Address:

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

Telephone:

+ 358 - 9 - 191 28087 (office)

Fax :

+ 358 - 9 - 191 28060

E-mail:

jan.vonplato(at)helsinki(dot)fi

New book!

Research interests

After I "quit probability" in 1992, I worked for some years on elementary intuitionistic axiomatics, especially intuitionistic geometry, related to the type theory group. (Gilles Kahn's implementation of my axiomatics of constructive geometry was one of the first such implementations.) The most important part of the group's work was Aarne Ranta's type-theoretical grammar. It led later to his Grammatical Framework (GF) that can be found displayed at his home page.

From 1997 on, I have mainly worked on proof theory, both systematically and with historical-foundational questions in mind. There are three books: Structural Proof Theory , written with Sara Negri and published by Cambridge University Press in 2001 (paperback edition 2008), Proof Analysis: A Contribution to Hilbert's Last Problem, written with Sara Negri, Cambridge University Press, 2011 and Logical Reasoning: First Principles & Deductive Machinery to appear in 2012. The last one began as an elementary textbook, but became also a statement about my views on logic more generally.

I had the good fortune of finding a handwritten manuscript version of Gentzen's doctoral thesis in February 2005. It turned out that the ms. contained a detailed proof of normalization for intuitionistic natural deduction. There is an English translation of the proof in item II.39.

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.

13. Five questions on probability. In A. Hajek and V. Hendricks, eds, Five Questions on Probability and Statistics, pp. 149-162, Automatic Press 2009.

3. Probability and causality
14. 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.

15. 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.

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

4. History of science

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

18. 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.

19. 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.

20. 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.

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

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

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

24. 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.

25. 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 Analysis: A Contribution to Hilbert's Last Problem, written with Sara Negri. Cambridge University Press, 2011 (in press).

3. The Logician's QED. A first book in logic, to appear in 2011.

4. From Hilbert's program to Gentzen's program, in E. Menzler-Trott, Logic's Lost Genius, pp. 365-402, American Mathematical Society, Providence, Rhode Island 2007.

5. Proof theory of classical and intuitionistic logic, in L. Haaparanta, ed, History of Modern Logic, pp. 499-515, Oxford Univers ity Press, 2009.

2. Foundations of geometry

6. 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).

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

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

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

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

11. A dialogue on the foundations of geometry. In Approaching Truth: Essays in Honour of Ilkka Niiniluoto, ed. S. Pihlstr\"om et al., pp. 83-97, College Publications, London 2007.

12. Combinatorial analysis of proofs in projective and affine geometry, Annals of Pure and Applied Logic, vol. 162 (2010), pp. 144-161.

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

14. 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.

15. 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.

16. Order in open intervals of computable reals, Mathematical Structures in Computer Science, vol. 9 (1999), pp. 103-108, Introduction.

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

18. 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

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

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

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

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

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

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

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

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

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

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

29. Normal derivability in modal logic, Mathematical Logic Quarterly, vol. 51 (2005), pp. 632-638

30. Gentzen's original proof of the consistency of arithmetic revisited. In G. Primiero and S. Rahman (eds.) Acts of Knowledge - History, Philosophy and Logic, pp. 151-171, College Publications, London 2009.

31. A sequent calculus isomorphic to Gentzen's natural deduction. The Review of Symbolic Logic, vol. 3 (2010), pp. 000-000.

32. Aristotle's deductive logic: a proof-theoretical study. To appear in the proceedings of the Martin-Loef conference, Uppsala, May 2009.

See also item 12 above.

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

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

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

36. 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.

37. In the shadows of the Loewenheim-Skolem theorem: Early combinatorial analyses of mathematical proofs, The Bulletin of Symbolic Logic, vol. 13 (2007), pp. 189-225.

38. The development of proof theory. In Stanford Encyclopaedia of Philosophy, on-line edition, April 2008.

39. Gentzen's proof of normalization for intuitionistic natural deduction. The Bulletin of Symbolic Logic, vol. 14 (2008), pp. 240-257.

40. Gentzen's logic. In Handbook of the History of Logic. Volume 5. Logic from Russell to Church, D. Gabbay and J. Woods, eds, pp. 667-721, Elsevier 2009.

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, vol. 12 (2006), pp. 492-494.