[FOM] Girard's new program

[Alasdair Urquhart]

Many thanks to FOM subscribers for the helpful
follow-ups to my posting asking for clarification
of Jean-Yves Girard's new program of ludics.
I hope to find the time to look at some of the
articles recommended.

However, I had in mind a somewhat more
basic question in posing my original query.
Girard claims in his BSL article to have made 
very deep progress in the foundations of mathematics.
His article also contains rather strongly worded 
polemics against traditional approaches to the foundations
of mathematics.  

On reading his article, what I seem to get out of it
is that it is a kind of abstract account of a sequent
calculus related to linear logic, together with a kind
of game-theoretical semantics associated with it
(I proffer these remarks with diffidence, as Girard's
article is far from clearly written).

So, my question is:  can somebody explain just what is
this basic new advance in foundational studies?