# Göran SundholmLeiden University | LEI · Leiden University Institute for Philosophy

Göran Sundholm

B.Phil., M.A., D.Phil. (Oxon)

## About

84

Publications

5,297

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1,077

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Introduction

Additional affiliations

July 2019 - present

**Leiden University**

Position

- Professor Emeritus

September 1987 - June 2019

July 1985 - September 1987

Education

October 1976 - April 1981

January 1975 - September 1976

September 1972 - December 1974

## Publications

Publications (84)

A close reading and running commentary on the first half of Frege's Grundlagen der Arithmetik, § 17.

Abstract of a paper read at the conference
The Classical Model of Science II
Free University, Amsterdam,
August, 2-5, 2011

The exaugural lecture considers three encounters between Gottlob Frege and die Grosse Politik of his times. It also offers customary thanks and some reminiscences of the 32 years that I held the Chair of Logic at Leiden.

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 con...

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 th...

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 th...

After some observations on the conference performance of Kevin Mulligan, the chapter notes shortcomings in the English epistemic vocabulary concerning the crucial terms knowledge, science, evidence, certainty, proof, demonstration, and proposition.

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. Krip...

« On the unreliability of the logical principles » : A new French translation of L. E. J. Brouwer’s 1908 article with annotations and commentary
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...

My original training as a philosopher, at Uppsala and at Oxford, was ruggedly analytical. Also the notion of an analytic judgement, or ‘proposition’, or ‘sentence’, or ‘statement’, (one did not overly distinguish these notions) was repeatedly treated of by excellent teachers and colleagues. There were aficionados of Quine and experts on Kant among...

The paper presents a framework of distinctions for the philosophy of logic in which the interrelations between some central logical notions, such as statement, judgement (-act), judgement (made), proposition (al content), consequence, and inference are spelled out.

The spring of 1980 I spent as visiting lecturer at Utrecht. The volume of Heyting’s Collected Papers had not yet been put together, and his philosophical papers could not be found at Oxford. Accordingly, I availed myself of the opportunities offered by Dutch libraries and read the relevant papers. A couple of years earlier, I had learned about Cons...

The paper traces nineteenth century devopments in the form of judgement from the traditional ‘S is P’ to the type theoretical a:A ; via Bolzano’s ‘A is true’, Brentano’s a+(a-) , Frege’s P(a) is true, and the Cambridge truth-makers and Heyting’s proof-explanations for the constructive logical constants.

Inference versus consequence, an invited lecture at the LOGICA 1997 conference at Castle Liblice, was part of a series of articles for which I did research during a Stockholm sabbatical in the autumn of 1995. The article seems to have been fairly effective in getting its point across and addresses a topic highly germane to the Uppsala workshop. Owi...

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”.

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this oppositio...

The term Proof Theory shows a certain ambiguity. In the fifties when Stig Kanger carried out his logical work it stood for a cluster of topics pertaining to the syntactic turnstile ⊢, that is, the syntactic counterpart to the semantical notion of (logical) consequence ⊨. On the other hand, and more narrowly, it also stood for investigations of the...

This chapter tells how, within a century, the notions of judgment and inference were driven out of logical theory and replaced by propositions and (logical) consequence. Systematic considerations guide the treatment. The history is unashamedly Whiggish: the current position is shown as the outcome, or even culmination, of a historical development.

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...

Brouwer’s demonstration of his Bar Theorem gives rise to provocative questions regarding the proper explanation of the logical
connectives within intuitionistic and constructivist frameworks, respectively, and, more generally, regarding the role of
logic within intuitionism. It is the purpose of the present note to discuss a number of these issues,...

A Timeline of Medieval LogiciansA Guide to the Literature

Drawing upon Martin-Lf’s semantic framework for his constructive type theory, semantic values are assigned also to natural-deduction
derivations, while observing the crucial distinction between (logical) consequence among propositions and inference among
judgements. Derivations in Gentzen’s (1934–5) format with derivable formulae dependent upon ope...

The position indicated by the term “antirealism” has come to the fore in philosophical discussion during the last thirty years, largely as a result of the writings of Michael Dummett.1Prima facie one would expect an antirealist critique of realism to comprise two parts: a negative part (as the name indicates) criticising the realist view, and a pos...

It is a moot question whether Jan Wolefiski himself knows how many articles he has written. 300? 350? It is, however, a fact true and certain that a considerable part of these articles deals with the ins and out of the history of Polish logic. I have not digested all of his oeuvre, but I have read quite a lot. In my opinion, Jan Wolenski has writte...

The meaning of a sentence determines how the truth of the proposition expressed by the sentence may be proved and hence one would expect proof theory to be influenced by meaning-theoretical considerations. In the present chapter we consider a proposal that also reverses the above prior-ities and determines meaning in terms of proof. The proposal or...

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...

An implication is a proposition, a consequence is a relation between propositions, and an inference is act of passage from
certain premise-judgements to another conclusion-judgement: a proposition is true, a consequence holds, whereas an inference
is valid. The paper examines interrelations, differences, refinements and linguistic renderings of the...

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 declarati...

In the present paper I wish to regard constructive logic as a self-contained system for the treatment of epistemological issues; the explanations of the constructivist logical notions are cast in an epistemological mold already from the outset. The discussion offered here intends to make explicit this implicit epistemic character of constructivism....

In the present paper I wish to regard constructive logic as a self-contained system for the treatment of epistemological issues; the explanations of the constructivist logical notions are cast in an epistemological mold already from the outset. The discussion offered here intends to make explicit this implicit epistemic character of constructivism....

Truth-maker analyses construe truth as existence of proof, a well-known example being that offered by Wittgenstein in theTractatus. The paper subsumes the intuitionistic view of truth as existence of proof under the general truth-maker scheme. Two generic
constraints on truth-maker analysis are noted and positioned with respect to the writings of M...

In the Trinity Term of 1977 I had the privilege of hearing Michael Dummett lecture in the Old Library at All Souls on the justification and criticism of logical laws, and subsequently I also assisted Mark Helme in the production of some unauthorised, not altogether successful, notes on these lectures. I can vividly recall my surprise when Prof. Dum...

Traditionally the subject matter of logic comprised judgements and inferences, that is, the products of certain (mental) acts. Indeed, Thomas Aquinas even characterized logic as the study of terms in ‘the second intention’, that is, such terms that themselves have mental entities as their intention, examples being the term ‘term’, the term ‘judgeme...

The meaning of a sentence determines how the truth of the proposition expressed by the sentence may be proved and hence one would expect proof theory to be influenced by meaning-theoretical considerations. In the present Chapter we consider a proposal that also reverses the above priorities and determines meaning in terms of proof. The proposal ori...

A reasonably complete presentation of the recursion-theretic and proof-theoretic aspects of the omega-rule in arithmetic is presented.
Key words:
Proof Theory of Arithmetic, Ordinal analysis - epsilon-nought, The OMEGA RULE, Recursive progressions, Infinitary Dialectica interpretation

Formal calculi of deduction have proved useful in logic and in the foundations of mathematics, otas well as in metamathematics. Examples of some of these uses are:

The paper traces nineteenth century devopments in the form of judgement from the traditional ‘S is P’ to the type theoretical
a:Aa\!:\!A
; via Bolzano’s ‘A is true’, Brentano’s a+
(a-)(a-)
, Frege’s P(a) is true, and the Cambridge truth-makers and Heyting’s proof-explanations for the constructive logical constants.

Propositions and operations both play a central role in the Phil-osophy of Logic as set out in Wittgensteins Tractatus. 1 The general prepositional form is amply treated of both in the work itself and in the substantial secondary literature. 2 The general form of an operation, on the other hand, has, to the best of my knowledge, received no scholar...

## Projects

Project (1)

To explore the current viability of pre-1930 style "atavistic" use of contentual formal languages, especially regarding the notions of inference and axioms, within the Philosophy of Logic and the Philosophy of Mathematics.