. (The three basic directions in the foundations of mathematics). (Bulletin de la Société Mathématique de Gréce), vol. 21 (1941), pp. 67–103.

In the foundations of mathematics there has been an ongoing debate about whether categorical foundations can replace set-theoretical foundations. The primary goal of this chapter is to provide a condensed summary of that debate. It addresses the two primary points of contention: technical adequacy and autonomy. Finally, it calls attention to a neglected feature of the debate, the claim that categorical foundations are more natural and readily useable, and how deeper investigation of that claim could prove fruitful for our understanding of mathematical thinking and mathematical practice.

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Carl Friedrich Gauss. Inaugural Lecture on Astronomy and Papers on the Foundations of Mathematics

National Mathematics Magazine ◽

10.2307/3028599 ◽

1938 ◽

Vol 12 (6) ◽

pp. 314

Author(s):

Martin A. Nordgaard ◽

G. Waldo Dunnington

Keyword(s):

Foundations Of Mathematics ◽

Inaugural Lecture

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Two Approaches to Foundations in Greek Mathematics: Apollonius and Geminus

Science in Context ◽

10.1017/s0269889710000037 ◽

2010 ◽

Vol 23 (2) ◽

pp. 151-186 ◽

Cited By ~ 4

Author(s):

Fabio Acerbi

Keyword(s):

Present Article ◽

Foundations Of Mathematics ◽

Previous Issue ◽

Greek Mathematics ◽

Set Up ◽

Key Characters

ArgumentThis article is the sequel to an article published in the previous issue of Science in Context that dealt with homeomeric lines (Acerbi 2010). The present article deals with foundational issues in Greek mathematics. It considers two key characters in the study of mathematical homeomery, namely, Apollonius and Geminus, and analyzes in detail their approaches to foundational themes as they are attested in ancient sources. The main historiographical result of this paper is to show that there was a well-established mathematical field of discourse in “foundations of mathematics,” a fact that is by no means obvious. The paper argues that the authors involved in this field of discourse set up a variety of philosophical, scholarly, and mathematical tools that they used in developing their investigations.

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