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  1. Jan von Plato (forthcoming). From Axiomatic Logic to Natural Deduction. Studia Logica:1-18.
    Recently discovered documents have shown how Gentzen had arrived at the final form of natural deduction, namely by trying out a great number of alternative formulations. What led him to natural deduction in the first place, other than the general idea of studying “mathematical inference as it appears in practice,” is not indicated anywhere in his publications or preserved manuscripts. It is suggested that formal work in axiomatic logic lies behind the birth of Gentzen’s natural deduction, rather than any single (...)
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  2. Jan Von Plato & Annika Siders (forthcoming). Normal Derivability in Classical Natural Deduction. Review of Symbolic Logic.
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  3. Jan von Plato (2013). Il Silenzio Delle Sirene: La Matematica Greca Antica. History and Philosophy of Logic 34 (4):381 - 392.
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  4. Jan von Plato (2012). Gentzen's Proof Systems: Byproducts in a Work of Genius. Bulletin of Symbolic Logic 18 (3):313-367.
    Gentzen's systems of natural deduction and sequent calculus were byproducts in his program of proving the consistency of arithmetic and analysis. It is suggested that the central component in his results on logical calculi was the use of a tree form for derivations. It allows the composition of derivations and the permutation of the order of application of rules, with a full control over the structure of derivations as a result. Recently found documents shed new light on the discovery of (...)
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  5. Jan von Plato (2011). A Sequent Calculus Isomorphic to Gentzen's Natural Deduction. Review of Symbolic Logic 4 (1):43-53.
    Gentzens natural deduction. Thereby the appearance of the cuts in translation is explained.
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  6. Jan von Plato (2011). Kurt Gödel: Essays for His Centennial. History and Philosophy of Logic 32 (4):402 - 404.
    History and Philosophy of Logic, Volume 32, Issue 4, Page 402-404, November 2011.
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  7. Jan von Plato (2010). Combinatorial Analysis of Proofs in Projective and Affine Geometry. Annals of Pure and Applied Logic 162 (2):144-161.
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  8. Jan von Plato (2009). Gentzen's Logic. In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier. 667-721.
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  9. Jan von Plato (2008). Gentzen Writes in the Published Version of His Doctoral Thesis Untersuchun-Gen Über Das Logische Schliessen (Investigations Into Logical Reasoning) That He Was Able to Prove the Normalization Theorem Only for Intuitionistic Natural Deduction, but Not for Classical. To Cover the Latter, He Developed Classical Sequent Calculus and Proved a Corresponding Theorem, the Famous Cut Elim. Bulletin of Symbolic Logic 14 (2).
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  10. Jan von Plato (2008). Proof Theory of Classical and Intuitionistic Logic. In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press.
  11. Jan von Plato & G. Gentzen (2008). Gentzen's Proof of Normalization for Natural Deduction. Bulletin of Symbolic Logic 14 (2):240 - 257.
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  12. Jan Von Plato (2007). In the Shadows of the Löwenheim-Skolem Theorem: Early Combinatorial Analyses of Mathematical Proofs. Bulletin of Symbolic Logic 13 (2):189-225.
    The Löwenheim-Skolem theorem was published in Skolem's long paper of 1920, with the first section dedicated to the theorem. The second section of the paper contains a proof-theoretical analysis of derivations in lattice theory. The main result, otherwise believed to have been established in the late 1980s, was a polynomial-time decision algorithm for these derivations. Skolem did not develop any notation for the representation of derivations, which makes the proofs of his results hard to follow. Such a formal notation is (...)
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  13. Jan von Plato (2006). David Hilbert's Lectures on the Foundations of Geometry 1891–1902. Edited by Hallett Michael and Majer Ulrich, Hilbert's David Lectures on the Foundations of Mathematics and Physics, 1891–1933, Vol. 1. Springer, Berlin, Heidelberg and New York, 2004, Xviii+ 661 Pp. [REVIEW] Bulletin of Symbolic Logic 12 (3):492-494.
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  14. Jan von Plato (2006). Normal Form and Existence Property for Derivations in Heyting Arithmetic. Acta Philosophica Fennica 78:159.
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  15. Jan von Plato (2005). Normal Derivability in Modal Logic. Mathematical Logic Quarterly 51 (6):632-638.
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  16. Sara Negri, Jan von Plato & Thierry Coquand (2004). Proof-Theoretical Analysis of Order Relations. Archive for Mathematical Logic 43 (3):297-309.
    A proof-theoretical analysis of elementary theories of order relations is effected through the formulation of order axioms as mathematical rules added to contraction-free sequent calculus. Among the results obtained are proof-theoretical formulations of conservativity theorems corresponding to Szpilrajn’s theorem on the extension of a partial order into a linear one. Decidability of the theories of partial and linear order for quantifier-free sequents is shown by giving terminating methods of proof-search.
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  17. Jan Von Plato (2003). Rereading Gentzen. Synthese 137 (1-2):195 - 209.
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  18. Jan von Plato (2003). Skolem's Discovery of Gödel-Dummett Logic. Studia Logica 73 (1):153 - 157.
    Attention is drawn to the fact that what is alternatively known as Dummett logic, Gödel logic, or Gödel-Dummett logic, was actually introduced by Skolem already in 1913. A related work of 1919 introduces implicative lattices, or Heyting algebras in today's terminology.
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  19. Jan von Plato (2002). Review: Vincent F. Hendricks, Stig Andur Pedersen, Klaus Frovin Jørgensen, Proof Theory, History and Philosophical Significance. [REVIEW] Bulletin of Symbolic Logic 8 (3):431-432.
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  20. Jan von Plato (2002). Proof Theory, History and Philosophical Significance, Edited by Hendricks Vincent F., Pedersen Stig Andur, and Jørgensen Klaus Frovin, Synthese Library, Vol. 292, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2000, Xii+ 244 Pp.—. [REVIEW] Bulletin of Symbolic Logic 8 (3):431-432.
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  21. Sara Negri & Jan von Plato (2001). Sequent Calculus in Natural Deduction Style. Journal of Symbolic Logic 66 (4):1803-1816.
    A sequent calculus is given in which the management of weakening and contraction is organized as in natural deduction. The latter has no explicit weakening or contraction, but vacuous and multiple discharges in rules that discharge assumptions. A comparison to natural deduction is given through translation of derivations between the two systems. It is proved that if a cut formula is never principal in a derivation leading to the right premiss of cut, it is a subformula of the conclusion. Therefore (...)
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  22. Sara Negri & Jan von Plato (2001). Structural Proof Theory. Cambridge University Press.
    A concise introduction to structural proof theory, a branch of logic studying the general structure of logical and mathematical proofs.
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  23. Jan von Plato (2001). A Proof of Gentzen's Hauptsatz Without Multicut. Archive for Mathematical Logic 40 (1):9-18.
    Gentzen's original proof of the Hauptsatz used a rule of multicut in the case that the right premiss of cut was derived by contraction. Cut elimination is here proved without multicut, by transforming suitably the derivation of the premiss of the contraction.
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  24. Jan von Plato (2001). Natural Deduction with General Elimination Rules. Archive for Mathematical Logic 40 (7):541-567.
    The structure of derivations in natural deduction is analyzed through isomorphism with a suitable sequent calculus, with twelve hidden convertibilities revealed in usual natural deduction. A general formulation of conjunction and implication elimination rules is given, analogous to disjunction elimination. Normalization through permutative conversions now applies in all cases. Derivations in normal form have all major premisses of elimination rules as assumptions. Conversion in any order terminates.Through the condition that in a cut-free derivation of the sequent Γ⇒C, no inactive weakening (...)
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  25. Jan von Plato (2001). Review: Dirk van Dalen, Mystic, Geometer, and Intuitionist. The Life of L. E. J. Brouwer. Volume 1. The Dawning Revolution. [REVIEW] Bulletin of Symbolic Logic 7 (1):62-65.
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  26. Sara Negri & Jan Von Plato (1998). Cut Elimination in the Presence of Axioms. Bulletin of Symbolic Logic 4 (4):418-435.
    A way is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive theories. All results are proved for systems in which also the rules of weakening and contraction can be eliminated. Applications include a system of predicate logic (...)
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  27. Sara Negri & Jan von Plato (1998). For Oiva Ketonen's 85th Birthday. Bulletin of Symbolic Logic 4 (4).
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  28. Jan von Plato (1997). Formalization of Hilbert's Geometry of Incidence and Parallelism. Synthese 110 (1):127-141.
    Three things are presented: How Hilbert changed the original construction postulates of his geometry into existential axioms; In what sense he formalized geometry; How elementary geometry is formalized to present day's standards.
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  29. Jan von Plato (1995). The Axioms of Constructive Geometry. Annals of Pure and Applied Logic 76 (2):169-200.
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  30. Jan Von Plato (1994). Illustrations of Method in Ptolemaic Astronomy. Grazer Philosophische Studien 49:63-75.
    Mathematical Astronomy as the most developed branch of ancient exact sciences has been widely discussed - especially epistemological issues e.g. concerning astronomy as a prime example of the distinction between instrumentalist and realist understanding of theories. In contrast to these the very methodology of ancient astronomy has received little attention. Following the work of Jaakko Hintikka and Unto Remes Aristarchus' method of determining the distance of the Sun is sketched and Ptolemy's solar model is discussed in detail.
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  31. P. Mäenpää & Jan von Plato (1990). The Logic of Euclidean Construction Procedures. Acta Philosophica Fennica 39:275-293.
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  32. Jan von Plato (1990). Probabilistic Causality From a Dynamical Point of View. Topoi 9 (2):101-108.
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  33. Jan von Plato (1989). De Finetti's Earliest Works on the Foundations of Probability. Erkenntnis 31 (2-3):263 - 282.
    Bruno de Finetti's earliest works on the foundations of probability are reviewed. These include the notion of exchangeability and the theory of random processes with independent increments. The latter theory relates to de Finetti's ideas for a probabilistic science more generally. Different aspects of his work are united by his foundational programme for a theory of subjective probabilities.
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  34. Jan von Plato (1986). Probabilistic Causality, Randomization and Mixtures. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:432 - 437.
    A formulation of probabilistic causality is given in terms of the theory of abstract dynamical systems. Causal factors are identified as invariants of motion of a system. Repetition of an experiment leads to the notion of stationarity, and causal factors yield a decomposition of the stationary probability law of the experiment into ergodic components. In these, statistical behaviour is uniform. Control of identified causal factors leads to a corresponding statistical law for the events, which is offered as a notion of (...)
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  35. Jan Von Plato (1983). The Method of Arbitrary Functions. British Journal for the Philosophy of Science 34 (1):37-47.
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  36. Jan Von Plato (1982). Probability and Determinism. Philosophy of Science 49 (1):51-66.
    This paper discusses different interpretations of probability in relation to determinism. It is argued that both objective and subjective views on probability can be compatible with deterministic as well as indeterministic situations. The possibility of a conceptual independence between probability and determinism is argued to hold on a general level. The subsequent philosophical analysis of recent advances in classical statistical mechanics (ergodic theory) is of independent interest, but also adds weight to the claim that it is possible to justify an (...)
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  37. Jan von Plato (1982). The Generalization of de Finetti's Representation Theorem to Stationary Probabilities. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1982:137 - 144.
    de Finetti's representation theorem of exchangeable probabilities as unique mixtures of Bernoullian probabilities is a special case of a result known as the ergodic decomposition theorem. It says that stationary probability measures are unique mixtures of ergodic measures. Stationarity implies convergence of relative frequencies, and ergodicity the uniqueness of limits. Ergodicity therefore captures exactly the idea of objective probability as a limit of relative frequency (up to a set of measure zero), without the unnecessary restriction to probabilistically independent events as (...)
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  38. Jan von Plato (1982). The Significance of the Ergodic Decomposition of Stationary Measures for the Interpretation of Probability. Synthese 53 (3):419 - 432.
    De Finetti's representation theorem is a special case of the ergodic decomposition of stationary probability measures. The problems of the interpretation of probabilities centred around de Finetti's theorem are extended to this more general situation. The ergodic decomposition theorem has a physical background in the ergodic theory of dynamical systems. Thereby the interpretations of probabilities in the cases of de Finetti's theorem and its generalization and in ergodic theory are systematically connected to each other.
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  39. Jan von Plato (1981). On Partial Exchangeability as a Generalization of Symmetry Principles. Erkenntnis 16 (1):53 - 59.
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  40. Jan von Plato (1981). Reductive Relations in Interpretations of Probability. Synthese 48 (1):61 - 75.
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