On the Topological Modelling of Ontological Objects: Substance in the Monadology
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Janusz Kaczmarek
Abstract
In this paper I explore a methodological problem: how can we use topology and topological concepts as a basis for making sense of ontological concepts and problems? I try to show that it is possible to describe some fundamental concepts of Leibniz’s Monadology using topology. Therefore, I shall treat monads as topologies, and substance as a set of topologies, with a certain topology distinguished as being the so-called dominant monad. This, as we shall see, furnishes some interesting theorems, comparable with those of systems theory and Leibniz’s own theory of substance.
Abstract
In this paper I explore a methodological problem: how can we use topology and topological concepts as a basis for making sense of ontological concepts and problems? I try to show that it is possible to describe some fundamental concepts of Leibniz’s Monadology using topology. Therefore, I shall treat monads as topologies, and substance as a set of topologies, with a certain topology distinguished as being the so-called dominant monad. This, as we shall see, furnishes some interesting theorems, comparable with those of systems theory and Leibniz’s own theory of substance.
Chapters in this book
- Frontmatter I
- Contents V
- Some Introductory Thoughts on Contemporary Polish Ontology VII
- On Essential Structures and Symmetries 1
- Prospects for an Animalistically Oriented Simple View 25
- How Long Does the Present Last? The Problem of Fissuration in Roman Ingarden’s Ontology 51
- The Subject’s Forms of Knowledge and the Question of Being 71
- The World as an Object of Formal Philosophy 87
- Logic and the Ontology of Language 109
- Benedict Bornstein’s Ontological Elements of Reality 133
- On the Topological Modelling of Ontological Objects: Substance in the Monadology 149
- Does Mathematical Possibility Imply Existence? 161
- Neologicism for Real(s) – Are We There Yet? 181
- Possible Worlds and Situations: How Can They Meet Up? 205
- The Ontologic of Actions 219
- “Physical Intentionality” and the Thomistic Theory of Formal Objects 245
- An Assessment of Contemporary Polish Ontology 271
- Author Index 295
Chapters in this book
- Frontmatter I
- Contents V
- Some Introductory Thoughts on Contemporary Polish Ontology VII
- On Essential Structures and Symmetries 1
- Prospects for an Animalistically Oriented Simple View 25
- How Long Does the Present Last? The Problem of Fissuration in Roman Ingarden’s Ontology 51
- The Subject’s Forms of Knowledge and the Question of Being 71
- The World as an Object of Formal Philosophy 87
- Logic and the Ontology of Language 109
- Benedict Bornstein’s Ontological Elements of Reality 133
- On the Topological Modelling of Ontological Objects: Substance in the Monadology 149
- Does Mathematical Possibility Imply Existence? 161
- Neologicism for Real(s) – Are We There Yet? 181
- Possible Worlds and Situations: How Can They Meet Up? 205
- The Ontologic of Actions 219
- “Physical Intentionality” and the Thomistic Theory of Formal Objects 245
- An Assessment of Contemporary Polish Ontology 271
- Author Index 295
