Mathesis Universalis, Computability and Proof

Mathesis Universalis, Computability and Proof

In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes "the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined"; in another fragment he takes the mathesis to be "the science of all things that are conc...

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Λεπτομέρειες βιβλιογραφικής εγγραφής
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Άλλοι συγγραφείς: Centrone, Stefania (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Negri, Sara (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Sarikaya, Deniz (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Schuster, Peter M. (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
Έκδοση:1st ed. 2019.
Σειρά:Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science ; 412
Θέματα:
Logic.
Mathematical logic.
Mathematical Logic and Foundations.
Mathematical Logic and Formal Languages.
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • 1. Introduction: Mathesis Universalis, Proof and Computation (Stefania Centrone)
  • 2. Diplomacy of Trust in the European Crisis (Enno Aufderheide)
  • 3. Mathesis Universalis and Homotopy Type Theory (Steve Awodey)
  • 4. Note on the Benefit of Proof Representations by Name (Matthias Baaz)
  • 5. Constructive Proofs of Negated Statements (Josef Berger and Gregor Svindland)
  • 6. Constructivism in Abstract Mathematics (Ulrich Berger)
  • 7. Addressing Circular Definitions via Systems of Proofs (Riccardo Bruni)
  • 8. The Monotone Completeness Theorem in Constructive Reverse Mathematics (Hajime Ishihara and Takako Nemoto)
  • 9. From Mathesis Universalis to Fixed Points and Related Set-Theoretic Concepts (Gerhard Jäger and Silvia Steila)
  • 10. Through an Inference Rule, Darkly (Roman Kuznets)
  • 11. Objectivity and Truth in Mathematics: A Sober Non-Platonist Perspective (Godehard Link)
  • 12. From Mathesis Universalis to Provability, Computability, and Constructivity (Klaus Mainzer)
  • 13. Analytic Equational Proof Systems for Combinatory Logic and λ-Calculus: a Survey (Pierluigi Minari)
  • 14. Computational Interpretations of Classical Reasoning: From the Epsilon Calculus to Stateful Programs (Thomas Powell)
  • 15. The Concepts of Proof and Ground (Dag Prawitz)
  • 16. On Relating Theories: Proof-Theoretical Reduction (Michael Rathjen and Michael Toppel)
  • 17. Program Extraction from Proofs: the Fan Theorem for Uniformly Coconvex Bars (Helmut Schwichtenberg)
  • 18. Counting and Numbers, from Pure Mathesis to Base Conversion Algorithms (Jan von Plato)
  • 19. Point-Free Spectra of Linear Spreads (Daniel Wessel). .

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