ARISTOTLE'S WORLD
ARISTOTLE'S WORLD
An Interactive Tutorial in Aristotelian Logic
Claus Brillowski
Welcome
Welcome
This is an interactive tutorial on Aristotelian logic - a philosophical logic designed to handle incomplete information and conflicting perceptions.
Unlike mathematical logic, Aristotelian logic does not require complete knowledge of the world. It is paraconsistent: contradictions do not cause everything to explode into nonsense. Instead, they signal that more information is needed.
This tutorial is based on the preprint "An Algebraic Model of Aristotelian Logic" available on ResearchGate:
This preprint contains the Syntax and a formal semantics based on domain theory, a branch of theoretical computer science. Here, we focus exclusively on the syntactic rules and their interactive exploration.
Tutorial Contents
Tutorial Contents
Work through the chapters in order. Each builds on the previous one.
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Why Aristotelian logic? The difference between mathematical and philosophical truth. The bent stick example. Paraconsistency .
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Building a world: predicates, individuals, and the “tabula rasa” of partial knowledge.
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A, E, I, O: the four categorical judgments. Symmetry and asymmetry. The tensor model. First inferences: subalternation and Barbara.
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Barbara, Celarent, Darii, Ferio, Baroco, Bocardo. Transitive closure. The fixed point as deductive closure.
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Subalternation, contrariety, subcontrariety, contradiction. How the square and fixedpoints work together. Outlook at Semantics.
How to Use This Tutorial
How to Use This Tutorial
There are three ways to use this tutorial.
First, you can use it interactively in the browser via the Wolfram Cloud. In this mode, the tutorial is designed for interactive exploration through sliders, buttons, and built-in examples. You do not need Mathematica installed for this.
Second, if you have a Mathematica license, you can use the tutorial as intended for direct code work: open the notebooks in your own Wolfram Cloud account or in Mathematica Desktop, modify the code, and evaluate input cells with Shift+Enter.
Third, you can work directly with the ArTensorLogic.wl package and its API. You can download the package from the supplementary material on ResearchGate and use it independently of the tutorial notebooks.
Currently only light mode is supported.
First, you can use it interactively in the browser via the Wolfram Cloud. In this mode, the tutorial is designed for interactive exploration through sliders, buttons, and built-in examples. You do not need Mathematica installed for this.
Second, if you have a Mathematica license, you can use the tutorial as intended for direct code work: open the notebooks in your own Wolfram Cloud account or in Mathematica Desktop, modify the code, and evaluate input cells with Shift+Enter.
Third, you can work directly with the ArTensorLogic.wl package and its API. You can download the package from the supplementary material on ResearchGate and use it independently of the tutorial notebooks.
Currently only light mode is supported.
Start Here
Start Here
Begin with the Preface, then work through Chapters 1-4 in order.