Von Plato, Jan
Overview
Works:  21 works in 110 publications in 4 languages and 1,929 library holdings 

Genres:  History Biography 
Roles:  Author, Creator, Other 
Classifications:  QA273, 519.2 
Publication Timeline
.
Most widely held works by
Jan Von Plato
Proof analysis : a contribution to Hilbert's last problem by
Sara Negri(
)
10 editions published between 2011 and 2014 in English and held by 717 WorldCat member libraries worldwide
"We shall discuss the notion of proof and then present an introductory example of the analysis of the structure of proofs. The contents of the book are outlined in the third and last section of this chapter. 1.1 The idea of a proof A proof in logic and mathematics is, traditionally, a deductive argument from some given assumptions to a conclusion. Proofs are meant to present conclusive evidence in the sense that the truth of the conclusion should follow necessarily from the truth of the assumptions. Proofs must be, in principle, communicable in every detail, so that their correctness can be checked. Detailed proofs are a means of presentation that need not follow in anyway the steps in finding things out. Still, it would be useful if there was a natural way from the latter steps to a proof, and equally useful if proofs also suggested the way the truths behind them were discovered. The presentation of proofs as deductive arguments began in ancient Greek axiomatic geometry. It took Gottlob Frege in 1879 to realize that mere axioms and definitions are not enough, but that also the logical steps that combine axioms into a proof have to be made, and indeed can be made, explicit. To this purpose, Frege formulated logic itself as an axiomatic discipline, completed with just two rules of inference for combining logical axioms. Axiomatic logic of the Fregean sort was studied and developed by Bertrand Russell, and later by David Hilbert and Paul Bernays and their students, in the first three decades of the twentieth century. Gradually logic came to be seen as a formal calculus instead of a system of reasoning: the language of logic was formalized and its rules of inference taken as part of an inductive definition of the class of formally provable formulas in the calculus"
10 editions published between 2011 and 2014 in English and held by 717 WorldCat member libraries worldwide
"We shall discuss the notion of proof and then present an introductory example of the analysis of the structure of proofs. The contents of the book are outlined in the third and last section of this chapter. 1.1 The idea of a proof A proof in logic and mathematics is, traditionally, a deductive argument from some given assumptions to a conclusion. Proofs are meant to present conclusive evidence in the sense that the truth of the conclusion should follow necessarily from the truth of the assumptions. Proofs must be, in principle, communicable in every detail, so that their correctness can be checked. Detailed proofs are a means of presentation that need not follow in anyway the steps in finding things out. Still, it would be useful if there was a natural way from the latter steps to a proof, and equally useful if proofs also suggested the way the truths behind them were discovered. The presentation of proofs as deductive arguments began in ancient Greek axiomatic geometry. It took Gottlob Frege in 1879 to realize that mere axioms and definitions are not enough, but that also the logical steps that combine axioms into a proof have to be made, and indeed can be made, explicit. To this purpose, Frege formulated logic itself as an axiomatic discipline, completed with just two rules of inference for combining logical axioms. Axiomatic logic of the Fregean sort was studied and developed by Bertrand Russell, and later by David Hilbert and Paul Bernays and their students, in the first three decades of the twentieth century. Gradually logic came to be seen as a formal calculus instead of a system of reasoning: the language of logic was formalized and its rules of inference taken as part of an inductive definition of the class of formally provable formulas in the calculus"
The great formal machinery works : theories of deduction and computation at the origins of the digital age by
Jan Von Plato(
)
11 editions published between 2017 and 2018 in English and held by 326 WorldCat member libraries worldwide
The information age owes its existence to a littleknown but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenthcentury German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later
11 editions published between 2017 and 2018 in English and held by 326 WorldCat member libraries worldwide
The information age owes its existence to a littleknown but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenthcentury German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later
Structural proof theory by
Sara Negri(
Book
)
15 editions published between 2001 and 2008 in English and Undetermined and held by 269 WorldCat member libraries worldwide
"This book is both a concise introduction to the central results and methods of structural proof theory and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics, and computer science." "The book contains a wealth of new results on prooftheoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory  natural deduction and sequent calculus. The authors emphasize the computational context of logical results." "A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated."Jacket
15 editions published between 2001 and 2008 in English and Undetermined and held by 269 WorldCat member libraries worldwide
"This book is both a concise introduction to the central results and methods of structural proof theory and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics, and computer science." "The book contains a wealth of new results on prooftheoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory  natural deduction and sequent calculus. The authors emphasize the computational context of logical results." "A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated."Jacket
Saved from the cellar : Gerhard Gentzen's shorthand notes on logic and foundations of mathematics by
Jan Von Plato(
)
15 editions published between 2017 and 2019 in English and German and held by 260 WorldCat member libraries worldwide
Gerhard Gentzen is best known for his development of the proof systems of natural deduction and sequent calculus, central in many areas of logic and computer science today. Another noteworthy achievement is his resolution of the embarrassing situation created by Gödel's incompleteness results, especially the second one about the unprovability of consistency of elementary arithmetic. After these successes, Gentzen dedicated the rest of his short life to the main problem of Hilbert's proof theory, the question of the consistency of analysis. He was arrested in the summer of 1945 with other professors of the German University of Prague and died soon afterward of starvation in a prison cell. Attempts at locating his lost manuscripts failed at the time, but several decades later, two slim folders of shorthand notes were found. In this volume, Jan von Plato gives an overview of Gentzen's life and scientific achievements, based on detailed archival and systematic studies, and essential for placing the translations of shorthand manuscripts that follow in the right setting. The materials in this book are singular in the way they show the birth and development of Gentzen's central ideas and results, sometimes in a welldeveloped form, and other times as flashes into the anatomy of the workings of a unique mind
15 editions published between 2017 and 2019 in English and German and held by 260 WorldCat member libraries worldwide
Gerhard Gentzen is best known for his development of the proof systems of natural deduction and sequent calculus, central in many areas of logic and computer science today. Another noteworthy achievement is his resolution of the embarrassing situation created by Gödel's incompleteness results, especially the second one about the unprovability of consistency of elementary arithmetic. After these successes, Gentzen dedicated the rest of his short life to the main problem of Hilbert's proof theory, the question of the consistency of analysis. He was arrested in the summer of 1945 with other professors of the German University of Prague and died soon afterward of starvation in a prison cell. Attempts at locating his lost manuscripts failed at the time, but several decades later, two slim folders of shorthand notes were found. In this volume, Jan von Plato gives an overview of Gentzen's life and scientific achievements, based on detailed archival and systematic studies, and essential for placing the translations of shorthand manuscripts that follow in the right setting. The materials in this book are singular in the way they show the birth and development of Gentzen's central ideas and results, sometimes in a welldeveloped form, and other times as flashes into the anatomy of the workings of a unique mind
Elements of logical reasoning by
Jan Von Plato(
Book
)
14 editions published between 2013 and 2014 in English and held by 168 WorldCat member libraries worldwide
"Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premisses have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics, and computer science"
14 editions published between 2013 and 2014 in English and held by 168 WorldCat member libraries worldwide
"Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premisses have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics, and computer science"
Logic's lost genius : the life of Gerhard Gentzen by
Eckart MenzlerTrott(
Book
)
8 editions published in 2001 in German and English and held by 88 WorldCat member libraries worldwide
"Gerhard Gentzen (19091945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called "proof theory", but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today." "The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945"Jacket
8 editions published in 2001 in German and English and held by 88 WorldCat member libraries worldwide
"Gerhard Gentzen (19091945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called "proof theory", but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today." "The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945"Jacket
Creating modern probability : its mathematics, physics, and philosophy in historical perspective by
Jan von Plato(
)
11 editions published between 1994 and 1998 in English and held by 67 WorldCat member libraries worldwide
This is the only book to chart the history and development of modern probability theory. It shows how in the first thirty years of this century probability theory became a mathematical science. The author also traces the development of probabilistic concepts and theories in statistical and quantum physics. There are chapters dealing with chance phenomena, as well as the main mathematical theories of today, together with their foundational and philosophical problems. Among the theorists whose work is treated at some length are Kolmogorov, von Mises and de Finetti. The principal audience for the book comprises philosophers and historians of science, mathematicians concerned with probability and statistics, and physicists. The book will also interest anyone fascinated by twentiethcentury scientific developments because the birth of modern probability is closely tied to the change from a determinist to an indeterminist worldview
11 editions published between 1994 and 1998 in English and held by 67 WorldCat member libraries worldwide
This is the only book to chart the history and development of modern probability theory. It shows how in the first thirty years of this century probability theory became a mathematical science. The author also traces the development of probabilistic concepts and theories in statistical and quantum physics. There are chapters dealing with chance phenomena, as well as the main mathematical theories of today, together with their foundational and philosophical problems. Among the theorists whose work is treated at some length are Kolmogorov, von Mises and de Finetti. The principal audience for the book comprises philosophers and historians of science, mathematicians concerned with probability and statistics, and physicists. The book will also interest anyone fascinated by twentiethcentury scientific developments because the birth of modern probability is closely tied to the change from a determinist to an indeterminist worldview
The interpretation of probabilities by
Jan Von Plato(
Book
)
10 editions published in 1980 in English and Finnish and held by 13 WorldCat member libraries worldwide
10 editions published in 1980 in English and Finnish and held by 13 WorldCat member libraries worldwide
Philosophie et religion : Platon Euthyphron by
JeanYves Chateau(
Book
)
1 edition published in 2005 in French and held by 4 WorldCat member libraries worldwide
1 edition published in 2005 in French and held by 4 WorldCat member libraries worldwide
The great formal machinery works digital age : theories of deduction and computation at the origins of the digital age by
Jan Von Plato(
Book
)
2 editions published in 2017 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2017 in English and held by 4 WorldCat member libraries worldwide
Creating modern probalitiy : its mathematics, physics and philosophy in historical perspective by
Jan Von Plato(
Book
)
2 editions published between 1995 and 1998 in English and held by 2 WorldCat member libraries worldwide
2 editions published between 1995 and 1998 in English and held by 2 WorldCat member libraries worldwide
Studia excellentia : essays in honour of Oiva Ketonen(
Book
)
2 editions published in 1977 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1977 in English and held by 2 WorldCat member libraries worldwide
The interpretation of probalities by
Jan Von Plato(
Book
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
From Gentzen to Jaskowski and back : algorithmic translation of derivations between the two main systems of natural deduction by
Jan Von Plato(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
That and "that" : essays in honour of S. Albert Kivinen(
Book
)
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
Studies in the history of philosophy(
Book
)
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
Epistemological problems of subjective probabilities by
Jan Von Plato(
Book
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
Reductive relations in interpretations of probability by
Jan Von Plato(
Book
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
Ein Leben, ein Werk : Gedanken über das wissenschaftliche Schaffen des finnischen Logikers Oiva Ketonen by
Jan Von Plato(
)
1 edition published in 2004 in German and held by 1 WorldCat member library worldwide
1 edition published in 2004 in German and held by 1 WorldCat member library worldwide
Foundations of objective probability by
Jan Von Plato(
Book
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
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Audience Level
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Related Identities
 Negri, Sara 1967 Author
 Gentzen, Gerhard
 MenzlerTrott, Eckart Other Author
 Ranta, Aarne
 Cambridge University Press Publisher
 Springer International Publishing AG Publisher
 Chateau, JeanYves
 Saarinen, Esa
 Niiniluoto, Ilkka
 Ketonen, Oiva
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