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On the Logical Geometry of Geometric Angles
In this paper we provide an analysis of the logical relations within the conceptual or lexical field of angles in 2D geometry. The basic tripartition...
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Universal Algebraic Geometry: Syntax and Semantics
In this paper, we give a general insight into the ideas that make ground for the develo** of universal algebraic geometry and logical geometry. We...
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Logical Hylomorphism Revisited: Aristotle, Tarski, and Corcoran
This paper proposes an approach to the demarcation of formal ontology and formal epistemology based on the dichotomy between substantial and dynamic...
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Logical Diagrams, Visualization Criteria, and Boolean Algebras
This paper considers logical diagrams as a method for visualizing information concerning logical/linguistic/conceptual systems. I introduce four...
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The Simplicity Degree of Tarski’s Euclidean Geometry of Ruler and Dividers is 5
We present an axiom system for the plane Euclidean geometry of ruler and dividers constructions, expressed in Tarski’s language, with points as the...
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What Is Geometry?
This introductory chapter has rather a philosophical, or more precisely a metamathematical character: It does not do mathematics, but talks about...
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On “Space” and “Geometry” in the Nineteenth Century
What did mathematicians mean by the words “space” and “geometry” in the nineteenth century? This chapter will try to answer this question, starting...
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Geometry and analysis in Anastácio da Cunha’s calculus
It is well known that over the eighteenth century the calculus moved away from its geometric origins; Euler, and later Lagrange, aspired to transform...
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Logical Methodology and the Structure of Logic Syllabi
This paper starts from a dissatisfaction with the way logic is currently taught in philosophy departments. In such a context, we would want logic to...
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Geometry: From Disorder to Order
The axiomatic Euclidean geometry was unique for 2000 years. Then, in the nineteenth century a certain modernity was established with the flourishing...
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The Direction-Theory of Parallels: Geometry and Philosophy in the Age of Kant
The direction-theory of parallels was a mathematical theory that gained enormous importance and popularity for about a century, from the 1770s to the...
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Contributions of Logical Analysis for Mathematics Education
In this paper, we support the claim that although mathematics aims at using non-ambiguous definitions and statements, the polysemy of natural...
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Encounters with Geometry — an Autobiography of Concepts
When we first learned long division at age eight I had fun working out examples where the problem was put at the top of the page and the long...
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Morphisms Between Aristotelian Diagrams
In logical geometry, Aristotelian diagrams are studied in a precise and systematic way. Although there has recently been a good amount of progress in...
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The Projective Geometry Over Partially Ordered Skew Fields
Derivative lattices associated with partially ordered linear spaces over partially ordered skew fields are considered. Properties of the convex...
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Brain and Its Universal Logical Model of Multi-Agent Biological Systems
We build a topological model, based on intuitionistic logic, for multi-agent biological systems (such as Physarum polycephalum , bacterial colonies or...
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Vetoing: Social, Logical and Mathematical Aspects
An alternative title of this chapter could be ‘On Vetoer in Language, Logic and Mathematics’ because this text can be considered as an example...
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Pieri’s 1898 Geometry of Position Memoir
This chapter contains an English translation of Mario Pieri’s 1898c memoir, The Principles of the Geometry of Position Composed into a Deductive...
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Investigating How the Activity, Classroom Discussion, and Exercise (ACE) Teaching Cycle Influences Learners’ Problem-Solving and Achievement in Circle Geometry
This chapter reports on how the ACE teaching cycle influenced participants’ problem-solving competence and achievements when learning the circle...