Logic List Mailing Archive

"Engineering the Concept of Collection", Oslo & Virtual

20-21 Jun 2022

CONF Engineering the Concept of Collection, Oslo/Zoom, 20-21 June

Engineering the Concept of Collection
Time and place: June 20, 2022–June 21, 2022, Georg Morgenstiernes hus,
University of Oslo room 452, and on Zoom

Speakers: Carolin Antos (Universität Konstanz), Neil Barton (University of
Oslo), Tim Button (University College London), Herman Cappelen (University
of Hong Kong and University of Oslo), Laura Crosilla (University of Oslo),
Kentaro Fujimoto (University of Bristol), Luca Incurvati (University of
Amsterdam), Øystein Linnebo (University of Oslo), Stewart Shapiro (Ohio
State University and University of Oslo)

The workshop will be hybrid (in-person and online). Registration is free
but is required to attend the workshop. Please fill in this form to


Registration deadline:  19th of June 2022, 5 pm (CET). You will receive the
Zoom invite by email in the evening of the 19th of June.

If you plan to attend in person in Oslo, please let the organisers know by
the 10th of June at the latest.

20th June

1030-1145 Herman Cappelen and Øystein Linnebo: Engineering the concept of
collection: introductory remarks
1145-1200 Break
1200-1315 Luca Incurvati: Inferential deflationism about objectified
1315-1415 Lunch
1415-1530 Kentaro Fujimoto: Plural, infinity, and impredicativity
1530-1545 Break
1545-1700 Laura Crosilla: On Weyl’s predicative concept of set

21st June

1030-1145 Tim Button: MOON theory: Mathematical Objects with Ontological
1145-1200 Break
1200-1315 Carolin Antos: Engineering the concept of set - in practice
1315-1415 Lunch
1415-1530 Neil Barton: Engineering Set-Theoretic Concepts
1530-1545 Break
1545-1700 Stewart Shapiro:  Semantic indeterminacy, concept sharpening, set


The history of mathematics and philosophy have seen many different concepts
of collection: a set (understood as a gathering into one of previously
available objects), a class (understood as defined by its membership
condition, not by its members), a mereological sum, etc. Indeed, even a
plurality (i.e. many objects) and a concept can be seen as a collection,
since it makes sense to talk about their members (or instances).

Alongside these longstanding debates about the nature of collections, there
are also questions of how exactly each conception should be made precise.
Recent attempts to make sense of the ontology of combinatorial sets, for
example, have proposed very different pictures of what they are like. This
is especially clear in the debates on the nature of our thought concerning
`the’ universe of sets: Does our concept of (combinatorial) set suffice to
determine a unique and maximal universe, or does our concept and talk of
sets admit of different multifarious interpretations?

These observations raise some general philosophical-mathematical questions.
What concepts of collection do we have? Which, if any, of these concepts
should we use? Or should we “(re-)engineer” one or more concepts of
collection to produce concepts that are fit for purpose?

Further questions may include:

Should we use a single concept of collection or different concepts for
different purposes? (Remember George Boolos: “I thought that set theory was
supposed to be a theory about all, `absolutely' all, the collections that
there are”.) Specifically, do we need both a combinatorial concept of set
and a logical concept of class (cf. Parsons 1974, Maddy 1983, Linnebo
2006)? Should we strive for a single true theory based on one or more
“correct” concepts of collection, or be pluralists and accept a multitude
of equally legitimate, but often competing, theories?

Can recent views on the nature of combinatorial sets (e.g. Hamkins,
Linnebo, Woodin) be understood as instances of conceptual engineering?

Dr. Neil Barton
Postdoctoral Researcher
IFIKK, Universitetet i Oslo
Web: https://neilbarton.net/
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