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Most innovative part of the Critical Philosophy of Mathematics

Performative interpretation of mathematics

From interpretation to practice

The performative practice of Mathematics

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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)

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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

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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)

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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

Ethics only applies to applied mathematics (pure mathematics is beyond any ethical discussion)

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)

This raises ethical challenges for any mathematical practice…”

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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