Karen François��Center for Logic and Philosophy of Science��Brussels University (Vrije Universiteit Brussel)�
Most innovative part of the Critical Philosophy of Mathematics
Performative interpretation of mathematics
From interpretation to practice
The performative practice of Mathematics
Positioning oneself (in relation to Skovsmose’s interest)
Phenomenologist (Husserl – Brouwer) (intuitionist foundation)
(Co-)Constructivist: Math as a human practice (founded in de LifeWorld)
Mathesis Universalis leads to the Crisis of EU Sciences (Husserl, 1936)
Politics of Mathematics (2008) (Latour- Laclau&Mouffe)
Research & intellectual (mostly) fathers
The Center for Logic & Philosophy of Science (CLPS) in Brussels
Research on mathematical practices (foundation of APMP Brussel 2010)
Ethnomathematics & Philosophy of Math Education
D’Ambrosio, Ascher, Bishop & Ernest, Skovsmose
Inspired by groundbreaking ideas of Skovsmose
Culture, diversity, equality
Background & Foreground (Skovsmose, O. 2014 Foregrounds)
“foregrounding may refer to students’ recognition of their own prospects in life, (…) Foregrounding is not an isolated individual act, but takes place in dialogue with others: students, friends, families, or teachers. (…)
foregrounding as a collective process.
I see foregrounding as being an important learning interact, bringing new dynamics to reflective inquiries.” (p.230)
Incommensurability
Platonic interpretation of Mathematics
Mathematics is just the inert architecture of Platonic heaven.
Mathematics exists outside the human space.
Mathematics exists ‘as such’: distinction of pure and applied mathematics
Critical Philosophy of Mathematics
Performative interpretation of Mathematics (weak position)
Skovsmose recognises mathematics as necessary being performative.
Mathematics contributes to the formation of worldviews and life-worlds. (p. 177)
Foundation of Performative Practice of Mathematics
Wittgenstein, L. (1922). Tractatus logico-philosophicus (Description)
Wittgenstein, L. (1953). Philosophical investigations. (Performance)
Discourse Theory
Ernesto Laclau & Chantal Mouffe, (1985). Hegemony and Socialist Strategy.
Jacob Torfing (1999) New Theories of Discourse
Michel Foucault (1989) The Archaeology of Knowledge