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The basic notions
The notions, at least the mathematical, are like the forms of matter, which are split in molecules, these in atoms, these in elementary particles...
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Thought Experiments in Mathematics: From Fiction to Facts
As in science and philosophy, thought experiments in mathematics link a problem to new epistemic resources that are unavailable in a given practice,...
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Abstraction: Mathematics Since the Twentieth Century
The revolutions in mathematics in the nineteenth century paved the way for rapid development and unprecedented expansion in mathematics in the...
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Modern Mathematics, Modern Art
In mathematics and in the arts, the first half of the nineteenth century marks a crucial turning point in the long march to modernity. In poetry, the...
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A Joint Logic of Problems and Propositions
AbstractIn a 1985 commentary to his collected works, Kolmogorov informed the reader that his 1932 paper On the interpretation of intuitionistic logic ...
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Rationalism
The question of whether the senses or the mind lead us to true knowledge is very old; it has been asked again and again throughout history and...
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Signs as a Theme in the Philosophy of Mathematical Practice
Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This...
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General Considerations and Kinematical Aspects of Motion
PappusPappusof Alexandria redefined the Euclidean construction game. AristotleAristotle and AugustineAugustineSt. pondered the nature of the...
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Logic Diagrams, Sacred Geometry and Neural Networks
In early modernity, one can find many spatial logic diagrams whose geometric forms share a family resemblance with religious art and symbols. The...
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Grete Hermann and Effective Methods in Geometry
Sometimes in the history of science we can find scientists who were not acknowledged at their time and only later the scientific community has...
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Introduction to the History and Philosophy of Mathematical Practice in Constructing the Reals
The ancient problem of the relationship of the continuous to the discrete, since its discovery by the Greeks, has posed a range of immensely fruitful...
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Translation of Form: a Model for Teaching Design Coding to Undergraduate Students
This study presents a Translation of Form (ToF) model aimed at fostering algorithmic thinking and computational design skills among architectural...
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Logical Accidents and the Problem of the Inside Corner
With the emergence of computational design, the production of architecture has come to be dominated by the algorithm, yet the presence of algorithmic...
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The Philosophy of Logic of John Corcoran
This article surveys the philosophy of logic of John Corcoran by focusing on some of its characteristic themes: his understanding of logic as formal...
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What Are Mathematical Practices? The Web-of-Practices Approach
This chapter can be considered as made up of two parts, a general discussion of the notion of mathematical practice and the limits of its use,...
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Thought Experiments in Mathematics: From Fiction to Facts
As in science and philosophy, thought experiments in mathematics link a problem to new epistemic resources that are unavailable in a given practice,...
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Mixed Political Inferences
The relation between logic and ethics is discussed through the reflections proposed by Corcoran. Although the latter claimed the inseparability of...
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Bayesian Perspectives on Mathematical Practice
Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies...
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Aristotle’s Relations: An Interpretation in Combinatory Logic
The usual modelling of the syllogisms of the Organon by a calculus of classes does not include relations. Aristotle may however have envisioned them...