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  1.  46
    On the Historical Transformations of the Square of Opposition as Semiotic Object.Ioannis M. Vandoulakis & Tatiana Yu Denisova - 2020 - Logica Universalis 14 (1):7-26.
    In this paper, we would show how the logical object “square of opposition”, viewed as semiotic object, has been historically transformed since its appearance in Aristotle’s texts until the works of Vasiliev. These transformations were accompanied each time with a new understanding and interpretation of Aristotle’s original text and, in the last case, with a transformation of its geometric configuration. The initial textual codification of the theory of opposition in Aristotle’s works is transformed into a diagrammatic one, based on a (...)
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  2.  34
    The Web as a Tool for Proving.Petros Stefaneas & Ioannis M. Vandoulakis - 2014 - In Harry Halpin & Alexandre Monnin (eds.), Philosophical Engineering: Toward a Philosophy of the Web. Wiley-Blackwell. pp. 149-167.
    This is the first interdisciplinary exploration of the philosophical foundations of the Web, a new area of inquiry that has important implications across a range of domains. - Contains twelve essays that bridge the fields of philosophy, cognitive science, and phenomenology. - Tackles questions such as the impact of Google on intelligence and epistemology, the philosophical status of digital objects, ethics on the Web, semantic and ontological changes caused by the Web, and the potential of the Web to serve as (...)
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  3.  48
    The Web as A Tool For Proving.Petros Stefaneas & Ioannis M. Vandoulakis - 2012 - Metaphilosophy 43 (4):480-498.
    The Web may critically transform the way we understand the activity of proving. The Web as a collaborative medium allows the active participation of people with different backgrounds, interests, viewpoints, and styles. Mathematical formal proofs are inadequate for capturing Web-based proofs. This article claims that Web provings can be studied as a particular type of Goguen's proof-events. Web-based proof-events have a social component, communication medium, prover-interpreter interaction, interpretation process, understanding and validation, historical component, and styles. To demonstrate its claim, the (...)
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  4. On Mathematical Proving.Ioannis M. Vandoulakis & Petros Stefaneas - 2015 - Journal of Artificial General Intelligence 6 (1):130–149.
    This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts in which (...)
     
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  5.  12
    The Web as a Tool for Proving.Petros Stefaneas & Ioannis M. Vandoulakis - 2013-12-13 - In Harry Halpin & Alexandre Monnin (eds.), Philosophical Engineering. Wiley. pp. 149–167.
    The Web may critically transform the way we understand the activity of proving. The Web as a collaborative medium allows the active participation of people with different backgrounds, interests, viewpoints, and styles. Mathematical formal proofs are inadequate for capturing Web‐based proofs. This chapter claims that Web provings can be studied as a particular type of Goguen's proof‐events. Web‐based proof‐events have a social component, communication medium, prover‐interpreter interaction, interpretation process, understanding and validation, historical component, and styles. To demonstrate its claim, the (...)
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  6.  9
    Self-reference and type distinctions in Greek philosophy and mathematics.Ioannis M. Vandoulakis - 2023 - In Jens Lemanski & Ingolf Max (eds.), Historia Logicae and its Modern Interpretation. London: College Publications. pp. 3-36.
    In this paper, we examine a fundamental problem that appears in Greek philosophy: the paradoxes of self-reference of the type of “Third Man” that appears first in Plato’s 'Parmenides', and is further discussed in Aristotle and the Peripatetic commentators and Proclus. We show that the various versions are analysed using different language, reflecting different understandings by Plato and the Platonists, such as Proclus, on the one hand, and the Peripatetics (Aristotle, Alexander, Eudemus), on the other hand. We show that the (...)
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  7.  26
    A Genetic Interpretation of Neo-Pythagorean Arithmetic.Ioannis M. Vandoulakis - 2010 - Oriens - Occidens 7:113-154.
    The style of arithmetic in the treatises the Neo-Pythagorean authors is strikingly different from that of the "Elements". Namely, it is characterised by the absence of proof in the Euclidean sense and a specific genetic approach to the construction of arithmetic that we are going to describe in our paper. Lack of mathematical sophistication has led certain historians to consider this type of mathematics as a feature of decadence of mathematics in this period [Tannery 1887; Heath 1921]. The alleged absence (...)
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  8.  37
    On A. A. Markov's Attitude towards Brouwer's Intuitionism.Ioannis M. Vandoulakis - 2015 - Philosophia Scientiae 19:143-158.
    The paper examines Andrei A. Markov’s critical attitude towards L.E.J. Brouwer’s intuitionism, as is expressed in his endnotes to the Russian translation of Heyting’s Intuitionism, published in Moscow in 1965. It is argued that Markov’s algorithmic approach was shaped under the impact of the mathematical style and values prevailing in the Petersburg mathematical school, which is characterized by the proclaimed primacy of applications and the search for rigor and effective solutions.
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  9.  32
    Proofs as Spatio-Temporal Processes.Petros Stefaneas & Ioannis M. Vandoulakis - 2014 - Philosophia Scientiae 18:111-125.
    The concept of proof can be studied from many different perspectives. Many types of proofs have been developed throughout history such as apodictic, dialectical, formal, constructive and non-constructive proofs, proofs by visualisation, assumption-based proofs, computer-generated proofs, etc. In this paper, we develop Goguen’s general concept of proof-events and the methodology of algebraic semiotics, in order to define the concept of mathematical style, which characterizes the proofs produced by different cultures, schools or scholars. In our view, style can be defined as (...)
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  10.  32
    Was Euclid's Approach to Arithmetic Axiomatic?Ioannis M. Vandoulakis - 1998 - Oriens - Occidens 2:141-181.
    The lack of specific arithmetical axioms in Book VII has puzzled historians of mathematics. It is hardly possible in our view to ascribe to the Greeks a conscious undertaking to axiomatize arithmetic. The view that associates the beginnings of the axiomatization of arithmetic with the works of Grassman [1861], Dedekind [1888] and Peano [1889] seems to be more plausible. In this connection a number of interesting historical problems have been raised, for instance, why arithmetic was axiomatized so late. This question (...)
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  11.  14
    On V.A. Yankov’s Hypothesis of the Rise of Greek Mathematics.Ioannis M. Vandoulakis - 2022 - In Alex Citkin & Ioannis M. Vandoulakis (eds.), V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics. Springer, Outstanding Contributions To Logic (volume 24). pp. 295-310.
    The paper examines the main points of Yankov’s hypothesis on the rise of Greek mathematics. The novelty of Yankov’s interpretation is that the rise of mathematics is examined within the context of the rise of ontological theories of the early Greek philosophers, which mark the beginning of rational thinking, as understood in the Western tradition.
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  12.  12
    On V.A. Yankov’s Contribution to the History of Foundations of Mathematics.Ioannis M. Vandoulakis - 2022 - In Alex Citkin & Ioannis M. Vandoulakis (eds.), V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics. Springer, Outstanding Contributions To Logic (volume 24). pp. 247-270.
    The paper examines Yankov’s contribution to the history of mathematical logic and the foundations of mathematics. It concerns the public communication of Markov’s critical attitude towards Brouwer’s intuitionistic mathematics from the point of view of his constructive mathematics and the commentary on A.S. Esenin-Vol’pin program of ultra-intuitionistic foundations of mathematics.
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  13. The Square of Opposition: Past, Present, and Future.Ioannis M. Vandoulakis & Jean-Yves Beziau - 2022 - In Jean-Yves Beziau & Ioannis Vandoulakis (eds.), The Exoteric Square of Opposition. Birkhauser. pp. 1-14.
  14.  10
    On the Transformations of the Square of Opposition from the Point of View of Institution Model Theory.Ioannis M. Vandoulakis, Yiannis Kiouvrekis & Petros Stefaneas - 2022 - In Jean-Yves Beziau & Ioannis Vandoulakis (eds.), The Exoteric Square of Opposition. Birkhauser. pp. 277-302.
    In recent decades, research in the square of opposition has increased. New interpretations, extensions, and generalizations have been suggested, both Aristotelian and non-Aristotelian ones. The paper attempts to compare different versions of the square of opposition. For this reason, we appeal to the wider categorical model-theoretic framework of the theory of institutions.
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  15.  10
    The Arbitrariness of the sign in Greek Mathematics.Ioannis M. Vandoulakis - 2019 - In Jean-Yves Beziau (ed.), The Arbitrariness of the Sign in Question. College Publications. pp. 379-397.
    This book is a collection of papers related to a workshop organized in Geneva in January 2017, part of a big event celebrating the centenary of Ferdinand de Saussure's famous "Cours de Linguistique Générale" (CLG). The topic of this workshop was THE FIRST PRINCIPLE, stated in the second section of the first part of the CLG entitled: THE ARBITRARINESS OF THE SIGN. -/- Discussions are developed according to the three perspectives presented in the call for papers: -/- (1) The details (...)
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  16.  11
    V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics.Alex Citkin & Ioannis M. Vandoulakis (eds.) - 2022 - Springer, Outstanding Contributions To Logic (volume 24).
    This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory (...)
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  17. Collective Discovery Events: Web-based Mathematical Problem-solving with Codelets.Ioannis M. Vandoulakis, Harry Foundalis, Maricarmen Martínez & Petros Stefaneas - 2014 - In Tarek R. Besold, Marco Schorlemmer & Alan Smaill (eds.), Computational Creativity Research: Towards Creative Machines. Springer, Atlantis Thinking Machines (Book 7), Atlantis. pp. 371-392.
    While collaboration has always played an important role in many cases of discovery and creation, recent developments such as the web facilitate and encourage collaboration at scales never seen before, even in areas such as mathematics, where contributions by single individuals have historically been the norm. This new scenario poses a challenge at the theoretical level, as it brings out the importance of various issues which, as of yet, have not been sufficiently central to the study of problem-solving, discovery, and (...)
     
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  18. Modelling, Logical and Philosophical Aspects of Foundations of Science.Ioannis M. Vandoulakis & Petros Stefaneas (eds.) - 2016 - Lambert Academic Publishing.
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  19. Mathematical Proving as Multi-Agent Spatio-Temporal Activity.Ioannis M. Vandoulakis & Petros Stefaneas - 2016 - In Ioannis M. Vandoulakis & Petros Stefaneas (eds.), Modelling, Logical and Philosophical Aspects of Foundations of Science. Lambert Academic Publishing. pp. 183-200.
  20. On the Interpretations of the History of Diophantine Analysis: A Comparative Study of Alternate Perspectives.Ioannis M. Vandoulakis - 2018 - Ganita Bharati 40 (3):115-152.
    Essay Review of “Les Arithmétiques de Diophante. Lecture historique et mathématique” by Roshdi Rashed and Christian Houzel, and Histoire de l’analyse diophantienne classique : d’Abū Kamil à Fermat by Roshdi Rashed.
     
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  21. Proof-events in History of Mathematics.Ioannis M. Vandoulakis & Petros Stefaneas - 2013 - Ganita Bharati 35 (1-4):119-157.
    In this paper, we suggest the broader concept of proof-event, introduced by Joseph Goguen, as a fundamental methodological tool for studying proofs in history of mathematics. In this framework, proof is understood not as a purely syntactic object, but as a social process that involves at least two agents; this highlights the communicational aspect of proving. We claim that historians of mathematics essentially study proof-events in their research, since the mathematical proofs they face in the extant sources involve many informal (...)
     
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  22.  72
    Plato’s Third Man Paradox: its Logic and History.Ioannis M. Vandoulakis - 2009 - Archives Internationale D’Histoire des Sciences 59 (162):3-52.
    In Plato’s Parmenides 132a-133b, the widely known Third Man Paradox is stated, which has special interest for the history of logical reasoning. It is important for philosophers because it is often thought to be a devastating argument to Plato’s theory of Forms. Some philosophers have even viewed Aristotle’s theory of predication and the categories as inspired by reflection on it [Owen 1966]. For the historians of logic it is attractive, because of the phenomenon of self-reference that involves. Bocheński denies any (...)
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  23. Symmetry: Art and Science.Ioannis M. Vandoulakis, Dénes Nagy, Ryuji Takaki, Ritsuko Izuhara, Shozo Ishihara & Yoshinori Teshima (eds.) - 2019 - Kanazawa: The International Society for the Interdisciplinary Study of Symmetry.
    Proceedings of the 11th Interdisciplinary Symmetry Congress-Festival of the International Society for the Interdisciplinary Study of Symmetry. Special Theme: “Tradition and Innovation in Symmetry - Katachi”.
     
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  24.  53
    The Readings of Apollonius' On the Cutting off of a Ratio.Ioannis M. Vandoulakis - 2012 - Arabic Sciences and Philosophy 22 (1):137-149.
    ExtractDuring the second half of the twentieth century an attention of historians of mathematics shifted to mathematics of the Late Antiquity and its subsequent development by mathematicians of the Arabic world. Many critical editions of works of mathematicians of the Hellenistic era have made their appearance, giving rise to a new, more detailed historical picture. Among these are the critical editions of the works of Diophantus, Apollonius, Archimedes, Pappus, Diocles, and others.Send article to KindleTo send this article to your Kindle, (...)
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  25. On a Possible Relation Between Greek Mathematics and Eleatic Philosophy.Ioannis M. Vandoulakis - 2024 - In Jean- Timothy J. Madigan & Jean-Yves Beziau (eds.), Universal Logic, Ethics, and Truth. Birkhäuser. pp. 217-230.
    In this paper, we approach the problem of the relationship between Greek mathematics and Eleatic philosophy from a new perspective, which leads us to a reappraisal of Szabó’s hypothesis about the origin of mathematics out of Eleatic philosophy. We claim that Parmenidean philosophy, particularly its semantic core, has possibly been shaped by reflexion on the Pythagoreans’ mathematical practice, particularly in arithmetic. Furthermore, Pythagorean arithmetic originates not from another domain outside mathematics but from counting, i.e., it has its roots in man’s (...)
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