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Geometry of Definable Sets
In the previous chapter we saw examples of mathematical structures that are simple enough to allow a complete analysis of the parametrically...
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Hume’s View of Geometry
I start by considering Mark Steiner’s startling claim that Hume takes geometry to be synthetic a priori, which engenders the Kantian challenge to...
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Demarcating Descartes’s geometry with clarity and distinctness
Descartes’s doctrine of clarity and distinctness states that whatever is clearly and distinctly perceived is true. This paper looks at his early...
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Peano’s Geometry: From Empirical Foundations to Abstract Development
In Principii di Geometria (1889b) and ‘Sui fondamenti della Geometria’ (1894) Peano offers axiomatic presentations of projective geometry. There...
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Husserlian Phenomenology of Limit-Problems: a “‘Geometry’ of Lived Experience”?
The proper way in which limit-problems [ Grenzprobleme ]—birth, death, dreamless sleep, the “prior to birth” [ das vor der Geburt ], the “after death” [ da...
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Language Without a Code: Islamic Geometry and Modernity
Do geometric patterns characterizing many surface treatments in Islamic cultures represent? If so, can pattern function as an image? The question of...
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Geometry, mechanics, and experience: a historico-philosophical musing
Euclidean geometry, statics, and classical mechanics, being in some sense the simplest physical theories based on a full-fledged mathematical...
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Parmenides, the Founder of Abstract Geometry: Enriques Interpreter of the Eleatic Thought
The interpretation of Parmenides’ Περί Φύσεως is a fascinating topic to which philosophers, historians of philosophy and scientists have dedicated...
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Grothendieck’s theory of schemes and the algebra–geometry duality
We shall address from a conceptual perspective the duality between algebra and geometry in the framework of the refoundation of algebraic geometry...
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The Esoteric Geometry of Poetic Reason
What I have called the esoteric function lies at the heart of poetic reason. In this chapter I outline a geometry of poetic reason based on the...
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Geometry from the Materialist and Idealist Perspectives
In this chapter, I consider – from the two perspectives (Idealist and Materialist) – our geometric beliefs: their acquisition, truth and warrant. I...
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Symmetry and partial belief geometry
When beliefs are quantified as credences, they are related to each other in terms of closeness and accuracy. The “accuracy first” approach in formal...
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The elliptope and the geometry of correlations
The Pearson correlation coefficient and the elliptope inequality • Why the quantum correlations saturate the elliptope • Why our raffles do not...
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Non-Euclidean Geometry
Four-dimensional theories match Virtual Reality because here time and space are configured through mutable lines. Since the discovery of...
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Pre-Reflective Self-Consciousness & Projective Geometry
We argue that the projective geometrical component of the Projective Consciousness Model (PCM) can account for key aspects of pre-reflective...
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Frege on intuition and objecthood in projective geometry
In recent years, several scholars have been investigating Frege’s mathematical background, especially in geometry, in order to put his general views...
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Mathematics embodied: Merleau-Ponty on geometry and algebra as fields of motor enaction
This paper aims to clarify Merleau-Ponty’s contribution to an embodied-enactive account of mathematical cognition. I first identify the main points...
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Geometry and Spinozan Science
This chapter is devoted, in part, to develo** an example of Spinozan science in practice, and exhibiting the role of geometry therein. In this...
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The Classical Style in Contemporary Geometry: Views from a Person Working in the Field
As is well known, geometry undergone revolutionary shifts of paradigm during all the last century. This in many cases implies, for instance in the...