[FOM] Troelstra's Paradox and Markov's Principle

[Harvey Friedman]

Of course I like very much that you put links to such papers with
obvious f.o.m. content along with Abstract on the FOM, and I will soon
take a look. I haven't thought about the Creating Subject (Creative
Subject) for a long time, but I remember this as a major idea in the
foundations of intuitionistic logic going back to Brouwer?

So I assume there is the broader question of how to set up the
foundations of intuitionistic logic hopefully with more coherence than
one has at the moment?

In any case, it would be even more valuable if there was a short piece
of the kind I was describing concerning foundations of intuitionistic
logic or intuitionism or constructivity, where we are with it, and in
particular the role of the Creating Subject, and so forth.
Intuitionism seems tp be remarkably stable under many
"interpretations" even if they are rather rough/vague, and that seems
to make it very likely to me that there is a lot more to be discovered
concerning its foundations.

Harvey

On Fri, Dec 16, 2016 at 5:31 AM, Mark van Atten <vanattenmark at gmail.com> wrote:
> A preprint of this paper is now available at
> https://hal.archives-ouvertes.fr/hal-01415603
>
> Abstract:
>
> 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 others do not. After a presentation of the Theory of the
> Creating Subject and the paradox, I argue that the paradox
> moreover depends on Markov's Principle, in a form that no
> intuitionist should accept. A postscript discusses a new
> version of the paradox that Troelstra has proposed in
> reaction to my argument.
>
> Best wishes,
> Mark.
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