Search results for 'the mathematical Continuum' (try it on Scholar)

1000+ found
Order:
  1. Anne Newstead (2001). Aristotle and Modern Mathematical Theories of the Continuum. In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang
    This paper is on Aristotle's conception of the continuum. It is argued that although Aristotle did not have the modern conception of real numbers, his account of the continuum does mirror the topology of the real number continuum in modern mathematics especially as seen in the work of Georg Cantor. Some differences are noted, particularly as regards Aristotle's conception of number and the modern conception of real numbers. The issue of whether Aristotle had the notion of open (...)
    Translate
      Direct download  
     
    Export citation  
     
    My bibliography  
  2.  1
    Stathis Livadas (2009). The Leap From the Ego of Temporal Consciousness to the Phenomenology of Mathematical Continuum. 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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography  
  3. Solomon Feferman, Is the Continuum Hypothesis a Definite Mathematical Problem?
    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.
    Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  4.  6
    Giuseppe Longo (1999). The Mathematical Continuum, From Intuition to Logic. In Jean Petitot, Franscisco J. Varela, Barnard Pacoud & Jean-Michel Roy (eds.), Naturalizing Phenomenology. Stanford University Press
    Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  5.  32
    Eduardo Castro (2013). Defending the Indispensability Argument: Atoms, Infinity and the Continuum. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 44 (1):41-61.
    This paper defends the Quine-Putnam mathematical indispensability argument against two objections raised by Penelope Maddy. The objections concern scientific practices regarding the development of the atomic theory and the role of applied mathematics in the continuum and infinity. I present two alternative accounts by Stephen Brush and Alan Chalmers on the atomic theory. I argue that these two theories are consistent with Quine’s theory of scientific confirmation. I advance some novel versions of the indispensability argument. I argue that (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  6.  2
    Claude Laflamme (2001). Bartoszynski Tomek. On the Structure of Measurable Filters on a Countable Set. Real Analysis Exchange, Vol. 17 No. 2 (1992), Pp. 681–701. Bartoszynski Tomek and Shelah Saharon. Intersection of Archive for Mathematical Logic, Vol. 31 (1992), Pp. 221–226. Bartoszynski Tomek and Judah Haim. Measure and Category—Filters on Ω. Set Theory of the Continuum, Edited by Judah H., Just W., and Woodin H., Mathematical Sciences Research Institute Publications, Vol. 26, Springer-Verlag, New York, Berlin, Heidelberg .. [REVIEW] Bulletin of Symbolic Logic 7 (3):388-389.
    Direct download  
     
    Export citation  
     
    My bibliography  
  7.  1
    Juris Steprāns (2005). Shelah S.. On Cardinal Invariants of the Continuum. Axiomatic Set Theory, Translated and Edited by Martin DA, Baumgartner J., and Shelah S., Contemporary Mathematics, Vol. 31. American Mathematical Society, Providence, 1984, Pp. 183–207. [REVIEW] Bulletin of Symbolic Logic 11 (3):451-453.
    Direct download  
     
    Export citation  
     
    My bibliography  
  8. Heike Mildenberger (2002). Blass Andreas. Simple Cardinal Characteristics of the Continuum. Set Theory of the Reals, Edited by Judah Haim, Israel Mathematical Conference Proceedings, Vol. 6, Gelbart Research Institute for Mathematical Sciences, Bar-Ilan University, Ramat-Gan 1993, Distributed by the American Mathematical Society, Providence, Pp. 63–90. [REVIEW] Bulletin of Symbolic Logic 8 (4):552-553.
    Direct download  
     
    Export citation  
     
    My bibliography  
  9. Joel W. Robbin (1997). Sprinkle H D. A Development of Cardinals in “The Consistency of the Continuum Hypothesis.” Proceedings of the American Mathematical Society, Vol. 7 (1956), Pp. 289–291. [REVIEW] Journal of Symbolic Logic 31 (4):663-663.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  10.  31
    Matthew E. Moore (2007). The Genesis of the Peircean Continuum. Transactions of the Charles S. Peirce Society 43 (3):425 - 469.
    : In the Cambridge Conferences Lectures of 1898 Peirce defines a continuum as a "collection of so vast a multitude" that its elements "become welded into one another." He links the transinfinity (the "vast multitude") of a continuum to the confusion of its elements by a line of mathematical reasoning closely related to Cantor's Theorem. I trace the mathematical and philosophical roots of this conception of continuity, and examine its unresolved tensions, which arise mainly from difficulties (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  11.  14
    Richard Jozsa (1986). An Approach to the Modelling of the Physical Continuum. British Journal for the Philosophy of Science 37 (4):395-404.
    We describe a way of constructing models for the continuum which does not require an underlying structure of points. With a condition of spatial homogeneity the models have the mathematical structure of a sheaf.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  12.  11
    Anne Newstead & James Franklin (2008). On the Reality of the Continuum Discussion Note: A Reply to Ormell, 'Russell's Moment of Candour', "Philosophy". Philosophy 83 (323):117-127.
    This paper discusses an argument for the reality of the classical mathematical continuum. An inference to the best explanation type of argument is used to defend the idea that real numbers exist even when they cannot be constructively specified as with the "indefinable numbers".
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  13.  36
    Anne Newstead & Franklin James (2008). On the Reality of the Continuum. Philosophy 83 (1):117-28.
    In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In practice, this means excluding (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  14.  6
    Arthur L. Rubin & Jean E. Rubin (1993). Weak Forms of the Axiom of Choice and the Generalized Continuum Hypothesis. Mathematical Logic Quarterly 39 (1):7-22.
    In this paper we study some statements similar to the Partition Principle and the Trichotomy. We prove some relationships between these statements, the Axiom of Choice, and the Generalized Continuum Hypothesis. We also prove some independence results. MSC: 03E25, 03E50, 04A25, 04A50.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  15.  85
    John L. Bell (2000). Hermann Weyl on Intuition and the Continuum. Philosophia Mathematica 8 (3):259-273.
    Hermann Weyl, one of the twentieth century's greatest mathematicians, was unusual in possessing acute literary and philosophical sensibilities—sensibilities to which he gave full expression in his writings. In this paper I use quotations from these writings to provide a sketch of Weyl's philosophical orientation, following which I attempt to elucidate his views on the mathematical continuum, bringing out the central role he assigned to intuition.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  16.  7
    Paul J. Cohen (1966). Set Theory and the Continuum Hypothesis. New York, W. A. Benjamin.
  17.  33
    Janet Folina (2008). Intuition Between the Analytic-Continental Divide: Hermann Weyl's Philosophy of the Continuum. Philosophia Mathematica 16 (1):25-55.
    Though logical positivism is part of Kant's complex legacy, positivists rejected both Kant's theory of intuition and his classification of mathematical knowledge as synthetic a priori. This paper considers some lingering defenses of intuition in mathematics during the early part of the twentieth century, as logical positivism was born. In particular, it focuses on the difficult and changing views of Hermann Weyl about the proper role of intuition in mathematics. I argue that it was not intuition in general, but (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  18.  20
    Richard Tieszen (2000). The Philosophical Background of Weyl's Mathematical Constructivism. Philosophia Mathematica 8 (3):274-301.
    Weyl's inclination toward constructivism in the foundations of mathematics runs through his entire career, starting with Das Kontinuum. Why was Weyl inclined toward constructivism? I argue that Weyl's general views on foundations were shaped by a type of transcendental idealism in which it is held that mathematical knowledge must be founded on intuition. Kant and Fichte had an impact on Weyl but HusserFs transcendental idealism was even more influential. I discuss Weyl's views on vicious circularity, existence claims, meaning, the (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  19.  14
    Stuart Elden (2001). The Place of Geometry: Heidegger's Mathematical Excursus on Aristotle. Heythrop Journal 42 (3):311–328.
    ‘The Place of Geometry’ discusses the excursus on mathematics from Heidegger's 1924–25 lecture course on Platonic dialogues, which has been published as Volume 19 of the Gesamtausgabe as Plato's Sophist, as a starting point for an examination of geometry in Euclid, Aristotle and Descartes. One of the crucial points Heidegger makes is that in Aristotle there is a fundamental difference between arithmetic and geometry, because the mode of their connection is different. The units of geometry are positioned, the units of (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  20.  31
    Paul Thompson (1998). The Nature and Role of Intuition in Mathematical Epistemology. Philosophia 26 (3-4):279-319.
    Great intuitions are fundamental to conjecture and discovery in mathematics. In this paper, we investigate the role that intuition plays in mathematical thinking. We review key events in the history of mathematics where paradoxes have emerged from mathematicians' most intuitive concepts and convictions, and where the resulting difficulties led to heated controversies and debates. Examples are drawn from Riemannian geometry, set theory and the analytic theory of the continuum, and include the Continuum Hypothesis, the Tarski-Banach Paradox, and (...)
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography  
  21.  3
    José Enrique García Pascua (2003). Aquiles, la Tortuga y el infinito. Revista de Filosofía (Madrid) 28 (2):215-236.
    This paper shows an analysis of some found solutions for the famous aporia of the race between Achilles and the Tortoise. As an introduction, we present the mechanical solution, to establish that it is not in the field of matters of fact where you can resolve a purely rational problem like the one raised by Zeno of Elea. And so, the main part of the article is dedicated to the mathematical solutions, which face the problem under the point of (...)
    No categories
    Translate
      Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  22.  2
    José García García (1994). A. Bowie: estética y subjetividad. Logos 28 (2):337-348.
    This paper shows an analysis of some found solutions for the famous aporia of the race between Achilles and the Tortoise. As an introduction, we present the mechanical solution, to establish that it is not in the field of matters of fact where you can resolve a purely rational problem like the one raised by Zeno of Elea. And so, the main part of the article is dedicated to the mathematical solutions, which face the problem under the point of (...)
    No categories
    Translate
      Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  23. Colin Rittberg (2015). How Woodin Changed His Mind: New Thoughts on the Continuum Hypothesis. Archive for History of Exact Sciences 69 (2):125-151.
    The Continuum Problem has inspired set theorists and philosophers since the days of Cantorian set theory. In the last 15 years, W. Hugh Woodin, a leading set theorist, has not only taken it upon himself to engage in this question, he has also changed his mind about the answer. This paper illustrates Woodin’s solutions to the problem, starting in Sect. 3 with his 1999–2004 argument that Cantor’s hypothesis about the continuum was incorrect. From 2010 onwards, Woodin presents a (...)
    No categories
    Direct download  
     
    Export citation  
     
    My bibliography  
  24.  3
    Jakob Kellner & Saharon Shelah (2012). Creature Forcing and Large Continuum: The Joy of Halving. Archive for Mathematical Logic 51 (1-2):49-70.
    For ${f,g\in\omega^\omega}$ let ${c^\forall_{f,g}}$ be the minimal number of uniform g-splitting trees needed to cover the uniform f-splitting tree, i.e., for every branch ν of the f-tree, one of the g-trees contains ν. Let ${c^\exists_{f,g}}$ be the dual notion: For every branch ν, one of the g-trees guesses ν(m) infinitely often. We show that it is consistent that ${c^\exists_{f_\epsilon,g_\epsilon}{=}c^\forall_{f_\epsilon,g_\epsilon}{=}\kappa_\epsilon}$ for continuum many pairwise different cardinals ${\kappa_\epsilon}$ and suitable pairs ${(f_\epsilon,g_\epsilon)}$ . For the proof we introduce a new mixed-limit creature (...)
    No categories
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  25.  18
    Stephen Pollard (2007). Mathematical Determinacy and the Transferability of Aboutness. Synthese 159 (1):83-98.
    Competent speakers of natural languages can borrow reference from one another. You can arrange for your utterances of ‘Kirksville’ to refer to the same thing as my utterances of ‘Kirksville’. We can then talk about the same thing when we discuss Kirksville. In cases like this, you borrow “ aboutness ” from me by borrowing reference. Now suppose I wish to initiate a line of reasoning applicable to any prime number. I might signal my intention by saying, “Let p be (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  26.  2
    Kurt Gödel (1940). The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory. Princeton University Press;.
  27.  6
    Sara Negri & Daniele Soravia (1999). The Continuum as a Formal Space. Archive for Mathematical Logic 38 (7):423-447.
    A constructive definition of the continuum based on formal topology is given and its basic properties studied. A natural notion of Cauchy sequence is introduced and Cauchy completeness is proved. Other results include elementary proofs of the Baire and Cantor theorems. From a classical standpoint, formal reals are seen to be equivalent to the usual reals. Lastly, the relation of real numbers as a formal space to other approaches to constructive real numbers is determined.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  28.  4
    Ramez L. Sami (1989). Turing Determinacy and the Continuum Hypothesis. Archive for Mathematical Logic 28 (3):149-154.
    From the hypothesis that all Turing closed games are determined we prove: (1) the Continuum Hypothesis and (2) every subset of ℵ1 is constructible from a real.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  29.  6
    Colin Hamlin (forthcoming). Towards a Theory of Universes: Structure Theory and the Mathematical Universe Hypothesis. Synthese:1-21.
    The maturation of the physical image has made apparent the limits of our scientific understanding of fundamental reality. These limitations serve as motivation for a new form of metaphysical inquiry that restricts itself to broadly scientific methods. Contributing towards this goal we combine the mathematical universe hypothesis as developed by Max Tegmark with the axioms of Stewart Shapiro’s structure theory. The result is a theory we call the Theory of the Structural Multiverse. The focus is on informal theory development (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  30.  3
    András Hajnal (1956). On a Consistency Theorem Connected with the Generalized Continuum Problem. Mathematical Logic Quarterly 2 (8‐9):131-136.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  31.  2
    Stephen H. Hechler (1973). Powers of Singular Cardinals and a Strong Form of The Negation of The Generalized Continuum Hypothesis. Mathematical Logic Quarterly 19 (3‐6):83-84.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  32.  19
    Peter Roeper (2006). The Aristotelian Continuum. A Formal Characterization. Notre Dame Journal of Formal Logic 47 (2):211-232.
    While the classical account of the linear continuum takes it to be a totality of points, which are its ultimate parts, Aristotle conceives of it as continuous and infinitely divisible, without ultimate parts. A formal account of this conception can be given employing a theory of quantification for nonatomic domains and a theory of region-based topology.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  33. Solomon Feferman, Conceptual Structuralism and the Continuum.
    • This comes from my general view of the nature of mathematics, that it is humanly based and that it deals with more or less clear conceptions of mathematical structures; for want of a better word, I call that view conceptual structuralism.
    Direct download  
     
    Export citation  
     
    My bibliography  
  34.  5
    Carl J. Posy (2000). Epistemology, Ontology and the Continuum. In Emily Grosholz & Herbert Breger (eds.), The Growth of Mathematical Knowledge. Kluwer Academic Publishers 199--219.
    No categories
    Direct download  
     
    Export citation  
     
    My bibliography  
  35.  23
    Rudolf Carnap (1952). The Continuum of Inductive Methods. [Chicago]University of Chicago Press.
  36.  7
    Simon D. Smith (2015). Kant’s Mathematical Sublime and the Role of the Infinite: Reply to Crowther. Kantian Review 20 (1):99-120.
    This paper offers an analysis of KantNature is thus sublime in those of its appearances the intuition of which brings with them the idea of its infinitys interpretation of this species of aesthetic experience, and I reject his interpretation as not being reflective of Kant’s actual position. I go on to show that the experience of the mathematical sublime is necessarily connected with the progression of the imagination in its move towards the infinite.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  37.  9
    Kajsa Bråting (2012). Ambiguities of Fundamental Concepts in Mathematical Analysis During the Mid-Nineteenth Century. Foundations of Science 17 (4):301-320.
    In this paper we consider the major development of mathematical analysis during the mid-nineteenth century. On the basis of Jahnke’s (Hist Math 20(3):265–284, 1993 ) distinction between considering mathematics as an empirical science based on time and space and considering mathematics as a purely conceptual science we discuss the Swedish nineteenth century mathematician E.G. Björling’s general view of real- and complexvalued functions. We argue that Björling had a tendency to sometimes consider mathematical objects in a naturalistic way. One (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  38.  10
    Alexander Abian (1973). The Consistency of the Continuum Hypothesis Via Synergistic Models. Mathematical Logic Quarterly 19 (13):193-198.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  39.  3
    Roy O. Davies (1962). Equivalence to the Continuum Hypothesis of a Certain Proposition of Elementary Plane Geometry. Mathematical Logic Quarterly 8 (2):109-111.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  40.  2
    Rolf Schock (1971). On the Axiom of Choice and the Continuum Hypothesis. Mathematical Logic Quarterly 17 (1):35-37.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  41.  1
    Frederick Bagemihl (1959). Some Results Connected with the Continuum Hypothesis. Mathematical Logic Quarterly 5 (7‐13):97-116.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  42.  1
    Keith J. Devlin (1980). Concerning the Consistency of the Souslin Hypothesis with the Continuum Hypothesis. Annals of Mathematical Logic 19 (1-2):115-125.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  43. Jacques Grassin (1981). Δ11‐Good Inductive Definitions Over The Continuum. Mathematical Logic Quarterly 27 (1):11-16.
  44.  6
    Philipp Bagus & David Howden (2012). The Continuing Continuum Problem of Deposits and Loans. Journal of Business Ethics 106 (3):295-300.
    Barnett and Block (J Bus Ethics 18(2):179–194, 2011 ) argue that one cannot distinguish between deposits and loans due to the continuum problem of maturities and because future goods do not exist—both essential characteristics that distinguish deposit from loan contracts. In a similar way but leading to opposite conclusions (Cachanosky, forthcoming) maintains that both maturity mismatching and fractional reserve banking are ethically justified as these contracts are equivalent. We argue herein that the economic and legal differences between genuine deposit (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   12 citations  
  45.  96
    Gualtiero Piccinini (2003). Alan Turing and the Mathematical Objection. Minds and Machines 13 (1):23-48.
    This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a (...)
    Direct download (14 more)  
     
    Export citation  
     
    My bibliography   11 citations  
  46.  15
    Geoffrey K. Pullum (2011). On the Mathematical Foundations of Syntactic Structures. Journal of Logic, Language and Information 20 (3):277-296.
    Chomsky’s highly influential Syntactic Structures ( SS ) has been much praised its originality, explicitness, and relevance for subsequent cognitive science. Such claims are greatly overstated. SS contains no proof that English is beyond the power of finite state description (it is not clear that Chomsky ever gave a sound mathematical argument for that claim). The approach advocated by SS springs directly out of the work of the mathematical logician Emil Post on formalizing proof, but few linguists are (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  47.  89
    Imre Lakatos (ed.) (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.
    Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   158 citations  
  48.  3
    Michel Blay (1999). Reasoning with the Infinite: From the Closed World to the Mathematical Universe. University of Chicago Press.
    "One of Michael Blay's many fine achievements in Reasoning with the Infinite is to make us realize how velocity, and later instantaneous velocity, came to play a vital part in the development of a rigorous mathematical science of motion. ...
    No categories
    Direct download  
     
    Export citation  
     
    My bibliography   2 citations  
  49.  22
    Flavia Padovani (2011). Hans Reichenbach.The Concept of Probability in the Mathematical Representation of Reality. Trans. And Ed. Frederick Eberhardt and Clark Glymour. Chicago: Open Court, 2008. Pp. Xi+154. $34.97. [REVIEW] Hopos: The Journal of the International Society for the History of Philosophy of Science 1 (2):344-347.
    Hans Reichenbach has been not only one of the founding fathers of logical empiricism but also one of the most prominent figures in the philosophy of science of the past century. While some of his ideas continue to be of interest in current philosophical programs, an important part of his early work has been neglected, and some of it has been unavailable to English readers. Among Reichenbach’s overlooked (and untranslated) early works, his doctoral thesis of 1915, The Concept of Probability (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  50.  23
    Max Tegmark (2008). The Mathematical Universe. Foundations of Physics 38 (2):101-150.
    I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   15 citations  
1 — 50 / 1000