Benedict Bornstein’s Ontological Elements of Reality
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Krzysztof Śleziński
Abstract
Bornstein arrived at an original mathematical system of relationships and categorical-ontological structures: i.e. a general ontology, or a metaphysics in the broader meaning of that term. Metaphysics, as a theoretical and mathematical science, is concerned with all of being and/or being generally. It is, therefore, a universal and pure mathematical science - mathesis universalis - of the kind sought after by Plato, Descartes, Leibniz and Hoene-Wroński. In this article, Bornstein’s algebraico-geometrical logic, known as “topologic”, will be treated as a spatial representation of algebraic logic. The representation is effected through an application of Descartes’s co-ordinates to logic, and by making use of the correspondences between duality in logic and in (projective) geometry. The spatialization of logic enables us to give it a clear structural and architectonic character - one which brings out the “order” internal to this domain. The foundations of geometrical logic as such are dealt with, and the architectonics responsible for governing its elements is highlighted. The second half of the 20th century saw work being undertaken on spatial logic that is still ongoing today, and whose precursor is undoubtedly Bornstein, making it all the more worthwhile that we pay attention to the results of his own ontological research.
Abstract
Bornstein arrived at an original mathematical system of relationships and categorical-ontological structures: i.e. a general ontology, or a metaphysics in the broader meaning of that term. Metaphysics, as a theoretical and mathematical science, is concerned with all of being and/or being generally. It is, therefore, a universal and pure mathematical science - mathesis universalis - of the kind sought after by Plato, Descartes, Leibniz and Hoene-Wroński. In this article, Bornstein’s algebraico-geometrical logic, known as “topologic”, will be treated as a spatial representation of algebraic logic. The representation is effected through an application of Descartes’s co-ordinates to logic, and by making use of the correspondences between duality in logic and in (projective) geometry. The spatialization of logic enables us to give it a clear structural and architectonic character - one which brings out the “order” internal to this domain. The foundations of geometrical logic as such are dealt with, and the architectonics responsible for governing its elements is highlighted. The second half of the 20th century saw work being undertaken on spatial logic that is still ongoing today, and whose precursor is undoubtedly Bornstein, making it all the more worthwhile that we pay attention to the results of his own ontological research.
Kapitel in diesem Buch
- 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
Kapitel in diesem Buch
- 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
