What is a Higher Level Set?

Philosophia Mathematica:nkw032 (2016)
  Copy   BIBTEX


Structuralist foundations of mathematics aim for an ‘invariant’ conception of mathematics. But what should be their basic objects? Two leading answers emerge: higher groupoids or higher categories. I argue in favor of the former over the latter. First, I explain why to choose between them we need to ask the question of what is the correct ‘categorified’ version of a set. Second, I argue in favor of groupoids over categories as ‘categorified’ sets by introducing a pre-formal understanding of groupoids as abstract shapes. This conclusion lends further support to the perspective taken by the Univalent Foundations of mathematics.



    Upload a copy of this work     Papers currently archived: 89,764

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Supervenience and explanation.Harold Kincaid - 1988 - Synthese 77 (November):251-81.
Higher type categories.Martin Dowd - 1993 - Mathematical Logic Quarterly 39 (1):251-254.
The principles of mathematics revisited.Jaakko Hintikka - 1996 - New York: Cambridge University Press.
The Principles of Mathematics Revisited.Jaakko Hintikka - 1996 - New York: Cambridge University Press.
Interventionism and Higher-level Causation.Vera Hoffmann-Kolss - 2014 - International Studies in the Philosophy of Science 28 (1):49-64.
Categories without Structures.Andrei Rodin - 2011 - Philosophia Mathematica 19 (1):20-46.
Of skyhooks and the coevolution of scientific disciplines.Donald R. Franceschetti - 1999 - Behavioral and Brain Sciences 22 (5):836-837.
Wide physical realization.Wim de Muijnck - 2003 - Inquiry: An Interdisciplinary Journal of Philosophy 46 (1):97 – 111.


Added to PP

63 (#228,909)

6 months
7 (#174,021)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A meaning explanation for HoTT.Dimitris Tsementzis - 2020 - Synthese 197 (2):651-680.

Add more citations

References found in this work

What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Abstract.[author unknown] - 2011 - Dialogue and Universalism 21 (4):447-449.
What Scientific Theories Could Not Be.Hans Halvorson - 2012 - Philosophy of Science 79 (2):183-206.

View all 42 references / Add more references