FOM: Re: constructive mathematics

Wim van Gessel wvgessel at
Mon May 29 04:46:47 EDT 2000

On May 27 Dr Jeffrey Ketland wrote:

#Goes *against* subjectivism? I don't understand. The following is an extract
#of what Arend Heyting wrote in his 1956: Intuitionism: An Introduction
#(This is part of an excellent dialogue, between the characters called
#"Class" (classical mathematician), "Form" (a formalist, seems to refer to a
#mixture of Hilbert and Carnap), "Int" (an intuitionist, seems to refer to
#Brouwer), "Letter" (a sort of finitist formalist), "Prag" (a pragmatist,
#seems a bit like Quine) and a mysterious character called "Sign"):
This mysterious chap is without doubt a representant of the 'Signifika'
movement of the early 20-th century in the Netherlands.
The word 'Signifika', or 'significs' in English, seems to be coined by
one Lady Victoria Welby, in an article 'Sense, meaning and Interpretation',
in the British Journal 'Mind', 1896 . Clearly the word didn't stick.
The leading figure of the 'Signifika' movement was Mannoury, who wrote
several books on the subject. He was a mathematician himself, who inspired
Brouwer and wrote a critical article when his dissertation on the
Foundations of Mathematics appeared in 1907 .
The focal point of the movement was a brand of critical language philosophy,
akin to the Wiener Kreis and the analytical philosophy in the Aglo-Saxon
world. It had some idealist/socialist overtones as well, due to the
involvement of the Dutch writer Frederik van Eeden. Brouwer was strongly
involved in it, and so were Evert Beth and Henri Borel at some point
in time.

My second remark about Jeffrey Ketland's contribution is that it would
be wrong to simply identify Brouwer's and Heyting's views on
intuitionistic mathematics. Brouwer had a strong aversion against
formalism (in fact he had some unpleasant exchanges with Hilbert).
Heyting had a more pragmatic attitude, and it is probably fair to say
that Heyting was more interested in the formal, technical development
of the subject than in its underlying philosophy.


Wim van Gessel


"Significs will be the wireless telegraphy between all sorts and
conditions of men in the future as compared with the communication
of 100 years ago."
(Lady Victoria Welby in a letter to Fred. van Eeden, Nov 11, 1908.
Quoted from "Signifika - een Inleiding" by prof. G. Mannoury,
the Hague, Netherlands, 1949)

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