Bolzano and Contemporary Metaphysics

(Affiliated Workshop, English)

nalytic Philosophy's great grandfather Bernard Bolzano is well known for his contributions to logic and the philosophy of mathematics. It is less well known that Bolzano also made significant contributions to metaphysics, in particular to mereology and to the theory of objective non-causal dependence. Both fields have gained increasing attention in current analytic metaphysics, and it can be shown that Bolzano's ideas often contain important and original contributions to the contemporary debate. The workshop will bring together recent work on Bolzano's metaphysics from historical as well as from systematic perspectives.
Speakers:

(1) Anna Bellomo

(2) Benjamin Schnieder

(3) Kevin Mulligan **Schedule.**

16:00--16:05 Welcome

16:05--17:20 Anna Bellomo: *Bolzano, geometry, and the part-whole principle*

Short break

17:25--18:40 Benjamin Schnieder: *tba*

Short break

18:45--20:00 Kevin Mulligan: *Grounding in Austro-German Philosophy (1890-1927)***Abstracts.****Anna Bellomo: Bolzano, geometry, and the part-whole principle**

Set theory, the current foundation of mainstream mathematics, originated in the mid 19th century. It is uncontroversial among historians of mathematics that some of Bolzano's mathematical ideas anticipated set theoretic concepts (see e.g. [1], p. 75). It

It has been argued in the literature that Bolzano accepted this set-theoretic principle of equality of size

If Mancosu's hypothesis is true, then Bolzano must have adopted in geometry a principle of equality of size which is

Maintaining two separate criteria for comparisons of size -- one-to-one correspondence in pure mathematics and part-whole in geometry -- runs against Bolzano's overall preference for general and unifying treatments of mathematical concepts such as size. However, our hypothesis is that the necessity of adopting two different criteria for equality of size stems from Bolzano's views on pure mathematics versus geometry, and in particular on the objects that they are dealing with. To be more precise, our hypothesis is that the ''pure quantities'' (

The aim of this talk is thus to evaluate Mancosu's hypothesis by investigating Bolzano's views on pure quantities versus special -- in particular geometrical -- quantities. We will focus on Bolzano's later mathematico-philosophical production (from the 1830s onwards), that is, his mathematical views as spelled out in the

References:

-- J. Ferreirós.

-- P. Mancosu. ''Measuring the size of infinite collections of natural numbers: Was Cantor?s theory of infinite number inevitable?'' In:

This paper looks at some claims employong grounding and related notions such as foundation between 1890 and 1927: logical truths ground logical norms; facts ground truths & correctness of attitudes; essence grounds modes of being; causal order grounds temporal order; values ground oughts; non-normative facts ground in a sui generis way values.

Further details coming soon

Chair: Stefan Roski

Time: 16:00-20:00, 13 September 2018 (Thursday)

Location: SR 1.005

Anna Bellomo

(University of Amsterdam, Netherlands)

Benjamin Schnieder

(University of Hamburg, Germany)

Kevin Mulligan

(University of Italian Switzerland, Lugano; University of Geneva, )

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Last update: 2014-04-01.