On Essential Structures and Symmetries
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Tomasz Bigaj
Abstract
The main goal of the paper is to revisit the concept of a symmetry for relational structures in light of the ontological position dubbed “essentialist structuralism”. It is argued that the standard definition of the notion of a symmetry commits us to the existence of non-qualitative, haecceitistic differences between possible worlds. An alternative notion of symmetry is developed, based on the distinction between essential and contingent structures. It is claimed that this new concept is better suited for the doctrine of structuralism, and moreover it offers a new perspective on some well-known problems in the foundation of physical theories, such as the problem of permutation invariance in quantum mechanics and diffeomorphism invariance in general relativity.
Abstract
The main goal of the paper is to revisit the concept of a symmetry for relational structures in light of the ontological position dubbed “essentialist structuralism”. It is argued that the standard definition of the notion of a symmetry commits us to the existence of non-qualitative, haecceitistic differences between possible worlds. An alternative notion of symmetry is developed, based on the distinction between essential and contingent structures. It is claimed that this new concept is better suited for the doctrine of structuralism, and moreover it offers a new perspective on some well-known problems in the foundation of physical theories, such as the problem of permutation invariance in quantum mechanics and diffeomorphism invariance in general relativity.
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
