## VISUALIZATION OF ORDINALS (2007)

### BibTeX

@MISC{Löwe07visualizationof,

author = {Benedikt Löwe},

title = {VISUALIZATION OF ORDINALS },

year = {2007}

}

### OpenURL

### Abstract

We describe the pictorial representations of infinite ordinals used in teaching set theory, and discuss a possible use in naturalistic foundations of mathematics.

### Citations

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Naturalism in Mathematics
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- 1997
(Show Context)
Citation Context ...the use of these means by mathematicians tells us nothing about mathematics. In this paper, we shall take a decidedly anti-foundationalist stance, following Maddy’s maxim of Naturalism in Mathematics =-=(Mad97)-=-. We be2 To give just one example: “Talk of this mysterious faculty of intuition is tainted with an air of occult mysticism.” (Che97, p. 121) 3 Cf. (Kva97; Kva00), the discussion between Brown and Fol... |

16 | Believing the axioms i - Maddy - 1988 |

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15 |
Proofs without words: Exercises in visual thinking
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- 1993
(Show Context)
Citation Context ...epresentations of mathematical structures. (Lei07)”. 4 Cf. (Núñ04). 5 Visualization has always played a major rôle in the didactics of mathematics, cf.—as a completely unrepresentative sample—, e.g., =-=(Nel93)-=- and (Pai01). Recently, it has become a major focus in philosophy of mathematics as well, as witnessed by (Man05) and the other papers in the collection (ManJørPed05).Visualization of ordinals 3 “Tak... |

13 | Mathematical Reasoning with Diagrams: From Intuition to Automation - Jamnik - 2001 |

10 |
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- Núñez
- 2005
(Show Context)
Citation Context ...iew: “There is nothing ‘mystic’ about intuition: whenever mathematicians speak of intuition, they refer to non-conceptual/non-propositional representations of mathematical structures. (Lei07)”. 4 Cf. =-=(Núñ04)-=-. 5 Visualization has always played a major rôle in the didactics of mathematics, cf.—as a completely unrepresentative sample—, e.g., (Nel93) and (Pai01). Recently, it has become a major focus in phil... |

6 |
Epistemology of visual thinking in elementary real analysis
- Giaquinto
- 1994
(Show Context)
Citation Context ...: “Talk of this mysterious faculty of intuition is tainted with an air of occult mysticism.” (Che97, p. 121) 3 Cf. (Kva97; Kva00), the discussion between Brown and Folina (Bro97; Fol99), (Rot00), and =-=(Gia94)-=-. In his recent project on informal provability, Leitgeb agrees with our point of view: “There is nothing ‘mystic’ about intuition: whenever mathematicians speak of intuition, they refer to non-concep... |

5 | Believing the axioms ii - Maddy - 1988 |

3 |
Visualization in logic and mathematics
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- 2005
(Show Context)
Citation Context ...e in the didactics of mathematics, cf.—as a completely unrepresentative sample—, e.g., (Nel93) and (Pai01). Recently, it has become a major focus in philosophy of mathematics as well, as witnessed by =-=(Man05)-=- and the other papers in the collection (ManJørPed05).Visualization of ordinals 3 “Take a line and a point that does not lie on the line . . . ” “. . . and draw the unique parallel through the point.... |

3 | Mathematics and Phenomenology. The correspondence between Oskar - Mancosu, Ryckman - 2002 |

1 | Barwise Hammer, Logical Reasoning with diagrams - Allwein, Jon - 1996 |

1 | Getting in Touch with Numbers: Intuition and Mathematical Platonism, Philosophy and Phenomenological Research 57 - Cheyne - 1997 |

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1 | Platonism and metaphor in the texts of mathematics - Headley |

1 | Wittgenstein on semantics of geometrical figures - Kvasz, Tarski - 1997 |

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1 | explanation and reasoning styles in mathematics, Papers from the meeting “Mathematics as Rational Activity” held at - Visualization |

1 |
Intuiting Mathematical Objects Using Diagrams and Kinetigrams
- Pais
(Show Context)
Citation Context ...ns of mathematical structures. (Lei07)”. 4 Cf. (Núñ04). 5 Visualization has always played a major rôle in the didactics of mathematics, cf.—as a completely unrepresentative sample—, e.g., (Nel93) and =-=(Pai01)-=-. Recently, it has become a major focus in philosophy of mathematics as well, as witnessed by (Man05) and the other papers in the collection (ManJørPed05).Visualization of ordinals 3 “Take a line and... |

1 | Vorlesungen über die Neuere Geometrie, SpringerVerlag 1926 [Grundlehren der mathematischen Wissenschaften 23 - Pasch |

1 |
Mathematics as sign
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(Show Context)
Citation Context ...t one example: “Talk of this mysterious faculty of intuition is tainted with an air of occult mysticism.” (Che97, p. 121) 3 Cf. (Kva97; Kva00), the discussion between Brown and Folina (Bro97; Fol99), =-=(Rot00)-=-, and (Gia94). In his recent project on informal provability, Leitgeb agrees with our point of view: “There is nothing ‘mystic’ about intuition: whenever mathematicians speak of intuition, they refer ... |

1 | Review of ‘Infinitary Combinatorics and the Axiom of Determinateness’ by Eugene M - Steel - 1979 |