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  1. Critical Plural Logic.Salvatore Florio & Øystein Linnebo - forthcoming - Philosophia Mathematica.
    What is the relation between some things and the set of these things? Mathematical practice does not provide a univocal answer. On the one hand, it relies on ordinary plural talk, which is implicitly committed to a traditional form of plural logic. On the other hand, mathematical practice favors a liberal view of definitions which entails that traditional plural logic must be restricted. We explore this predicament and develop a "critical" alternative to traditional plural logic.
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  2. J. I. Friedman. Proper Classes as Members of Extended Sets. Mathematische Annalen, Vol. 83 , Pp. 232–240.J. B. Paris - 1975 - Journal of Symbolic Logic 40 (3):462.
  3. Mathematical Knowledge.Mary Leng, Alexander Paseau & Michael Potter (eds.) - 2007 - Oxford University Press.
    What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions.
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  4. Note on the Significance of the New Logic.Frederique Janssen-Lauret - 2018 - The Reasoner 6 (12):47-48.
    Brief note explaining the content, importance, and historical context of my joint translation of Quine's The Significance of the New Logic with my single-authored historical-philosophical essay 'Willard Van Orman Quine's Philosophical Development in the 1930s and 1940s'.
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  5. Foundations of Set Theory.Abraham Adolf Fraenkel & Yehoshua Bar-Hillel - 1958 - North-Holland.
    HISTORICAL INTRODUCTION In Abstract Set Theory) the elements of the theory of sets were presented in a chiefly generic way: the fundamental concepts were ...
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  6. Understanding the Infinite I: Niceness, Robustness, and Realism†: Articles.David Corfield - 2010 - Philosophia Mathematica 18 (3):253-275.
    This paper treats the situation where a single mathematical construction satisfies a multitude of interesting mathematical properties. The examples treated are all infinitely large entities. The clustering of properties is termed ‘niceness’ by the mathematician Michiel Hazewinkel, a concept we compare to the ‘robustness’ described by the philosopher of science William Wimsatt. In the final part of the paper, we bring our findings to bear on the question of realism which concerns not whether mathematical entities exist as abstract objects, but (...)
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  7. Cantor’s Proof in the Full Definable Universe.Laureano Luna & William Taylor - 2010 - Australasian Journal of Logic 9:10-25.
    Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the (...)
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  8. Cantor’s Absolute in Metaphysics and Mathematics.Kai Hauser - 2013 - International Philosophical Quarterly 53 (2):161-188.
    This paper explores the metaphysical roots of Cantor’s conception of absolute infinity in order to shed some light on two basic issues that also affect the mathematical theory of sets: the viability of Cantor’s distinction between sets and inconsistent multiplicities, and the intrinsic justification of strong axioms of infinity that are studied in contemporary set theory.
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  9. Hennie Frederick C.. Analysis of Bilateral Iterative Networks. Transactions of the I.R.E. Professional Group on Circuit Theory, Vol. CT-6 No. 1 , Pp. 35–45. [REVIEW]Edward F. Moore - 1959 - Journal of Symbolic Logic 24 (3):259-260.
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  10. Relevant First-Order Logic LP# and Curry’s Paradox Resolution.Jaykov Foukzon - 2015 - Pure and Applied Mathematics Journal Volume 4, Issue 1-1, January 2015 DOI: 10.11648/J.Pamj.S.2015040101.12.
    In 1942 Haskell B. Curry presented what is now called Curry's paradox which can be found in a logic independently of its stand on negation. In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this article the non-classical resolution of Curry’s Paradox and Shaw-Kwei' sparadox without rejection any contraction postulate is proposed. In additional relevant paraconsistent logic C ̌_n^#,1≤n<ω, in fact,provide an effective way of circumventing triviality of da Costa’s paraconsistent Set Theories〖NF〗n^C.
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  11. Transfinite Recursion and Computation in the Iterative Conception of Set.Benjamin Rin - 2015 - Synthese 192 (8):2437-2462.
    Transfinite recursion is an essential component of set theory. In this paper, we seek intrinsically justified reasons for believing in recursion and the notions of higher computation that surround it. In doing this, we consider several kinds of recursion principles and prove results concerning their relation to one another. We then consider philosophical motivations for these formal principles coming from the idea that computational notions lie at the core of our conception of set. This is significant because, while the iterative (...)
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  12. Metaphysical Myths, Mathematical Practice: The Ontology and Epistemology of the Exact Sciences.Jody Azzouni - 1994 - Cambridge University Press.
    Most philosophers of mathematics try to show either that the sort of knowledge mathematicians have is similar to the sort of knowledge specialists in the empirical sciences have or that the kind of knowledge mathematicians have, although apparently about objects such as numbers, sets, and so on, isn't really about those sorts of things as well. Jody Azzouni argues that mathematical knowledge really is a special kind of knowledge with its own special means of gathering evidence. He analyses the linguistic (...)
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  13. Groundedness - Its Logic and Metaphysics.Jönne Kriener - 2014 - Dissertation, Birkbeck College, University of London
    In philosophical logic, a certain family of model constructions has received particular attention. Prominent examples are the cumulative hierarchy of well-founded sets, and Kripke's least fixed point models of grounded truth. I develop a general formal theory of groundedness and explain how the well-founded sets, Cantor's extended number-sequence and Kripke's concepts of semantic groundedness are all instances of the general concept, and how the general framework illuminates these cases. Then, I develop a new approach to a grounded theory of proper (...)
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  14. Analysis of Bilateral Iterative Networks.Frederick C. Hennie - 1959 - Journal of Symbolic Logic 24 (3):259-260.
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  15. Encoded Pilots for Iterative Receiver Improvement.Hyuck M. Kwon, Khurram Hassan, Ashutosh Goyal, Mi-Kyung Oh, Dong-Jo Park & Yong Hoon Lee - 2005 - Complexity 4:5.
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  16. Review of Some Iterative Root-Finding Methods From a Dynamical Point of View. [REVIEW]Sergio Amat, Sonia Busquier & Sergio Plaza - 2004 - Scientia 10:3-35.
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  17. The Elusiveness of Sets.Max Black - 1971 - Review of Metaphysics 24 (4):614-636.
    NOWADAYS, even schoolchildren babble about "null sets" and "singletons" and "one-one correspondences," as if they knew what they were talking about. But if they understand even less than their teachers, which seems likely, they must be using the technical jargon with only an illusion of understanding. Beginners are taught that a set having three members is a single thing, wholly constituted by its members but distinct from them. After this, the theological doctrine of the Trinity as "three in one" should (...)
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  18. Iterativity Vs. Habituality: On the Iterative Interpretation of Perfective Sentences.Alessandro Lenci & Pier Marco Bertinetto - 2000 - In Achille Varzi, James Higginbotham & Fabio Pianesi (eds.), Speaking of Events. Oxford University Press.
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  19. NIIA: Nonparametric Iterative Imputation Algorithm.Shichao Zhang, Zhi Jin & Xiaofeng Zhu - 2008 - In Tu-Bao Ho & Zhi-Hua Zhou (eds.), Pricai 2008: Trends in Artificial Intelligence. Springer. pp. 544--555.
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  20. Discovery of Clusters From Proximity Data: An Approach Using Iterative Adjustment of Binary Classifications.Shoji Hirano & Shusaku Tsumoto - 2008 - In S. Iwata, Y. Oshawa, S. Tsumoto, N. Zhong, Y. Shi & L. Magnani (eds.), Communications and Discoveries From Multidisciplinary Data. Springer. pp. 251--268.
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  21. Indefinite Extensibility—Dialetheic Style.Graham Priest - 2013 - Studia Logica 101 (6):1263-1275.
    In recent years, many people writing on set theory have invoked the notion of an indefinitely extensible concept. The notion, it is usually claimed, plays an important role in solving the paradoxes of absolute infinity. It is not clear, however, how the notion should be formulated in a coherent way, since it appears to run into a number of problems concerning, for example, unrestricted quantification. In fact, the notion makes perfectly good sense if one endorses a dialetheic solution to the (...)
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  22. Philosophy of Mathematics in the Warsaw Mathematical School.Roman Murawski - 2010 - Axiomathes 20 (2-3):279-293.
    The aim of this paper is to present and discuss the philosophical views concerning mathematics of the founders of the so called Warsaw Mathematical School, i.e., Wacław Sierpiński, Zygmunt Janiszewski and Stefan Mazurkiewicz. Their interest in the philosophy of mathematics and their philosophical papers will be considered. We shall try to answer the question whether their philosophical views influenced their proper mathematical investigations. Their views towards set theory and its rôle in mathematics will be emphasized.
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  23. Review: Frederick C. Hennie, Analysis of Bilateral Iterative Networks. [REVIEW]Edward F. Moore - 1959 - Journal of Symbolic Logic 24 (3):259-260.
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  24. Review: Frederick C. Hennie III, Iterative Arrays of Logical Circuits. [REVIEW]Albert A. Mullin - 1962 - Journal of Symbolic Logic 27 (1):106-107.
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  25. Implementing Mathematical Objects in Set Theory.Thomas Forster - 2007 - Logique Et Analyse 50 (197):79-86.
    In general little thought is given to the general question of how to implement mathematical objects in set theory. It is clear that—at various times in the past—people have gone to considerable lengths to devise implementations with nice properties. There is a litera- ture on the evolution of the Wiener-Kuratowski ordered pair, and a discussion by Quine of the merits of an ordered-pair implemen- tation that makes every set an ordered pair. The implementation of ordinals as Von Neumann ordinals is (...)
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  26. Zermelo and Russell's Paradox: Is There a Universal Set?G. Landini - 2013 - Philosophia Mathematica 21 (2):180-199.
    Zermelo once wrote that he had anticipated Russell's contradiction of the set of all sets that are not members of themselves. Is this sufficient for having anticipated Russell's Paradox — the paradox that revealed the untenability of the logical notion of a set as an extension? This paper argues that it is not sufficient and offers criteria that are necessary and sufficient for having discovered Russell's Paradox. It is shown that there is ample evidence that Russell satisfied the criteria and (...)
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  27. Enlarging One's Stall or How Did All of These Sets Get in Here?M. Wilson - 2013 - Philosophia Mathematica 21 (2):157-179.
    Following historical developments, this article traces two basic motives for employing sets within a physical setting and discusses whether they truly pose a problem for ‘mathematical naturalism’.
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  28. The Hyperuniverse Program.Tatiana Arrigoni & Sy-David Friedman - 2013 - Bulletin of Symbolic Logic 19 (1):77-96.
    The Hyperuniverse Program is a new approach to set-theoretic truth which is based on justifiable principles and leads to the resolution of many questions independent from ZFC. The purpose of this paper is to present this program, to illustrate its mathematical content and implications, and to discuss its philosophical assumptions.
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  29. Splitting the Μονάς.Claudio Majolino - 2011 - New Yearbook for Phenomenology and Phenomenological Philosophy 11:187-213.
    This paper assesses the philosophical heritage of Jacob Klein’s thought through an analysis of the key tenets of his Greek Mathematical Thought and theOrigin of Algebra. Threads of Klein’s thought are distinguished and subsequently singled out (phenomenological, epistemological, and anti-ontological; historical, ontological, and critical), and the peculiar way in which Klein’s project brings together ontology and history of mathematics is investigated. Plato’s theoretical logistic and Klein’s understanding thereof are questioned—especially the claim that the Platonic distinction between practical and theoretical logistic (...)
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  30. V = L and Intuitive Plausibility in Set Theory. A Case Study.Tatiana Arrigoni - 2011 - Bulletin of Symbolic Logic 17 (3):337-360.
    What counts as an intuitively plausible set theoretic content (notion, axiom or theorem) has been a matter of much debate in contemporary philosophy of mathematics. In this paper I develop a critical appraisal of the issue. I analyze first R. B. Jensen's positions on the epistemic status of the axiom of constructibility. I then formulate and discuss a view of intuitiveness in set theory that assumes it to hinge basically on mathematical success. At the same time, I present accounts of (...)
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  31. On Arbitrary Sets and ZFC.José Ferreirós - 2011 - Bulletin of Symbolic Logic 17 (3):361-393.
    Set theory deals with the most fundamental existence questions in mathematics—questions which affect other areas of mathematics, from the real numbers to structures of all kinds, but which are posed as dealing with the existence of sets. Especially noteworthy are principles establishing the existence of some infinite sets, the so-called “arbitrary sets.” This paper is devoted to an analysis of the motivating goal of studying arbitrary sets, usually referred to under the labels of quasi-combinatorialism or combinatorial maximality. After explaining what (...)
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  32. Wokół problemu realizmu teoriomnogościowego.Krzysztof Wójtowicz - 1995 - Filozofia Nauki 4.
    The paper is devoted to the problem of the existence of mathematical objects. The ideas of Godel and the Quine-Putnam indispensability argument are discussed. A „qualitative” version of this argument, in which the results of reverse mathematics are used, is presented.
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  33. Status hipotezy kontinuum w świetle koncepcji Woodina.Krzysztof Wójtowicz - 2011 - Filozofia Nauki 19 (4):67-82.
    In the article, Woodin’s program (for setting up axioms, which decide the continuum hypothesis) is presented, and some philosophical aspects of it are discussed. In particular, the general problem of justifying axioms of set theory is discussed in the context of the relation between set theory and mainstream mathematics.
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  34. The Structure of Causal Sets.Christian Wüthrich - 2012 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 43 (2):223-241.
    More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case of a physical theory predestined to be interpreted in structuralist terms. It is shown how employing structuralism lends itself to a natural interpretation of the physical meaning of causal set theory. Conversely, the conceptually exceptionally clear case of causal sets is used as a foil to illustrate how a (...)
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  35. The Simple Consistency of Naive Set Theory Using Metavaluations.Ross T. Brady - 2014 - Journal of Philosophical Logic 43 (2-3):261-281.
    The main aim is to extend the range of logics which solve the set-theoretic paradoxes, over and above what was achieved by earlier work in the area. In doing this, the paper also provides a link between metacomplete logics and those that solve the paradoxes, by finally establishing that all M1-metacomplete logics can be used as a basis for naive set theory. In doing so, we manage to reach logics that are very close in their axiomatization to that of the (...)
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  36. Gödel's Modernism: On Set Theoretic Incompleteness, Revisited.Juliette Kennedy - 2009 - In Sten Lindström, Erik Palmgren, Krister Segerberg & Viggo Stoltenberg-Hansen (eds.), Logicism, Intuitionism and Formalism: What has become of them? Springer.
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  37. Impure Sets Are Not Located: A Fregean Argument.Roy T. Cook - 2012 - Thought: A Journal of Philosophy 1 (3):219-229.
    It is sometimes suggested that impure sets are spatially co-located with their members (and hence are located in space). Sets, however, are in important respects like numbers. In particular, sets are connected to concepts in much the same manner as numbers are connected to concepts—in both cases, they are fundamentally abstracts of (or corresponding to) concepts. This parallel between the structure of sets and the structure of numbers suggests that the metaphysics of sets and the metaphysics of numbers should parallel (...)
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  38. Monads and Sets: On Leibniz, Gödel, and the Reflection Principle.Mark Van Atten - unknown
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  39. Universal Sets for Pointsets Properly on the N Th Level of the Projective Hierarchy.Greg Hjorth, Leigh Humphries & Arnold W. Miller - 2013 - Journal of Symbolic Logic 78 (1):237-244.
    The Axiom of Projective Determinacy implies the existence of a universal $\utilde{\Pi}^{1}_{n}\setminus\utilde{\Delta}^{1}_{n}$ set for every $n \geq 1$. Assuming $\text{\upshape MA}(\aleph_{1})+\aleph_{1}=\aleph_{1}^{\mathbb{L}}$ there exists a universal $\utilde{\Pi}^{1}_{1}\setminus\utilde{\Delta}^{1}_{1}$ set. In ZFC there is a universal $\utilde{\Pi}^{0}_{\alpha}\setminus\utilde{\Delta}^{0}_{\alpha}$ set for every $\alpha$.
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  40. On Balzer's Small Set Solution to Russell's Paradox.Michael S. Pollanen - 1993 - Journal of Value Inquiry 27 (3-4):541-541.
    The objective of this paper is to show that Russell's paradox cannot be solved just by defining a class as what is classified, as Balzer thinks. It can be solved not by defining a class, as he does, but by rejecting the assumption on which the validity of argument is based, that is, not conceding the truth of the disjunctive premise that a class is either an instance of itself or not an instance of itself.
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  41. What Constitutes a Formal Analogy?Kenneth Olson & Gilbert Plumer - 2002 - In Hans V. Hansen, Christopher W. Tindale, J. Anthony Blair, Ralph H. Johnson & Robert C. Pinto (eds.), Argumentation and its Applications [CD-ROM]. Ontario Society for the Study of Argumentation. pp. 1-8.
    There is ample justification for having analogical material in standardized tests for graduate school admission, perhaps especially for law school. We think that formal-analogy questions should compare different scenarios whose structure is the same in terms of the number of objects and the formal properties of their relations. The paper deals with this narrower question of how legitimately to have formal analogy test items, and the broader question of what constitutes a formal analogy in general.
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  42. Michael Potter Tom Ricketts, Eds. The Cambridge Companion to Frege. Cambridge: Cambridge University Press, 2010. Isbn 978-0-521-62479-4. Pp. XVII+639. [REVIEW]G. Landini - 2012 - Philosophia Mathematica 20 (3):372-387.
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  43. Sets Whose Members Might Not Exist + Essentialism Possible Worlds.T. Baldwin - unknown
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  44. The Iterative Use of Ν with the Imperf. And Aor. Indic.R. C. Seaton - 1889 - The Classical Review 3 (8):343-345.
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  45. Plural Quantification and the Iterative Concept of Set.Stephen Pollard - 1985 - Philosophy Research Archives 11:579-587.
    Arecent paper by George Boolos suggests that it is philosophically respectable to use monadic second order logic in one’s explication of the iterative concept of set. I shall here give a partial indication of the new range of theories of the iterative hierarchy which are thus madeavailable to philosophers of set theory.
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  46. Is the Continuum Hypothesis a Definite Mathematical Problem?Solomon Feferman - manuscript
    The purpose of this article is to explain why I believe that the Continuum Hypothesis (CH) is not a definite mathematical problem. My reason for that is that the concept of arbitrary set essential to its formulation is vague or underdetermined and there is no way to sharpen it without violating what it is supposed to be about. In addition, there is considerable circumstantial evidence to support the view that CH is not definite.
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  47. Abstract of Comments: Mathematical Epistemology: What is the Question?Penelope Maddy - 1982 - Noûs 16 (1):106 - 107.
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  48. Are Subclasses Parts of Classes?Alex Oliver - 1994 - Analysis 54 (4):215 - 223.
    The fundamental thesis of David Lewis's "Parts of Classes" is that the nonempty subsets of a set are mereological parts of it. This paper shows that Lewis's considerations in favor of this thesis are unpersuasive. First, common speech provides no support. Second, the formal analogy between mereology and the Boolean algebra of sets can be explained without accepting the thesis. Third, it is very doubtful that the thesis is fruitful. Certainly, Lewis's claim that it helps us understand set theory is (...)
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  49. Parts of Singletons.Pat Reeder - 2010 - Journal of Philosophy 107 (10):501-533.
  50. Retrieving the Mathematical Mission of the Continuum Concept From the Transfinitely Reductionist Debris of Cantor’s Paradise. Extended Abstract.Edward G. Belaga - forthcoming - International Journal of Pure and Applied Mathematics.
    What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the transfinite deadlock of (...)
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