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Invariance and Necessity
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Gila Sher
Abstract
Properties and relations in general have a certain degree of invariance, and some types of properties/relations have a stronger degree of invariance than others. In this paper I will show how the degrees of invariance of different types of properties are associated with, and explain, the modal force of the laws governing them. This explains differences in the modal force of laws/principles of different disciplines, starting with logic and mathematics and proceeding to physics and biology.
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Abstract
Properties and relations in general have a certain degree of invariance, and some types of properties/relations have a stronger degree of invariance than others. In this paper I will show how the degrees of invariance of different types of properties are associated with, and explain, the modal force of the laws governing them. This explains differences in the modal force of laws/principles of different disciplines, starting with logic and mathematics and proceeding to physics and biology.
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Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Preface IX
-
Part I: Philosophy of Logic
- Link’s Revenge: A Case Study in Natural Language Mereology 3
- Universal Translatability: An Optimality- Based Justification of (Classical) Logic 37
- Invariance and Necessity 55
- Translations Between Logics: A Survey 71
- On the Relation of Logic to Metalogic 91
- Free Logic and the Quantified Argument Calculus 105
- Dependencies Between Quantifiers Vs. Dependencies Between Variables 117
- Three Types and Traditions of Logic: Syllogistic, Calculus and Predicate Logic 133
- Truth, Paradox, and the Procedural Conception of Fregean Sense 153
- Wittgenstein and Frege on Assertion 169
- Assertions and Their Justification: Demonstration and Self-Evidence 183
- Surprises in Logic: When Dynamic Formality Meets Interactive Compositionality 197
-
Part II: Philosophy of Mathematics
- Neologicist Foundations: Inconsistent Abstraction Principles and Part-Whole 215
- What Hilbert and Bernays Meant by “Finitism” 249
- Wittgenstein and Turing 263
- Remarks on Two Papers of Paul Bernays 297
- The Significance of the Curry-Howard Isomorphism 313
- Reductions of Mathematics: Foundation or Horizon? 327
- What Are the Axioms for Numbers and Who Invented Them? 343
-
Part III: Wittgenstein
- Following a Rule: Waismann’s Variation 359
- Propositions in Wittgenstein and Ramsey 375
- An Unexpected Feature of Classical Propositional Logic in the Tractatus 385
- Ontology in Tractatus Logico-Philosophicus: A Topological Approach 397
- Adding 4.0241 to TLP 415
- Understanding Wittgenstein’s Wood Sellers 429
- On the Infinite, In-Potentia: Discovery of the Hidden Revision of Philosophical Investigations and Its Relation to TS 209 Through the Eyes of Wittgensteinian Mathematics 441
- Incomplete Pictures and Specific Forms: Wittgenstein Around 1930 457
- „Man kann die Menschen nicht zum Guten führen“ – Zur Logik des moralischen Urteils bei Wittgenstein und Hegel 473
- Der Status mathematischer und religiöser Sätze bei Wittgenstein 485
- Gutes Sehen 499
- Wittgenstein’s Conjecture 515
- Index of Names 535
- Index of Subjects 539
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Preface IX
-
Part I: Philosophy of Logic
- Link’s Revenge: A Case Study in Natural Language Mereology 3
- Universal Translatability: An Optimality- Based Justification of (Classical) Logic 37
- Invariance and Necessity 55
- Translations Between Logics: A Survey 71
- On the Relation of Logic to Metalogic 91
- Free Logic and the Quantified Argument Calculus 105
- Dependencies Between Quantifiers Vs. Dependencies Between Variables 117
- Three Types and Traditions of Logic: Syllogistic, Calculus and Predicate Logic 133
- Truth, Paradox, and the Procedural Conception of Fregean Sense 153
- Wittgenstein and Frege on Assertion 169
- Assertions and Their Justification: Demonstration and Self-Evidence 183
- Surprises in Logic: When Dynamic Formality Meets Interactive Compositionality 197
-
Part II: Philosophy of Mathematics
- Neologicist Foundations: Inconsistent Abstraction Principles and Part-Whole 215
- What Hilbert and Bernays Meant by “Finitism” 249
- Wittgenstein and Turing 263
- Remarks on Two Papers of Paul Bernays 297
- The Significance of the Curry-Howard Isomorphism 313
- Reductions of Mathematics: Foundation or Horizon? 327
- What Are the Axioms for Numbers and Who Invented Them? 343
-
Part III: Wittgenstein
- Following a Rule: Waismann’s Variation 359
- Propositions in Wittgenstein and Ramsey 375
- An Unexpected Feature of Classical Propositional Logic in the Tractatus 385
- Ontology in Tractatus Logico-Philosophicus: A Topological Approach 397
- Adding 4.0241 to TLP 415
- Understanding Wittgenstein’s Wood Sellers 429
- On the Infinite, In-Potentia: Discovery of the Hidden Revision of Philosophical Investigations and Its Relation to TS 209 Through the Eyes of Wittgensteinian Mathematics 441
- Incomplete Pictures and Specific Forms: Wittgenstein Around 1930 457
- „Man kann die Menschen nicht zum Guten führen“ – Zur Logik des moralischen Urteils bei Wittgenstein und Hegel 473
- Der Status mathematischer und religiöser Sätze bei Wittgenstein 485
- Gutes Sehen 499
- Wittgenstein’s Conjecture 515
- Index of Names 535
- Index of Subjects 539
