phenomenology in the Current Epistemological Edifice.Stathis Livadas - 2018 - Proceedings of the XXIII World Congress of Philosophy 75:133-140.
    This article tries to establish the relevance of phenomenological analysis within the current epistemological edifice, in particular, with regard to certain key issues of the epistemology of our time, this last one meant as a philosophy of science. In doing so, it is primarily based, on the one hand, on certain Husserlian texts mainly those published in Logical Investigations, Formal and Transcendental Logic and the Phenomenology of Time Consciousness and, on the other, on certain developments, essentially running from the beginning (...)
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  16.  9
    Is There an Ontology of Infinity?Stathis Livadas - 2020 - Foundations of Science 25 (3):519-540.
    In this article I try to articulate a defensible argumentation against the idea of an ontology of infinity. My position is phenomenologically motivated and in this virtue strongly influenced by the Husserlian reduction of the ontological being to a process of subjective constitution within the immanence of consciousness. However taking into account the historical charge and the depth of the question of infinity over the centuries I also include a brief review of the platonic and aristotelian views and also those (...)
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  17.  16
    The Transcendental Source of Logic by Way of Phenomenology.Stathis Livadas - 2018 - Axiomathes 28 (3):325-344.
    In this article I am going to argue for the possibility of a transcendental source of logic based on a phenomenologically motivated approach. My aim will be essentially carried out in two succeeding steps of reduction: the first one will be the indication of existence of an inherent temporal factor conditioning formal predicative discourse and the second one, based on a supplementary reduction of objective temporality, will be a recourse to a time-constituting origin which has to be assumed as a (...)
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  18. Weyl's Conception of the Continuum in a Husserlian Transcendental Perspective.Stathis Livadas - 2017 - Studia Philosophica Estonica 10 (1):99-124.
    This article attempts to broaden the phenomenologically motivated perspective of H. Weyl's Das Kontinuum in the hope of elucidating the differences between the intuitive and mathematical continuum and further providing a deeper phenomenological interpretation. It is known that Weyl sought to develop an arithmetically based theory of continuum with the reasoning that one should be based on the naturally accessible domain of natural numbers and on the classical first-order predicate calculus to found a theory of mathematical continuum free of impredicative (...)
     
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  19.  8
    Extending the Non-Extendible: Shades of Infinity in Large Cardinals and Forcing Theories.Stathis Livadas - 2018 - Axiomathes 28 (5):565-586.
    This is an article whose intended scope is to deal with the question of infinity in formal mathematics, mainly in the context of the theory of large cardinals as it has developed over time since Cantor’s introduction of the theory of transfinite numbers in the late nineteenth century. A special focus has been given to this theory’s interrelation with the forcing theory, introduced by P. Cohen in his lectures of 1963 and further extended and deepened since then, which leads to (...)
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  20.  7
    The Leap From the Ego of Temporal Consciousness to the Phenomenology of Mathematical Continuum.Stathis Livadas - 2009 - Manuscrito 32 (2):321-356.
    This article attempts to link the notion of absolute ego as the ultimate subjectivity of consciousness in continental tradition with a phenomenology of Mathematical Continuum as this term is generally established following Cantor’s pioneering ideas on the properties and cardinalities of sets. My motivation stems mainly from the inherent ambiguities underlying the nature and properties of this fundamental mathematical notion which, in my view, cannot be resolved in principle by the analytical means of any formal language not even by the (...)
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  21.  8
    The Transcendence of Time in the Epistemology of Observation From a Phenomenological Standpoint.Stathis Livadas - 2011 - Manuscrito 34 (2):435-468.
    In this article I deal with time as a notion of epistemological content associated though with the notion of a subjective consciousness co-constitutive of physical reality. In this phenomenologically grounded approach I attempt to establish a ‘metaphysical’ aspect of time, within a strictly pistemological context, in the sense of an underlying absolute subjectivity which is non-objectifiable within objective temporality and thus non-susceptible of any ontological designation. My arguments stem, on the one hand, from a version of quantum-mechanical theory in view (...)
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  22.  1
    Is Existence an Ontologically Sound Term?Stathis Livadas - 2021 - International Philosophical Quarterly 61 (4):439-461.
    This article deals with the question of existence by considering the way in which phenomenology has faced this issue. To provide an argument against the ontological certainties typical of idealism and realism, I try to show the possibility of a subjective reduction of the question of existence and to highlight the way in which the concept of existence may be “undermined” by this reduction. A prominent place is given to the concept of infinity for radically reassessing the content and scope (...)
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