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The recent development of Non Euclidean geometries presented new view of geometrical space which contrasts with the traditional view of geometrical space. I suggest that there is an epistemological break between The Euclidean geometry and non Euclidean geometries. My focus will be on two points. To illustrate the ontological foundation of the Euclidean and the Kantian space from one side and to explain the constructive nature of non Euclidean space. Therefore, I will choose group theory to indicate to the constructive process of geometrical space. I propose that the transcendental method is a relevant method to investigate the problem of space. Therefore, I choose Ernst Cassirer as one of the Marburg school members who firmly confirmed the richness of the transcendental method for explaining exact sciences. I will also discuss the logical foundations of geometrical space, and my primary aim is to ascertain the effectiveness of functional relational thought in constructing of geometrical space. These goals will be illustrated throughout the problems and issues which I will raise in this study.

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Mohamed Sayed Hassan has BA in Philosophy from Ain Shams University, Cairo, and MA in History and Philosophy of Science from Leeds University, Uk and PhD from Durham University,Uk. He is Presently a lecturer at Ain Shams University, Egypt. His research interests include Philosophy and History of Science and Philosophy of Perception.

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