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View article: Charles Parsons April 13, 1933 – April 19, 2024
Charles Parsons April 13, 1933 – April 19, 2024 Open
Charles Dacre Parsons passed away on April 19, 2024, aged 91. In this obituary, four of his PhD students and one colleague and collaborator discuss, in an order (roughly) determined by the development of Parsons’s career, his engagement wi…
View article: Kurt Gödel Maxims and Philosophical Remarks vol XV: Volume XV of the Max Phil Notebooks
Kurt Gödel Maxims and Philosophical Remarks vol XV: Volume XV of the Max Phil Notebooks Open
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View article: Intuition, Iteration, Induction
Intuition, Iteration, Induction Open
Brouwer’s view on induction has relatively recently been characterised as one on which it is not only intuitive (as expected) but functional, by van Dalen. He claims that Brouwer’s ‘Ur-intuition’ also yields the recursor. Appealing to Huss…
View article: Natural constructive proofs of A via A → B, proof paradoxes, and impredicativity
Natural constructive proofs of A via A → B, proof paradoxes, and impredicativity Open
Guided by a passage in Kreisel, this is a discussion of the relations between the phenomena in the title, with special attention to the method of analysis and synthesis in Greek geometry, fixed point theorems, and Kreisel's contact with Gö…
View article: BSL volume 27 issue 3 Cover and Front matter
BSL volume 27 issue 3 Cover and Front matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
View article: Kurt Gödel Maxims and Philosophical Remarks, vol XII
Kurt Gödel Maxims and Philosophical Remarks, vol XII Open
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View article: Kurt Gödel Maxims and Philosophical Remarks Volume XI of the Max Phil Notebooks
Kurt Gödel Maxims and Philosophical Remarks Volume XI of the Max Phil Notebooks Open
International audience
View article: BSL volume 26 issue 2 Cover and Front matter
BSL volume 26 issue 2 Cover and Front matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
View article: Dummett's objection to the ontological route to intuitionistic logic: a rejoinder
Dummett's objection to the ontological route to intuitionistic logic: a rejoinder Open
In 'The philosophical basis of intuitionistic logic', Michael Dummett discusses two routes towards accepting intuitionistic rather than classical logic in number theory, one meaning-theoretical (his own) and the other ontological (Brouwer …
View article: Weyl and intuitionistic infinitesimals
Weyl and intuitionistic infinitesimals Open
As Weyl was interested in infinitesimal analysis and for some years embraced Brouwer's intuitionism, which he continued to see as an ideal even after he had convinced himself that it is a practical necessity for science to go beyond intuit…
View article: Predicativity and parametric polymorphism of Brouwerian implication
Predicativity and parametric polymorphism of Brouwerian implication Open
A common objection to the definition of intuitionistic implication in the Proof Interpretation is that it is impredicative. I discuss the history of that objection, argue that in Brouwer's writings predicativity of implication is ensured t…
View article: Intuition, iteration, induction
Intuition, iteration, induction Open
In Mathematical Thought and Its Objects, Charles Parsons argues that our knowledge of the iterability of functions on the natural numbers and of the validity of complete induction is not intuitive knowledge ; Brouwer disagrees on both coun…
View article: Corrigenda to Essays on Gödel's Reception of Leibniz, Husserl, and Brouwer
Corrigenda to Essays on Gödel's Reception of Leibniz, Husserl, and Brouwer Open
A list of corrections to the book Essays on Gödel's Reception of Leibniz, Husserl, and Brouwer (Springer, 2015).
View article: Troelstra's Paradox and Markov's Principle
Troelstra's Paradox and Markov's Principle Open
A prominent problem for the Theory of the Creating Subject is Troelstra's Paradox. As is well known, the construction of that paradox depends on the acceptability of a certain impredicativity, of a kind that some intuitionists accept and o…
View article: Corrigenda to Essays on Gödel's Reception of Leibniz, Husserl, and Brouwer
Corrigenda to Essays on Gödel's Reception of Leibniz, Husserl, and Brouwer Open
A list of corrections to the book Essays on Gödel's Reception of Leibniz, Husserl, and Brouwer (Springer, 2015).
View article: Troelstra's Paradox and Markov's Principle
Troelstra's Paradox and Markov's Principle Open
A prominent problem for the Theory of the Creating Subject is Troelstra's Paradox. As is well known, the construction of that paradox depends on the acceptability of a certain impredicativity, of a kind that some intuitionists accept and o…
View article: Kant and real numbers
Kant and real numbers Open
Kant held that under the concept of √2 falls a geometrical magnitude, but not a number. In particular, he explicitly distinguished this root from potentially infinite converging sequences of rationals. Like Kant, Brouwer based his foundati…
View article: Kurt Gödel Maxims and Philosophical Remarks Volume X
Kurt Gödel Maxims and Philosophical Remarks Volume X Open
International audience
View article: L.E.J. Brouwer's ‘Unreliability of the Logical Principles’: A New Translation, with an Introduction
L.E.J. Brouwer's ‘Unreliability of the Logical Principles’: A New Translation, with an Introduction Open
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 Br…
View article: Troelstra's Paradox and Markov's Principle
Troelstra's Paradox and Markov's Principle Open
A prominent problem for the Theory of the Creating Subject is
Troelstra's Paradox. As is well known, the construction of that
paradox depends on the acceptability of a certain impredicativity, of
a kind that some intuitionists accept an…
View article: Gödel’s Dialectica Interpretation and Leibniz
Gödel’s Dialectica Interpretation and Leibniz Open
In an envelope of material relating to his work on the translation and revision of the Dialectica paper in 1968, Gödel kept a note that is in shorthand but in which one immediately notices the longhand name “Leibniz”. When transcribed and …