Göran Sundholm | Universiteit Leiden (original) (raw)

Papers by Göran Sundholm

Philosophy of Logic and Mathematics, 2019

Revue internationale de philosophie, 2004

Dans Revue internationale de philosophie Revue internationale de philosophie 2004/4 (n° 230) 2004... more Dans Revue internationale de philosophie Revue internationale de philosophie 2004/4 (n° 230) 2004/4 (n° 230), pages 401 à 410

History and Philosophy of Logic, 2001

A detailed chronology is offered for the writing of Frege's central philosophical essays from the... more A detailed chronology is offered for the writing of Frege's central philosophical essays from the early 1890s. Particular attention is given to (the distinction between) Sinn and Bedeutung. Suggestions are made as to the origin of the examples concerning the Morning Star/Evening Star and August Bebel's views on the return of Alsace-Lorraine. Likely sources are offered for Frege's use of the terms Bestimmungsweise, Art des Gegebenseins and Sinn und Bedeutung. 10 In his letter of reply Husserl thanks Frege for a number of off-prints; FB, however, is not mentioned among them. Nevertheless, Husserl did possess a copy of the FB booklet, for information concerning which see KS, pp. 431±434. 11 WB, p. 48.

Topoi, 2018

The two different layers of logical theory-epistemological and ontological-are considered and exp... more The two different layers of logical theory-epistemological and ontological-are considered and explained. Special attention is given to epistemic assumptions of the kind that a judgement is granted as known, and their role in validating rules of inference, namely to aid the inferential preservation of epistemic matters from premise judgements to conclusion judgement, while ordinary Natural Deduction assumptions (that propositions are true) serve to establish the holding of consequence from antecedent propositions to succedent proposition.

History and Philosophy of Logic, 2016

We present a new English translation of L.E.J. Brouwer's paper 'De onbetrouwbaarheid der logische... more We present a new English translation of L.E.J. Brouwer's paper 'De onbetrouwbaarheid der logische principes' (The unreliability of the logical principles) of 1908, together with a philosophical and historical introduction. In this paper Brouwer for the first time objected to the idea that the Principle of the Excluded Middle is valid. We discuss the circumstances under which the manuscript was submitted and accepted, Brouwer's ideas on the principle of the excluded middle, its consistency and partial validity, and his argument against the possibility of absolutely undecidable propositions. We note that principled objections to the general excluded middle similar to Brouwer's had been advanced in print by Jules Molk two years before. Finally, we discuss the influence on George Griss' negationless mathematics. keywords: Luitzen Egbertus Jan Brouwer, George Griss, intuitionism, Jules Molk, principle of the excluded middle 4 Among the references in Kohnstamm (1907) we note on pp. 387-388 Husserl's Logische Untersuchungen and Meinong's Gegenstandstheorie, and, indeed, on p. 403, Brouwer's dissertation-'a stern Dutch book' (een ernstig Hollandsch boek). However, that reference just concerns Brouwer's adoption (Brouwer, 1907, p. 104) of Poincaré's remark that the world started rotating only with Copernicus. 5 Much later, in 1949, Brouwer mentioned in a letter to David van Dantzig his 'belief that psychological pictures of intuitionistic mathematics, however interesting they may be, never can be adequate' (

Logic, Epistemology, and the Unity of Science, 2014

The first half of the paper discusses recursive versus constructive functions and, following Heyt... more The first half of the paper discusses recursive versus constructive functions and, following Heyting, stresses that from a constructive point the former cannot replace the latter. The second half of the paper treats of the Kreisel-Myhill theory CS for Brouwer’s Creating Subject, and its relation to BHK meaning-explanations and Kripke’s Schema. Kripke’s Schema is reformulated as a principle and shown to be classically valid. Assuming existence of a verification-object for this principle, a modification of a proof of conservativeness of Van Dalen’s, is shown to give a relative BHK meaning explanation for the Kreisel-Myhill connective. The result offers an explanation of why Kripke’s Schema can be used as a replacement of the Theory of Creating Subject when formulating Brouwerian counter-examples. It also shows that the Theory of Creating Subject is classically valid.

Handbook of Philosophical Logic, 2001

One Hundred Years of Intuitionism (1907–2007), 2008

3. As Kleene showed (Kleene and Vesley 1965, pp. 87-88), a condition is that the bar is decidable... more 3. As Kleene showed (Kleene and Vesley 1965, pp. 87-88), a condition is that the bar is decidable. Brouwer does not make this condition explicit, but in his proofs of 1924 (Brouwer 1924D2) and 1927 (Brouwer 1927B), it is satisfied, because there the bar is defined by an application of the continuity principle for choice sequences. The proof from 1954 (Brouwer 1954A), however, in which the bar is neither defined so as to be decidable, nor explicitly required to be, is incorrect. This seems to have been an oversight on Brouwer's part, rather than an overgeneralization, as the method he gives to construct the well-ordering depends on the decidability of the bar. See on this point also Veldman 2006. 4. Here we note and accept an ambiguity. In the primary sense, a demonstration is the act by and in which knowledge is acquired; this corresponds to Brouwer's 'Beweis'. But we also use 'demonstration' to translate Brouwer's 'Beweisführung', which is not an act but an object, namely the act objectified.

Revue d'histoire des sciences, 2014

Dans son article majeur « Que les principes de la logique ne sont pas fiables » de 1908, L. E. J.... more Dans son article majeur « Que les principes de la logique ne sont pas fiables » de 1908, L. E. J. Brouwer tire pour la premiere fois les consequences revisionnistes de la vue generale de la logique presentee dans sa these de doctorat de 1907, en rejetant le principe du tiers exclu. Nous presentons ici une nouvelle traduction francaise et une introduction philosophique et historique.

Peter Aczel: Predicate logic over a type setup There are a variety of closely related notions aim... more Peter Aczel: Predicate logic over a type setup There are a variety of closely related notions aimed at capturing the abstract structure of type dependency in the syntax and semantics of dependent type theories. Examples of such notions are category with attributes, category with families, category with display maps, contextual category, comprehension category, and there are more. The notion of a type setup is yet one more such notion, which differs from the others in taking a more syntactic approach in its explicit use of contexts, as finite lists of typed variable declarations. This makes it closer to the syntax of dependent type theories, while still abstracting away from the usual inductive structure of syntax and the corresponding recursive definition of substitution. Predicate logic over a type setup is simply defined as a sorted predicate logic where the sorts are the types of the type setup and the sorted terms and substitution are also given by the type setup. Logic over a t...

Nordic Journal of Philosophical Logic, 1998

The first part of the paper presents a framework of distinctions for the philosophy of logic in w... more The first part of the paper presents a framework of distinctions for the philosophy of logic in which the interrelations between some central logical notions, such as judgement(-act), judgement (made), proposition(al content), consequence, and inference are spelled out, In the second half the system of MacColl is measured against the distinctions offered in the framework.

In his seminal paper « On the unreliability of the logical principles » of 1908, L. E. J. Brouwer... more In his seminal paper « On the unreliability of the logical principles » of 1908, L. E. J. Brouwer draws for the first time the revisionistic consequences of the general view on logic that he had presented in his dissertation of 1907, by rejecting the principle of the excluded middle. We present here a new French translation as well as a philosophical and historical introduction.

Topoi, 2012

The possibility of error is related to the existence a norm. Connections are spelled out to the n... more The possibility of error is related to the existence a norm. Connections are spelled out to the notion of infallibility and to that of a modifying predicate, to traditional truth theories in connection with ''truth of things'', as well as the primacy of the negative cases, for instance ''false friend''. Keywords Error Á Norm Á Infallibility Á Modifying predicate History, so far as history has anything to say about it, does teach that right and wrong are real distinctions.

Theoria, 2008

Distinguant la notion de construction-acte et de construction-objet en reference a Brouwer et Hey... more Distinguant la notion de construction-acte et de construction-objet en reference a Brouwer et Heyting, l'A. confronte sa propre definition de la preuve-acte et de la preuve-objet a la position anti-realiste de Prawitz concernant la philosophie de la logique et des mathematiques. L'A. examine les points suivants: 1) l'interpretation semantique de la deduction naturelle des arbres de derivation; 2) la relation entre les notions de conservation et d'harmonie; 3) la formulation des principes fondamentaux de Dummett; 4) les principes et la signification constructive de l'implication.

Alfred Tarski and the Vienna Circle, 1999

Tradition is classical. Surely, nothing could be more pleonastic than that? The logical tradition... more Tradition is classical. Surely, nothing could be more pleonastic than that? The logical tradition, certainly, was squarely classical from Bolzano to Carnap, with, say, Frege, Moore, Russell and the Wittgenstein of the Tractatus as intermediaries. Propositions are construed as being in themselves true-or-false. Indeed, in this tradition, a declarative sentence S expresses a proposition (or is a proposition, depending on what version of the theory that is adopted) by being true-or-false. So the meaningfulness of a sentence consists in its being true-or-false. But S is true-orfalse, or so they say, only when S is true, or when S is false. On the classical account the presumption of bivalence is built into the very notion of meaningfulness: there is no difference between asserting that Λ is a proposition and asserting that A is true-or-false. The matter came to the fore in the foundations of set theory. In his first attempt at giving an application criterion for sets Cantor noted: Eine Mannigfaltigkeit (ein Inbegriff, eine Menge) von Elementen, die irgendwelcher Begriffssphäre angehören, nenne ich wohldefiniert, wenn auf Grund ihrer Definition und infolge des logischen Prinzips vom ausgeschlossenen Dritten es als intern bestimmt angesehen werden muss, sowohl ob irgendein derselben Begriffssphäre angehöriges Objekt zu der gedachten Mannigfaltigkeit gehört oder nicht, wie auch, ob zwei zur Mannigfaltigkeit gehörige Objekte trotz formaler Unterschiede in der Art des Gegebenseins einander gleich sind oder nicht.' Here Cantor's reference to the Law of the Excluded Third is, in my opinion, of the above kind, where meaningfulness, rather than logicality, is at issue: when α is a set, and a an object from the right 'concept sphere', α e α has to be a well-put statement, that is, it must be determinately true-or-false. 2 The passage continues: Im allgemeinen werden die betreffenden Entscheidungen nicht mit den zu Gebote stehenden Methoden oder Fähigkeiten in Wirklichkeit sicher und genau ausführbar sein; daraufkommt es aber hierdurch nicht an, sondern allein auf die interne Determination, welche in konkreten Fällen, wo die Zwecke fordern, durch Vervollkommnung der Hilfsmittel zu einer aktuellen (externen) Determination auszubilden ist. The issue concerning the actual execution of methods of evaluation and decision was a bone of contention between Cantor and Kronecker. The Cantorian point of view was followed by Zermelo in his axiomatization, where definite Eigenschaften were used in the formulation of the Axiom der Aussonderung? Similarly, Frege imposed a very strict sharpness condition of complete determination on his propositional functions ("concepts"). Also he allowed for the possibility that human agents might not be able to execute the required decision. 4 Wittgenstein stressed similar points hi the Tractatus. A sentence must have trueor-false bipolarity in order to be able to say anything. The possibility of human 135

Judgement and the Epistemic Foundation of Logic, 2012

Lingua e Stile, 1999

Lingua e Stile ISSN : 0024-385X. Numero: 1, marzo 1999, Indice. DOI: 10.1417/11653. Interview wit... more Lingua e Stile ISSN : 0024-385X. Numero: 1, marzo 1999, Indice. DOI: 10.1417/11653. Interview with Michael Dummett Göran Sundholm, Peter Pagin, pp. 133-0 € 7 [pdf 590K ...

Philosophy of Logic and Mathematics, 2019

Revue internationale de philosophie, 2004

Dans Revue internationale de philosophie Revue internationale de philosophie 2004/4 (n° 230) 2004... more Dans Revue internationale de philosophie Revue internationale de philosophie 2004/4 (n° 230) 2004/4 (n° 230), pages 401 à 410

History and Philosophy of Logic, 2001

A detailed chronology is offered for the writing of Frege's central philosophical essays from the... more A detailed chronology is offered for the writing of Frege's central philosophical essays from the early 1890s. Particular attention is given to (the distinction between) Sinn and Bedeutung. Suggestions are made as to the origin of the examples concerning the Morning Star/Evening Star and August Bebel's views on the return of Alsace-Lorraine. Likely sources are offered for Frege's use of the terms Bestimmungsweise, Art des Gegebenseins and Sinn und Bedeutung. 10 In his letter of reply Husserl thanks Frege for a number of off-prints; FB, however, is not mentioned among them. Nevertheless, Husserl did possess a copy of the FB booklet, for information concerning which see KS, pp. 431±434. 11 WB, p. 48.

Topoi, 2018

The two different layers of logical theory-epistemological and ontological-are considered and exp... more The two different layers of logical theory-epistemological and ontological-are considered and explained. Special attention is given to epistemic assumptions of the kind that a judgement is granted as known, and their role in validating rules of inference, namely to aid the inferential preservation of epistemic matters from premise judgements to conclusion judgement, while ordinary Natural Deduction assumptions (that propositions are true) serve to establish the holding of consequence from antecedent propositions to succedent proposition.

History and Philosophy of Logic, 2016

We present a new English translation of L.E.J. Brouwer's paper 'De onbetrouwbaarheid der logische... more We present a new English translation of L.E.J. Brouwer's paper 'De onbetrouwbaarheid der logische principes' (The unreliability of the logical principles) of 1908, together with a philosophical and historical introduction. In this paper Brouwer for the first time objected to the idea that the Principle of the Excluded Middle is valid. We discuss the circumstances under which the manuscript was submitted and accepted, Brouwer's ideas on the principle of the excluded middle, its consistency and partial validity, and his argument against the possibility of absolutely undecidable propositions. We note that principled objections to the general excluded middle similar to Brouwer's had been advanced in print by Jules Molk two years before. Finally, we discuss the influence on George Griss' negationless mathematics. keywords: Luitzen Egbertus Jan Brouwer, George Griss, intuitionism, Jules Molk, principle of the excluded middle 4 Among the references in Kohnstamm (1907) we note on pp. 387-388 Husserl's Logische Untersuchungen and Meinong's Gegenstandstheorie, and, indeed, on p. 403, Brouwer's dissertation-'a stern Dutch book' (een ernstig Hollandsch boek). However, that reference just concerns Brouwer's adoption (Brouwer, 1907, p. 104) of Poincaré's remark that the world started rotating only with Copernicus. 5 Much later, in 1949, Brouwer mentioned in a letter to David van Dantzig his 'belief that psychological pictures of intuitionistic mathematics, however interesting they may be, never can be adequate' (

Logic, Epistemology, and the Unity of Science, 2014

The first half of the paper discusses recursive versus constructive functions and, following Heyt... more The first half of the paper discusses recursive versus constructive functions and, following Heyting, stresses that from a constructive point the former cannot replace the latter. The second half of the paper treats of the Kreisel-Myhill theory CS for Brouwer’s Creating Subject, and its relation to BHK meaning-explanations and Kripke’s Schema. Kripke’s Schema is reformulated as a principle and shown to be classically valid. Assuming existence of a verification-object for this principle, a modification of a proof of conservativeness of Van Dalen’s, is shown to give a relative BHK meaning explanation for the Kreisel-Myhill connective. The result offers an explanation of why Kripke’s Schema can be used as a replacement of the Theory of Creating Subject when formulating Brouwerian counter-examples. It also shows that the Theory of Creating Subject is classically valid.

Handbook of Philosophical Logic, 2001

One Hundred Years of Intuitionism (1907–2007), 2008

3. As Kleene showed (Kleene and Vesley 1965, pp. 87-88), a condition is that the bar is decidable... more 3. As Kleene showed (Kleene and Vesley 1965, pp. 87-88), a condition is that the bar is decidable. Brouwer does not make this condition explicit, but in his proofs of 1924 (Brouwer 1924D2) and 1927 (Brouwer 1927B), it is satisfied, because there the bar is defined by an application of the continuity principle for choice sequences. The proof from 1954 (Brouwer 1954A), however, in which the bar is neither defined so as to be decidable, nor explicitly required to be, is incorrect. This seems to have been an oversight on Brouwer's part, rather than an overgeneralization, as the method he gives to construct the well-ordering depends on the decidability of the bar. See on this point also Veldman 2006. 4. Here we note and accept an ambiguity. In the primary sense, a demonstration is the act by and in which knowledge is acquired; this corresponds to Brouwer's 'Beweis'. But we also use 'demonstration' to translate Brouwer's 'Beweisführung', which is not an act but an object, namely the act objectified.

Revue d'histoire des sciences, 2014

Dans son article majeur « Que les principes de la logique ne sont pas fiables » de 1908, L. E. J.... more Dans son article majeur « Que les principes de la logique ne sont pas fiables » de 1908, L. E. J. Brouwer tire pour la premiere fois les consequences revisionnistes de la vue generale de la logique presentee dans sa these de doctorat de 1907, en rejetant le principe du tiers exclu. Nous presentons ici une nouvelle traduction francaise et une introduction philosophique et historique.

Peter Aczel: Predicate logic over a type setup There are a variety of closely related notions aim... more Peter Aczel: Predicate logic over a type setup There are a variety of closely related notions aimed at capturing the abstract structure of type dependency in the syntax and semantics of dependent type theories. Examples of such notions are category with attributes, category with families, category with display maps, contextual category, comprehension category, and there are more. The notion of a type setup is yet one more such notion, which differs from the others in taking a more syntactic approach in its explicit use of contexts, as finite lists of typed variable declarations. This makes it closer to the syntax of dependent type theories, while still abstracting away from the usual inductive structure of syntax and the corresponding recursive definition of substitution. Predicate logic over a type setup is simply defined as a sorted predicate logic where the sorts are the types of the type setup and the sorted terms and substitution are also given by the type setup. Logic over a t...

Nordic Journal of Philosophical Logic, 1998

The first part of the paper presents a framework of distinctions for the philosophy of logic in w... more The first part of the paper presents a framework of distinctions for the philosophy of logic in which the interrelations between some central logical notions, such as judgement(-act), judgement (made), proposition(al content), consequence, and inference are spelled out, In the second half the system of MacColl is measured against the distinctions offered in the framework.

In his seminal paper « On the unreliability of the logical principles » of 1908, L. E. J. Brouwer... more In his seminal paper « On the unreliability of the logical principles » of 1908, L. E. J. Brouwer draws for the first time the revisionistic consequences of the general view on logic that he had presented in his dissertation of 1907, by rejecting the principle of the excluded middle. We present here a new French translation as well as a philosophical and historical introduction.

Topoi, 2012

The possibility of error is related to the existence a norm. Connections are spelled out to the n... more The possibility of error is related to the existence a norm. Connections are spelled out to the notion of infallibility and to that of a modifying predicate, to traditional truth theories in connection with ''truth of things'', as well as the primacy of the negative cases, for instance ''false friend''. Keywords Error Á Norm Á Infallibility Á Modifying predicate History, so far as history has anything to say about it, does teach that right and wrong are real distinctions.

Theoria, 2008

Distinguant la notion de construction-acte et de construction-objet en reference a Brouwer et Hey... more Distinguant la notion de construction-acte et de construction-objet en reference a Brouwer et Heyting, l'A. confronte sa propre definition de la preuve-acte et de la preuve-objet a la position anti-realiste de Prawitz concernant la philosophie de la logique et des mathematiques. L'A. examine les points suivants: 1) l'interpretation semantique de la deduction naturelle des arbres de derivation; 2) la relation entre les notions de conservation et d'harmonie; 3) la formulation des principes fondamentaux de Dummett; 4) les principes et la signification constructive de l'implication.

Alfred Tarski and the Vienna Circle, 1999

Tradition is classical. Surely, nothing could be more pleonastic than that? The logical tradition... more Tradition is classical. Surely, nothing could be more pleonastic than that? The logical tradition, certainly, was squarely classical from Bolzano to Carnap, with, say, Frege, Moore, Russell and the Wittgenstein of the Tractatus as intermediaries. Propositions are construed as being in themselves true-or-false. Indeed, in this tradition, a declarative sentence S expresses a proposition (or is a proposition, depending on what version of the theory that is adopted) by being true-or-false. So the meaningfulness of a sentence consists in its being true-or-false. But S is true-orfalse, or so they say, only when S is true, or when S is false. On the classical account the presumption of bivalence is built into the very notion of meaningfulness: there is no difference between asserting that Λ is a proposition and asserting that A is true-or-false. The matter came to the fore in the foundations of set theory. In his first attempt at giving an application criterion for sets Cantor noted: Eine Mannigfaltigkeit (ein Inbegriff, eine Menge) von Elementen, die irgendwelcher Begriffssphäre angehören, nenne ich wohldefiniert, wenn auf Grund ihrer Definition und infolge des logischen Prinzips vom ausgeschlossenen Dritten es als intern bestimmt angesehen werden muss, sowohl ob irgendein derselben Begriffssphäre angehöriges Objekt zu der gedachten Mannigfaltigkeit gehört oder nicht, wie auch, ob zwei zur Mannigfaltigkeit gehörige Objekte trotz formaler Unterschiede in der Art des Gegebenseins einander gleich sind oder nicht.' Here Cantor's reference to the Law of the Excluded Third is, in my opinion, of the above kind, where meaningfulness, rather than logicality, is at issue: when α is a set, and a an object from the right 'concept sphere', α e α has to be a well-put statement, that is, it must be determinately true-or-false. 2 The passage continues: Im allgemeinen werden die betreffenden Entscheidungen nicht mit den zu Gebote stehenden Methoden oder Fähigkeiten in Wirklichkeit sicher und genau ausführbar sein; daraufkommt es aber hierdurch nicht an, sondern allein auf die interne Determination, welche in konkreten Fällen, wo die Zwecke fordern, durch Vervollkommnung der Hilfsmittel zu einer aktuellen (externen) Determination auszubilden ist. The issue concerning the actual execution of methods of evaluation and decision was a bone of contention between Cantor and Kronecker. The Cantorian point of view was followed by Zermelo in his axiomatization, where definite Eigenschaften were used in the formulation of the Axiom der Aussonderung? Similarly, Frege imposed a very strict sharpness condition of complete determination on his propositional functions ("concepts"). Also he allowed for the possibility that human agents might not be able to execute the required decision. 4 Wittgenstein stressed similar points hi the Tractatus. A sentence must have trueor-false bipolarity in order to be able to say anything. The possibility of human 135

Judgement and the Epistemic Foundation of Logic, 2012

Lingua e Stile, 1999

Lingua e Stile ISSN : 0024-385X. Numero: 1, marzo 1999, Indice. DOI: 10.1417/11653. Interview wit... more Lingua e Stile ISSN : 0024-385X. Numero: 1, marzo 1999, Indice. DOI: 10.1417/11653. Interview with Michael Dummett Göran Sundholm, Peter Pagin, pp. 133-0 € 7 [pdf 590K ...

A running commentary is offered on the first half of GLA, § 17, and suggests that Frege anticipat... more A running commentary is offered on the first half of GLA, § 17, and suggests that Frege anticipated the method of demonstration used by Paul Bernays for the DeductionTheorem.

The paper discusses where in Kreisel's work his eponymous "Dictum" can be found and offers novel ... more The paper discusses where in Kreisel's work his eponymous "Dictum" can be found and offers novel relevant evidence.

A distinction is drwan between Natural Deduction assuptions (antecedent propositions ) that serve... more A distinction is drwan between Natural Deduction assuptions (antecedent propositions ) that serve to establish the holding of consequence and epistemic assumptions that serve as premises of inferences.

My Oxford 1983doctoral dissertation

Different logical frameworks define their own logical concepts in their own technical terms. Some... more Different logical frameworks define their own logical concepts in their own technical terms. Some key concepts in logic – such as validity for example, judgment, proposition or inference – end up having radically different meaning: validity may be defined in Model Theory as what is true in every model, but what could it mean in Proof Theory which does not use models? In today's context of logical pluralism, this plurality of definitions and uses of logical concepts makes communication between logics a challenge.

This workshop intends to explore the meaning of key logical concepts, over and beyond their specific meaning in each local logical framework, by investigating the history of logic. Thus, a focus will be made each morning:
first in Ancient logic – Michel Crubellier, Judgment and Proposition in Aristotle (in French) –
then in Medieval logic – Barbara Bartocci, Consequentia and Argumentatio: Medievals on consequences and inferences.
Göran Sundholm will give a talk each afternoon on history and philosophy of logic.
Each session is provided with long discussion time, and the speakers have provided a list of central texts to read beforehand in order to prepare for the discussions, as well as a complementary bibliography for further reading.