On the Brouwerian concept of negative continuity

Martino, Enrico

doi:10.1007/bf00649482

Cited by 5 publications

(6 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Different explanations of this proof are given in the literature [31,34,37,43,44] [39, appendix B]. Niekus [32] comments that Brouwer's proof 'is vague and deviates essentially from all his other uses of choice sequences' (p. 32), and also 'This proof of the negative continuity theorem is so vague that it allows many reconstructions.…”

Section: The Negative Continuity Proof Of 1927mentioning

confidence: 99%

Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey

Fletcher

2020

J Philos Logic

View full text Add to dashboard Cite

I survey Brouwer’s weak counterexamples to classical theorems, with a view to discovering (i) what useful mathematical work is done by weak counterexamples; (ii) whether they are rigorous mathematical proofs or just plausibility arguments; (iii) the role of Brouwer’s notion of the creative subject in them, and whether the creative subject is really necessary for them; (iv) what axioms for the creative subject are needed; (v) what relation there is between these arguments and Brouwer’s theory of choice sequences. I refute one of Brouwer’s claims with a weak counterexample of my own. I also examine Brouwer’s 1927 proof of the negative continuity theorem, which appears to be a weak counterexample reliant on both the creative subject and the concept of choice sequence; I argue that it provides a good justification for the weak continuity principle, but it is not a weak counterexample and it does not depend essentially on the creative subject.

show abstract

Section: The Negative Continuity Proof Of 1927mentioning

confidence: 99%

Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey

Fletcher

2020

J Philos Logic

View full text Add to dashboard Cite

show abstract

“…, a n , whereas for the later i ν b n+1 cannot increase and c n+1 cannot decrease. 113 Now, as long as b n+1 and c n+1 retain the same distinct values, the corresponding i v contain the element a 1 , . .…”

Section: A Brouwer's Implicit Use Of Mp In 1918mentioning

confidence: 99%

“…But in the definition and proof under discussion here, the wider notion is meant. ]113 [Note MvA: An increase of b n+1 would make the left end element smaller with respect to ⊏, and a decrease of c n+1 would make the right end element greater; but the sequence i is supposed to be decreasing. ]…”

mentioning

confidence: 99%

The Creating Subject, the Brouwer–Kripke Schema, and infinite proofs

Atten¹

2018

Indagationes Mathematicae

View full text Add to dashboard Cite

Forthcoming in Indagationes Mathematicae. AbstractKripke's Schema (better the Brouwer-Kripke Schema) and the Kreisel-Troelstra Theory of the Creating Subject were introduced around the same time for the same purpose, that of analysing Brouwer's 'Creating Subject arguments'; other applications have been found since. I first look in detail at a representative choice of Brouwer's arguments. Then I discuss the original use of the Schema and the Theory, their justification from a Brouwerian perspective, and instances of the Schema that can in fact be found in Brouwer's own writings. Finally, I defend the Schema and the Theory against a number of objections that have been made.

show abstract

“…Troelstra discusses three possible ones, and there are others, see e.g. Posy 1976 andMartino 1985, all different. It is also the only Brouwerian choice sequence discussed in van Atten 2007 (p. 108-109), a recent study on the phenomenology of choice sequences.…”

Section: The Definition Of a Spreadmentioning

confidence: 99%

Brouwer's Incomplete Objects

Niekus¹

2010

History and Philosophy of Logic

View full text Add to dashboard Cite

Abstract. Brouwer's papers after 1945 are characterized by a technique, known as the method of the creating subject. It has been supposed that the method was radically new in his work, since Brouwer seems to introduce an idealized mathematician into his mathematical practice. A newly opened source, the unpublished text of a lecture of Brouwer from 1934, fully supports the conclusions of our analysis that: -There is no idealized mathematician involved in the method.-The method was not new at all.-Brouwer uses an incomplete sequence, also known as choice sequence, in this method, which is special. The method does not take its place in the standard works on choice sequences.

show abstract

On the Brouwerian concept of negative continuity

Cited by 5 publications

References 4 publications

Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey

Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey

The Creating Subject, the Brouwer–Kripke Schema, and infinite proofs

Brouwer's Incomplete Objects

Contact Info

Product

Resources

About