Lifeworld and Mathematics

The article “Lifeworld and Mathematics” has been inspired by well-known scientists, from whom are listed here: Edmund Husserl, Jürgen Habermas, Reuben Hersh, Martin Heidegger, Hartmut von Hentig and Knut Radbruch. Basic for this article is Husserl’s phenomenological lifeworld analysis of the mathematized modern natural science. Habermas, in whose social theory the concept of lifeworld has also a central meaning, recommends a theoretic communicational approach for the lifeworld analysis which answers the question about the intersubjective constitution of the lifeworld in the sense of the american pragmatism. Hersh has a pragmatic understanding of mathematics so that he views mathematics as a social, cultural, historical reality. Heidegger saw the basic character of the modern knowledge attitude in the new knowledge claim named the “mathematical” which is not deducable out of mathematics. Hentig has offered the book “Magier oder Magister? Über die Einheit der Wissenschaft im Verständigungsprozess”, in which he discusses generally the role of the science in our society, while doing so he considers as necessary a democratically activated general understanding of scientific actions. Already 1991 Radbruch has pointed out in a lecture at the Darmstadt Seminar about “general mathematics” the analysis of conditions and realizations of the mathematical as task of general mathematics. 1 Lifeworld and Inworld The concept “lifeworld” has been introduced into philosophy by Edmund Husserl in his late work “The crisis of the european sciences and the transcendental phenomenology” (see [Hu54]). With the term “lifeworld” Husserl names in the frame of his phenomenological philosophy the concrete context of the world. This context is intersubjectively experienced by humans in original evidence and is therefore ordered before the objective-scientific cognition of the world. Husserl founded on the “lifeworld” concept his fundamental critic about the development of science. For him the scientists have chanced the ideal of objectivity, which has to be understood only methodically, into an independently made “objectivism” by which the relationship of the research to the responsibility of the acting human being is lost. To overcome by it the occuring sense-crisis of science, Husserl recommends to make conscious that and how the objectivistic imagined world Lifeworld and Mathematics 23 arises out of human achievements which are founded on the lifeworld as the extensive horizon of human cognition and action. Husserl’s phenomenological lifeworld analysis of the mathematized modern natural science has been extended by Alfred Schütz with a phenomenological analysis of the social lifeworld [SL79]. Schütz understands the lifeworld as the transcendental frame of possible everyday experiences of the recognizing and acting subject. Jürgen Habermas, in whose social theory the concept of lifeworld has also a central meaning, criticizes the approach of Schütz: On the one hand Schütz tends to start out from an intersubjectively constituted lifeworld, without to clarify how the lifeworld is intersubjectively produced (a problem of which Schütz knew that also Husserl has not solved it); on the other hand he takes over Husserl’s philosophical view of consciousness to comprehend the “experiencing subject” as the last reference point of the lifeworld analysis [Ha81; vol.2, p.197f]. Habermas recommends a theoretic communicational approach for the lifeworld analysis which answers the question about the intersubjective constitution of the lifeworld in the sense of the american pragmatism. A convincing understanding of mathematics has also to be pragmatically founded, as it is for instance realized by Reuben Hersh in his 1997 appeared book “What is mathematics, really?” [He97]. Hence, the treatment of the theme “lifeworld and mathematics” shall be based in this paper on Habermas’ concept of lifeworld, which has therefore be more explicated in detail. Jürgen Habermas introduces in his main work “Theorie des kommunikativen Handelns” [Ha81] “lifeworld” as a complementary concept to the “communicative action”. Habermas understands action and therefore communicative action as mastering of situations. “The concept of communicative action cuts out of the mastering of situations first of all two aspects: the teleological aspect of the realization of the mastering of purposes (or the execution of a plan of action) and the communicative aspect of the interpretation of a situation and the achieving of an agreement. In the communicative action the participants pursue their plans on the basis of common definitions of situations in mutual agreements.” [Ha81; vol.2, p.193] For the unification of common definitions of situations the lifeworld is fundamental because “communicatively acting subjects communicate always in the horizon of a lifeworld. [...] This lifeworld background serves as a source for defining situations which are presupposed by the participants as unproblematic.” [Ha81, vo.1, p.107] For the situation-oriented communication “the lifeworld is a reservoir of self-evident facts or unshakable convictions which the communication participants utilize for interpretation processes. But single elements and determined self-evident facts are only mobilized in the form of consentaneous and at the same time of problematic knowledge if they become relevant for some situation. [...Out of an understanding-oriented view] we are able to think the lifeworld as a culturally transmitted and linguistically organized supply of explanation patterns.” [Ha81; vol.2, p.189] To be able in answering the question about the intersubjective constitution and reproduction of the lifeworld, Habermas goes back to the social psychology of the american pragmatist Georg Herbert Mead. Mead, who is interested