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In his famous essay "The Origin of Geometry' Husserl claimed that language is the embodiment (Sprachleib) of geometry. Husserl's argument for this striking thesis starts from the question as to how the objectivity of geometry is to be understood, given that it is an abstract science dealing with ideal objects. His answer is that the existence of written demonstrations enables people to reactivate the fundamental experiences which formed geometrical practices and share the self-evidence of the ideal truths thereby grasped in a way which vindicates their objectivity. This answer is compared with positions advocated by Russell and Merleau-Ponty. Russell's work shows that the conception of self-evidence Husserl employs is not tenable; but Russell's emphasis on the importance of formal proofs in logic and mathematics provides an alternative vindication of the role of language as the embodiment of truth in mathematics and geometry. Merleau-Ponty offers a different approach which draws on the importance of language in upholding the traditions which sustain abstract sciences such as geometry, but since he downgrades the significance of formal proofs it is not clear what the role of language is supposed to be.

DOI: 10.1007/978-3-319-01616-0_16

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