Address:

Department of Philosophy, P.O.Box 24, 00014 University of Helsinki, Finland.

Telephone:

+ 358 - 9 - 191 29243 (office)

Fax :

+ 358 - 9 - 191 29229

E-mail:

jan.vonplato(at)helsinki(dot)fi

Research interests

My present research is mainly in logic and foundations of mathematics, particularly, proof theory, constructive geometry, and elementary intuitionistic axiomatics and logical issues related to the latter. Latest work is the book Structural Proof Theory , written with Sara Negri and published by Cambridge University Press in 2001.

Thematic List of Publications

I History and philosophy of science

1. General

2. Interpretations of probability

3. Probability and causality

4. History of science

II Logic and foundations

1. General

2. Foundations of geometry

3. Intuitionism

4. Proof theory

5. History and philosophy of logic

III Reviews

I History and philosophy of science

1. General
1. Creating Modern Probability: Its Mathematics, Physics and Philosophy in Historical Perspective, Cambridge University Press 1994, 3rd printing (paperback) 1998. Fourth printing 2000.

2. The rise of probabilistic thinking, in T.\ Baldwin, ed, Cambridge History of Philosophy 1870--1945, pp.\ 621--628, Cambridge University Press 2003.

2. Interpretations of probability

3. On partial exchangeability as a generalization of symmetry principles, Erkenntnis, vol. 16 (1981), pp. 53-59.

4. Reductive relations in interpretations of probability, Synthese, vol. 48 (1981), pp. 61-75.

5. Probability and determinism, Philosophy of Science, vol. 49 (1982), pp. 52-66.

6. The generalization of de Finetti's theorem to stationary probabilities, in P. Asquith and T. Nickles, eds, PSA 1982, vol. 1, pp. 137-144, Philosophy of Science Association, East Lansing, Michigan 1982.

7. The significance of the ergodic decomposition of stationary probabilities for the interpretation of probability, Synthese, vol. 52 (1983), pp. 419-432.

8. The method of arbitrary functions, The British Journal for the Philosophy of Science, vol. 33 (1983), pp. 37-47.

9. Ergodic theory and the foundations of probability, in B. Skyrms and W.L. Harper, eds, Causation, Chance and Credence. Proceedings of the Irvine Conference on Probability and Causation, vol. 1, pp. 257-277, Kluwer, Dordrecht 1988.

10. Probability in dynamical systems, in J. Fenstad et al., eds, Logic, Methodology, and Philosophy of Science VIII, pp. 427-443, North-Holland, Amsterdam 1989.

11. de Finetti's earliest works on the foundations of probability, Erkenntnis, vol. 31 (1989), pp. 263-282.

12. Finite partial exchangeability, Statistics \& Probability Letters, vol. 11 (1991), pp. 91-94, Abstract.

3. Probability and causality
13. Probabilistic causality, randomization and mixtures, in A. Fine and P. Mach-amer, eds, PSA 1986, vol. 1, pp. 432-437, Philosophy of Science Association, East Lansing, Michigan 1986.

14. Description of experiments in physics: a dynamical approach, in E.I. Bitsakis and C.A. Nicolaides, eds, The Concept of Probability, pp. 199-206, Kluwer, Dordrecht 1989.

15. Probabilistic causality from a dynamical point of view, Topoi, vol. 8 (1990), pp. 11-18.

4. History of science

16. Nicole Oresme and the ergodicity of rotations, Acta Philosophica Fennica, vol. 32 (1981), pp. 190-197.

17. Instability and the accumulation of small effects, in M. Heidelberger and L. Kr\"uger, eds, Probability and Conceptual Change in Scientific Thought, pp. 77-93, B. Kleine Verlag, Bielefeld 1982.

18. Classical physics and determinism, in M. Heidelberger, L. Kr\"uger and R. Rheinwald, eds, Probability Since 1800, pp. 415-429, B. Kleine Verlag, Bielefeld 1983.

19. Probabilistic physics the classical way, in L. Kr\"uger, G. Gigerenzer, and M. Morgan, eds, The Probabilistic Revolution, vol. 2, pp. 379-407, MIT Press, Cambridge 1987.

20. Boltzmann's ergodic hypothesis, Archive for History of Exact Sciences, vol. 42 (1991), pp. 71-89. Summary.

21. Oresme's proof of the ergodicity of rotations of a circle through an irrational angle, Historia Mathematica, vol. 20 (1993), pp. 428-433. Summary.

22. Illustrations of method in Ptolemaic astronomy, Grazer Philosophische Studien, vol. 48 (1994/5), pp. 69-82.

23. Theory and experiment in the study of Brownian motion and radioactivity, (with comments by Manfred Stoeckler: How to learn from experiments), in D. Anapolitanos et al., eds, Philosophy and the Many Faces of Science, pp. 144-154, Rowman & Littlefield, 1998.

24. A. N. Kolmogorov, Grundlagen der Wahrscheinlichkeitsrechnung (1933), in I. Grattan-Guinness, ed, Landmarks in Western Mathematics: Case Studies 1640--1940, pp. 960-969, Elsevier 2005.

II Logic and foundations

1. General
1. Structural Proof Theory , written with Sara Negri. Contents. Cambridge University Press, 2001, xvii + 257 p.. Connected to the book is an interactive sequent calculus proof editor that can be found through Aarne Ranta's home page.

2. Proof theory of classical and intuitionistic logic, in L. Haaparanta, ed, History of Modern Logic, Oxford University Press, in press.

3. From Hilbert's program to Gentzen's program, to appear in E. Menzler-Trott, Logic's Lost Genius, AMS, Providence, Rhode Island.

2. Foundations of geometry

4. The logic of Euclidean construction procedures, (together with Petri M\"aenp\"a\"a, in L. Haaparanta et al., eds, Logic, Language and Intentionality, pp. 275-293 (= Acta Philosophica Fennica, vol. 49, 1990).

5. The axioms of constructive geometry, Annals of Pure and Applied Logic, vol. 76 (1995), pp. 169-200, Abstract.

6. Formalization of Hilbert's geometry of incidence and parallelism, Synthese, vol. 110 (1997), pp. 127-141, Abstract.

7. A constructive theory of ordered affine geometry , (dvi file), Indagationes Mathematicae, vol. 9 (1998), pp. 549-562. Summary.

8. The decision problem in projective and affine geometry. Submitted for publication.

9. A constructive approach to Sylvester's conjecture, Journal of Universal Computer Science, vol. 11 (2005), pp. 2165-2178.

10. A dialogue on the foundations of geometry, to appear.

3. Intuitionism
11. Chance against constructibility, in J. Hintikka, ed, Essays on the Development of the Foundations of Mathematics, pp. 263-281, Kluwer, Dordrecht 1995.

12. Organization and development of a constructive axiomatization , (dvi file) , in S. Berardi and M. Coppo, eds, Types for Proofs and Programs, pp. 288-296 (LNCS, vol. 1158), Springer, Berlin 1996.

13. From Kripke models to algebraic counter-valuations, (with Sara Negri), in H. de Swart, ed, Automated Reasoning with Analytic Tableaux and Related Methods, pp. 247-261 (LNAI, vol. 1397), Springer, Berlin 1998, Summary.

14. Order in open intervals of computable reals, Mathematical Structures in Computer Science, vol. 9 (1999), pp. 103-108, href="http:intintr.html"> Introduction.

15. Positive lattices, in P. Schuster et al., eds, Reuniting the Antipodes, pp. 185-197, Kluwer, Dordrecht 2001.

16. The duality of classical and constructive notions and proofs, (with Sara Negri), in L. Crosilla and P. Schuster, eds, From Sets and Types to Topology and Analysis: Practicable Foundations of Constructive Mathematics, pp. 149-161, Oxford Logic Guides, Oxford 2005.

4. Proof theory

17. Cut elimination in the presence of axioms, (with Sara Negri), The Bulletin of Symbolic Logic, vol. 4 (1998), pp. 418-435.

18. A problem of normal form in natural deduction, Mathematical Logic Quarterly, vol. 46 (2000), pp. 121-124.

19. A proof of Gentzen's Hauptsatz without multicut, Archive for Mathematical Logic, vol. 40 (2001), pp. 9-18.

20. Natural deduction with general elimination rules, Archive for Mathematical Logic, vol. 40 (2001), pp. 541-567.

21. Sequent calculus in natural deduction style, (with Sara Negri), The Journal of Symbolic Logic, vol. 65, 2001, pp. 1803-1816, Abstract.

22. Permutability of rules in lattice theory, (with Sara Negri), Algebra Universalis, vol. 48 (2002), pp. 473-477.

23. Translations from natural deduction to sequent calculus, Mathematical Logic Quarterly , vol. 49 (2003), pp. 435-443.

24. Proof systems for lattice theory, (with Sara Negri), Mathematical Structures in Computer Science , vol. 14 (2004), pp. 507-526

25. Proof-theoretical analysis of order relations, (with Sara Negri and Thierry Coquand), Archive for Mathematical Logic}, vol. 43 (2004), pp. 297-309.

26. Natural deduction: some recent developments, (scheduled to appear in the proceedings of the Dresden Summer School 2003).

27. Normal derivability in modal logic, Mathematical Logic Quarterly, vol. 51, pp. 632-638.

28. Gentzen's original proof of the consistency of arithmetic revisited. Submitted for publication.

29. A sequent calculus with derivations isomorphic to those in Gentzen's natural deduction. Submitted for publication.

5. History and philosophy of logic
30. Gentzen und die Beweistheorie, in E. Menzler-Trott, Gentzens Problem: mathematische Logik im nationalsozialistischen Deutschland, pp. 313-328, Birkh\"auser, Basel 2001.

31. Rereading Gentzen, Synthese, vol. 173 (2003), pp. 195-209.

32. Skolem's discovery of Goedel-Dummett logic, Studia Logica, vol. 73 (2003), pp. 153-157.

33. Ein Leben, ein Werk -- Gedanken \"uber das wissenschaftliche Schaffen des finnischen Logikers Oiva Ketonen, in R. Seising, ed, Form, Zahl, Ordnung: Studien zur Wissenschafts- und Technikgeschichte, pp. 427-435, Franz Steiner Verlag, Stuttgart 2004.

34. Gentzen's logic, a chapter to appear in vol. V of the Handbook of the History and Philosophy of Logic, D. Gabbay and J. Woods, eds, Elsevier.

35. In the shadows of the Loewenheim-Skolem theorem: Early combinatorial analyses of mathematical proofs, The Bulletin of Symbolic Logic, in press.

1. Review of Niiniluoto, I. and R. Tuomela, Theoretical Concepts and Hypothe-tico-Inductive Inference, in Arkhimedes, vol. 27 (1975), pp. 54--57 [in Finnish].

2. Review of Dirk van Dalen, L. E. J. Brouwer: Mystic, Geometer, and Intuitionist, in The Bulletin of Symbolic Logic, vol. 7 (2001), pp. 129--132.

3. Review of Ptolemy's Almagest, edited and annotated by G. J. Toomer, and of David Pingree, Preceptum Canonis Ptolomei, in Isis: An International Review Devoted to the History of Science and Its Cultural Influences, vol. 92 (2001), pp. 149-150.

4. Review of V. Hendricks et al., eds, Proof Theory: History and Philosophical Significance, in The Bulletin of Symbolic Logic, vol. 8 (2002), pp. 431--432.

5. Essay review of Kurt G\"odel, Collected Works IV--V: Correspondence, ed. S. Feferman et al., The Bulletin of Symbolic Logic, vol. 10 (2004), pp. 558--563.

6. Review of David Hilbert's Lectures on the Foundations of Geometry, 1891--1902, ed. by M. Hallett and U. Majer, The Bulletin of Symbolic Logic, in press.