Natural and Formal Infinities

By David Tall. 2001

93 citations recorded by the source corpus.

Subfields: Cognitive Neuroscience, History and Philosophy of Science, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/47a84358805aaaf8ca0e2cddddd3f4880589e4d9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Cognitive Neuroscience

1. Jack Pegg
2. Stella Vosniadou
3. Xenia Vamvakoussi
4. David Tall

In History and Philosophy of Science

1. Jack Pegg
2. Stella Vosniadou
3. Xenia Vamvakoussi
4. David Tall

In Mathematical Physics

1. Jack Pegg
2. Stella Vosniadou
3. Xenia Vamvakoussi
4. David Tall

Citations in the corpus

• Introducing Three Worlds of Mathematics (2004, background): “…is that the idea of ‘three worlds of mathematics’ that arose in my discussions with Anna Poynter, and have been published in their application to vectors in Watson, Spirou and Tall (2002) and acknowledged in Watson (2002) have ramifications that need careful consideration and long term reflection.”
• Understanding the structure of the set of rational numbers: a conceptual change approach (2004, background): “The concept of infinity has various aspects, among which actual infinity is the most difficult to grasp (Fischbein, 1987; Lakoff & Nunez, 2000; Tall, 2001; Tirosh, 1991).”
• The fundamental cycle of concept construction underlying various theoretical frameworks (2005, background): “…empirical abstraction (of properties of perceived objects) and pseudo-empirical abstraction (of properties of actions on perceived objects), Gray & Tall (2001) suggested that there were (at least) three different ways of constructing mathematical concepts: from a focus on perception of objects…”
• Building Theories: The Three Worlds of Mathematics. (2004, background): “In Gray and Tall (2001), we presented the idea that there were thr·ee (or possibly fom) fundamentally different types of object: • those that arise through empirical abstraction (in the seuse of Piaget) by which is meant the study of objects to discover theu properties those that arise flam what…”
• Some Historical Issues and Paradoxes Regarding the Concept of Infinity: An Apos Analysis: Part 2 (2005, unknown): “These include Aristotle, Archimedes, Cantor, Brouwer, Hobbes, Taylor (see Moore, 1995, 1999, 2002), and Tall (2001).”